subject:(Hamiltonian dynamics)

Georgia Tech

1. Berman, Simon Abraham. Classical mechanisms of recollision and high harmonic generation.

Degree: PhD, Physics, 2019, Georgia Tech

► Thirty years after the demonstration of the production of high laser harmonics through nonlinear laser-gas interaction, high harmonic generation (HHG) is being used to probe… (more)

▼ Thirty years after the demonstration of the production of high laser harmonics through nonlinear laser-gas interaction, high harmonic generation (HHG) is being used to probe molecular dynamics in real time and is realizing its technological potential as a tabletop source of attosecond pulses in the XUV to soft X-ray range. Despite experimental progress, theoretical efforts have been stymied by the excessive computational cost of first-principles simulations and the difficulty of systematically deriving reduced models for the non-perturbative, multiscale interaction of an intense laser pulse with a macroscopic gas of atoms. In this thesis, we investigate first-principles reduced models for HHG using classical mechanics. On the microscopic level, we examine the recollision process—the laser-driven collision of an ionized electron with its parent ion—that drives HHG. Using nonlinear dynamics, we elucidate the indispensable role played by the ionic potential during recollisions in the strong-field limit. On the macroscopic level, we show that the intense laser-gas interaction can be cast as a classical field theory. Borrowing a technique from plasma physics, we systematically derive a hierarchy of reduced Hamiltonian models for the self-consistent interaction between the laser and the atoms during pulse propagation. The reduced models can accommodate either classical or quantum electron dynamics, and in both cases, simulations over experimentally-relevant propagation distances are feasible. We build a classical model based on these simulations which agrees quantitatively with the quantum model for the propagation of the dominant components of the laser field. Subsequently, we use the classical model to trace the coherent buildup of harmonic radiation to its origin in phase space. In a simplified geometry, we show that the anomalously high frequency radiation seen in simulations results from the delicate interplay between electron trapping and higher energy recollisions brought on by propagation effects. Advisors/Committee Members: Chandre, Cristel (advisor), Uzer, Turgay (advisor), Berger, Claire (committee member), Cvitanovic, Predrag (committee member), Kennedy, Brian (committee member), de la Llave, Rafael (committee member), Lorin, Emmanuel (committee member), Shadwick, Bradley (committee member).

Subjects/Keywords: Attosecond physics; Hamiltonian systems; Nonlinear dynamics

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APA (6^th Edition):

Berman, S. A. (2019). Classical mechanisms of recollision and high harmonic generation. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/61214

Chicago Manual of Style (16^th Edition):

Berman, Simon Abraham. “Classical mechanisms of recollision and high harmonic generation.” 2019. Doctoral Dissertation, Georgia Tech. Accessed March 07, 2021. http://hdl.handle.net/1853/61214.

MLA Handbook (7^th Edition):

Berman, Simon Abraham. “Classical mechanisms of recollision and high harmonic generation.” 2019. Web. 07 Mar 2021.

Vancouver:

Berman SA. Classical mechanisms of recollision and high harmonic generation. [Internet] [Doctoral dissertation]. Georgia Tech; 2019. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/1853/61214.

Council of Science Editors:

Berman SA. Classical mechanisms of recollision and high harmonic generation. [Doctoral Dissertation]. Georgia Tech; 2019. Available from: http://hdl.handle.net/1853/61214

New Jersey Institute of Technology

2. Basarab, Casayndra H. Hamiltonian bifurcations in Schrodinger trimers.

Degree: PhD, Mathematical Sciences, 2016, New Jersey Institute of Technology

URL: https://digitalcommons.njit.edu/dissertations/87

► The phase space of the three-mode discrete NLS in the nonlinear regime with periodic boundary conditions is investigated by reducing the degree of freedom… (more)

Subjects/Keywords: Hamiltonian systems; Nonlinear dynamics; Nonlinear Schrodinger equation; Hamiltonian hopf bifurcation; Chaos; Mathematics

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APA (6^th Edition):

Basarab, C. H. (2016). Hamiltonian bifurcations in Schrodinger trimers. (Doctoral Dissertation). New Jersey Institute of Technology. Retrieved from https://digitalcommons.njit.edu/dissertations/87

Chicago Manual of Style (16^th Edition):

Basarab, Casayndra H. “Hamiltonian bifurcations in Schrodinger trimers.” 2016. Doctoral Dissertation, New Jersey Institute of Technology. Accessed March 07, 2021. https://digitalcommons.njit.edu/dissertations/87.

MLA Handbook (7^th Edition):

Basarab, Casayndra H. “Hamiltonian bifurcations in Schrodinger trimers.” 2016. Web. 07 Mar 2021.

