You searched for subject:(Fokker Planck equation).
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University of Sydney
1.
Noble, Patrick.
Stochastic processes in Astrophysics
.
Degree: 2013, University of Sydney
URL: http://hdl.handle.net/2123/10013 
► This thesis makes two contributions to the solar literature. The first is the development and application of a formal statistical framework for describing short-term (daily)…
(more)
▼ This thesis makes two contributions to the solar literature. The first is the development and application of a formal statistical framework for describing short-term (daily) variation in the level of magnetic activity on the Sun. Modelling changes on this time-scale is important because rapid developments of magnetic structures on the sun have important consequences for the space weather experienced on Earth (Committee On The Societal & Economic Impacts Of Severe Space Weather Events, 2008). The second concerns how energetic particles released from the Sun travel through the solar wind. The contribution from this thesis is to resolve a mathematical discrepancy in theoretical models for the transport of charged particles.
Subjects/Keywords: Sunspot Number;
Space Weather;
Fokker-Planck Equation
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APA (6th Edition):
Noble, P. (2013). Stochastic processes in Astrophysics
. (Thesis). University of Sydney. Retrieved from http://hdl.handle.net/2123/10013
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Noble, Patrick. “Stochastic processes in Astrophysics
.” 2013. Thesis, University of Sydney. Accessed March 04, 2021.
http://hdl.handle.net/2123/10013.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Noble, Patrick. “Stochastic processes in Astrophysics
.” 2013. Web. 04 Mar 2021.
Vancouver:
Noble P. Stochastic processes in Astrophysics
. [Internet] [Thesis]. University of Sydney; 2013. [cited 2021 Mar 04].
Available from: http://hdl.handle.net/2123/10013.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Noble P. Stochastic processes in Astrophysics
. [Thesis]. University of Sydney; 2013. Available from: http://hdl.handle.net/2123/10013
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Penn State University
2.
Cheng, Wen.
Approximate Solutions to Second Order Parabolic Equations with Applications to Option Pricing.
Degree: 2011, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/12454
► In this thesis, we consider second order parabolic equations with coefficients that vary both in space and in time (non-autonomous). We derive closed-form approx- imations…
(more)
▼ In this thesis, we consider second order parabolic equations with coefficients that vary both in space and in time (non-autonomous). We derive closed-form approx- imations to the associated fundamental solution by extending the Dyson-Taylor commutator method recently developed by Costantinescu, Costanzino, Mazzucato and Nistor for autonomous equations. We establish error bounds in Sobolev spaces and show that, by including enough terms, our approximation can be proven to be accurate to arbitrary high order in the short-time limit. We show how our method can give an approximation of the solution for any fixed time and within any given tolerance. To extend our results to large time, we introduce the so called boot- strap scheme, and show that the total error is still under control in this scheme, but the short time limitation can be removed. For applications, we adapt our ideas to Kolmogorov backward equations that appear in various research fields, such as option pricing. We also numerically compare our results with many other methods in the literature and show that our Dyson-Taylor Commutator method is algorithmically more elementary, it works for more general PDEs, and it gives fairly accurate approximations that are good enough in practice.
Advisors/Committee Members: Victor Nistor, Dissertation Advisor/Co-Advisor, Victor Nistor, Committee Chair/Co-Chair, Anna L Mazzucato, Committee Chair/Co-Chair, John C Liechty, Committee Member, Alexei Novikov, Committee Member.
Subjects/Keywords: Green function; Fokker Planck equation; parabolic equation; Option Pricing
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APA (6th Edition):
Cheng, W. (2011). Approximate Solutions to Second Order Parabolic Equations with Applications to Option Pricing. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/12454
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Cheng, Wen. “Approximate Solutions to Second Order Parabolic Equations with Applications to Option Pricing.” 2011. Thesis, Penn State University. Accessed March 04, 2021.
https://submit-etda.libraries.psu.edu/catalog/12454.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Cheng, Wen. “Approximate Solutions to Second Order Parabolic Equations with Applications to Option Pricing.” 2011. Web. 04 Mar 2021.
Vancouver:
Cheng W. Approximate Solutions to Second Order Parabolic Equations with Applications to Option Pricing. [Internet] [Thesis]. Penn State University; 2011. [cited 2021 Mar 04].
Available from: https://submit-etda.libraries.psu.edu/catalog/12454.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Cheng W. Approximate Solutions to Second Order Parabolic Equations with Applications to Option Pricing. [Thesis]. Penn State University; 2011. Available from: https://submit-etda.libraries.psu.edu/catalog/12454
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Texas Tech University
3.
Liu, Han.
Escape time distribution for stochastic flows.
Degree: Mathematics and Statistics, 2011, Texas Tech University
URL: http://hdl.handle.net/2346/ETD-TTU-2011-08-1590
► The model is based on models developed at the Federal Reserve Board of Governors by Robert Martin, PhD. His models were used to model data…
(more)
▼ The model is based on models developed at the Federal Reserve
Board of Governors by Robert Martin, PhD. His models were used to
model data arising from subprime mortgages. They are very simple
but capture data very well. In this thesis we used his model and
derived the partial differential equations describing the time
history of the corresponding distributions. In the case of
Brownian motion this reduced to just the
Fokker-
Planck equation
and in the case of the jump process we followed the derivation in
the notes by Roger Brockett. In doing this, a deep understanding
of how to use and manipulate the It\
o formula and other aspects
of stochastic differential equations is gained.
We assume x, as a weighted variable, to evaluate the borrower's
ability to continue making payments, refinance, default or pay
off. It is scaled so that 0 represents default and 1 represents
paid. For each treatment we assume the approximation difference
equation x
n+1=(1+r)x
n-sε
n as the model where the
parameters r and s are two positive constants to be
determined. r stands for the growth rate which is a positive
real number in (0,1). The sε
n term as the bad
accidents such as divorce, job loss, career moves, etc. which can
dramatically affect the ability to pay. After 10,000 treatments,
we will find the histograms which are obtained by recording the
frequency of those jump time points. We will then analyze and
explain our results of simulation based on the histograms of the
escape time distributions.
Advisors/Committee Members: Martin, Clyde F. (Committee Chair), Drager, Lance D. (committee member).
Subjects/Keywords: Poisson counter; Brownian motion; Stochastic differential equation; Fokker-planck equation
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APA (6th Edition):
Liu, H. (2011). Escape time distribution for stochastic flows. (Thesis). Texas Tech University. Retrieved from http://hdl.handle.net/2346/ETD-TTU-2011-08-1590
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Liu, Han. “Escape time distribution for stochastic flows.” 2011. Thesis, Texas Tech University. Accessed March 04, 2021.
http://hdl.handle.net/2346/ETD-TTU-2011-08-1590.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Liu, Han. “Escape time distribution for stochastic flows.” 2011. Web. 04 Mar 2021.
Vancouver:
Liu H. Escape time distribution for stochastic flows. [Internet] [Thesis]. Texas Tech University; 2011. [cited 2021 Mar 04].
Available from: http://hdl.handle.net/2346/ETD-TTU-2011-08-1590.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Liu H. Escape time distribution for stochastic flows. [Thesis]. Texas Tech University; 2011. Available from: http://hdl.handle.net/2346/ETD-TTU-2011-08-1590
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Kansas
4.
Li, Xi.
Dynamics of A Degenerate Fokker-Planck Equation and Its Application.
Degree: PhD, Mathematics, 2015, University of Kansas
URL: http://hdl.handle.net/1808/21706
► In this project, a Fokker-Planck equation with two singular points is studied. The equation is derived from a stochastic evolution equation, LMM-SABR model, which is…
(more)
▼ In this project, a
Fokker-
Planck equation with two singular points is studied. The
equation is derived from a stochastic evolution
equation, LMM-SABR model, which is widely used in financial industry. It is difficult to directly study the original
equation due to the singularity. As an alternative approach, we introduce appropriate modifications to certain terms of original
Fokker-
Planck equation at each singular point so that the modified
equation has a stationary solution. With the stable stationary solution, the intermediate behavior of the modified
Fokker-
Planck equation can be captured and described to some extent. The non-modified solutions are compared to modified solutions within finite time and a relatively concrete estimation is given in terms of the modification parameter and the given finite time. We also study some possible modifications. For each modification, the properties of the stationary solution are given. Some numerical results of the time-evolution solutions for these modified equations are also included. As an attempt, we have initiated in this project the study of the difference between the modified and non-modified stochastic differential equations (SDEs). Although no complete analytical results are available, our initial work appears pointing in a promising direction, based on the numerical simulation results that we have observed. The further study of the SDEs will be carried out in the future work.
Advisors/Committee Members: Liu, Weishi (advisor), Liu, Weishi (cmtemember), Hu, Yaozhong (cmtemember), Stanislavova, Milena (cmtemember), Van Vleck, Erik (cmtemember), Zhang, Jianbo (cmtemember).
Subjects/Keywords: Mathematics; Applied mathematics; Degenerate; Dynamics; Fokker-Planck Equation; Stochastic Differential Equation
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APA (6th Edition):
Li, X. (2015). Dynamics of A Degenerate Fokker-Planck Equation and Its Application. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/21706
Chicago Manual of Style (16th Edition):
Li, Xi. “Dynamics of A Degenerate Fokker-Planck Equation and Its Application.” 2015. Doctoral Dissertation, University of Kansas. Accessed March 04, 2021.
http://hdl.handle.net/1808/21706.
MLA Handbook (7th Edition):
Li, Xi. “Dynamics of A Degenerate Fokker-Planck Equation and Its Application.” 2015. Web. 04 Mar 2021.
Vancouver:
Li X. Dynamics of A Degenerate Fokker-Planck Equation and Its Application. [Internet] [Doctoral dissertation]. University of Kansas; 2015. [cited 2021 Mar 04].
Available from: http://hdl.handle.net/1808/21706.
Council of Science Editors:
Li X. Dynamics of A Degenerate Fokker-Planck Equation and Its Application. [Doctoral Dissertation]. University of Kansas; 2015. Available from: http://hdl.handle.net/1808/21706
Universidade Estadual de Campinas
5.
Alarcon LLacctarimay, Cesar Juan, 1982-.
Modelagem da distribuição de matéria em um anel em presença de Shepherds, via equação de Fokker-Planck: Modeling the distribution of matter in a ring in the presence of sheperds, via Fokker-Planck equation.
Degree: 2012, Universidade Estadual de Campinas
URL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/278457
► Abstract: In this thesis we intend to model the distribution of matter in a thin stellar ring immersed in the gravitational field of one and…
(more)
▼ Abstract: In this thesis we intend to model the distribution of matter in a thin stellar ring immersed in the gravitational field of one and two shepherd satellites using the
Fokker-
Planck equation. In particular, we study the evolution of a thin ring around a central monopole. The diffusion coefficients are calculated and written in terms of a ¿potential¿ similar to the usual Rosenbluth potentials. In this case, we consider that the particles follow a Gaussian distribution. We solve the 1-dimensional
Fokker-
Planck equation for the ring particles distribution function using the finite difference method (implicit Euler version). We show that the ring is a stable configuration for long time evolutions in the absence or in the presence of shepherds. We also studied the change in the mass density of the ring for different configurations. In all of the cases, it is observed a maximum negative variation of the density near the location of the shepherd due to dynamical effects
Advisors/Committee Members: UNIVERSIDADE ESTADUAL DE CAMPINAS (CRUESP), Ujevic Tonino, Maximiliano (advisor), Tonino, Maximiliano Ujevic (advisor), Ramos Caro, Javier Fernando (coadvisor), Chinellato, Carola Dobrigkeit, 1952- (coadvisor), Universidade Estadual de Campinas. Instituto de Física Gleb Wataghin (institution), Programa de Pós-Graduação em Física (nameofprogram), Antonelli, Alex (committee member), Koning, Maurice de (committee member), Zanchin, Vilson Tonin (committee member), Lugones, German (committee member).
Subjects/Keywords: Planetas e satélites; Anéis planetários; Mecânica celeste; Fokker-Planck, Equação de; Planets and satellites; Planetary rings; Celestial mechanics; Fokker-Planck equation
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APA (6th Edition):
Alarcon LLacctarimay, Cesar Juan, 1. (2012). Modelagem da distribuição de matéria em um anel em presença de Shepherds, via equação de Fokker-Planck: Modeling the distribution of matter in a ring in the presence of sheperds, via Fokker-Planck equation. (Thesis). Universidade Estadual de Campinas. Retrieved from http://repositorio.unicamp.br/jspui/handle/REPOSIP/278457
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Alarcon LLacctarimay, Cesar Juan, 1982-. “Modelagem da distribuição de matéria em um anel em presença de Shepherds, via equação de Fokker-Planck: Modeling the distribution of matter in a ring in the presence of sheperds, via Fokker-Planck equation.” 2012. Thesis, Universidade Estadual de Campinas. Accessed March 04, 2021.
http://repositorio.unicamp.br/jspui/handle/REPOSIP/278457.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Alarcon LLacctarimay, Cesar Juan, 1982-. “Modelagem da distribuição de matéria em um anel em presença de Shepherds, via equação de Fokker-Planck: Modeling the distribution of matter in a ring in the presence of sheperds, via Fokker-Planck equation.” 2012. Web. 04 Mar 2021.
