You searched for +publisher:"Georgia Tech" +contributor:("Bonetto, Federico").
Showing records 1 – 16 of
16 total matches.
No search limiters apply to these results.
Georgia Tech
1.
Bolding, Mark M.
Topics in dynamics: First passage probabilities and chaotic properties of the physical wind-tree model.
Degree: PhD, Mathematics, 2018, Georgia Tech
URL: http://hdl.handle.net/1853/59931 
► We prove that the evolution of the "most chaotic" dynamical systems consists of three different stages. Consider a finite Markov partition (coarse graining) X of…
(more)
▼ We prove that the evolution of the "most chaotic" dynamical systems consists of three different stages. Consider a finite Markov partition (coarse graining) X of the phase space of a system. In the first short time interval there is a hierarchy with respect to the values of the first passage probabilities for the elements of X and therefore predictions can be made about which element an orbit will most likely hit. In the third infinitely long time interval there is an opposite hierarchy of the elements of X and therefore analogous finite time predictions can be made. Our results demonstrate that finite time predictions for the evolution of strongly chaotic dynamical systems are possible. We then show that mathematical billiards generated by the motion of a point particle do not adequately describe the dynamics of real physical particles within the same domain (billiard table), and introduce a new model for diffusion intended to revitalize the Ehrenfests’ Wind-Tree model.
Advisors/Committee Members: Matzinger, Heinrich (advisor), Bunimovich, Leonid (advisor), Bonetto, Federico (advisor), Goldsztein, Guillermo (advisor).
Subjects/Keywords: Dynamical systems; Chaos
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Bolding, M. M. (2018). Topics in dynamics: First passage probabilities and chaotic properties of the physical wind-tree model. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/59931
Chicago Manual of Style (16th Edition):
Bolding, Mark M. “Topics in dynamics: First passage probabilities and chaotic properties of the physical wind-tree model.” 2018. Doctoral Dissertation, Georgia Tech. Accessed April 11, 2021.
http://hdl.handle.net/1853/59931.
MLA Handbook (7th Edition):
Bolding, Mark M. “Topics in dynamics: First passage probabilities and chaotic properties of the physical wind-tree model.” 2018. Web. 11 Apr 2021.
Vancouver:
Bolding MM. Topics in dynamics: First passage probabilities and chaotic properties of the physical wind-tree model. [Internet] [Doctoral dissertation]. Georgia Tech; 2018. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1853/59931.
Council of Science Editors:
Bolding MM. Topics in dynamics: First passage probabilities and chaotic properties of the physical wind-tree model. [Doctoral Dissertation]. Georgia Tech; 2018. Available from: http://hdl.handle.net/1853/59931
2.
Viana Camejo, Mikel.
Results on invariant whiskered tori for fibered holomorphic maps and on compensated domains.
Degree: PhD, Mathematics, 2018, Georgia Tech
URL: http://hdl.handle.net/1853/59176
We present a very general theory that includes results on the persistence of quasi-periodic orbits of systems subject to quasi-periodic perturbations.
Advisors/Committee Members: Loss, Michael (committee member), Zeng, Chongchun (committee member), Jorba, Angel (committee member), Bonetto, Federico (committee member).Subjects/Keywords: Quasi-periodic dynamics; KAM theory; Lower dimensional elliptic tori; Skew-products; Compensated domains
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Viana Camejo, M. (2018). Results on invariant whiskered tori for fibered holomorphic maps and on compensated domains. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/59176
Chicago Manual of Style (16th Edition):
Viana Camejo, Mikel. “Results on invariant whiskered tori for fibered holomorphic maps and on compensated domains.” 2018. Doctoral Dissertation, Georgia Tech. Accessed April 11, 2021.
http://hdl.handle.net/1853/59176.
MLA Handbook (7th Edition):
Viana Camejo, Mikel. “Results on invariant whiskered tori for fibered holomorphic maps and on compensated domains.” 2018. Web. 11 Apr 2021.
Vancouver:
Viana Camejo M. Results on invariant whiskered tori for fibered holomorphic maps and on compensated domains. [Internet] [Doctoral dissertation]. Georgia Tech; 2018. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1853/59176.
Council of Science Editors:
Viana Camejo M. Results on invariant whiskered tori for fibered holomorphic maps and on compensated domains. [Doctoral Dissertation]. Georgia Tech; 2018. Available from: http://hdl.handle.net/1853/59176
Georgia Tech
3.
Kieffer, Thomas Forrest.
The Maxwell-Pauli Equations.
Degree: PhD, Mathematics, 2020, Georgia Tech
URL: http://hdl.handle.net/1853/62787
► We study the quantum mechanical many-body problem of N ≥ 1 non-relativistic electrons with spin interacting with their self-generated classical electromagnetic field and K ≥…
(more)
▼ We study the quantum mechanical many-body problem of N ≥ 1 non-relativistic
electrons with spin interacting with their self-generated classical electromagnetic field and K ≥ 0 static nuclei. We model the dynamics of the electrons
and their self-generated electromagnetic field using the so-called many-body
Maxwell-Pauli equations. The main result of this thesis is to construct time
global, finite-energy, weak solutions to the many-body Maxwell-Pauli equations
under the assumption that the fine structure constant α and the nuclear charges
are not too large. The assumptions on the size of α and the nuclear charges
ensure that we have energetic stability for this system, i.e., the absolute ground
state energy exists. The work in this thesis serves as an initial step towards understanding the connection between the energetic stability of matter in quantum
mechanics and the well-posedness of the corresponding dynamical equations.