Vancouver:

Basarab CH. Hamiltonian bifurcations in Schrodinger trimers. [Internet] [Doctoral dissertation]. New Jersey Institute of Technology; 2016. [cited 2021 Mar 07]. Available from: https://digitalcommons.njit.edu/dissertations/87.

Council of Science Editors:

Basarab CH. Hamiltonian bifurcations in Schrodinger trimers. [Doctoral Dissertation]. New Jersey Institute of Technology; 2016. Available from: https://digitalcommons.njit.edu/dissertations/87

3. Korepanov, Alexey. Small Perturbations In Hard Balls Dynamics.

Degree: 2013, University of Alabama – Birmingham

URL: http://contentdm.mhsl.uab.edu/u?/etd,1538

►

This dissertation consists of three articles written in cooperation with F. Bonetto,N. Chernov, J. Lebowitz and N. Simanyi. The common theme is small perturbationsof hard… (more)

▼

This dissertation consists of three articles written in cooperation with F. Bonetto,N. Chernov, J. Lebowitz and N. Simanyi. The common theme is small perturbationsof hard balls dynamics on a flat table with obstacles. While the original dynamicspreserves the Lebesgue measure and is hyperbolic and ergodic for all models that wehave considered, even smallest perturbations may significantly change the nature ofthe dynamics. Physically observable invariant measure may become singular withrespect to Lebesgue measure, or even fail to exist. In some cases the dynamicscollapses to a continuum of degenerate stable regimes.In Spatial Structure of Stationary Nonequilibrium States in the ThermostattedPeriodic Lorentz Gas we consider a single particle in a two-dimensional periodicarray of convex obstacles. The particle is subject to a constant electric field as well asa Gaussian thermostat which keeps the energy constant. This model provides a localapproximation to the one without thermostat. We study properties of projectionsof the invariant physically observable (SRB) measure – despite its singular nature,projections on the space coordinates have continuous densities.In Stable regimes for hard disks in a channel with twisting walls we consider asystem of N hard disks in a two-dimensional channel with slightly modified rulesof collisions with walls. While with zero perturbation the system is ergodic (thisis proven for N = 2 and expected to be true for N > 2), for arbitrarily smallperturbations it tends to collapse to the attractive submanifolds of the phase space.In Speed Distribution of N Particles in the Thermostated Periodic Lorentz Gaswith a Field we study a system of N point particles moving on a two-dimensional toruswith convex obstacles or random scatterers and a constant electric field. Particles areconnected by a common Gaussian thermostat that keeps the kinetic energy constant.We show that for small fields the velocity distribution of the particles is independentof the nature of scattering.

PhD

1 online resource (x, 64 pages)

Applied Mathematics

billiards, dynamical systems, ergodic theory, Gaussian thermostat, lorentz gas

UNRESTRICTED

Advisors/Committee Members: Nikolai Chernov, Nandor Simanyi, Kawai,Ryoichi Belbas,Stavros Friedman,Mark.

Subjects/Keywords: Dynamics.<; br>; Perturbation (Mathematics)<; br>; Hamiltonian systems.

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APA (6^th Edition):

Korepanov, A. (2013). Small Perturbations In Hard Balls Dynamics. (Thesis). University of Alabama – Birmingham. Retrieved from http://contentdm.mhsl.uab.edu/u?/etd,1538

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Korepanov, Alexey. “Small Perturbations In Hard Balls Dynamics.” 2013. Thesis, University of Alabama – Birmingham. Accessed March 07, 2021. http://contentdm.mhsl.uab.edu/u?/etd,1538.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Korepanov, Alexey. “Small Perturbations In Hard Balls Dynamics.” 2013. Web. 07 Mar 2021.

Vancouver:

Korepanov A. Small Perturbations In Hard Balls Dynamics. [Internet] [Thesis]. University of Alabama – Birmingham; 2013. [cited 2021 Mar 07]. Available from: http://contentdm.mhsl.uab.edu/u?/etd,1538.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Korepanov A. Small Perturbations In Hard Balls Dynamics. [Thesis]. University of Alabama – Birmingham; 2013. Available from: http://contentdm.mhsl.uab.edu/u?/etd,1538

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

NSYSU

4. Chin, Pei-Hao. Gauge field induced spin dynamics and spin conductivity in the Luttinger semiconductor system.

Degree: Master, Physics, 2015, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0606115-140740

► The main goal of this research is to realize the spin dynamics and the spin current in the non-spherical Luttinger Hamiltonian, which is a 4… (more)

Subjects/Keywords: Berry curvature; Luttinger Hamiltonian; semi-classical method; electron dynamics; spin current

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APA (6^th Edition):

Chin, P. (2015). Gauge field induced spin dynamics and spin conductivity in the Luttinger semiconductor system. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0606115-140740

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Chin, Pei-Hao. “Gauge field induced spin dynamics and spin conductivity in the Luttinger semiconductor system.” 2015. Thesis, NSYSU. Accessed March 07, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0606115-140740.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Chin, Pei-Hao. “Gauge field induced spin dynamics and spin conductivity in the Luttinger semiconductor system.” 2015. Web. 07 Mar 2021.