Vancouver:
Alarcon LLacctarimay, Cesar Juan 1. Modelagem da distribuição de matéria em um anel em presença de Shepherds, via equação de Fokker-Planck: Modeling the distribution of matter in a ring in the presence of sheperds, via Fokker-Planck equation. [Internet] [Thesis]. Universidade Estadual de Campinas; 2012. [cited 2021 Mar 04].
Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/278457.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Alarcon LLacctarimay, Cesar Juan 1. Modelagem da distribuição de matéria em um anel em presença de Shepherds, via equação de Fokker-Planck: Modeling the distribution of matter in a ring in the presence of sheperds, via Fokker-Planck equation. [Thesis]. Universidade Estadual de Campinas; 2012. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/278457
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Delaware
6.
Zeng, Yun.
Mathematical modeling and stochastic simulation of soft materials.
Degree: PhD, University of Delaware, Department of Mathematical Sciences, 2014, University of Delaware
URL: http://udspace.udel.edu/handle/19716/16840
► Soft materials are all around us; they may appear as consumer products, foods, or biological materials. The interest in studying the properties of soft materials…
(more)
▼ Soft materials are all around us; they may appear as consumer products, foods, or biological materials. The interest in studying the properties of soft materials both experimentally and theoretically has steadily increased due to their wide range of industrial applications. One example of a soft material is wormlike micellar solutions. Depending on the temperature and composition, these solvent-surfactant-salt mixtures may exhibit close to mono-exponential or, alternatively, power-law or stretched-exponential stress decay. Of particular interest to this thesis is the development of stochastic models that can capture the stress relaxation behavior of such materials in the small strain limit, which is non-exponential in time as opposed to exponential. Continuous time random walk (CTRW) or subordinated Langevin processes are utilized to model systems exhibiting non-exponential relaxation behavior or anomalous diffusion. Stochastic simulations using the CTRW approach or the subordination method are carried out in this thesis for one-dimensional systems in which the probability density distribution of particle positions is described by a fractional
Fokker-
Planck equation (FFPE). The equivalence of the CTRW simulation and the subordination simulation with that of the FFPE is analyzed through the simulation of an ensemble of particle trajectories. The simulated particle dynamics suggest that CTRW processes or subordinated Langevin dynamics can be included in soft material mesoscale dynamics to capture the anomalous transport. To model the non-exponential stress relaxation dynamics of soft gel systems (three-dimensional fluids), stochastic models are simulated using transient network theory as developed and combined with the CTRW and subordinated Langevin processes. This approach enables us to connect the microstructural dynamics of certain soft gel-like materials with macroscale experimental observations by examining the material properties under homogeneous shear flow conditions. The study shows that transient network models combined with CTRW or subordination processes can successfully predict the non-exponential stress relaxation dynamics of soft materials. Future work should include the understanding of this class of models for other types of flows, e.g. inhomogeneous flows, as well as inclusion of the CTRW approach in a transient network model with the network topology tracked.
Advisors/Committee Members: Cook, L. Pamela.
Subjects/Keywords: Colloids.; Stochastic models.; Random walks (Mathematics); Fokker-Planck equation.
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APA (6th Edition):
Zeng, Y. (2014). Mathematical modeling and stochastic simulation of soft materials. (Doctoral Dissertation). University of Delaware. Retrieved from http://udspace.udel.edu/handle/19716/16840
Chicago Manual of Style (16th Edition):
Zeng, Yun. “Mathematical modeling and stochastic simulation of soft materials.” 2014. Doctoral Dissertation, University of Delaware. Accessed March 04, 2021.
http://udspace.udel.edu/handle/19716/16840.
MLA Handbook (7th Edition):
Zeng, Yun. “Mathematical modeling and stochastic simulation of soft materials.” 2014. Web. 04 Mar 2021.
Vancouver:
Zeng Y. Mathematical modeling and stochastic simulation of soft materials. [Internet] [Doctoral dissertation]. University of Delaware; 2014. [cited 2021 Mar 04].
Available from: http://udspace.udel.edu/handle/19716/16840.
Council of Science Editors:
Zeng Y. Mathematical modeling and stochastic simulation of soft materials. [Doctoral Dissertation]. University of Delaware; 2014. Available from: http://udspace.udel.edu/handle/19716/16840
Kansas State University
7.
Islam, Md Atiqul.
Cyanobacterial harmful algal bloom modeling in eutrophic water
bodies.
Degree: MS, Department of Biological &
Agricultural Engineering, 2020, Kansas State University
URL: http://hdl.handle.net/2097/40914
► Harmful algal bloom (or HAB) is a global phenomenon in the rising trend of environmental concerns that impacts public health and the economy through declining…
(more)
▼ Harmful algal bloom (or HAB) is a global phenomenon in
the rising trend of environmental concerns that impacts public
health and the economy through declining water quality and
toxicity. A rapid increase in cyanobacteria concentrations in water
bodies is a primary cause of HABs. Enhanced eutrophication and
warmer climate are considered vital driving factors for the
proliferation of HAB events in the United States and worldwide.
Dynamic modeling of cyanobacteria concentrations can help manage
and reduce the impact of toxic blooms by better understanding the
conditions for cyanobacteria growth and providing recommendations
for early advisory warnings to the public for eutrophic water
bodies in the agriculture dominated watersheds of the Midwest. In
this study, sub-daily time series of cyanobacteria concentration
and other environmental, physical-chemical variables were collected
at the USGS sites in southcentral Kansas at Cheney Reservoir near
the City of Wichita and in northeast Kansas at Kansas River near
Wamego. Statistical analysis of the data revealed positive
correlations between cyanobacteria concentration and water
temperature, irradiation, phosphorus concentration, and storage
volume. Correlation of dissolved oxygen depletion with
cyanobacteria growth indicated an adverse impact of HABs on aquatic
systems. A process-based mathematical framework for the kinetics of
cyanobacteria growth was implemented at two sites considering
bacteria natural growth, non-predatory loss, outflow washout, and
accounting for the changes in water temperature (T), solar
irradiance (I), and available nutrients (phosphorus [P] and
nitrogen [N]). Four models were developed to facilitate examination
of potential data limitation in sampling and continuous
observations: (i) T-based, (ii) T, I-based, (iii) T, I, P- based,
and (iv) complete four-factor model (T, I, P, N-based). The models
were calibrated using continuous observations in 2013 - 2014 with
time intervals from 2 days to 15 days (NSE = 0.41 to 0.71), and
validated for 2018 (NSE = 0.56).
Simulations revealed model
efficiency in short-term (one day to bi-weekly) forecasting of
cyanobacteria concentration for both nutrient-rich sites. The
performance of TIP-based and TIPN-based models was found acceptable
for long-term forecasting in the Cheney Reservoir. Data sampling at
a 15-day interval was found adequate for the forecasting of
cyanobacteria growth. A stochastic modeling approach was applied to
the TIPN model that converted a kinetic growth model to a modified
Fokker-
Planck equation for the probability density function of the
cyanobacteria concentration to account for variability in influent
nutrient concentrations and their impact on HABs. Several single
storm event scenarios were simulated to evaluate the impact of high
nutrient runoff into the lake on cyanobacteria. Stochastic model
simulations showed that mechanistic modeling forecasting
uncertainty increased along time propagation and higher uncertainty
in initial concentrations of the cyanobacteria. The process-based…
Advisors/Committee Members: Aleksey Y. Sheshukov.
Subjects/Keywords: Cyanobacteria; Harmful Algal Blooms; Process-based model;
Fokker-Planck equation
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APA ·
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Manager
APA (6th Edition):
Islam, M. A. (2020). Cyanobacterial harmful algal bloom modeling in eutrophic water
bodies. (Masters Thesis). Kansas State University. Retrieved from http://hdl.handle.net/2097/40914
Chicago Manual of Style (16th Edition):
Islam, Md Atiqul. “Cyanobacterial harmful algal bloom modeling in eutrophic water
bodies.” 2020. Masters Thesis, Kansas State University. Accessed March 04, 2021.
http://hdl.handle.net/2097/40914.
MLA Handbook (7th Edition):
Islam, Md Atiqul. “Cyanobacterial harmful algal bloom modeling in eutrophic water
bodies.” 2020. Web. 04 Mar 2021.
Vancouver:
Islam MA. Cyanobacterial harmful algal bloom modeling in eutrophic water
bodies. [Internet] [Masters thesis]. Kansas State University; 2020. [cited 2021 Mar 04].
Available from: http://hdl.handle.net/2097/40914.
Council of Science Editors:
Islam MA. Cyanobacterial harmful algal bloom modeling in eutrophic water
bodies. [Masters Thesis]. Kansas State University; 2020. Available from: http://hdl.handle.net/2097/40914
8.
Khaldi nee Bouzaghti, Yamina.
Interprétation probabiliste des EDP et processus de diffusion.
Degree: 2007, Université M'Hamed Bougara Boumerdès
URL: http://dlibrary.univ-boumerdes.dz:8080/jspui/handle/123456789/844
► 106 p. ; ill. ; 30 cm
The objective of this work is to show the bond between the partial derivative equations of the second…
(more)
▼ 106 p. ; ill. ; 30 cm
The objective of this work is to show the bond between the partial derivative equations
of the second order and the stochastic processes of diffusion like having some results obtained recently on the partial derivative equations by probabilistic methods.
Many solutions of partial derivative equations of the second order can be written like
the hope of a functional calculus of a process of diffusion. The probabilistic formulas, often known as formulas of Feynman-Kac, constitute a tool which makes it possible to show many results on the partial derivative equation corresponding by probabilistic methods. The Brownian movement is, amongst other things, the major tool of the model of Black and Scholes and is used to build the majority of the models of credits in finance. The systems appearing in the applications are often subjected to disturbances which one can regard as random. One gives initially the probabilistic interpretation of the equation of heat thanks to the Brownian movement. The relationship between the Brownian movement and the equation of heat is illustrated between certain systems of partial derivative equations, the physical problems from which they result and the stochastic differential equations. One shows then that the results obtained for the Laplacian can be generalized with the operators of the second order with variable coefficients, the Brownian movement, being, in this case, replaced by a process of diffusion. The practical point of view of modelling is studied in particular through the algorithms of numerical resolution of Euler and Milstein by the means of some problems. The stochastic differential equations find an application significant in finance. It is the object of the last part of this work in which one is interested particularly in the evaluation of options in the model of Black and Scholes
Subjects/Keywords: 106 p.; ill.; 30 cm; Processus de diffusion; Fokker-Planck, Equation de
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APA (6th Edition):
Khaldi nee Bouzaghti, Y. (2007). Interprétation probabiliste des EDP et processus de diffusion. (Thesis). Université M'Hamed Bougara Boumerdès. Retrieved from http://dlibrary.univ-boumerdes.dz:8080/jspui/handle/123456789/844
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Khaldi nee Bouzaghti, Yamina. “Interprétation probabiliste des EDP et processus de diffusion.” 2007. Thesis, Université M'Hamed Bougara Boumerdès. Accessed March 04, 2021.
http://dlibrary.univ-boumerdes.dz:8080/jspui/handle/123456789/844.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Khaldi nee Bouzaghti, Yamina. “Interprétation probabiliste des EDP et processus de diffusion.” 2007. Web. 04 Mar 2021.
Vancouver:
Khaldi nee Bouzaghti Y. Interprétation probabiliste des EDP et processus de diffusion. [Internet] [Thesis]. Université M'Hamed Bougara Boumerdès; 2007. [cited 2021 Mar 04].
Available from: http://dlibrary.univ-boumerdes.dz:8080/jspui/handle/123456789/844.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Khaldi nee Bouzaghti Y. Interprétation probabiliste des EDP et processus de diffusion. [Thesis]. Université M'Hamed Bougara Boumerdès; 2007. Available from: http://dlibrary.univ-boumerdes.dz:8080/jspui/handle/123456789/844
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of California – Irvine
9.
Wang, Dongyong.
Numerical Methods for Reaction Diffusion Systems in High Spatial Dimensions.