Advisors/Committee Members: Loss, Michael (advisor), Kennedy, Brian (committee member), Harrell, Evans (committee member), Bonetto, Federico (committee member), Zeng, Chongchun (committee member).
Subjects/Keywords: Mathematical Physics; The Analysis of Partial Differential Equations
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Kieffer, T. F. (2020). The Maxwell-Pauli Equations. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/62787
Chicago Manual of Style (16th Edition):
Kieffer, Thomas Forrest. “The Maxwell-Pauli Equations.” 2020. Doctoral Dissertation, Georgia Tech. Accessed April 11, 2021.
http://hdl.handle.net/1853/62787.
MLA Handbook (7th Edition):
Kieffer, Thomas Forrest. “The Maxwell-Pauli Equations.” 2020. Web. 11 Apr 2021.
Vancouver:
Kieffer TF. The Maxwell-Pauli Equations. [Internet] [Doctoral dissertation]. Georgia Tech; 2020. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1853/62787.
Council of Science Editors:
Kieffer TF. The Maxwell-Pauli Equations. [Doctoral Dissertation]. Georgia Tech; 2020. Available from: http://hdl.handle.net/1853/62787
Georgia Tech
4.
Beck, Brian Michael.
Localization and tomographic imaging for spatially aware mobile radio networks.
Degree: PhD, Electrical and Computer Engineering, 2016, Georgia Tech
URL: http://hdl.handle.net/1853/59151
► Mobile wireless sensors and networks have many potential applications, and have attracted much industry and academic interest in the past decade. This work pursues research…
(more)
▼ Mobile wireless sensors and networks have many potential applications, and have attracted much industry and academic interest in the past decade. This work pursues research
which enhances the spatial awareness of such networks. Specifically, in this work we focus on original contributions to the spatial topics of interference/spectrum mapping, cooperative ultra-wideband (UWB) localization and tracking, uncooperative emitter localization,
and active mapping of the radio frequency (RF) shadowing environment. Toward contributions in these areas, we introduce the Cognitive Spectrum Operations Testbed (CSOT), which was designed specifically for spatially oriented wireless network research. The system consists of eight mobile nodes, each with software defined radio (SDR) and UWB capabilities. The CSOT’s hardware and software are first demonstrated in an interference mapping experiment, which is used to optimize the positioning of a relay node. We then utilize CSOT to pursue high accuracy, cooperative indoor localization and tracking. This research utilizes fusion of both UWB ranging and odometry data. The experimental results demonstrate average positioning error of < 2 cm, and drops the requirement of pre-surveying the positions of anchor nodes. With precise localization in hand, we then use CSOT to explore the field of radio tomographic imaging (RTI). For our RTI work, UWB signal strength data is employed to produce accurate images of the RF shadowing environment. A major contribution of this work is its deployment in a completely uncalibrated network. All necessary parameters are estimated directly from the data. We show performance improvements through simulation and experiment, and via comparison with other techniques. Finally, we apply the uncalibrated network principle to the uncooperative emitter localization problem. We develop algorithms to model the effects of uncalibrated sensors on the data covariance and mitigate them. Further simulations and experimental results demonstrate significant localization performance improvements over naive methods.
Advisors/Committee Members: Ma, Xiaoli (advisor), Baxley, Robert J. (committee member), Chang, Gee-Kung (committee member), Weitnauer, Mary Ann (committee member), Bonetto, Federico (committee member).
Subjects/Keywords: Radio tomographic imaging; Localization; Ultra wideband; Sensor registration; Calibration
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Beck, B. M. (2016). Localization and tomographic imaging for spatially aware mobile radio networks. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/59151
Chicago Manual of Style (16th Edition):
Beck, Brian Michael. “Localization and tomographic imaging for spatially aware mobile radio networks.” 2016. Doctoral Dissertation, Georgia Tech. Accessed April 11, 2021.
http://hdl.handle.net/1853/59151.
MLA Handbook (7th Edition):
Beck, Brian Michael. “Localization and tomographic imaging for spatially aware mobile radio networks.” 2016. Web. 11 Apr 2021.
Vancouver:
Beck BM. Localization and tomographic imaging for spatially aware mobile radio networks. [Internet] [Doctoral dissertation]. Georgia Tech; 2016. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1853/59151.
Council of Science Editors:
Beck BM. Localization and tomographic imaging for spatially aware mobile radio networks. [Doctoral Dissertation]. Georgia Tech; 2016. Available from: http://hdl.handle.net/1853/59151
Georgia Tech
5.
Yoon, Yong Eun.
Prediction of limit cycle oscillations in piecewise linear systems.
Degree: PhD, Aerospace Engineering, 2019, Georgia Tech
URL: http://hdl.handle.net/1853/61280
► The exact mathematical model of most of mechanical and/or electrical systems involves the piecewise linear system, which consists of linear parts along with piecewise nonlinearities.…
(more)
▼ The exact mathematical model of most of mechanical and/or electrical systems involves the piecewise linear system, which consists of linear parts along with piecewise nonlinearities. Piecewise linear systems can possess a periodic solution called a limit-cycle oscillation (LCO), which can seriously undermine the system performance depending on the amplitude and the
frequency of the LCO. Therefore, how to analyze LCO and its parameters of piecewise linear systems is one of the primary concerns for the control and system engineers of the system. This thesis work presents a novel framework to predict and analyze LCO of piecewise linear systems. On top of the well-known piecewise linear analysis we apply the Floquet theory to identify LCO parameters and determine the stability of the LCO. The introduction of Floquet theory to piecewise linear systems is allowed through transforming piecewise nonlinearities to corresponding equivalent analytic functions. In addition, the establishment of switching equation provides another necessary condition to predict LCO parameters. We take an example of a realistic flight control system to demonstrate the effectiveness and efficiency of our framework.