Vancouver:

Chin P. Gauge field induced spin dynamics and spin conductivity in the Luttinger semiconductor system. [Internet] [Thesis]. NSYSU; 2015. [cited 2021 Mar 07]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0606115-140740.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Chin P. Gauge field induced spin dynamics and spin conductivity in the Luttinger semiconductor system. [Thesis]. NSYSU; 2015. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0606115-140740

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Colorado

5. Mosovsky, Brock Alan. Finite-Time Transport in Aperiodic Dynamical Systems.

Degree: PhD, Applied Mathematics, 2013, University of Colorado

URL: https://scholar.colorado.edu/appm_gradetds/57

► In this dissertation, we consider the problem of quantifying finite-time transport in aperiodic dynamical systems. To address this problem, we concentrate primarily on a… (more)

Subjects/Keywords: Chaos; Dynamical Systems; Hamiltonian Dynamics; Lagrangian; Transport; Applied Mathematics; Mathematics; Physics

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APA (6^th Edition):

Mosovsky, B. A. (2013). Finite-Time Transport in Aperiodic Dynamical Systems. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/57

Chicago Manual of Style (16^th Edition):

Mosovsky, Brock Alan. “Finite-Time Transport in Aperiodic Dynamical Systems.” 2013. Doctoral Dissertation, University of Colorado. Accessed March 07, 2021. https://scholar.colorado.edu/appm_gradetds/57.

MLA Handbook (7^th Edition):

Mosovsky, Brock Alan. “Finite-Time Transport in Aperiodic Dynamical Systems.” 2013. Web. 07 Mar 2021.

Vancouver:

Mosovsky BA. Finite-Time Transport in Aperiodic Dynamical Systems. [Internet] [Doctoral dissertation]. University of Colorado; 2013. [cited 2021 Mar 07]. Available from: https://scholar.colorado.edu/appm_gradetds/57.

Council of Science Editors:

Mosovsky BA. Finite-Time Transport in Aperiodic Dynamical Systems. [Doctoral Dissertation]. University of Colorado; 2013. Available from: https://scholar.colorado.edu/appm_gradetds/57

Delft University of Technology

6. Driessen, D.M. (author). Large Deviations for Markov Jump Processes and Hamiltonian Trajectories.

Degree: 2015, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:3762ee57-0e0e-4012-bb35-157bd14961bf

►

This master thesis is concerned with Large Deviation Theory in combination with Lagrangian and Hamiltonian dynamics. In particular, the Large Deviation behaviour of the empirical… (more)

Subjects/Keywords: Large Deviation Theory; Markov Jump Processes; Hamiltonian dynamics; Lagrangian

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APA (6^th Edition):

Driessen, D. M. (. (2015). Large Deviations for Markov Jump Processes and Hamiltonian Trajectories. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:3762ee57-0e0e-4012-bb35-157bd14961bf

Chicago Manual of Style (16^th Edition):

Driessen, D M (author). “Large Deviations for Markov Jump Processes and Hamiltonian Trajectories.” 2015. Masters Thesis, Delft University of Technology. Accessed March 07, 2021. http://resolver.tudelft.nl/uuid:3762ee57-0e0e-4012-bb35-157bd14961bf.

MLA Handbook (7^th Edition):

Driessen, D M (author). “Large Deviations for Markov Jump Processes and Hamiltonian Trajectories.” 2015. Web. 07 Mar 2021.

Vancouver:

Driessen DM(. Large Deviations for Markov Jump Processes and Hamiltonian Trajectories. [Internet] [Masters thesis]. Delft University of Technology; 2015. [cited 2021 Mar 07]. Available from: http://resolver.tudelft.nl/uuid:3762ee57-0e0e-4012-bb35-157bd14961bf.