Degree: Mathematics, 2014, University of California – Irvine
URL: http://www.escholarship.org/uc/item/8191p3n3
► Reaction diffusion equations are widely used to model biological phenomena and in some situation, the spatial dimension can be much larger. Numerical efficiently solving high-dimensional…
(more)
▼ Reaction diffusion equations are widely used to model biological phenomena and in some situation, the spatial dimension can be much larger. Numerical efficiently solving high-dimensional reaction-diffusion equations is a huge challenge. To solve the high-dimensional equation, the ``curse of dimensions" has to be dealt with. Also, an efficiently time integration method is needed to solve the afterwords time dependent problem. The sparse grid technique can deal with the problem, and the semi-implicit integration factor method can handles the second one. The combination of two methods will be an efficient method to solve high-dimensional reaction-diffusion equations.
Subjects/Keywords: Mathematics; Fokker-Planck Equation; hair follicle cycle; high dimensions; implicit methods; reaction-diffusion; sparse grid
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APA (6th Edition):
Wang, D. (2014). Numerical Methods for Reaction Diffusion Systems in High Spatial Dimensions. (Thesis). University of California – Irvine. Retrieved from http://www.escholarship.org/uc/item/8191p3n3
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Wang, Dongyong. “Numerical Methods for Reaction Diffusion Systems in High Spatial Dimensions.” 2014. Thesis, University of California – Irvine. Accessed March 04, 2021.
http://www.escholarship.org/uc/item/8191p3n3.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Wang, Dongyong. “Numerical Methods for Reaction Diffusion Systems in High Spatial Dimensions.” 2014. Web. 04 Mar 2021.
Vancouver:
Wang D. Numerical Methods for Reaction Diffusion Systems in High Spatial Dimensions. [Internet] [Thesis]. University of California – Irvine; 2014. [cited 2021 Mar 04].
Available from: http://www.escholarship.org/uc/item/8191p3n3.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Wang D. Numerical Methods for Reaction Diffusion Systems in High Spatial Dimensions. [Thesis]. University of California – Irvine; 2014. Available from: http://www.escholarship.org/uc/item/8191p3n3
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Utah State University
10.
Spencer, Joseph Andrew.
A 2D Finite Element/1D Fourier Solution To The Fokker-Planck Equation.
Degree: PhD, Physics, 2012, Utah State University
URL: https://digitalcommons.usu.edu/etd/1257
► Plasma, the fourth state of matter, is a gas in which a significant portion of the atoms are ionized. It is estimated that more…
(more)
▼ Plasma, the fourth state of matter, is a gas in which a significant portion of the atoms are ionized. It is estimated that more than 99% of the material in the visible universe is in the plasma state. The process that stars, including our sun, combine atomic nuclei and produce large amounts of energy is called thermonuclear fusion. It is anticipated future energy demands will be met by large terrestrial devices harnessing the energy of nuclear fusion. A gas hot enough to produce the number of atomic collisions needed for fusion is necessarily in the plasma state. Therefore, plasmas are of great interest to researchers studying nuclear fusion. Stars are massive enough that the gravitational attraction heats and confines the plasma. Gravitational confinement cannot be used to confine fusion plasmas on Earth. Material containers cause cooling, which prevent a plasma from maintaining the high temperature needed for fusion. Fortunately plasmas have electrical properties, which allow them to be controlled by strong magnetic fields.
Although serious research into controlled thermonuclear fusion began over 60 years ago, only a couple of man-made devices are even close to obtaining more energy from fusion than is put into them. One difficulty lies in understanding the physics of particle collisions. A relative few particle collisions result in the fusion of atomic nuclei, while the vast majority of collisions are understood in terms of the electrostatic force between particles. My work has been to create an a computer code, which can be executed in parallel on supercomputers, to quickly and accurately calculate the evolution of a plasma due to particle collisions. This work explains the physics and mathematics underlying our code, as well as several tests which demonstrate the code is working as expected.
Advisors/Committee Members: Eric D. Held, W. Farrell Edwards, James T. Wheeler, ;.
Subjects/Keywords: 2D; 1D; Finite Element; Solution; Fokker-Planck Equation; Physical Sciences and Mathematics; Physics
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APA (6th Edition):
Spencer, J. A. (2012). A 2D Finite Element/1D Fourier Solution To The Fokker-Planck Equation. (Doctoral Dissertation). Utah State University. Retrieved from https://digitalcommons.usu.edu/etd/1257
Chicago Manual of Style (16th Edition):
Spencer, Joseph Andrew. “A 2D Finite Element/1D Fourier Solution To The Fokker-Planck Equation.” 2012. Doctoral Dissertation, Utah State University. Accessed March 04, 2021.
https://digitalcommons.usu.edu/etd/1257.
MLA Handbook (7th Edition):
Spencer, Joseph Andrew. “A 2D Finite Element/1D Fourier Solution To The Fokker-Planck Equation.” 2012. Web. 04 Mar 2021.
Vancouver:
Spencer JA. A 2D Finite Element/1D Fourier Solution To The Fokker-Planck Equation. [Internet] [Doctoral dissertation]. Utah State University; 2012. [cited 2021 Mar 04].
Available from: https://digitalcommons.usu.edu/etd/1257.
Council of Science Editors:
Spencer JA. A 2D Finite Element/1D Fourier Solution To The Fokker-Planck Equation. [Doctoral Dissertation]. Utah State University; 2012. Available from: https://digitalcommons.usu.edu/etd/1257
Louisiana State University
11.
Ghadipasha, Navid.
A Model-Centric Framework for Advanced Operation of Crystallization Processes.
Degree: PhD, Chemical Engineering, 2017, Louisiana State University
URL: etd-06262017-150243
;
https://digitalcommons.lsu.edu/gradschool_dissertations/4304
► Crystallization is the main physical separation process in many chemical industries. It is an old unit operation which can separate solids of high purity from…
(more)
▼ Crystallization is the main physical separation process in many chemical industries. It is an old unit operation which can separate solids of high purity from liquids, and is widely applied in the production of food, pharmaceuticals, and fine chemicals. While industries in crystallization operation quite rely on rule-of-thumb techniques to fulfill their requirement, the move towards a scientific- and technological- based approach is becoming more important as it provides a mechanism for driving crystallization processes optimally and in more depth without increasing costs. Optimal operation of industrial crystallizers is a prerequisite these days for achieving the stringent requirements of the consumer-driven manufacturing.
To achieve this, a generic and flexible model centric framework is developed for the advanced operation of crystallization processes. The framework deploys the modern software environment combined with the design of a state-of-the-art 1-L crystallization laboratory facility. The emphasis is on developing an economically and practically feasible implementation which can be applied for the optimal operation of various crystallization systems by pharmaceutical industries. The key developments in the framework have occurred in three broad categories:
i. Modeling: Using an advanced modeling tool is intended for accurate representation of the behavior of the physical system. This is the cornerstone of any simulation, optimization or model-based control approach.
ii. Monitoring: Applying a novel image-based technique for online characterization of the particulate processes. This is a promising method for direct tracking of particle size and size distribution with high adaptability for real-time application
iii. Control: Proposing numerous model-based strategies for advanced control of the crystallization system. These strategies enable us to investigate the role of model complexity on real-time control design. Furthermore, the effect of model imperfections, process uncertainty and decision variables on optimal operation of the process can be evaluated.
Overall, results from this work presents a robust platform for further research in the area of crystal engineering. Most of the developments described will pave the way for future set of activities being targeted towards extending and adapting advanced modeling, monitoring and control concepts for different crystallization processes.
Subjects/Keywords: Model-based Control; Particle Size Distribution; Fokker-Planck Equation; Image analysis; Crystallization
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APA (6th Edition):
Ghadipasha, N. (2017). A Model-Centric Framework for Advanced Operation of Crystallization Processes. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-06262017-150243 ; https://digitalcommons.lsu.edu/gradschool_dissertations/4304
Chicago Manual of Style (16th Edition):
Ghadipasha, Navid. “A Model-Centric Framework for Advanced Operation of Crystallization Processes.” 2017. Doctoral Dissertation, Louisiana State University. Accessed March 04, 2021.
etd-06262017-150243 ; https://digitalcommons.lsu.edu/gradschool_dissertations/4304.
MLA Handbook (7th Edition):
Ghadipasha, Navid. “A Model-Centric Framework for Advanced Operation of Crystallization Processes.” 2017. Web. 04 Mar 2021.
Vancouver:
Ghadipasha N. A Model-Centric Framework for Advanced Operation of Crystallization Processes. [Internet] [Doctoral dissertation]. Louisiana State University; 2017. [cited 2021 Mar 04].
Available from: etd-06262017-150243 ; https://digitalcommons.lsu.edu/gradschool_dissertations/4304.
Council of Science Editors:
Ghadipasha N. A Model-Centric Framework for Advanced Operation of Crystallization Processes. [Doctoral Dissertation]. Louisiana State University; 2017. Available from: etd-06262017-150243 ; https://digitalcommons.lsu.edu/gradschool_dissertations/4304
Louisiana State University
12.
Ghadipasha, Navid.
A Model-based Framework to Control the Crystal Size Distribution.
Degree: MSChE, Chemical Engineering, 2015, Louisiana State University
URL: etd-04082015-104914
;
https://digitalcommons.lsu.edu/gradschool_theses/4237
► Crystallization is an old unit operation in the industry which is widely used as a separation process due to its ability to produce highly valued…
(more)
▼ Crystallization is an old unit operation in the industry which is widely used as a separation process due to its ability to produce highly valued chemical with high purity. Despite the long history of batch crystallization, industry still relies on rule of- thumb techniques for their crystallization processes. Thus, any method to improve the products characteristics such as size and morphology will be highly valued. Advances in robustness and accuracy of automated in situ sensors give the possibility to move towards an engineering based approach by implementing the real-time monitoring and control of the process. The research undertaken here investigates the development of an advanced framework for the operation of crystallization processes. This project builds upon the synergy among the research teams at LSU and at the University of Cagliari. The proposed methodology comprises of exploiting an advanced model to simulate the process, On-line implementation of the image-based approach within a feedback loop in a completely automated feedback fashion and implementation of model-free control technology. In situ measurement of crystals’ size distribution by using image-based technique and wavelet-fractal algorithm is implemented in a real-time environment for inferring the particles characteristics captured at different time of the experiment. This technique is becoming increasingly more attractive due to availability of high speed imaging devices and powerful computers at reasonable costs and the adaptability to real time application. The process is modelled by means of a stochastic approach. This is an alternative method to the traditional population balance which leads to a more straightforward model that can be solved analytically and obtain the CSD over time. The simplicity of the model gives the possibility to properly implement an automatic control strategy.
Subjects/Keywords: Real-time control; Neural network; Fokker-Planck equation; Image analysis; Non-isothermal antisolvent crystallization
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APA ·
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CSE |
Export
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APA (6th Edition):
Ghadipasha, N. (2015). A Model-based Framework to Control the Crystal Size Distribution. (Masters Thesis). Louisiana State University. Retrieved from etd-04082015-104914 ; https://digitalcommons.lsu.edu/gradschool_theses/4237
Chicago Manual of Style (16th Edition):
Ghadipasha, Navid. “A Model-based Framework to Control the Crystal Size Distribution.” 2015. Masters Thesis, Louisiana State University. Accessed March 04, 2021.
etd-04082015-104914 ; https://digitalcommons.lsu.edu/gradschool_theses/4237.
MLA Handbook (7th Edition):
Ghadipasha, Navid. “A Model-based Framework to Control the Crystal Size Distribution.” 2015. Web. 04 Mar 2021.
Vancouver:
Ghadipasha N. A Model-based Framework to Control the Crystal Size Distribution. [Internet] [Masters thesis]. Louisiana State University; 2015. [cited 2021 Mar 04].
Available from: etd-04082015-104914 ; https://digitalcommons.lsu.edu/gradschool_theses/4237.
Council of Science Editors:
Ghadipasha N. A Model-based Framework to Control the Crystal Size Distribution. [Masters Thesis]. Louisiana State University; 2015. Available from: etd-04082015-104914 ; https://digitalcommons.lsu.edu/gradschool_theses/4237
Simon Fraser University
13.
Chen, Tianhong.
A theoretical and numerical study for the Fokker-Planck equation.
Degree: 1992, Simon Fraser University
URL: http://summit.sfu.ca/item/3695
Subjects/Keywords: Fokker-Planck equation.; Differential equations, Partial.
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APA (6th Edition):
Chen, T. (1992). A theoretical and numerical study for the Fokker-Planck equation. (Thesis). Simon Fraser University. Retrieved from http://summit.sfu.ca/item/3695
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Chen, Tianhong. “A theoretical and numerical study for the Fokker-Planck equation.” 1992. Thesis, Simon Fraser University. Accessed March 04, 2021.
http://summit.sfu.ca/item/3695.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Chen, Tianhong. “A theoretical and numerical study for the Fokker-Planck equation.” 1992. Web. 04 Mar 2021.