Advisors/Committee Members: Johnson, Eric N. (advisor), Feron, Eric M. (advisor), Prasad, Jonnalagadda V. R. (committee member), Egerstedt, Magnus B. (committee member), Bonetto, Federico (committee member).
Subjects/Keywords: Limit-cycle oscillation; Piecewise linear system; Floquet theory
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Yoon, Y. E. (2019). Prediction of limit cycle oscillations in piecewise linear systems. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/61280
Chicago Manual of Style (16th Edition):
Yoon, Yong Eun. “Prediction of limit cycle oscillations in piecewise linear systems.” 2019. Doctoral Dissertation, Georgia Tech. Accessed April 11, 2021.
http://hdl.handle.net/1853/61280.
MLA Handbook (7th Edition):
Yoon, Yong Eun. “Prediction of limit cycle oscillations in piecewise linear systems.” 2019. Web. 11 Apr 2021.
Vancouver:
Yoon YE. Prediction of limit cycle oscillations in piecewise linear systems. [Internet] [Doctoral dissertation]. Georgia Tech; 2019. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1853/61280.
Council of Science Editors:
Yoon YE. Prediction of limit cycle oscillations in piecewise linear systems. [Doctoral Dissertation]. Georgia Tech; 2019. Available from: http://hdl.handle.net/1853/61280
Georgia Tech
6.
Chen, Jiangning.
Text-classification methods and the mathematical theory of Principal Components.
Degree: PhD, Mathematics, 2019, Georgia Tech
URL: http://hdl.handle.net/1853/61686
► This thesis studies three topics. First of all, in text classification, one may use Principal Components Analysis (PCA) as a dimension reduction technique, or with…
(more)
▼ This thesis studies three topics. First of all, in text classification, one may use Principal Components Analysis (PCA) as a dimension reduction technique, or with few topics even as unsupervised classification method. We investigate how useful it is for real life problems. The problem is that, often times the spectrum of the covariance matrix is wrongly estimated due to the ratio between sample space dimension over feature space dimension not being large enough. We show how to reconstruct the spectrum of the ground truth covariance matrix, given the spectrum of the estimated covariance for multivariate normal vectors. We then present an algorithm for reconstruction the spectrum in the case of sparse matrices related to text classification. In the second part, we concentrate on schemes of PCA estimators. Consider the problem of finding the least eigenvalue and eigenvector of ground truth covariance matrix, a famous classical estimator are due to Krasulina. We state the convergence proof of Krasulina for the least eigenvalue and corresponding eigenvector, and then find their convergence rate. In the last part, we consider the application problem, text classification, in the supervised view with traditional Naive-Bayes method. We find out an updated Naive-Bayes method with a new loss function, which loses the unbiased property of traditional Naive-Bayes method, but obtains a smaller variance of the estimator.
Advisors/Committee Members: Matzinger, Heinrich (advisor), Lounici, Karim (advisor), Popescu, Ionel (committee member), Huo, Xiaoming (committee member), Bonetto, Federico (committee member).
Subjects/Keywords: Text-classification; NLP; PCA; Online PCA; Incremental scheme; Naive Bayes; Partial labeling; KL divergence
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Chen, J. (2019). Text-classification methods and the mathematical theory of Principal Components. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/61686
Chicago Manual of Style (16th Edition):
Chen, Jiangning. “Text-classification methods and the mathematical theory of Principal Components.” 2019. Doctoral Dissertation, Georgia Tech. Accessed April 11, 2021.
http://hdl.handle.net/1853/61686.
MLA Handbook (7th Edition):
Chen, Jiangning. “Text-classification methods and the mathematical theory of Principal Components.” 2019. Web. 11 Apr 2021.
Vancouver:
Chen J. Text-classification methods and the mathematical theory of Principal Components. [Internet] [Doctoral dissertation]. Georgia Tech; 2019. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1853/61686.
Council of Science Editors:
Chen J. Text-classification methods and the mathematical theory of Principal Components. [Doctoral Dissertation]. Georgia Tech; 2019. Available from: http://hdl.handle.net/1853/61686
Georgia Tech
7.
Sharma, Kamal.
Transport in low-dimensional interacting systems.
Degree: PhD, Physics, 2019, Georgia Tech
URL: http://hdl.handle.net/1853/62339
► One-dimensional quantum many-body systems have been an interesting area of theoretical research since last 90 years. However, advances in fabrication technologies has led to influx…
(more)
▼ One-dimensional quantum many-body systems have been an interesting area of theoretical research since last 90 years. However, advances in fabrication technologies has led to influx of real materials and devices that are one-dimensional or quasi one-dimensional. These devices have brought back a renewed interest in understating the physics of such systems. However, the established Luttinger liquid theory has some limitations due to absence of scattering processes at finite temperatures. Further, any arbitrarily weak interaction potential between Luttinger liquid bosons leads to divergences already in the first order calculation. We adopt the low energy one-dimensional Wigner crystal as the strongly interacting regime of Luttinger liquid. We show that the violation of the Wiedemann-Franz law can be demonstrated by calculating correction to thermal conductance of a non-linear interacting Wigner crystal.