Council of Science Editors:

Driessen DM(. Large Deviations for Markov Jump Processes and Hamiltonian Trajectories. [Masters Thesis]. Delft University of Technology; 2015. Available from: http://resolver.tudelft.nl/uuid:3762ee57-0e0e-4012-bb35-157bd14961bf

Delft University of Technology

7. Singh, Niels (author). A Hamiltonian Reduction Method for Nonlinear Dynamics.

Degree: 2015, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:bc6a6d49-8ea4-4aca-ace6-0cd6934070da

►

Nonlinear analysis of dynamic problems has become important for modern industrial design applications. The increasing pressure on airlines to decrease fuel costs demands the design… (more)

▼

Nonlinear analysis of dynamic problems has become important for modern industrial design applications. The increasing pressure on airlines to decrease fuel costs demands the design of more efficient aircraft. This requires aircraft manufacturing companies to design lighter structural components. The result is the need for more realistic and accurate modelling of critical structural components. Over the years, more powerful finite element discretization methods and improved numerical methods and programming techniques for dynamic analyses of structures have been introduced. Despite these advances and the increase in available computer power, the analysis of nonlinear dynamic problems is yet a computationally demanding task, implying it is very expensive. To reduce the computational time of nonlinear finite element analyses, reduction methods have been developed. These methods have as aim to reduce the number of degrees of freedom, while retaining sufficient accuracy of the solution. Recently, a new reduction method, applicable to nonlinear static stability problems, has been developed at Delft University of Technology. The aim of this thesis is to extend the reduction method for statics to nonlinear dynamics. This is achieved by using the Hamiltonian formulation to describe the motion of a system. A reduced order model (ROM) is constructed for free vibrations, forced vibrations and damped vibrations, using Hamilton’s equations of motion. These are integrated to obtain the response of the ROM, in terms of displacements and momenta. The displacements of the full finite element model are computed by back-substituting the reduced response into the displacement expansion. The ROM is implemented in a finite element framework. The ROM is applied to beams, to plates as well as to shells. Overall, good agreement is found between the ROM and Abaqus. The big advantage of the ROM is found when the computational times for beams and plates are compared to that of Abaqus. A drastic reduction in time is observed for the ROM, while still maintaining accurate results. The ROM thus saves valuable computational time.

Aerospace Structures and Computational Mechanics

Advisors/Committee Members: Abdalla, Mostafa (mentor), Turteltaub, Sergio (graduation committee), Alijani, Farbod (graduation committee), van Kampen, Erik-jan (graduation committee), Delft University of Technology (degree granting institution).

Subjects/Keywords: Reduced order model; Nonlinear dynamics; Finite Element Method; Hamiltonian mechanics

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APA (6^th Edition):

Singh, N. (. (2015). A Hamiltonian Reduction Method for Nonlinear Dynamics. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:bc6a6d49-8ea4-4aca-ace6-0cd6934070da

Chicago Manual of Style (16^th Edition):

Singh, Niels (author). “A Hamiltonian Reduction Method for Nonlinear Dynamics.” 2015. Masters Thesis, Delft University of Technology. Accessed March 07, 2021. http://resolver.tudelft.nl/uuid:bc6a6d49-8ea4-4aca-ace6-0cd6934070da.

MLA Handbook (7^th Edition):

Singh, Niels (author). “A Hamiltonian Reduction Method for Nonlinear Dynamics.” 2015. Web. 07 Mar 2021.

Vancouver:

Singh N(. A Hamiltonian Reduction Method for Nonlinear Dynamics. [Internet] [Masters thesis]. Delft University of Technology; 2015. [cited 2021 Mar 07]. Available from: http://resolver.tudelft.nl/uuid:bc6a6d49-8ea4-4aca-ace6-0cd6934070da.

Council of Science Editors:

Singh N(. A Hamiltonian Reduction Method for Nonlinear Dynamics. [Masters Thesis]. Delft University of Technology; 2015. Available from: http://resolver.tudelft.nl/uuid:bc6a6d49-8ea4-4aca-ace6-0cd6934070da

University of Texas – Austin

8. Holder, Benjamin Peirce, 1976-. Coherent control of cold atoms in a[n] optical lattice.

Degree: PhD, Physics, 2007, University of Texas – Austin

URL: http://hdl.handle.net/2152/3251

► The dynamics of non-interacting, ultracold alkali atoms in the presence of counter-propagating lasers (optical lattice systems) is considered theoretically. The center of mass motion of… (more)

Subjects/Keywords: Lattice dynamics; Atoms; Hamiltonian systems

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APA (6^th Edition):

Holder, Benjamin Peirce, 1. (2007). Coherent control of cold atoms in a[n] optical lattice. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/3251

Chicago Manual of Style (16^th Edition):

Holder, Benjamin Peirce, 1976-. “Coherent control of cold atoms in a[n] optical lattice.” 2007. Doctoral Dissertation, University of Texas – Austin. Accessed March 07, 2021. http://hdl.handle.net/2152/3251.

MLA Handbook (7^th Edition):

Holder, Benjamin Peirce, 1976-. “Coherent control of cold atoms in a[n] optical lattice.” 2007. Web. 07 Mar 2021.

Vancouver:

Holder, Benjamin Peirce 1. Coherent control of cold atoms in a[n] optical lattice. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2007. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/2152/3251.