Vancouver:
Chen T. A theoretical and numerical study for the Fokker-Planck equation. [Internet] [Thesis]. Simon Fraser University; 1992. [cited 2021 Mar 04].
Available from: http://summit.sfu.ca/item/3695.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Chen T. A theoretical and numerical study for the Fokker-Planck equation. [Thesis]. Simon Fraser University; 1992. Available from: http://summit.sfu.ca/item/3695
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of New South Wales
14.
Straka, Peter.
Continuous time random walk limit processes.
Degree: Mathematics & Statistics, 2011, University of New South Wales
URL: http://handle.unsw.edu.au/1959.4/50906
;
https://unsworks.unsw.edu.au/fapi/datastream/unsworks:9800/SOURCE02?view=true
► Continuous Time Random Walks (CTRWs) provide stochastic models for the random movement of any entity, e.g. a particle, a derivative price, etc. They are given…
(more)
▼ Continuous Time Random Walks (CTRWs) provide stochastic models for the random movement of any entity, e.g. a particle, a derivative price, etc. They are given by a sequence of random waiting times, each of which is followed by a random jump. The distribution of a jump possibly depends on the preceding (or succeeding) waiting time. After every jump, the CTRW is renewed. Waiting times with infinite means usually model long trapping times of particles, slow relaxation to equilibrium, or the system’s dependence on its history. Jumps with infinite variance usually model extremely fast dispersion. The rate at which the distribution of the limit process spreads in space can stay constant or can accelerate or decelerate, with transient behaviour from short to long times being possible. CTRW limits are hence versatile models for anomalous sub- or superdiffusion, and have found applications in a wide range of fields including biology, physics, hydrology, finance and ecology.This thesis is concerned with scaling limits of CTRWs on the level of stochastic processes. Similar to the convergence of random walks to Brownian motion, we identify limit processes when waiting times and jump lengths are rescaled to zero. We then show that these limit processes are jump-diffusions whose time evolution is governed by the inverse of an increasing additive process. Moreover, it turns out that there can be two different limit processes, depending on whether the length of a jump depends on the preceding or the succeeding waiting time. For independentidentically distributed waiting times, we show the existence of a governing “generalized
Fokker-
Planck equation,” which is a partial differential
equation whose solutions are given by the densities of CTRW limit process. Finally, we establish a continuous semi-Markov property for CTRW limits by embedding them into Markov processes. This property can then be used to resolve problems which arise from the missing Markov property of CTRW limits.
Advisors/Committee Members: Henry, Bruce Ian, Mathematics & Statistics, Faculty of Science, UNSW, Goldys, Ben, Mathematics & Statistics, Faculty of Science, UNSW.
Subjects/Keywords: Levy process; Random Walk; Stochastic process limit; Anomalous transport; Anomalous diffusion; Fokker-Planck equation
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APA (6th Edition):
Straka, P. (2011). Continuous time random walk limit processes. (Doctoral Dissertation). University of New South Wales. Retrieved from http://handle.unsw.edu.au/1959.4/50906 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:9800/SOURCE02?view=true
Chicago Manual of Style (16th Edition):
Straka, Peter. “Continuous time random walk limit processes.” 2011. Doctoral Dissertation, University of New South Wales. Accessed March 04, 2021.
http://handle.unsw.edu.au/1959.4/50906 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:9800/SOURCE02?view=true.
MLA Handbook (7th Edition):
Straka, Peter. “Continuous time random walk limit processes.” 2011. Web. 04 Mar 2021.
Vancouver:
Straka P. Continuous time random walk limit processes. [Internet] [Doctoral dissertation]. University of New South Wales; 2011. [cited 2021 Mar 04].
Available from: http://handle.unsw.edu.au/1959.4/50906 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:9800/SOURCE02?view=true.
Council of Science Editors:
Straka P. Continuous time random walk limit processes. [Doctoral Dissertation]. University of New South Wales; 2011. Available from: http://handle.unsw.edu.au/1959.4/50906 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:9800/SOURCE02?view=true
15.
Cesar Menezes Vieira.
Modelo contÃnuo para distribuiÃÃo e fluxo de partÃculas em meios superamortecidos.
Degree: Master, 2013, Universidade Federal do Ceará
URL: http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=10407
;
► Sistemas estocÃsticos sÃo sistemas que apresentam essencialmente um elemento imprevisÃvel, proveniente do acaso. Alguns exemplos desse tipo de sistema sÃo o movimento aleatÃrio de partÃculas…
(more)
▼ Sistemas estocÃsticos sÃo sistemas que apresentam essencialmente um elemento imprevisÃvel, proveniente do acaso. Alguns exemplos desse tipo de sistema sÃo o movimento aleatÃrio de partÃculas imersas em um fluido e distribuiÃÃes de velocidade de um fluido em escoamentos turbulentos. A equaÃÃo de Fokker-Planck à um formalismo para descrever a evoluÃÃo de sistemas estocÃsticos em geral, sendo tambÃm eficiente quando a contribuiÃÃo estocÃstica à irrelevante, resultando em um sistema determinÃstico. Pode ser aplicada tanto a sistemas que estÃo prÃximos do estado de equilÃbrio quanto a sistemas fora do equilÃbrio. No intuito de modelar partÃculas imersas em um meio, estudamos o movimento de partÃculas que interagem com forÃas repulsivas e de curto alcance. Estudamos esse sistema no regime superamortecido e à temperatura nula, isto Ã, sem levar em conta efeitos tÃrmicos, utilizando dois potenciais de interaÃÃo distintos. Por meio da equaÃÃo de Fokker-Planck, foi desenvolvido em trabalhos anteriores um modelo que descreve o comportamento macroscÃpico do sistema a partir de uma equaÃÃo contÃnua, em regimes estacionÃrios e nÃo-estacionÃrios. Segundo o modelo, a densidade de energia potencial de interaÃÃo (up) à proporcional ao quadrado da densidade de partÃculas, up=a
ho 2, onde a à uma constante que depende do potencial de interaÃÃo. Neste trabalho, tentamos aperfeiÃoar este modelo, fazendo uma modificaÃÃo neste na construÃÃo de a, passando a ser uma funÃÃo da densidade, a(
ho), isto Ã, considerando a possibilidade de outras formas de nÃo-linearidade. Nossos resultados sugerem que, sob certas circunstÃncias, em especial para o potencial de Yukawa, o modelo que propomos consegue prever bem os resultados de simulaÃÃo de dinÃmica molecular. Para este mesmo potencial, vimos que a dependÃncia da densidade de energia potencial de interaÃÃo (up) com a densidade de partÃculas (
ho) nem sempre à quadrÃtica. Por outro lado, para o segundo potencial estudado, que permite transiÃÃes estruturais com a variaÃÃo de densidade, a simplicidade do modelo nÃo foi suficiente para prever o perfil de densidade.
Stochastic systems typically present an element of randomness ( extit{e.g.} the random motion of particles inside a overdamped fluid, velocity distributions into turbulent flow, etc.). The Fokker-Planck equation is a formalism useful to describe the temporal evolution of stochastic systems in general, and it is also efficient when the stochastic element is negligible, yielding a deterministic system. It can be applied both to systems far from equilibrium and systems which are close to a state of equilibrium. In order to model particles inside a medium, we study the motion of particles which interact with each other through short-range repulsive potentials. Using the Fokker-Planck equation, a model has been previously developed in order to explain both stationary and non-stationary behaviour of the system. According to the model, the interaction energy density (up) is proportional to the square of the density of…
Advisors/Committee Members: Andrà Auto Moreira.
Subjects/Keywords: FISICA DA MATERIA CONDENSADA; DinÃmica molecular; Coarse-graining; EquaÃÃo de Fokker-Planck; MecÃnica EstatÃstica; Molecular Dynamics; Coarse-graining; Fokker-Planck equation; Statistical Mechanics
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APA ·
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APA (6th Edition):
Vieira, C. M. (2013). Modelo contÃnuo para distribuiÃÃo e fluxo de partÃculas em meios superamortecidos. (Masters Thesis). Universidade Federal do Ceará. Retrieved from http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=10407 ;
Chicago Manual of Style (16th Edition):
Vieira, Cesar Menezes. “Modelo contÃnuo para distribuiÃÃo e fluxo de partÃculas em meios superamortecidos.” 2013. Masters Thesis, Universidade Federal do Ceará. Accessed March 04, 2021.
http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=10407 ;.
MLA Handbook (7th Edition):
Vieira, Cesar Menezes. “Modelo contÃnuo para distribuiÃÃo e fluxo de partÃculas em meios superamortecidos.” 2013. Web. 04 Mar 2021.
Vancouver:
Vieira CM. Modelo contÃnuo para distribuiÃÃo e fluxo de partÃculas em meios superamortecidos. [Internet] [Masters thesis]. Universidade Federal do Ceará 2013. [cited 2021 Mar 04].
Available from: http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=10407 ;.
Council of Science Editors:
Vieira CM. Modelo contÃnuo para distribuiÃÃo e fluxo de partÃculas em meios superamortecidos. [Masters Thesis]. Universidade Federal do Ceará 2013. Available from: http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=10407 ;
16.
ARAÚJO, Hugo de Andrade.
Transições de fase do modelo de Foraging e difusão anômala
.
Degree: 2013, Universidade Federal de Pernambuco
URL: http://repositorio.ufpe.br/handle/123456789/17100
► Nesta Dissertac¸ ˜ao estudamos a dinˆamica energ´etica das buscas aleat ´orias aplicadas ao problema de foraging, em que animais buscam por comida ou parceiros em…
(more)
▼ Nesta Dissertac¸ ˜ao estudamos a dinˆamica energ´etica das buscas aleat ´orias aplicadas ao
problema de foraging, em que animais buscam por comida ou parceiros em ambientes
escassos. Discutiremos, inicialmente, um modelo estat´ıstico de caminhadas aleat ´orias
utilizando as distribuic¸ ˜oes de L´evy para os tamanhos dos passos de busca, as quais tˆem
sido reportadas na literatura como estrat´egias de eficiˆencia ´otima para o problema. Em
seguida vamos incluir no modelo ganhos e perdas de energia na caminhada aleat ´ oria de
busca, e abordaremos a dinˆamica energ´etica do processo de busca unidimensional com
extremos absorventes. Vamos discutir a transic¸ ˜ao de fase que o buscador experimenta
de um estado ativo (“vivo”), t´ıpico de ambientes com abundˆancia de recursos, para um
estado est´atico absorvente (“morto”), onde a busca ´e encerrada pela falta de energia
oriunda do encontro de recursos. Obteremos os expoentes cr´ıticos relativos a essa
transic¸ ˜ao atrav´es de abordagens te ´ oricas, tais como o m´etodo de primeira passagem
para o estado de energia nula, e num´ericas, baseadas na hip´otese de escala. Mostraremos
a independˆencia destes expoentes com a forma funcional da func¸ ˜ao gasto de energia. Por
fim, faremos uma breve revis˜ao da literatura sobre a equac¸ ˜ao de
Fokker-
Planck canˆonica
e tamb´em sobre as suas vers˜oes utilizando derivadas fracion´arias, numa prepararac¸ ˜ao
para uma futura abordagem, durante o programa de Doutorado, do problema da busca
aleat´oria envolvendo difus˜oes anˆomalas (por exemplo, superdifus˜ao) via equac¸ ˜oes
diferenciais.
Advisors/Committee Members: RAPOSO, Ernesto Carneiro Pessoa (advisor), http://lattes.cnpq.br/4321118621178584 (advisor).
Subjects/Keywords: Caminhadas Aleat´ orias;
Distribuic¸ ˜ao de L´evy;
Foraging;
Transic¸ ˜oes de fase;
Equac¸ ˜ao de Fokker-Planck;
Random Walks;
L´evy Distribution;
Foraging;
Phase Transition;
Fokker- Planck Equation
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APA (6th Edition):
ARAÚJO, H. d. A. (2013). Transições de fase do modelo de Foraging e difusão anômala
. (Thesis). Universidade Federal de Pernambuco. Retrieved from http://repositorio.ufpe.br/handle/123456789/17100
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
ARAÚJO, Hugo de Andrade. “Transições de fase do modelo de Foraging e difusão anômala
.” 2013. Thesis, Universidade Federal de Pernambuco. Accessed March 04, 2021.
http://repositorio.ufpe.br/handle/123456789/17100.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
ARAÚJO, Hugo de Andrade. “Transições de fase do modelo de Foraging e difusão anômala
.” 2013. Web. 04 Mar 2021.