Advisors/Committee Members: Pustilnik, Michael (advisor), Zangwill, Andrew (committee member), Davidovic, Dragomir (committee member), Bonetto, Federico (committee member), Kindermann, Markus (committee member).
Subjects/Keywords: One-dimensional; Quantum; Wire; Physics; Thermal; Conductance; Luttinger liquid; Non-fermi; Bosonization; Wiedemann; Franz; Wigner; Crystal; Haldane; Kamal; Sharma
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Sharma, K. (2019). Transport in low-dimensional interacting systems. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/62339
Chicago Manual of Style (16th Edition):
Sharma, Kamal. “Transport in low-dimensional interacting systems.” 2019. Doctoral Dissertation, Georgia Tech. Accessed April 11, 2021.
http://hdl.handle.net/1853/62339.
MLA Handbook (7th Edition):
Sharma, Kamal. “Transport in low-dimensional interacting systems.” 2019. Web. 11 Apr 2021.
Vancouver:
Sharma K. Transport in low-dimensional interacting systems. [Internet] [Doctoral dissertation]. Georgia Tech; 2019. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1853/62339.
Council of Science Editors:
Sharma K. Transport in low-dimensional interacting systems. [Doctoral Dissertation]. Georgia Tech; 2019. Available from: http://hdl.handle.net/1853/62339
Georgia Tech
8.
Gallandat, Noris Andre.
Enhanced Ambient Heat Rejection in Passive Thermal Management Systems.
Degree: PhD, Mechanical Engineering, 2015, Georgia Tech
URL: http://hdl.handle.net/1853/56183
► The combined trends of increasing computing power with the miniaturization of electronic devices brought about new challenges in terms of ambient heat rejection. The most…
(more)
▼ The combined trends of increasing computing power with the miniaturization of electronic devices brought about new challenges in terms of ambient heat rejection. The most simple and reliable ambient heat rejection method is natural air convection. However, this technique is limited in terms of the cooling power that can be dealt with. This work presents two technologies that can potentially increase the heat rejection rate to ambient air without using any moving part, thus ensuring a high reliability. The first technology considered uses ionic wind to increase the air flow through cooling passages. Ionic wind occurs when a high voltage potential is applied to an electrode with a large curvature – typically a thin wire or a needle. Due to the strong electric potential close to the electrode, a Corona discharge occurs and air molecules are ionized. The resulting ions induce an air flow through collisions with neutral molecules. In this study, the Corona current is characterized experimentally and a numerical procedure is developed to solve the electrohydrodynamics. A custom-built test bench is used to validate the numerical model experimentally. It is shown that ionic wind can increase the heat removal rate by up to 100% as compared to natural convection only. The second cooling enhancement technology considered is the addition of a chimney on top of the heat sink to increase the air flow through the cooling channels. A semi-analytical model based on thermal- and fluid equivalent resistance networks is developed. The model is validated using a commercial CFD package. Finally, a thermo-economic study is performed using genetic algorithms in order to compare the performance of both technologies versus natural convection only. A Pareto front combining the three technologies is constructed, allowing for cost-effective design decisions based on the cooling power requirements.
Advisors/Committee Members: Mayor, J.Rhett (advisor), Bonetto, Federico (committee member), Garimella, Srinivas (committee member), Ghiaasiaan, Mostafa (committee member), Jeter, Sheldon (committee member).
Subjects/Keywords: Ambient Heat Rejection; Ionic Wind; Enhanced Convection
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Gallandat, N. A. (2015). Enhanced Ambient Heat Rejection in Passive Thermal Management Systems. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/56183
Chicago Manual of Style (16th Edition):
Gallandat, Noris Andre. “Enhanced Ambient Heat Rejection in Passive Thermal Management Systems.” 2015. Doctoral Dissertation, Georgia Tech. Accessed April 11, 2021.
http://hdl.handle.net/1853/56183.
MLA Handbook (7th Edition):
Gallandat, Noris Andre. “Enhanced Ambient Heat Rejection in Passive Thermal Management Systems.” 2015. Web. 11 Apr 2021.
Vancouver:
Gallandat NA. Enhanced Ambient Heat Rejection in Passive Thermal Management Systems. [Internet] [Doctoral dissertation]. Georgia Tech; 2015. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1853/56183.
Council of Science Editors:
Gallandat NA. Enhanced Ambient Heat Rejection in Passive Thermal Management Systems. [Doctoral Dissertation]. Georgia Tech; 2015. Available from: http://hdl.handle.net/1853/56183
9.
Loewe Yanez, Benjamin Andres.
Bridges between quantum and classical mechanics: Directed polymers, flocking and transitionless quanum driving.