Council of Science Editors:

Holder, Benjamin Peirce 1. Coherent control of cold atoms in a[n] optical lattice. [Doctoral Dissertation]. University of Texas – Austin; 2007. Available from: http://hdl.handle.net/2152/3251

University of Georgia

9. Zhang, Jun. Hamiltonian dynamics and persistent homology.

Degree: 2017, University of Georgia

URL: http://hdl.handle.net/10724/36582

► In this dissertation, we first develop an alternative method of persistent homology from filtered chain complex level, called Floer-Novikov persistent theory. Then we apply it… (more)

Subjects/Keywords: Hamiltonian dynamics; Hamiltonian Floer theory; persistent homology; non-Archimedean orthogonality; singular value decomposition; barcode; generalized boundary depth; egg-beater model

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APA (6^th Edition):

Zhang, J. (2017). Hamiltonian dynamics and persistent homology. (Thesis). University of Georgia. Retrieved from http://hdl.handle.net/10724/36582

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Zhang, Jun. “Hamiltonian dynamics and persistent homology.” 2017. Thesis, University of Georgia. Accessed March 07, 2021. http://hdl.handle.net/10724/36582.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Zhang, Jun. “Hamiltonian dynamics and persistent homology.” 2017. Web. 07 Mar 2021.

Vancouver:

Zhang J. Hamiltonian dynamics and persistent homology. [Internet] [Thesis]. University of Georgia; 2017. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/10724/36582.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Zhang J. Hamiltonian dynamics and persistent homology. [Thesis]. University of Georgia; 2017. Available from: http://hdl.handle.net/10724/36582

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

10. Berman, Simon. Classical mechanisms of recollision and high harmonic generation : Mécanismes classiques de recollisions et génération d'harmoniques d'ordres élevés.

Degree: Docteur es, Physique et sciences de la matière, 2018, Aix-Marseille; Georgia institute of technology

URL: http://www.theses.fr/2018AIXM0494

►

Trente ans après la démonstration de la production d'harmoniques laser par interaction laser-gaz non linéaire, la génération d'harmoniques d’ordre élevées (HHG) est utilisée pour sonder… (more)

▼

Trente ans après la démonstration de la production d'harmoniques laser par interaction laser-gaz non linéaire, la génération d'harmoniques d’ordre élevées (HHG) est utilisée pour sonder la dynamique moléculaire et réalise son potentiel technologique comme source compacte d'impulsions attosecondes XUV à la gamme de rayons X. Malgré les progrès expérimentaux, le coût de calcul excessif des simulations fondées sur les premiers principes et la difficulté de dériver systématiquement des modèles réduits pour l'interaction non perturbatif et à échelles multiples d'une impulsion laser intense avec un gaz macroscopique d'atomes ont entravé les efforts théoriques. Dans cette thèse, nous étudions des modèles réduits de premier principe pour HHG utilisant la mécanique classique. En utilisant la dynamique non linéaire, nous élucidons le rôle indispensable joué par le potentiel ionique lors des recollisions dans la limite du champ fort. Ensuite, en empruntant une technique de la physique des plasmas, nous dérivons systématiquement une hiérarchie de modèles hamiltoniens réduits pour l’interaction cohérente entre le laser et les atomes lors de la propagation des impulsions. Les modèles réduits permettent une dynamique électronique soit classique, soit quantique. Nous construisons un modèle classique qui concorde quantitativement avec le modèle quantique pour la propagation des composantes dominantes du champ laser. Dans une géométrie simplifiée, nous montrons que le rayonnement à fréquence anormalement élevée observé dans les simulations résulte de l’interaction délicate entre le piégeage d’électrons et les recollisions de plus grande énergie provoqués par les effets de propagation.

Thirty years after the demonstration of the production of high laser harmonics through nonlinear laser-gas interaction, high harmonic generation (HHG) is being used to probe molecular dynamics in real time and is realizing its technological potential as a tabletop source of attosecond pulses in the XUV to soft X-ray range. Despite experimental progress, theoretical efforts have been stymied by the excessive computational cost of first-principles simulations and the difficulty of systematically deriving reduced models for the non-perturbative, multiscale interaction of an intense laser pulse with a macroscopic gas of atoms. In this thesis, we investigate first-principles reduced models for HHG using classical mechanics. Using nonlinear dynamics, we elucidate the indispensable role played by the ionic potential during recollisions in the strong-field limit. Then, borrowing a technique from plasma physics, we systematically derive a hierarchy of reduced Hamiltonian models for the self-consistent interaction between the laser and the atoms during pulse propagation. The reduced models can accommodate either classical or quantum electron dynamics. We build a classical model which agrees quantitatively with the quantum model for the propagation of the dominant components of the laser field. In a simplified geometry, we show that the anomalously high…

Advisors/Committee Members: Chandre, Cristel (thesis director), Uzer, Turgay (thesis director).