Vancouver:
ARAÚJO HdA. Transições de fase do modelo de Foraging e difusão anômala
. [Internet] [Thesis]. Universidade Federal de Pernambuco; 2013. [cited 2021 Mar 04].
Available from: http://repositorio.ufpe.br/handle/123456789/17100.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
ARAÚJO HdA. Transições de fase do modelo de Foraging e difusão anômala
. [Thesis]. Universidade Federal de Pernambuco; 2013. Available from: http://repositorio.ufpe.br/handle/123456789/17100
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Université de Bordeaux I
17.
Mallet, Jessy.
Contribution à la modélisation et à la simulation numérique multi-échelle du transport cinétique électronique dans un plasma chaud : A couple problems of linear dynamics in Banach spaces.
Degree: Docteur es, Mathématiques appliquées et calcul scientifique, 2012, Université de Bordeaux I
URL: http://www.theses.fr/2012BOR14584
► En physique des plasmas, le transport des électrons peut être décrit d'un point de vue cinétique ou d'un point de vue hydrodynamique.En théorie cinétique, une…
(more)
▼ En physique des plasmas, le transport des électrons peut être décrit d'un point de vue cinétique ou d'un point de vue hydrodynamique.En théorie cinétique, une équation de Fokker-Planck couplée aux équations de Maxwell est utilisée habituellement pour décrire l'évolution des électrons dans un plasma collisionnel. Plus précisément la solution de l'équation cinétique est une fonction de distribution non négative f spécifiant la densité des particules en fonction de la vitesse des particules, le temps et la position dans l'espace. Afin d'approcher la solution de ce problème cinétique, de nombreuses méthodes de calcul ont été développées. Ici, une méthode déterministe est proposée dans une géométrie plane. Cette méthode est basée sur différents schémas numériques d'ordre élevé . Chaque schéma déterministe utilisé présente de nombreuses propriétés fondamentales telles que la conservation du flux de particules, la préservation de la positivité de la fonction de distribution et la conservation de l'énergie. Cependant, le coût de calcul cinétique pour cette méthode précise est trop élevé pour être utilisé dans la pratique, en particulier dans un espace multidimensionnel.Afin de réduire ce temps de calcul, le plasma peut être décrit par un modèle hydrodynamique. Toutefois, pour les nouvelles cibles à haute énergie, les effets cinétiques sont trop importants pour les négliger et remplacer le calcul cinétique par des modèles habituels d'Euler macroscopiques. C'est pourquoi une approche alternative est proposée en considérant une description intermédiaire entre le modèle fluide et le modèle cinétique. Pour décrire le transport des électrons, le nouveau modèle réduit cinétique M1 est basé sur une approche aux moments pour le système Maxwell-Fokker-Planck. Ce modèle aux moments utilise des intégrations de la fonction de distribution des électrons sur la direction de propagation et ne retient que l'énergie des particules comme variable cinétique. La variable de vitesse est écrite en coordonnées sphériques et le modèle est défini en considérant le système de moments par rapport à la variable angulaire. La fermeture du système de moments est obtenue sous l'hypothèse que la fonction de distribution est une fonction d'entropie minimale. Ce modèle satisfait les propriétés fondamentales telles que la conservation de la positivité de la fonction de distribution, les lois de conservation pour les opérateurs de collision et la dissipation d'entropie. En outre une discrétisation entropique avec la variable de vitesse est proposée sur le modèle semi-discret. De plus, le modèle M1 peut être généralisé au modèle MN en considérant N moments donnés. Le modèle aux N-moments obtenu préserve également les propriétés fondamentales telles que les lois de conservation et la dissipation de l'entropie. Le schéma semi-discret associé préserve les propriétés de conservation et de décroissance de l'entropie.
In plasma physics, the transport of electrons can be described from a kinetic point of view or from an hydrodynamical point of view.Classically in…
Advisors/Committee Members: Dubroca, Bruno (thesis director), Humières, Emmanuel d' (thesis director).
Subjects/Keywords: Minimisation entropique; Équation Fokker-Planck-Landau; Équations de Maxwell; Système aux moments; Schéma entropique; Entropy minimization; Landau-Fokker-Planck equation; Maxwell equations; Moments systems; Entropic scheme
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APA ·
Chicago ·
MLA ·
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CSE |
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to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Mallet, J. (2012). Contribution à la modélisation et à la simulation numérique multi-échelle du transport cinétique électronique dans un plasma chaud : A couple problems of linear dynamics in Banach spaces. (Doctoral Dissertation). Université de Bordeaux I. Retrieved from http://www.theses.fr/2012BOR14584
Chicago Manual of Style (16th Edition):
Mallet, Jessy. “Contribution à la modélisation et à la simulation numérique multi-échelle du transport cinétique électronique dans un plasma chaud : A couple problems of linear dynamics in Banach spaces.” 2012. Doctoral Dissertation, Université de Bordeaux I. Accessed March 04, 2021.
http://www.theses.fr/2012BOR14584.
MLA Handbook (7th Edition):
Mallet, Jessy. “Contribution à la modélisation et à la simulation numérique multi-échelle du transport cinétique électronique dans un plasma chaud : A couple problems of linear dynamics in Banach spaces.” 2012. Web. 04 Mar 2021.
Vancouver:
Mallet J. Contribution à la modélisation et à la simulation numérique multi-échelle du transport cinétique électronique dans un plasma chaud : A couple problems of linear dynamics in Banach spaces. [Internet] [Doctoral dissertation]. Université de Bordeaux I; 2012. [cited 2021 Mar 04].
Available from: http://www.theses.fr/2012BOR14584.
Council of Science Editors:
Mallet J. Contribution à la modélisation et à la simulation numérique multi-échelle du transport cinétique électronique dans un plasma chaud : A couple problems of linear dynamics in Banach spaces. [Doctoral Dissertation]. Université de Bordeaux I; 2012. Available from: http://www.theses.fr/2012BOR14584
Pontifical Catholic University of Rio de Janeiro
18.
[No author].
[pt] ESTUDO DA DINÂMICA ESTOCÁSTICA DE REDISTRIBUIÇÃO DA
RIQUEZA USANDO UMA EQUAÇÃO DE FOKKER-PLANCK.
Degree: 2020, Pontifical Catholic University of Rio de Janeiro
URL: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=50971
► [pt] A dinâmica da distribuição da riqueza para o modelo conhecido em inglês como Yard-Sale Model (Modelo da Venda de Quintal) pode ser descrita através…
(more)
▼ [pt] A dinâmica da distribuição da riqueza para o
modelo conhecido em inglês como Yard-Sale Model (Modelo da Venda de
Quintal) pode ser descrita através de uma equação de Fokker-Planck
para a função densidade de probabilidade P(w, t) da riqueza w em um
instante t. Neste trabalho foi investigado o efeito de um arrasto
redistributivo não linear nessa dinâmica. Considera-se (I) uma
taxação do tipo linear por partes, onde apenas aqueles com riqueza
acima de um determinado valor são taxados, e, (II) uma taxação na
forma de lei de potência, que inclui os tipos progressivo e
regressivo. Em todos os casos, o total arrecadado é distribuído
igualmente. Analisou-se como essas regras podem modificar a
distribuição da riqueza numa população e, principalmente, o nível
de desigualdade medido pelo índice de Gini.
[en] The dynamics of wealth distribution for the
so-called Yard-Sale Model can be described by a Fokker-Planck
equation for the probability density function P(w, t) of wealth w
at time t. In this work, the effect of nonlinear redistributive
drifts was investigated. It was considered (I) a piecewise linear
tax, where only those with wealth above a certain threshold are
taxed, and, (II) a power-law tax that includes the progressive and
regressive types. In all cases, the collected amount of wealth is
redistributed equally. We analyze how these rules modify the
distribution of wealth across the population and, mainly, the
inequality level measured through the Gini index.
Advisors/Committee Members: CELIA BEATRIZ ANTENEODO DE PORTO.
Subjects/Keywords: [pt] EQUACAO DE FOKKER-PLANCK; [pt] MODELO DE AGENTES; [pt] DISTRIBUICAO DE RIQUEZA; [pt] DINAMICA ESTOCASTICA; [en] FOKKER-PLANCK EQUATION; [en] AGENT-BASED MODEL; [en] WEALTH DISTRIBUTION; [en] STOCHASTIC DYNAMICS
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APA (6th Edition):
author], [. (2020). [pt] ESTUDO DA DINÂMICA ESTOCÁSTICA DE REDISTRIBUIÇÃO DA
RIQUEZA USANDO UMA EQUAÇÃO DE FOKKER-PLANCK. (Thesis). Pontifical Catholic University of Rio de Janeiro. Retrieved from http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=50971
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
author], [No. “[pt] ESTUDO DA DINÂMICA ESTOCÁSTICA DE REDISTRIBUIÇÃO DA
RIQUEZA USANDO UMA EQUAÇÃO DE FOKKER-PLANCK.” 2020. Thesis, Pontifical Catholic University of Rio de Janeiro. Accessed March 04, 2021.
http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=50971.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
author], [No. “[pt] ESTUDO DA DINÂMICA ESTOCÁSTICA DE REDISTRIBUIÇÃO DA
RIQUEZA USANDO UMA EQUAÇÃO DE FOKKER-PLANCK.” 2020. Web. 04 Mar 2021.
Vancouver:
author] [. [pt] ESTUDO DA DINÂMICA ESTOCÁSTICA DE REDISTRIBUIÇÃO DA
RIQUEZA USANDO UMA EQUAÇÃO DE FOKKER-PLANCK. [Internet] [Thesis]. Pontifical Catholic University of Rio de Janeiro; 2020. [cited 2021 Mar 04].
Available from: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=50971.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
author] [. [pt] ESTUDO DA DINÂMICA ESTOCÁSTICA DE REDISTRIBUIÇÃO DA
RIQUEZA USANDO UMA EQUAÇÃO DE FOKKER-PLANCK. [Thesis]. Pontifical Catholic University of Rio de Janeiro; 2020. Available from: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=50971
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of British Columbia
19.
Lo, Joseph Quin Wai.
Pseudospectral methods in quantum and statistical mechanics.
Degree: PhD, Mathematics, 2008, University of British Columbia
URL: http://hdl.handle.net/2429/1298
► The pseudospectral method is a family of numerical methods for the solution of differential equations based on the expansion of basis functions defined on a…
(more)
▼ The pseudospectral method is a family of numerical methods for the solution of differential equations based on the expansion of basis functions defined on a set of grid points. In this thesis, the relationship between the distribution of grid points and the accuracy and convergence of the solution is emphasized. The polynomial and sinc pseudospectral methods are extensively studied along with many applications to quantum and statistical mechanics involving the Fokker-Planck and Schroedinger equations.
The grid points used in the polynomial methods coincide with the points of quadrature, which are defined by a set of polynomials orthogonal with respect to a weight function. The choice of the weight function plays an important role in the convergence of the solution. It is observed that rapid convergence is usually achieved when the weight function is chosen to be the square of the ground-state eigenfunction of the problem. The sinc method usually provides a slow convergence as the grid points are uniformly distributed regardless of the behaviour of the solution.
For both polynomial and sinc methods, the convergence rate can be improved by redistributing the grid points to more appropriate positions through a transformation of coordinates. The transformation method discussed in this thesis preserves the orthogonality of the basis functions and provides simple expressions for the construction of discretized matrix operators. The convergence rate can be improved by several times in the evaluation of loosely bound eigenstates with an exponential or hyperbolic sine transformation.
The transformation can be defined explicitly or implicitly. An explicit transformation is based on a predefined mapping function, while an implicit transformation is constructed by an appropriate set of grid points determined by the behaviour of the solution. The methodologies of these transformations are discussed with some applications to 1D and 2D problems. The implicit transformation is also used as a moving mesh method for the time-dependent Smoluchowski equation when a function with localized behaviour is used as the initial condition.
Subjects/Keywords: Pseudospectral methods; Fokker-Planck equation; Schroedinger equation; Interpolation
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APA (6th Edition):
Lo, J. Q. W. (2008). Pseudospectral methods in quantum and statistical mechanics. (Doctoral Dissertation). University of British Columbia. Retrieved from http://hdl.handle.net/2429/1298
Chicago Manual of Style (16th Edition):
Lo, Joseph Quin Wai. “Pseudospectral methods in quantum and statistical mechanics.” 2008. Doctoral Dissertation, University of British Columbia. Accessed March 04, 2021.
http://hdl.handle.net/2429/1298.
MLA Handbook (7th Edition):
Lo, Joseph Quin Wai. “Pseudospectral methods in quantum and statistical mechanics.” 2008. Web. 04 Mar 2021.