Degree: PhD, Physics, 2017, Georgia Tech
URL: http://hdl.handle.net/1853/58276
► Often considered separated worlds, classical and quantum mechanics share numerous connections with one another. Indeed, as classical mechanics corresponds to a limiting case of quantum…
(more)
▼ Often considered separated worlds, classical and quantum mechanics share numerous connections with one another. Indeed, as classical mechanics corresponds to a limiting case of quantum mechanics, certain concepts and elements of physical intuition developed in one theory can be and have been used to tackle issues in the other. Nevertheless, these connections do not only cover conceptual issues but also numerous techniques. Indeed, the inherently probabilistic nature of quantum mechanics and its close resemblance to Markovian stochastic processes opens the door to the application of a broad range of powerful methods, initially developed for quantum mechanics, in classical equilibrium and non-equilibrium statistical mechanics. In this thesis we develop progress in three subjects by taking advantage of either a conceptual or a methodological connection between quantum and classical mechanics. First, we develop the well-known mapping between systems of strongly repelling, two-dimensional directed lines and systems of one-dimensional fermions in order to extend the directed polymer problem to richer geometries. By expressing path integrals in generalized curvilinear coordinates, we successfully generalize the model to settings such as polymers anchored to curved edges, polymers constrained to uneven walls, and polymers constrained to curved surfaces. In each case, we identify the Hamiltonian of an analogous quantum system, which, because of the new geometry of each setting, develops features such as a time- and position-dependent mass and an external electromagnetic vector potential. Along the way, we perform an in-depth analysis of the approximations made and establish regimes of their validity. Finally, in order to obtain analytical results, we employ an extension of the time-dependent perturbation theory scheme of quantum mechanics to imaginary time. Complementing this with the assumption of ground-state dominance, we obtain compact expressions for universal shifts in the free energies of the various systems that allows for isolation of the effects of the distinct geometrical properties of each system. The second piece of work presented into this thesis relates to the non-equilibrium setting of active particles. Strongly interacting, self-propelled particles can form a spontaneously flowing, polar (i.e. motionally aligned), active fluid. The study of the connection between the microscopic dynamics of a single, self-propelled particle and the macroscopic dynamics of a liquid comprising such particles can yield insights into experimentally realizable active flows, but this connection is well understood in only a few select cases. Here, we introduce a model of self-propelled particles that is based on an analogy with the motion of an electron subject to strong spin-orbit coupling. We find that, within our model, self-propelled particles experience an analog of the Heisenberg uncertainly principle that instead relates positional and rotational noise. An extension to many-component (and hence more classical) spinors, under…
Advisors/Committee Members: Goldbart, Paul M. (advisor), Cvitanovic, Predrag (committee member), Pustilnik, Michael (committee member), Matsumoto, Elisabetta (committee member), Bonetto, Federico (committee member).
Subjects/Keywords: Directed polymers; Quantum analogies; Path integrals; Self-propelled particles; Flocking transition; Spin-orbit coupling; Transitionless quantum driving; Semi-classical expansion
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Loewe Yanez, B. A. (2017). Bridges between quantum and classical mechanics: Directed polymers, flocking and transitionless quanum driving. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/58276
Chicago Manual of Style (16th Edition):
Loewe Yanez, Benjamin Andres. “Bridges between quantum and classical mechanics: Directed polymers, flocking and transitionless quanum driving.” 2017. Doctoral Dissertation, Georgia Tech. Accessed April 11, 2021.
http://hdl.handle.net/1853/58276.
MLA Handbook (7th Edition):
Loewe Yanez, Benjamin Andres. “Bridges between quantum and classical mechanics: Directed polymers, flocking and transitionless quanum driving.” 2017. Web. 11 Apr 2021.
Vancouver:
Loewe Yanez BA. Bridges between quantum and classical mechanics: Directed polymers, flocking and transitionless quanum driving. [Internet] [Doctoral dissertation]. Georgia Tech; 2017. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1853/58276.
Council of Science Editors:
Loewe Yanez BA. Bridges between quantum and classical mechanics: Directed polymers, flocking and transitionless quanum driving. [Doctoral Dissertation]. Georgia Tech; 2017. Available from: http://hdl.handle.net/1853/58276
10.
Cheriyan, Vinod.
Models of human behavior with applications to finance and pricing.
Degree: PhD, Industrial and Systems Engineering, 2014, Georgia Tech
URL: http://hdl.handle.net/1853/52310
► This thesis presents two classes of models of boundedly rational decision makers - one with application to finance and the other to pricing. It consists…
(more)
▼ This thesis presents two classes of models of boundedly rational decision makers - one with application to finance and the other to pricing. It consists of three parts.
The first part of the thesis investigates the impact of investors' boundedly rational forecasting on asset price bubbles. We present a class of models, called extrapolation-correction models, of boundedly rational investor behavior. That is, the investors in our model, quite reasonably, use data available to them, i.e. past price data, to form forecasts about future prices. We relate the model parameters to various behavioral aspects like investor memory, caution/confidence, and panic. We present the resulting dynamical system model of asset price bubbles and relate the behavior of the dynamical system to the parameters capturing investor forecasting behavior. We show that, depending on the behavioral parameters, the associated dynamical system can converge to the fundamental value, go into predictable price cycles, or go into unpredictable price cycles. In particular, we find that the greater the weight investors' forecasts put on the most recent observations, the greater the tendency for the asset prices to exhibit cycles, forming positive and negative bubbles. We also find that when forecasts are strongly affected by recent prices, the price process becomes chaotic and it becomes increasingly difficult to forecast future prices accurately.
The second part of the thesis addresses the question: How do investors make their price forecasts? We present the design of an experiment where investors participate in a virtual asset market run over a computer network. During the course of the experiment, the participants report their price forecasts and enter buy and sell orders. The computer software determines the market clearing prices. Despite full disclosure of the assets' dividends and the fundamental value, the price trajectories in all three experimental sessions exhibited cycles. We calibrated various models, including rational expectations based models and the extrapolation-correction family of models presented in the first part of the thesis. The results indicate that rational expectations hypothesis does not provide an accurate model of forecast formation. Moreover, a simple one-parameter exponential smoothing model is much better at modeling forecast formation, with the extrapolation-correction models making the fit slightly better.