Subjects/Keywords: Mécanique hamiltonienne; Dynamique non-Linéaire; Physique attoseconde; Hamiltonian systems; Nonlinear dynamics; Attosecond physics; 530

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APA (6^th Edition):

Berman, S. (2018). Classical mechanisms of recollision and high harmonic generation : Mécanismes classiques de recollisions et génération d'harmoniques d'ordres élevés. (Doctoral Dissertation). Aix-Marseille; Georgia institute of technology. Retrieved from http://www.theses.fr/2018AIXM0494

Chicago Manual of Style (16^th Edition):

Berman, Simon. “Classical mechanisms of recollision and high harmonic generation : Mécanismes classiques de recollisions et génération d'harmoniques d'ordres élevés.” 2018. Doctoral Dissertation, Aix-Marseille; Georgia institute of technology. Accessed March 07, 2021. http://www.theses.fr/2018AIXM0494.

MLA Handbook (7^th Edition):

Berman, Simon. “Classical mechanisms of recollision and high harmonic generation : Mécanismes classiques de recollisions et génération d'harmoniques d'ordres élevés.” 2018. Web. 07 Mar 2021.

Vancouver:

Berman S. Classical mechanisms of recollision and high harmonic generation : Mécanismes classiques de recollisions et génération d'harmoniques d'ordres élevés. [Internet] [Doctoral dissertation]. Aix-Marseille; Georgia institute of technology; 2018. [cited 2021 Mar 07]. Available from: http://www.theses.fr/2018AIXM0494.

Council of Science Editors:

Berman S. Classical mechanisms of recollision and high harmonic generation : Mécanismes classiques de recollisions et génération d'harmoniques d'ordres élevés. [Doctoral Dissertation]. Aix-Marseille; Georgia institute of technology; 2018. Available from: http://www.theses.fr/2018AIXM0494

University of Maryland

11. Galante, Joseph Robert. Cometary Escape in the Restricted Circular Planar Three Body Problem.

Degree: Mathematics, 2011, University of Maryland

URL: http://hdl.handle.net/1903/11641

► The classical principle of least action says that orbits of mechanical systems extremize action; an important subclass are those orbits that minimize action. This principle… (more)

Subjects/Keywords: Mathematics; Celestial Mechanics; Dynamical Systems; Hamiltonian Dynamics; Instabilities; Rigorous Numerics; Variational Methods

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APA (6^th Edition):

Galante, J. R. (2011). Cometary Escape in the Restricted Circular Planar Three Body Problem. (Thesis). University of Maryland. Retrieved from http://hdl.handle.net/1903/11641

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Galante, Joseph Robert. “Cometary Escape in the Restricted Circular Planar Three Body Problem.” 2011. Thesis, University of Maryland. Accessed March 07, 2021. http://hdl.handle.net/1903/11641.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Galante, Joseph Robert. “Cometary Escape in the Restricted Circular Planar Three Body Problem.” 2011. Web. 07 Mar 2021.

Vancouver:

Galante JR. Cometary Escape in the Restricted Circular Planar Three Body Problem. [Internet] [Thesis]. University of Maryland; 2011. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/1903/11641.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Galante JR. Cometary Escape in the Restricted Circular Planar Three Body Problem. [Thesis]. University of Maryland; 2011. Available from: http://hdl.handle.net/1903/11641

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Virginia Tech

12. Zhong, Jun. Geometrical Investigation on Escape Dynamics in the Presence of Dissipative and Gyroscopic Forces.

Degree: PhD, Engineering Mechanics, 2020, Virginia Tech

URL: http://hdl.handle.net/10919/97363

► Transition or escape events are very common in daily life, such as the snap-through of plant leaves and the flipping over of umbrellas on a… (more)