Vancouver:
Lo JQW. Pseudospectral methods in quantum and statistical mechanics. [Internet] [Doctoral dissertation]. University of British Columbia; 2008. [cited 2021 Mar 04].
Available from: http://hdl.handle.net/2429/1298.
Council of Science Editors:
Lo JQW. Pseudospectral methods in quantum and statistical mechanics. [Doctoral Dissertation]. University of British Columbia; 2008. Available from: http://hdl.handle.net/2429/1298
Universitat de Barcelona
20.
Sancho, José M.
Aplicaciones de la dinámica de Fokker-Planck.
Degree: 1980, Universitat de Barcelona
URL: http://hdl.handle.net/10803/666108
► El estudio de la dinámica de un sistema físico macroscópico mediante sus ecuaciones microscópicas del movimiento tiene un interés innegable, pero posee también unas limitaciones…
(more)
▼ El estudio de la dinámica de un sistema físico macroscópico mediante sus ecuaciones microscópicas del movimiento tiene un interés innegable, pero posee también unas limitaciones muy poderosas. En primer lugar no siempre son bien conocidos sus componentes microscópicos ni las ecuaciones dinámicas que éstos obedecen. En segundo lugar, aún conociendo bien los componentes internos del Sistema y sus ecuaciones del movimiento, el numero de éstas es tan elevado (del orden del número de Avogrado) que su tratamiento puede resultar imposible en la práctica. Por úl.timo, el hech.o de que la observación .sea siempre macroscópica nos asegura que bastan pocas variables (llamadas relevantes, “gruesas” o macroscópicas) para dar una buena descripción de las procesos que tienen lugar en esos sitemas. Esta ultima situación ha conducido a postular ecuaciones fenomenológicas del movimiento, para estas variables, basadas en principios físicos muy generales, como pueden ser: la conservación de masa, de la energia, del momento, etc; siendo la mayoria de ellas ecuaciones de continuidad.
Estas ecuaciones fenomenológicas consiguieron explicar muchos de los fenómenos obs.ervados, pero quedaba todavía par explicar las fluctuaciones completamente aleatorias que, por otra parte, también eran observadas. Dado el caracter completamente det.erminista de tales ecuaciones fenomenológicas, estaba claro que de ellas no se podía derivar ningun tipo de fenómeno probabilístico, como son las fluctuaciones.
Todas estas consideraciones han hecho que en los últimos años haya aumentado considerablemente el interés por explicar los problemas estadísticos referidos al equilibrio y al no equilibrio mediante ecuaciones diferenciales estocásticas para las variables relevantes del problema en estudio. El éxito de la descripción de los sistemas macroscópicos en términos de variables relevantes es debido principalmente a que el número elevado de grados de libertad que se han eliminado, que eran de variación rápida en el tiempo y corta en el espacio, se han tenido en cuenta dejando fluctuar a las variables relevantes.
Así pues, en analogía con la idea de Langevin para la dinámica de una partícula browniana la dinámica de estos sistemas más complicados puede ser descrita mediante ecuaciones diferenciales de primer orden en el tiempo del tipo de la ecuación de Langevin en las que una parte es determinista y otra estocástica. Aunque existen otro tipo de descripciones nos limitaremos en este trabajo al estudio de las ecuaciones del tipo de Langevin.
Advisors/Committee Members: Universitat de Barcelona. Facultat de Física, [email protected] (authoremail), false (authoremailshow), Garrido, L. (Luis), 1930- (director).
Subjects/Keywords: Equació de Fokker-Planck; Fokker-Planck, Ecuación de; Fokker-Planck equation; Ciències Experimentals i Matemàtiques; 53
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APA ·
Chicago ·
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CSE |
Export
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Manager
APA (6th Edition):
Sancho, J. M. (1980). Aplicaciones de la dinámica de Fokker-Planck. (Thesis). Universitat de Barcelona. Retrieved from http://hdl.handle.net/10803/666108
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Sancho, José M. “Aplicaciones de la dinámica de Fokker-Planck.” 1980. Thesis, Universitat de Barcelona. Accessed March 04, 2021.
http://hdl.handle.net/10803/666108.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Sancho, José M. “Aplicaciones de la dinámica de Fokker-Planck.” 1980. Web. 04 Mar 2021.
Vancouver:
Sancho JM. Aplicaciones de la dinámica de Fokker-Planck. [Internet] [Thesis]. Universitat de Barcelona; 1980. [cited 2021 Mar 04].
Available from: http://hdl.handle.net/10803/666108.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Sancho JM. Aplicaciones de la dinámica de Fokker-Planck. [Thesis]. Universitat de Barcelona; 1980. Available from: http://hdl.handle.net/10803/666108
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Michigan
21.
Park, Sang H.
Nonlinear trajectory navigation.
Degree: PhD, Electrical engineering, 2007, University of Michigan
URL: http://hdl.handle.net/2027.42/126532
► Trajectory navigation entails the solution of many different problems that arise due to uncertain knowledge of the spacecraft state, including orbit prediction, correction maneuver design,…
(more)
▼ Trajectory navigation entails the solution of many different problems that arise due to uncertain knowledge of the spacecraft state, including orbit prediction, correction maneuver design, and trajectory estimation. In practice, these problems are usually solved based on an assumption that linear dynamical models sufficiently approximate the local trajectory dynamics and their associated statistics. However, astrodynamics problems are nonlinear in general and linear spacecraft dynamics models can fail to characterize the true trajectory dynamics when the system is
subject to a highly unstable environment or when mapped over a long time period. This limits the performance of traditional navigation techniques and can make it difficult to perform precision analysis or robust navigation. This dissertation presents an alternate method for spacecraft trajectory navigation based on a nonlinear local trajectory model and their statistics in an analytic framework. For a given reference trajectory, we first solve for the higher order Taylor series terms that describe the localized nonlinear motion and develop an analytic expression for the relative solution flow. We then discuss the nonlinear dynamical mapping of a spacecraft's probability density function by solving the
Fokker-
Planck equation for a deterministic system. From this result we derive an analytic method for orbit uncertainty propagation which can replicate Monte-Carlo simulations with the benefit of added flexibility in initial orbit statistics. Using this approach, we introduce the concept of the statistically correct trajectory where we directly incorporate statistical information about an orbit state into the trajectory design process. As an extension of this concept, we define a nonlinear statistical targeting method where we solve for a correction maneuver which intercepts the desired target on average. Then we apply our results to a Bayesian filtering problem to obtain a general filtering algorithm for optimal estimation of the posterior conditional density function incorporating nonlinearity into the filtering process. Finally, we derive practical Kalman-type filters by applying our nonlinear relative solutions into the standard filters and show that these filters provide superior performance over linear filtering methods based on realistic trajectory and uncertainty models. The examples we consider are a conventional Hohmann transfer from the Earth to Moon using a simple two-body model, a strongly unstable transfer trajectory in the Hill three-body problem from the vicinity of L
2 through several orbits, and to the navigation of a spacecraft in a halo orbit in the restricted three-body problem. For each of these examples we show the benefits of using our nonlinear trajectory navigation techniques as compared to traditional linear navigation techniques.
Advisors/Committee Members: Scheeres, Daniel J. (advisor).
Subjects/Keywords: Fokker-planck Equation; Hamiltonian Dynamics; Navigation; Nonlinear Trajectory
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APA (6th Edition):
Park, S. H. (2007). Nonlinear trajectory navigation. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/126532
Chicago Manual of Style (16th Edition):
Park, Sang H. “Nonlinear trajectory navigation.” 2007. Doctoral Dissertation, University of Michigan. Accessed March 04, 2021.
http://hdl.handle.net/2027.42/126532.
MLA Handbook (7th Edition):
Park, Sang H. “Nonlinear trajectory navigation.” 2007. Web. 04 Mar 2021.
Vancouver:
Park SH. Nonlinear trajectory navigation. [Internet] [Doctoral dissertation]. University of Michigan; 2007. [cited 2021 Mar 04].
Available from: http://hdl.handle.net/2027.42/126532.
Council of Science Editors:
Park SH. Nonlinear trajectory navigation. [Doctoral Dissertation]. University of Michigan; 2007. Available from: http://hdl.handle.net/2027.42/126532
22.
Khaldi nee Bouzaghti, Yamina.
Interprétation probabiliste des EDP et processus de diffusion.
Degree: 2007, Université M'Hamed Bougara Boumerdès
URL: http://dlibrary.univ-boumerdes.dz:8080/jspui/handle/123456789/369
106 p. ; ill. ; 30 cm
Subjects/Keywords: Processus stochastique; Processus de diffusion; Fokker-Planck, Equation de
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APA (6th Edition):
Khaldi nee Bouzaghti, Y. (2007). Interprétation probabiliste des EDP et processus de diffusion. (Thesis). Université M'Hamed Bougara Boumerdès. Retrieved from http://dlibrary.univ-boumerdes.dz:8080/jspui/handle/123456789/369
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Khaldi nee Bouzaghti, Yamina. “Interprétation probabiliste des EDP et processus de diffusion.” 2007. Thesis, Université M'Hamed Bougara Boumerdès. Accessed March 04, 2021.
http://dlibrary.univ-boumerdes.dz:8080/jspui/handle/123456789/369.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Khaldi nee Bouzaghti, Yamina. “Interprétation probabiliste des EDP et processus de diffusion.” 2007. Web. 04 Mar 2021.
Vancouver:
Khaldi nee Bouzaghti Y. Interprétation probabiliste des EDP et processus de diffusion. [Internet] [Thesis]. Université M'Hamed Bougara Boumerdès; 2007. [cited 2021 Mar 04].
Available from: http://dlibrary.univ-boumerdes.dz:8080/jspui/handle/123456789/369.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Khaldi nee Bouzaghti Y. Interprétation probabiliste des EDP et processus de diffusion. [Thesis]. Université M'Hamed Bougara Boumerdès; 2007. Available from: http://dlibrary.univ-boumerdes.dz:8080/jspui/handle/123456789/369
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Texas A&M University
23.
Kumar, Mrinal.
Design and Analysis of Stochastic Dynamical Systems with Fokker-Planck Equation.
Degree: PhD, Aerospace Engineering, 2011, Texas A&M University
URL: http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7500
► This dissertation addresses design and analysis aspects of stochastic dynamical systems using Fokker-Planck equation (FPE). A new numerical methodology based on the partition of unity…
(more)
▼ This dissertation addresses design and analysis aspects of stochastic dynamical
systems using
Fokker-
Planck equation (FPE). A new numerical methodology based
on the partition of unity meshless paradigm is developed to tackle the greatest hurdle
in successful numerical solution of FPE, namely the curse of dimensionality. A local
variational form of the
Fokker-
Planck operator is developed with provision for h-
and p- refinement. The resulting high dimensional weak form integrals are evaluated
using quasi Monte-Carlo techniques. Spectral analysis of the discretized
Fokker-
Planck operator, followed by spurious mode rejection is employed to construct a
new semi-analytical algorithm to obtain near real-time approximations of transient
FPE response of high dimensional nonlinear dynamical systems in terms of a reduced
subset of admissible modes. Numerical evidence is provided showing that the curse
of dimensionality associated with FPE is broken by the proposed technique, while
providing problem size reduction of several orders of magnitude.
In addition, a simple modification of norm in the variational formulation is shown
to improve quality of approximation significantly while keeping the problem size fixed.
Norm modification is also employed as part of a recursive methodology for tracking
the optimal finite domain to solve FPE numerically.
The basic tools developed to solve FPE are applied to solving problems in nonlinear stochastic optimal control and nonlinear filtering. A policy iteration algorithm for
stochastic dynamical systems is implemented in which successive approximations of
a forced backward Kolmogorov
equation (BKE) is shown to converge to the solution
of the corresponding Hamilton Jacobi Bellman (HJB)
equation. Several examples,
including a four-state missile autopilot design for pitch control, are considered.
Application of the FPE solver to nonlinear filtering is considered with special emphasis
on situations involving long durations of propagation in between measurement
updates, which is implemented as a weak form of the Bayes rule. A nonlinear filter
is formulated that provides complete probabilistic state information conditioned on
measurements. Examples with long propagation times are considered to demonstrate
benefits of using the FPE based approach to filtering.
Advisors/Committee Members: Chakravorty, Suman (advisor), Junkins, John L. (advisor), Vadali, Srinivas R. (committee member), Hyland, David (committee member), Bhattacharyya, Shankar P. (committee member).