The third part of the thesis explores a different aspect of customer rationality - that of customer impatience - and its effect on pricing of product versions. We consider a setting in which impatient customers are faced with frequent product introductions, for example, products like Apple iPhones. This raises the following questions regarding customers: Given the pricing strategy of the firm, what are the optimal buying behaviors of the customers? How does customer buying behavior change in relation to impatience? We consider two settings. In the first setting, the firm offers a trade-in price for existing…
Advisors/Committee Members: Kleywegt, Anton J. (advisor), Bonetto, Federico (committee member), Subramanian, Ravi (committee member), Tovey, Craig A. (committee member), Goldberg, David A. (committee member).
Subjects/Keywords: Bounded rationality; Asset price bubbles; Dynamical system; Behavioral experiments; Forecast formation; Experimental economics; Product pricing; Customer impatience
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Cheriyan, V. (2014). Models of human behavior with applications to finance and pricing. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/52310
Chicago Manual of Style (16th Edition):
Cheriyan, Vinod. “Models of human behavior with applications to finance and pricing.” 2014. Doctoral Dissertation, Georgia Tech. Accessed April 11, 2021.
http://hdl.handle.net/1853/52310.
MLA Handbook (7th Edition):
Cheriyan, Vinod. “Models of human behavior with applications to finance and pricing.” 2014. Web. 11 Apr 2021.
Vancouver:
Cheriyan V. Models of human behavior with applications to finance and pricing. [Internet] [Doctoral dissertation]. Georgia Tech; 2014. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1853/52310.
Council of Science Editors:
Cheriyan V. Models of human behavior with applications to finance and pricing. [Doctoral Dissertation]. Georgia Tech; 2014. Available from: http://hdl.handle.net/1853/52310
11.
Nah, Seungjoo.
Kondo temperature of a quantum dot.
Degree: PhD, Physics, 2011, Georgia Tech
URL: http://hdl.handle.net/1853/41137
► The low-energy properties of quantum dot systems are dominated by the Kondo effect. We study the dependence of the characteristic energy scale of the effect,…
(more)
▼ The low-energy properties of quantum dot systems are dominated by the Kondo effect. We study the dependence of the characteristic energy scale of the effect, the Kondo temperature, on the gate voltage, which controls the number of electrons in the strongly blockaded dot. We show that in order to obtain the correct Kondo temperature as a function of the gate voltage, it is crucial to take into account the presence of many energy levels in the dot. The dependence turns out to be very different from that in the conventional single-level Anderson impurity model. Unlike in the latter, the Kondo temperature cannot be characterized by a single parameter, such as the ratio of the tunneling-induced width of the energy levels in the dot and the charging energy.
Advisors/Committee Members: Pustilnik, Michael (Committee Chair), Apalkov, Vadym (Committee Member), Bonetto, Federico (Committee Member), Geller, Michael (Committee Member), Kindermann, Markus (Committee Member), Landman, Uzi (Committee Member).
Subjects/Keywords: Disorder; Single electron transistors; Mesoscopic fluctuations; Renormalization group; Nanoscience; Quantum dots; Kondo effect
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Nah, S. (2011). Kondo temperature of a quantum dot. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/41137
Chicago Manual of Style (16th Edition):
Nah, Seungjoo. “Kondo temperature of a quantum dot.” 2011. Doctoral Dissertation, Georgia Tech. Accessed April 11, 2021.
http://hdl.handle.net/1853/41137.
MLA Handbook (7th Edition):
Nah, Seungjoo. “Kondo temperature of a quantum dot.” 2011. Web. 11 Apr 2021.
Vancouver:
Nah S. Kondo temperature of a quantum dot. [Internet] [Doctoral dissertation]. Georgia Tech; 2011. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1853/41137.
Council of Science Editors:
Nah S. Kondo temperature of a quantum dot. [Doctoral Dissertation]. Georgia Tech; 2011. Available from: http://hdl.handle.net/1853/41137
12.
Vaidyanathan, Ranjini.
Thermostated Kac models.
Degree: PhD, Mathematics, 2015, Georgia Tech
URL: http://hdl.handle.net/1853/54446
► We consider a model of N particles interacting through a Kac-style collision process, with m particles among them interacting, in addition, with a thermostat. When…
(more)
▼ We consider a model of N particles interacting through a Kac-style collision process, with m particles among them interacting, in addition, with a thermostat. When m = N, we show exponential approach to the equilibrium canonical distribution in terms of the L2 norm, in relative entropy, and in the Gabetta-Toscani-Wennberg (GTW) metric, at a rate independent of N. When m < N , the exponential rate of approach to equilibrium in L2 is shown to behave as m/N for N large, while the relative entropy and the GTW distance from equilibrium exhibit (at least) an "eventually exponential” decay, with a rate scaling as m/N
2 for large N. As an allied project, we obtain a rigorous microscopic description of the thermostat used, based on a model of a tagged particle colliding with an infinite gas in equilibrium at the thermostat temperature. These results are based on joint work with
Federico Bonetto, Michael Loss and Hagop Tossounian.
Advisors/Committee Members: Bonetto, Federico (advisor), Loss, Michael (committee member), de la Llave, Rafael (committee member), Harrell, Evans (committee member), Wiesenfeld, Kurt (committee member).