▼ Transition or escape events are very common in daily life, such as the snap-through of plant leaves and the flipping over of umbrellas on a windy day, the capsize of ships and boats on a rough sea. Some other engineering problems related to escape, such as the collapse of arch bridges subjected to seismic load and moving trucks, and the escape and recapture of the spacecraft, are also widely known. At first glance, these problems seem to be irrelated. However, from the perspective of mechanics, they have the same physical principle which essentially can be considered as the escape from the potential wells. A more specific exemplary representative is a rolling ball on a multi-well surface where the potential energy is from gravity. The purpose of this dissertation is to develop a theoretical-computational framework to understand how a transition event can occur if a certain energy is applied to the system. For a multi-well system, the potential wells are usually connected by saddle points so that the motion between the wells generally occurs around the saddle. Thus, knowing the local behavior around the saddle plays a vital role in understanding the global motion of the nonlinear system. The first topic aims to study the linearized dynamics around the saddle. In this study, an idealized ball rolling on both stationary and rotating surfaces will be used to reveal the dynamics. The effect of the gyroscopic force induced by the rotation of the surface and the energy dissipation will be considered. In the second work, the escape dynamics will be extended to the nonlinear system applied to the snap-through of a buckled beam. Due to the nonlinear behavior existing in the system, it is hard to get the analytical solutions so that numerical algorithms are needed. In this study, a bisection method is developed to search the transition boundary. By using such method, the transition boundary on a specific Poincar'e section is obtained for both the conservative and dissipative systems. Finally, we revisit the escape dynamics in the snap-through buckling from the perspective of the invariant manifold. The treatment for the conservative and dissipative systems is different. In the conservative system, we compute the invariant manifold of a periodic orbit, while in the dissipative system we compute the invariant manifold of a saddle point. The computational process for the conservative system consists of the computation of the periodic orbit and the globalization of the corresponding manifold. In the dissipative system, the invariant manifold can be found by solving a proper boundary-value problem. Based on these algorithms, the nonlinear transition tube and transition ellipsoid in the phase space can be obtained for the conservative and dissipative systems, respectively, which are qualitatively the same as the linearized dynamics. Advisors/Committee Members: Ross, Shane D. (committeechair), Virgin, Lawrie (committee member), Plaut, Raymond H. (committee member), Abaid, Nicole (committee member), Tarazaga, Pablo Alberto (committee member).

Subjects/Keywords: Escape dynamics; Invariant manifold; Transition tube; Transition ellipsoid; Hamiltonian system; Dissipative system; Gyroscopic system

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APA (6^th Edition):

Zhong, J. (2020). Geometrical Investigation on Escape Dynamics in the Presence of Dissipative and Gyroscopic Forces. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/97363

Chicago Manual of Style (16^th Edition):

Zhong, Jun. “Geometrical Investigation on Escape Dynamics in the Presence of Dissipative and Gyroscopic Forces.” 2020. Doctoral Dissertation, Virginia Tech. Accessed March 07, 2021. http://hdl.handle.net/10919/97363.

MLA Handbook (7^th Edition):

Zhong, Jun. “Geometrical Investigation on Escape Dynamics in the Presence of Dissipative and Gyroscopic Forces.” 2020. Web. 07 Mar 2021.

Vancouver:

Zhong J. Geometrical Investigation on Escape Dynamics in the Presence of Dissipative and Gyroscopic Forces. [Internet] [Doctoral dissertation]. Virginia Tech; 2020. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/10919/97363.

Council of Science Editors:

Zhong J. Geometrical Investigation on Escape Dynamics in the Presence of Dissipative and Gyroscopic Forces. [Doctoral Dissertation]. Virginia Tech; 2020. Available from: http://hdl.handle.net/10919/97363

University of North Texas

13. Kim, Won-Gyu, 1962-. A Study of Nonlinear Dynamics in an Internal Water Wave Field in a Deep Ocean.

Degree: 1996, University of North Texas

URL: https://digital.library.unt.edu/ark:/67531/metadc278092/

► The Hamiltonian of a stably stratified incompressible fluid in an internal water wave in a deep ocean is constructed. Studying the ocean internal wave field… (more)

Subjects/Keywords: ocean; waves; nonlinear dynamics; physics; Hamiltonian; Dynamics.; Nonlinear theories.

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APA (6^th Edition):

Kim, Won-Gyu, 1. (1996). A Study of Nonlinear Dynamics in an Internal Water Wave Field in a Deep Ocean. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc278092/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Kim, Won-Gyu, 1962-. “A Study of Nonlinear Dynamics in an Internal Water Wave Field in a Deep Ocean.” 1996. Thesis, University of North Texas. Accessed March 07, 2021. https://digital.library.unt.edu/ark:/67531/metadc278092/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Kim, Won-Gyu, 1962-. “A Study of Nonlinear Dynamics in an Internal Water Wave Field in a Deep Ocean.” 1996. Web. 07 Mar 2021.

Vancouver:

Kim, Won-Gyu 1. A Study of Nonlinear Dynamics in an Internal Water Wave Field in a Deep Ocean. [Internet] [Thesis]. University of North Texas; 1996. [cited 2021 Mar 07]. Available from: https://digital.library.unt.edu/ark:/67531/metadc278092/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Kim, Won-Gyu 1. A Study of Nonlinear Dynamics in an Internal Water Wave Field in a Deep Ocean. [Thesis]. University of North Texas; 1996. Available from: https://digital.library.unt.edu/ark:/67531/metadc278092/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Michigan

14. Penagaricano Munoa, Oier. A Perturbation Theory for Hamilton's Principal Function: Applications to Boundary Value Problems.