Subjects/Keywords: Stochastic dynamical systems; Fokker-Planck equation; Meshless finite-element methods; Nonlinear filtering; Stochastic optimal control; Partition of unity finite-element method
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APA (6th Edition):
Kumar, M. (2011). Design and Analysis of Stochastic Dynamical Systems with Fokker-Planck Equation. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7500
Chicago Manual of Style (16th Edition):
Kumar, Mrinal. “Design and Analysis of Stochastic Dynamical Systems with Fokker-Planck Equation.” 2011. Doctoral Dissertation, Texas A&M University. Accessed March 04, 2021.
http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7500.
MLA Handbook (7th Edition):
Kumar, Mrinal. “Design and Analysis of Stochastic Dynamical Systems with Fokker-Planck Equation.” 2011. Web. 04 Mar 2021.
Vancouver:
Kumar M. Design and Analysis of Stochastic Dynamical Systems with Fokker-Planck Equation. [Internet] [Doctoral dissertation]. Texas A&M University; 2011. [cited 2021 Mar 04].
Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7500.
Council of Science Editors:
Kumar M. Design and Analysis of Stochastic Dynamical Systems with Fokker-Planck Equation. [Doctoral Dissertation]. Texas A&M University; 2011. Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7500
Hong Kong University of Science and Technology
24.
Yang, Chen.
Quantum dissipation theory and its application to nonlinear spectroscopies.
Degree: 2001, Hong Kong University of Science and Technology
URL: http://repository.ust.hk/ir/Record/1783.1-4004
;
https://doi.org/10.14711/thesis-b692732
;
http://repository.ust.hk/ir/bitstream/1783.1-4004/1/th_redirect.html
► This thesis focuses on the study on the two most commonly used quantum dissipation theories, the Bloch-Redfield theory and Fokker-Planck equations and their applications in…
(more)
▼ This thesis focuses on the study on the two most commonly used quantum dissipation theories, the Bloch-Redfield theory and Fokker-Planck equations and their applications in nonlinear spectroscopies. After the spectrum conjugation to a dissipative mode was introduced, developed is the unified Redfield theory which satisfies the detailed-balance. Base on this unified Redfield theory, a generalized quantum Fokker-Planck equation is developed for both the T1-energy relaxation and the pure-T2 dephasing dissipation processes. The resulting dynamical semigroup Fokker-Planck equation preserves the general positivity of the reduced density operator and satisfies the detailed-balance relation up to the second-order moments at any temperatures. (Chapter 1). In order to understand the molecular dynamics in condensed phase theoretically and experimentally, the application of unified Redfield theory to transient absorption spectroscopies of molecules( Chapter 2) and the implementation of Fokker-Planck equation to transient absorption and fluorescence upconversion spectroscopies( Chapter 3 and Chapter 4) are discussed. Numerical demonstrations are carried out in a model molecule involving two Morse potential surfaces in the presence of the T1-vibrational relaxation and the pure T2-dephasing in both nuclear and electronic degrees of freedom. The pump-probe absorption and the time-frequency resolved fluorescence spectra are analyzed in terms of the dissiaptive dynamics. Chapter 5 presents an interesting application of quantum dissipation theories beyond the spectroscopies. Analyzed is the quantum transport in symmetric two-level systems under the influence of both dissipation and periodic driving.
Subjects/Keywords: Quantum theory
; Fokker-Planck equation
; Spectrum analysis
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APA (6th Edition):
Yang, C. (2001). Quantum dissipation theory and its application to nonlinear spectroscopies. (Thesis). Hong Kong University of Science and Technology. Retrieved from http://repository.ust.hk/ir/Record/1783.1-4004 ; https://doi.org/10.14711/thesis-b692732 ; http://repository.ust.hk/ir/bitstream/1783.1-4004/1/th_redirect.html
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Yang, Chen. “Quantum dissipation theory and its application to nonlinear spectroscopies.” 2001. Thesis, Hong Kong University of Science and Technology. Accessed March 04, 2021.
http://repository.ust.hk/ir/Record/1783.1-4004 ; https://doi.org/10.14711/thesis-b692732 ; http://repository.ust.hk/ir/bitstream/1783.1-4004/1/th_redirect.html.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Yang, Chen. “Quantum dissipation theory and its application to nonlinear spectroscopies.” 2001. Web. 04 Mar 2021.
Vancouver:
Yang C. Quantum dissipation theory and its application to nonlinear spectroscopies. [Internet] [Thesis]. Hong Kong University of Science and Technology; 2001. [cited 2021 Mar 04].
Available from: http://repository.ust.hk/ir/Record/1783.1-4004 ; https://doi.org/10.14711/thesis-b692732 ; http://repository.ust.hk/ir/bitstream/1783.1-4004/1/th_redirect.html.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Yang C. Quantum dissipation theory and its application to nonlinear spectroscopies. [Thesis]. Hong Kong University of Science and Technology; 2001. Available from: http://repository.ust.hk/ir/Record/1783.1-4004 ; https://doi.org/10.14711/thesis-b692732 ; http://repository.ust.hk/ir/bitstream/1783.1-4004/1/th_redirect.html
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Iowa State University
25.
Wang, Chi-Jen.
Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport.
Degree: 2013, Iowa State University
URL: https://lib.dr.iastate.edu/etd/13325
► We analyze both the spatiotemporal behavior of non-linear "reaction" models utilizing reaction-diffusion equations, and spatial transport problems on surfaces and in nanopores utilizing the relevant…
(more)
▼ We analyze both the spatiotemporal behavior of non-linear "reaction" models utilizing reaction-diffusion equations, and spatial transport problems on surfaces and in nanopores utilizing the relevant diffusion or Fokker-Planck equations.
The non-linear "reaction" models involve spatial discrete systems where "particles" reside at the sites of a periodic lattice: particles, X, spontaneously annihilate (X->O) at a specified rate p, and are autocatalytically created given the presence of nearby pairs of particles (O+2X->3X) at rates depending on the local configuration. [This reaction model is equivalent to a spatial epidemic model where sick individuals spontaneously recover (S->H), and healthy individuals are infected by pairs of sick neighbors (H+2S->3S).] The model exhibits a non-equilibrium phase-transition from a populated state to a vacuum state (with no particles) with increasing p. Near this transition, one can consider the propagation of interfaces separating the two states. Planar interfaces exhibit an orientation-dependence (leading to so-called generic two-phase coexistence), and curved interfaces enclosing droplets exhibit even richer behavior. These phenomena are analyzed utilizing the appropriate set of discrete reaction-diffusion equations (corresponding to lattice differential equations).
Diffusive transport of particles between islands or clusters of particles on a surface leads to coarsening of island arrays which can be analyzed by solution of an appropriate boundary value problem for the surface diffusion equation. We extend previous treatments to strongly anisotropic systems. Diffusion and passing of pairs of overdamped Langevin molecules in narrow nanopores can be described by the appropriate Fokker-Planck equations (corresponding to a high-dimensional diffusion equation). We provide the first analysis of this problem focusing on a characterization of the propensity of passing as a function of pore diameter.
Subjects/Keywords: coarsening and decay (ostwald ripening); Fokker-Planck equation; generic two-phase coexistence; overdamped Langevin particles passing; Schloegl's second model; Applied Mathematics
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APA (6th Edition):
Wang, C. (2013). Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport. (Thesis). Iowa State University. Retrieved from https://lib.dr.iastate.edu/etd/13325
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Wang, Chi-Jen. “Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport.” 2013. Thesis, Iowa State University. Accessed March 04, 2021.
https://lib.dr.iastate.edu/etd/13325.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Wang, Chi-Jen. “Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport.” 2013. Web. 04 Mar 2021.
Vancouver:
Wang C. Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport. [Internet] [Thesis]. Iowa State University; 2013. [cited 2021 Mar 04].
Available from: https://lib.dr.iastate.edu/etd/13325.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Wang C. Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport. [Thesis]. Iowa State University; 2013. Available from: https://lib.dr.iastate.edu/etd/13325
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Arizona
26.
PARLETTE, EDWARD BRUCE.
GENERALIZED FUNCTION SOLUTIONS TO THE FOKKER-PLANCK EQUATION.
Degree: 1985, University of Arizona
URL: http://hdl.handle.net/10150/187933
► In problems involving highly forward-peaked scattering, the Boltzmann transport equation can be simplified using the Fokker-Planck model. The purpose of this project was to develop…
(more)
▼ In problems involving highly forward-peaked scattering, the Boltzmann transport equation can be simplified using the Fokker-Planck model. The purpose of this project was to develop an analytical solution to the resulting Fokker-Planck equation. This analytical solution can then be used to benchmark numerical transport codes. A numerical solution to the Fokker-Planck equation was also developed. The analytical solution found is a generalized function. It satisfies the purpose of the project with two limitations. The first limitation is that the solution can only be evaluated for certain sources. The second limitation is that the solution can only be evaluated for small times. The moments of the Fokker-Planck equation can be evaluated for any time. The numerical solution developed works for all sources and all times. The analytical solution, then, provides an accurate and precise benchmark under certain conditions. The numerical solution provides a less accurate benchmark under all conditions.
Subjects/Keywords: Controlled fusion – Mathematical models.;
Fokker-Planck equation.
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APA (6th Edition):
PARLETTE, E. B. (1985). GENERALIZED FUNCTION SOLUTIONS TO THE FOKKER-PLANCK EQUATION.
(Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/187933
Chicago Manual of Style (16th Edition):
PARLETTE, EDWARD BRUCE. “GENERALIZED FUNCTION SOLUTIONS TO THE FOKKER-PLANCK EQUATION.
” 1985. Doctoral Dissertation, University of Arizona. Accessed March 04, 2021.
http://hdl.handle.net/10150/187933.
MLA Handbook (7th Edition):
PARLETTE, EDWARD BRUCE. “GENERALIZED FUNCTION SOLUTIONS TO THE FOKKER-PLANCK EQUATION.
” 1985. Web. 04 Mar 2021.
Vancouver:
PARLETTE EB. GENERALIZED FUNCTION SOLUTIONS TO THE FOKKER-PLANCK EQUATION.
[Internet] [Doctoral dissertation]. University of Arizona; 1985. [cited 2021 Mar 04].
Available from: http://hdl.handle.net/10150/187933.
Council of Science Editors:
PARLETTE EB. GENERALIZED FUNCTION SOLUTIONS TO THE FOKKER-PLANCK EQUATION.
[Doctoral Dissertation]. University of Arizona; 1985. Available from: http://hdl.handle.net/10150/187933
27.
Zhai, Haoyan.
The applications of discrete optimal transport in path planning and data clustering.
Degree: PhD, Mathematics, 2019, Georgia Tech
URL: http://hdl.handle.net/1853/61712
► Optimal transport introduces the concept of Wasserstein distance, which has been widely used in various applications in computational mathematics, machine learning as well as many…
(more)
▼ Optimal transport introduces the concept of Wasserstein distance, which has been widely used in various applications in computational mathematics, machine learning as well as many areas in engineering. Meanwhile, control theory and path planning is an active branch in mathematics and robotics, focusing on algorithms that calculate feasible or optimal paths for robotic systems. In this thesis, we use the properties of the gradient flows induced by Wasserstein-2 metric to design algorithms to handle different types of path planning and control problems. Also, we define the Wasserstein K-means problems on graphs and propose an efficient algorithm to solve it. First of all, we provide an algorithm to handle the path planning problem in unknown environments. We develop a deterministic approach with finite-step convergence guarantee. Also, there is a theoretical relation between this algorithm and the
Fokker-
Planck equations, which bounds the searching region of the algorithm. We use numerical examples to show the efficiency of the algorithm as well as to support the theoretical results. Then, we generalize the algorithm to solve the general control problem in the unknown environments and similar convergence results can be proven. Besides, there is an evidence that the algorithm is guided by the evolution of
Fokker-
Planck equation, and we use experiments to demonstrate our theorems. We move on to study the optimal path planning in flow field. In this case, the objective function, the traveling time or kinetic energy, is to be minimized with a given flow field. Following the idea of method of evolving junctions, we first transform the original infinite dimensional optimal control into a finite dimensional global optimization problem by introducing junctions located only on the discontinuity positions of the dynamics. To handle the global optimization, intermittent diffusion is used here to guarantee the completeness of the method. At last, we define the discrete Wasserstein-(1,p) distance that depends on the graph structure. With this distance function, we further propose the Wasserstein K-means problem on a general graph and provide an algorithm in the framework of Lloyd method. The key part of the algorithm is the calculation of discrete Wasserstein-(1,p) distance and the gradient flow induced by Wasserstein-2 metric to solve an optimization with objective function being a linear combination of Wasserstein-(1.p) distance. Examples and simulation results are provided in the thesis.
Advisors/Committee Members: Zhou, Haomin (advisor), Dieci, Luca (committee member), Kang, Sung Ha (committee member), Short, Martin (committee member), Zhang, Fumin (committee member).