Subjects/Keywords: Kinetic theory; Spectral gap; Heat bath
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Vaidyanathan, R. (2015). Thermostated Kac models. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/54446
Chicago Manual of Style (16th Edition):
Vaidyanathan, Ranjini. “Thermostated Kac models.” 2015. Doctoral Dissertation, Georgia Tech. Accessed April 11, 2021.
http://hdl.handle.net/1853/54446.
MLA Handbook (7th Edition):
Vaidyanathan, Ranjini. “Thermostated Kac models.” 2015. Web. 11 Apr 2021.
Vancouver:
Vaidyanathan R. Thermostated Kac models. [Internet] [Doctoral dissertation]. Georgia Tech; 2015. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1853/54446.
Council of Science Editors:
Vaidyanathan R. Thermostated Kac models. [Doctoral Dissertation]. Georgia Tech; 2015. Available from: http://hdl.handle.net/1853/54446
13.
Kim, Sang Kyu.
Error estimation and adaptive refinement technique in the method of moments.
Degree: PhD, Electrical and Computer Engineering, 2017, Georgia Tech
URL: http://hdl.handle.net/1853/58211
► The objective of this dissertation is to develop a reliable and computationally inexpensive adaptive h-refinement technique for the three-dimensional method of moments to reduce numerical…
(more)
▼ The objective of this dissertation is to develop a reliable and computationally inexpensive adaptive h-refinement technique for the three-dimensional method of moments to reduce numerical errors in electromagnetics efficiently. The adaptive refinement technique consists of an error estimator and a control algorithm. Error estimation plays an important role because it determines regions where error is large. Various error estimators are investigated and implemented. With the Pearson correlation coefficient, local error plots, and scatter plots comparing the estimated errors with actual errors, we evaluate reliability and efficiency of the error estimators. Based on the study of the initial error estimators, we invent new error estimators, which satisfy accuracy and efficiency simultaneously. The controller in the adaptive h-refinement technique is required to adjust mesh sizes and to maintain mesh quality over the regions that are identified for the refinement. The control algorithm distributes new nodes on the domains to be refined and employs the advancing front Delaunay algorithm to generate refined meshes. Since the quality of refined meshes can be aggravated during this procedure, we adopt Laplacian smoothing, which adjusts node positions by taking the average of their adjacent node positions. Numerical results of the error estimator assessment and the adaptive h-refinement technique will be presented and discussed.
Advisors/Committee Members: Peterson, Andrew F. (advisor), Scott, Waymond R. (committee member), Durgin, Gregory D. (committee member), Tentzeris, Emmanouil M. (committee member), Bonetto, Federico (committee member).
Subjects/Keywords: Method of moments; Error estimation; Adaptive refinement technique; Delaunay triangulation; Laplacian smoothing
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Kim, S. K. (2017). Error estimation and adaptive refinement technique in the method of moments. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/58211
Chicago Manual of Style (16th Edition):
Kim, Sang Kyu. “Error estimation and adaptive refinement technique in the method of moments.” 2017. Doctoral Dissertation, Georgia Tech. Accessed April 11, 2021.
http://hdl.handle.net/1853/58211.
MLA Handbook (7th Edition):
Kim, Sang Kyu. “Error estimation and adaptive refinement technique in the method of moments.” 2017. Web. 11 Apr 2021.
Vancouver:
Kim SK. Error estimation and adaptive refinement technique in the method of moments. [Internet] [Doctoral dissertation]. Georgia Tech; 2017. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1853/58211.
Council of Science Editors:
Kim SK. Error estimation and adaptive refinement technique in the method of moments. [Doctoral Dissertation]. Georgia Tech; 2017. Available from: http://hdl.handle.net/1853/58211
14.
Zhang, Lei.
Analysis and numerical methods in solid state physics and chemistry.
Degree: PhD, Mathematics, 2017, Georgia Tech
URL: http://hdl.handle.net/1853/58675
► In the first part of the paper, we consider an atomic model of deposition over a quasi-periodic medium, that is, a quasi-periodic version of the…
(more)
▼ In the first part of the paper, we consider an atomic model of deposition over a quasi-periodic medium, that is, a quasi-periodic version of the well-known Frenkel-Kontorova model. We consider the problem of whether there are quasi-periodic equilibria with a frequency that resonates with the frequencies of the medium. We show that there are always perturbative expansions. We also prove a KAM theorem in a-posterori form. We show that if there is an approximate solution of the equilibrium equation satisfying non-degeneracy conditions, we can adjust one parameter and obtain a true solution which is close to the approximate solution. The proof is based on an iterative method of the KAM type and a novel technique of supplementing the equilibrium equation with another equation that factors the linearization of equilibrium equation. In the second part of the paper, we consider a model related to Transition State Theory in chemical reactions. We consider a particle with an initial position on the reactant side of a time-dependent energy barrier and study the invariant manifolds and associated bundles using the parameterization method.
Advisors/Committee Members: de la Llave, Rafael (advisor), Bonetto, Federico (committee member), Loss, Michael (committee member), Uzer, Turgay (committee member), Zeng, Chongchun (committee member).
Subjects/Keywords: Mathematical physics; Dynamical system; Frennkel-Kontorova model; Normally hyperbolic invariant manifolds; Parameterization method
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Zhang, L. (2017). Analysis and numerical methods in solid state physics and chemistry. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/58675
Chicago Manual of Style (16th Edition):
Zhang, Lei. “Analysis and numerical methods in solid state physics and chemistry.” 2017. Doctoral Dissertation, Georgia Tech. Accessed April 11, 2021.
http://hdl.handle.net/1853/58675.
MLA Handbook (7th Edition):
Zhang, Lei. “Analysis and numerical methods in solid state physics and chemistry.” 2017. Web. 11 Apr 2021.
Vancouver:
Zhang L. Analysis and numerical methods in solid state physics and chemistry. [Internet] [Doctoral dissertation]. Georgia Tech; 2017. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1853/58675.
Council of Science Editors:
Zhang L. Analysis and numerical methods in solid state physics and chemistry. [Doctoral Dissertation]. Georgia Tech; 2017. Available from: http://hdl.handle.net/1853/58675
15.
Ghanta, Rohan.
The polaron hydrogenic atom in a strong magnetic field.
Degree: PhD, Mathematics, 2019, Georgia Tech
URL: http://hdl.handle.net/1853/61780
► It is shown that: (1) The ground-state electron density of a polaron bound in a Coulomb potential and exposed to a homogeneous magnetic field of…
(more)
▼ It is shown that: (1) The ground-state electron density of a polaron bound in a Coulomb potential and exposed to a homogeneous magnetic field of strength B–with its transverse electron coordinates integrated out and when scaled appropriately with the magnetic field strength–converges pointwise and in a weak sense as B → ∞ to the square of a hyperbolic secant function; (2) The ground state of a polaron bound in a symmetric Mexican hat- type potential, scaled appropriately with the electron-phonon coupling parameter, is unique and therefore rotation-invariant, but the minimizers of the corresponding Pekar problem are nonradial; in the strong-coupling limit under the assumption that these minimizers are unique up to rotation the ground-state electron density–when scaled appropriately with the electron-phonon coupling strength–converges in a weak sense to a rotational average of their densities.
Advisors/Committee Members: Loss, Michael (advisor), Bonetto, Federico (committee member), de la Llave, Rafael (committee member), Harrell, Evans (committee member), Kennedy, Brian (committee member).
Subjects/Keywords: Polaron; Strong magnetic fields
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Ghanta, R. (2019). The polaron hydrogenic atom in a strong magnetic field. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/61780
Chicago Manual of Style (16th Edition):
Ghanta, Rohan. “The polaron hydrogenic atom in a strong magnetic field.” 2019. Doctoral Dissertation, Georgia Tech. Accessed April 11, 2021.
http://hdl.handle.net/1853/61780.
MLA Handbook (7th Edition):
Ghanta, Rohan. “The polaron hydrogenic atom in a strong magnetic field.” 2019. Web. 11 Apr 2021.
Vancouver:
Ghanta R. The polaron hydrogenic atom in a strong magnetic field. [Internet] [Doctoral dissertation]. Georgia Tech; 2019. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1853/61780.
Council of Science Editors:
Ghanta R. The polaron hydrogenic atom in a strong magnetic field. [Doctoral Dissertation]. Georgia Tech; 2019. Available from: http://hdl.handle.net/1853/61780
Georgia Tech
16.
Grigo, Alexander.
Billiards and statistical mechanics.
Degree: PhD, Mathematics, 2009, Georgia Tech
URL: http://hdl.handle.net/1853/29610
► In this thesis we consider mathematical problems related to different aspects of hard sphere systems. In the first part we study planar billiards, which arise…
(more)
▼ In this thesis we consider mathematical problems related to different aspects of hard sphere systems.
In the first part we study planar billiards, which arise in the context of hard sphere systems when only one or two spheres are present. In particular we investigate the possibility of elliptic periodic orbits in the general construction of hyperbolic billiards. We show that if non-absolutely focusing components are present there can be elliptic periodic orbits with arbitrarily long free paths. Furthermore, we show that smooth stadium like billiards have elliptic periodic orbits for a large range of separation distances.
In the second part we consider hard sphere systems with a large number of particles, which we model by the Boltzmann equation. We develop a new approach to derive hydrodynamic limits, which is based on classical methods of geometric singular perturbation theory of ordinary differential equations. This method provides new geometric and dynamical interpretations of hydrodynamic limits, in particular, for the of the dissipative Boltzmann equation.
Advisors/Committee Members: Bunimovich, Leonid (Committee Chair), Bonetto, Federico (Committee Member), Chow, Shui-Nee (Committee Member), Cvitanovic, Predrag (Committee Member), Weiss, Howard (Committee Member).
Subjects/Keywords: Billiards; Boltzmann equation; Hamiltonian systems; Statistical mechanics; Ergodic theory; Dynamics; Transport theory
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Grigo, A. (2009). Billiards and statistical mechanics. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/29610
Chicago Manual of Style (16th Edition):
Grigo, Alexander. “Billiards and statistical mechanics.” 2009. Doctoral Dissertation, Georgia Tech. Accessed April 11, 2021.
http://hdl.handle.net/1853/29610.
MLA Handbook (7th Edition):
Grigo, Alexander. “Billiards and statistical mechanics.” 2009. Web. 11 Apr 2021.
Vancouver:
Grigo A. Billiards and statistical mechanics. [Internet] [Doctoral dissertation]. Georgia Tech; 2009. [cited 2021 Apr 11].
Available from: http://hdl.handle.net/1853/29610.
Council of Science Editors:
Grigo A. Billiards and statistical mechanics. [Doctoral Dissertation]. Georgia Tech; 2009. Available from: http://hdl.handle.net/1853/29610
. 
Open Access Theses and Dissertations