Subjects/Keywords: Optimal transport; Path planning; Fokker-Planck equation
…guided by the evolution of Fokker-Planck equation, and we
use experiments to demonstrate our… …x28;x) log ρ(x)dx,
Rd
the gradient flow is the famous Fokker-Planck equation… …guided by the evolution of the Fokker-Planck equation (FPE) in the Optimal
Transport… …equation.
1.2
Optimal path planning in partitioned flow fields
In the Fokker-Planck equation… …then the corresponding Fokker-Planck equation is
∂ρ
+ div(f (x)ρ) = βdiv…
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APA (6th Edition):
Zhai, H. (2019). The applications of discrete optimal transport in path planning and data clustering. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/61712
Chicago Manual of Style (16th Edition):
Zhai, Haoyan. “The applications of discrete optimal transport in path planning and data clustering.” 2019. Doctoral Dissertation, Georgia Tech. Accessed March 04, 2021.
http://hdl.handle.net/1853/61712.
MLA Handbook (7th Edition):
Zhai, Haoyan. “The applications of discrete optimal transport in path planning and data clustering.” 2019. Web. 04 Mar 2021.
Vancouver:
Zhai H. The applications of discrete optimal transport in path planning and data clustering. [Internet] [Doctoral dissertation]. Georgia Tech; 2019. [cited 2021 Mar 04].
Available from: http://hdl.handle.net/1853/61712.
Council of Science Editors:
Zhai H. The applications of discrete optimal transport in path planning and data clustering. [Doctoral Dissertation]. Georgia Tech; 2019. Available from: http://hdl.handle.net/1853/61712
University of British Columbia
28.
Leung, Ki Y.
Electron mobilities in binary rare gas mixtures.
Degree: MS- MSc, Chemistry, 1990, University of British Columbia
URL: http://hdl.handle.net/2429/29339
► This thesis presents a detailed study of the composition dependence of the thermal and transient mobility of electrons in binary rare gas mixtures. The time…
(more)
▼ This thesis presents a detailed study of the composition dependence of the thermal and transient mobility of electrons in binary rare gas mixtures. The time independent electron real mobility in binary inert gas mixtures is calculated versus mole fraction for different electric
field strengths. The deviations from the linear variation of the reciprocal of the mobility of the mixture with mole fraction, that is from Blanc's law, is determined and explained in detail. Very large deviations from the linear behavior were calculated for several binary mixtures at specific electric strengths, in particular for He-Xe mixtures. An interesting effect was observed whereby the electron mobility in He-Xe mixtures, for particular compositions and electron field strength could be greater than in pure He or less than in pure Xe.
The time dependent electron real mobility and the corresponding relaxation time, in particular for He-Ar and He-Ne mixtures are reported for a wide range of concentrations, field strengths (d.c. electric field), and frequencies (microwave electric field). For a He-Ar mixture, the time dependent electron mobility is strongly influenced by the Ramsauer-Townsend minimum and leads to the occurrence of an overshoot and a negative mobility in the transient mobility. For He-Ne, a mixture without the Ramsauer-Townsend minimum, the transient mobility increases monotonically towards the thermal value. The energy thermal relaxation times 1/Pτ for He-Ne, and Ne-Xe mixtures are calculated so as to find out the validity of the linear relationship between the 1/Pτ of the mixture and mole fraction. A Quadrature Discretization Method of solution of the time dependent Boltzmann-Fokker-Planck equation for electrons in binary inert gas mixture is employed in the study of the time dependent electron real mobility. The solution of the Fokker-Planck equation is based on the expansion of the solution in the eigenfunctions of the Fokker-Planck operator.
Subjects/Keywords: Electron mobility; Fokker-Planck equation; Gases, Rare
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APA (6th Edition):
Leung, K. Y. (1990). Electron mobilities in binary rare gas mixtures. (Masters Thesis). University of British Columbia. Retrieved from http://hdl.handle.net/2429/29339
Chicago Manual of Style (16th Edition):
Leung, Ki Y. “Electron mobilities in binary rare gas mixtures.” 1990. Masters Thesis, University of British Columbia. Accessed March 04, 2021.
http://hdl.handle.net/2429/29339.
MLA Handbook (7th Edition):
Leung, Ki Y. “Electron mobilities in binary rare gas mixtures.” 1990. Web. 04 Mar 2021.
Vancouver:
Leung KY. Electron mobilities in binary rare gas mixtures. [Internet] [Masters thesis]. University of British Columbia; 1990. [cited 2021 Mar 04].
Available from: http://hdl.handle.net/2429/29339.
Council of Science Editors:
Leung KY. Electron mobilities in binary rare gas mixtures. [Masters Thesis]. University of British Columbia; 1990. Available from: http://hdl.handle.net/2429/29339
University of Texas – Austin
29.
-2728-5566.
From confinement to clustering : decoding the structural and diffusive signatures of microscopic frustration.
Degree: PhD, Chemical engineering, 2016, University of Texas – Austin
URL: http://hdl.handle.net/2152/46440
► There are diverse technological contexts where fluids and suspensions are perturbed by applied fields like interfaces or intrinsically governed by complex interparticle potentials. When these…
(more)
▼ There are diverse technological contexts where fluids and suspensions are perturbed by applied fields like interfaces or intrinsically governed by complex interparticle potentials. When these interactions act over lengthscales comparable to the fluid particle size and become strong enough to frustrate particle packing or rearrangements, they drive systems to exhibit microscopically inhomogeneous (i.e., position-dependent) structural and relaxation responses. We use computer simulations and statistical-mechanical tools to find connections between such frustrating interactions and inhomogeneous fluid responses, which can profoundly impact macroscopic material properties and processing requirements. We first consider how to measure and predict the position-dependent and average diffusion coefficients of particles along inhomogeneous free-energy landscapes (i.e., potentials of mean force). Characterizing diffusion in such inhomogeneous fluids is crucial for modeling, e.g., the transit of colloids across microfluidic devices and of solutes through biological membranes. We validate a practical technique based on the
Fokker-
Planck diffusion formalism that measures diffusivities based solely on particle trajectory data. We focus on hard-sphere fluids confined to thin channels or subjected to external fields that impose density fluctuations at various wavelengths. We find, for example, that hydrodynamic predictions of tracer diffusion in confinement are surprisingly robust given non-continuum solvents. We also demonstrate that correlations between fluid static structure and diffusivity can qualitatively depend on the lengthscale of density fluctuations or the onset of supercooling. We next examine fluids governed by competing short-range attractions and long-range repulsions that drive formation of equilibrium cluster phases, which comprise monodisperse aggregates of monomers. The formation of such morphologies greatly impacts, e.g., the manufacturing of therapeutic protein solutions. We first address a major challenge in probing the real-space structure of such suspensions: detecting and characterizing cluster phases based on the static structure factor accessible via scattering experiments. Using computer simulations and liquid-state theory, we validate rules for interpreting low-wavenumber features in the structure factor in terms of cluster emergence, size, spatial distribution, etc. We then validate a thermodynamic model that predicts cluster size based on the strengths of monomer interactions, adapting classical nucleation theory to incorporate new empirical scalings for the surface energies of small stable droplets.
Advisors/Committee Members: Truskett, Thomas Michael, 1973- (advisor), Bonnecaze, Roger T. (committee member), Ganesan, Venkat (committee member), Lynd, Nathaniel A. (committee member), Makarov, Dmitrii E. (committee member).
Subjects/Keywords: Complex fluids; Colloidal suspensions; Diffusion coefficient; Fokker-Planck equation; Confined fluids; SALR fluids; Equilibrium clusters; Structure factor; Classical nucleation theory
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APA (6th Edition):
-2728-5566. (2016). From confinement to clustering : decoding the structural and diffusive signatures of microscopic frustration. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/46440
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Chicago Manual of Style (16th Edition):
-2728-5566. “From confinement to clustering : decoding the structural and diffusive signatures of microscopic frustration.” 2016. Doctoral Dissertation, University of Texas – Austin. Accessed March 04, 2021.
http://hdl.handle.net/2152/46440.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
MLA Handbook (7th Edition):
-2728-5566. “From confinement to clustering : decoding the structural and diffusive signatures of microscopic frustration.” 2016. Web. 04 Mar 2021.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Vancouver:
-2728-5566. From confinement to clustering : decoding the structural and diffusive signatures of microscopic frustration. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2016. [cited 2021 Mar 04].
Available from: http://hdl.handle.net/2152/46440.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Council of Science Editors:
-2728-5566. From confinement to clustering : decoding the structural and diffusive signatures of microscopic frustration. [Doctoral Dissertation]. University of Texas – Austin; 2016. Available from: http://hdl.handle.net/2152/46440
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
The Ohio State University
30.
Zhao, Lin.
Aggregate Modeling of Large-Scale Cyber-Physical
Systems.
Degree: PhD, Electrical and Computer Engineering, 2017, The Ohio State University
URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1512111263124549
► This dissertation delivers new theoretical and computational frameworks for systematically modeling the aggregate dynamics of large-scale cyber-physical systems. Particularly focused on the hierarchical demand response…
(more)
▼ This dissertation delivers new theoretical and
computational frameworks for systematically modeling the aggregate
dynamics of large-scale cyber-physical systems. Particularly
focused on the hierarchical demand response management system in
smart grid, we develop both control-oriented and
optimization-oriented aggregate models for coordinating a large
population of responsive loads, including both thermostatically
controlled loads (TCLs) and deferrable loads. For control-oriented
modeling, we develop a unified stochastic hybrid system (SHS)
framework to derive the partial differential equations (PDE) that
characterize the dynamical evolution of the load distribution. A
deterministic hybrid system is proposed for modeling general
individual responsive load. An SHS is proposed for modeling the
population dynamics after accounting for different
uncertainties.Existing literature usually derives the PDE based on
the physical principles and specifies the associated boundary
conditions heuristically. Our method is based on the adjoint
relation between the differential operator associated with the PDE
and the extended generator of the SHS process. In particular, it
enables us to determine the PDE boundary conditions directly from
the boundary condition satisfied by the SHS generator. The obtained
PDE model systematically generalizes many existing aggregate
models. It is fundamentally important for designing various
aggregate control strategies.The optimization-oriented modeling is
to characterize the constraint sets satisfied by the aggregate load
power, also known as the aggregate flexibility. We show that the
individual power flexibility can be modeled by a polytope and the
aggregate flexibility is the Minkowski sum of the individual
flexibility polytopes. Exact Minkowski sum of these polytopes is
computationally prohibitive. Therefore, we develop
optimization-based algorithms to approximate the aggregate
flexibility. For TCLs, we propose to approximate individual
flexibility polytopes using homothetic polytopes. This leads to
efficient algorithms to approximate the aggregate flexibility as
the Minkowski sum of homothetic polytopes reduces to just the
ordinary vector sum. We also provide extensive simulation to show
the significant performance improvement over the existing modeling
methods.Aggregate flexibility modeling of deferrable loads is more
challenging than that of TCLs due to the additional timing
constraints. A sufficient characterization (i.e., inner
approximation) of the aggregate flexibility with controllable model
complexity has not been proposed in the literature before. We
interpret the Minkowski sum as a projection operation and develop
an algorithm to inner approximate the projection optimally using
homothetic polytopes. The algorithm can be executed efficiently in
a distributed way. An energy arbitrage example is further employed
to demonstrate the application of the proposed
algorithm.
Advisors/Committee Members: Zhang, Wei (Advisor), Passino, Kevin (Committee Chair).
Subjects/Keywords: Electrical Engineering; aggregate modeling; Fokker-Planck equation; population dynamics; stochastic hybrid system; smart grid; cyber-physical system; boundary conditions
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APA (6th Edition):
Zhao, L. (2017). Aggregate Modeling of Large-Scale Cyber-Physical
Systems. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1512111263124549
Chicago Manual of Style (16th Edition):
Zhao, Lin. “Aggregate Modeling of Large-Scale Cyber-Physical
Systems.” 2017. Doctoral Dissertation, The Ohio State University. Accessed March 04, 2021.
http://rave.ohiolink.edu/etdc/view?acc_num=osu1512111263124549.
MLA Handbook (7th Edition):
Zhao, Lin. “Aggregate Modeling of Large-Scale Cyber-Physical
Systems.” 2017. Web. 04 Mar 2021.
Vancouver:
Zhao L. Aggregate Modeling of Large-Scale Cyber-Physical
Systems. [Internet] [Doctoral dissertation]. The Ohio State University; 2017. [cited 2021 Mar 04].
Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1512111263124549.
Council of Science Editors:
Zhao L. Aggregate Modeling of Large-Scale Cyber-Physical
Systems. [Doctoral Dissertation]. The Ohio State University; 2017. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1512111263124549
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Open Access Theses and Dissertations