Degree: PhD, Aerospace Engineering, 2010, University of Michigan

URL: http://hdl.handle.net/2027.42/78858

► This thesis introduces an analytical perturbation theory for Hamilton's principal function and Hamilton's characteristic function. Based on Hamilton's principle and the research carried out by… (more)

Subjects/Keywords: Hamiltonian Dynamics; Orbital Perturbations; Aerospace Engineering; Engineering

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APA (6^th Edition):

Penagaricano Munoa, O. (2010). A Perturbation Theory for Hamilton's Principal Function: Applications to Boundary Value Problems. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/78858

Chicago Manual of Style (16^th Edition):

Penagaricano Munoa, Oier. “A Perturbation Theory for Hamilton's Principal Function: Applications to Boundary Value Problems.” 2010. Doctoral Dissertation, University of Michigan. Accessed March 07, 2021. http://hdl.handle.net/2027.42/78858.

MLA Handbook (7^th Edition):

Penagaricano Munoa, Oier. “A Perturbation Theory for Hamilton's Principal Function: Applications to Boundary Value Problems.” 2010. Web. 07 Mar 2021.

Vancouver:

Penagaricano Munoa O. A Perturbation Theory for Hamilton's Principal Function: Applications to Boundary Value Problems. [Internet] [Doctoral dissertation]. University of Michigan; 2010. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/2027.42/78858.

Council of Science Editors:

Penagaricano Munoa O. A Perturbation Theory for Hamilton's Principal Function: Applications to Boundary Value Problems. [Doctoral Dissertation]. University of Michigan; 2010. Available from: http://hdl.handle.net/2027.42/78858

University of Michigan

15. 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 L₂ 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 (6^th 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 (16^th Edition):

Park, Sang H. “Nonlinear trajectory navigation.” 2007. Doctoral Dissertation, University of Michigan. Accessed March 07, 2021. http://hdl.handle.net/2027.42/126532.

MLA Handbook (7^th Edition):

Park, Sang H. “Nonlinear trajectory navigation.” 2007. Web. 07 Mar 2021.

Vancouver:

Park SH. Nonlinear trajectory navigation. [Internet] [Doctoral dissertation]. University of Michigan; 2007. [cited 2021 Mar 07]. 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

16. Rajan Nambiar A. Chaotic dynamics in model hamiltonian and dissipative systems;.

Degree: Physics, 2015, University of Calicut

URL: http://shodhganga.inflibnet.ac.in/handle/10603/38191

newline

Appendices p.149-151, References p.152-158

Advisors/Committee Members: P. Rameshan.

Subjects/Keywords: Chaotic dynamics; dissipative systems; model hamiltonian; Physics

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APA (6^th Edition):

A., R. N. (2015). Chaotic dynamics in model hamiltonian and dissipative systems;. (Thesis). University of Calicut. Retrieved from http://shodhganga.inflibnet.ac.in/handle/10603/38191

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

A., Rajan Nambiar. “Chaotic dynamics in model hamiltonian and dissipative systems;.” 2015. Thesis, University of Calicut. Accessed March 07, 2021. http://shodhganga.inflibnet.ac.in/handle/10603/38191.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

A., Rajan Nambiar. “Chaotic dynamics in model hamiltonian and dissipative systems;.” 2015. Web. 07 Mar 2021.

Vancouver:

A. RN. Chaotic dynamics in model hamiltonian and dissipative systems;. [Internet] [Thesis]. University of Calicut; 2015. [cited 2021 Mar 07]. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/38191.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

A. RN. Chaotic dynamics in model hamiltonian and dissipative systems;. [Thesis]. University of Calicut; 2015. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/38191

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

17. Cambon, Benjamin. Chaos hamiltonien dans les plasmas de fusion : Hamiltonian chaos into fusion plasmas.

Degree: Docteur es, Physique et sciences de la matière, 2015, Aix Marseille Université

URL: http://www.theses.fr/2015AIXM4035

►

Notre travail se portera sur l’étude de la trajectoire exacte d’une particule chargée dans un champ magnétique de type tokamak. Nous considérerons des particules tests… (more)

▼

Notre travail se portera sur l’étude de la trajectoire exacte d’une particule chargée dans un champ magnétique de type tokamak. Nous considérerons des particules tests plongées dans un champ magnétique indépendant du temps. Par définition, elles n’interagissent pas entre-elles et n’ont aucun effet sur le champ magnétique. Le but de notre étude sera alors de mettre en évidence des différences de comportement majeures entre d’une part les trajectoires des particules et d’autre part les lignes de champ magnétique. Nous commencerons dans une première partie par expliciter nos motivations. Les techniques employées aujourd’hui pour simuler la dynamique d’un plasma de fusion reposent sur des modèles magnétohydrodynamiques ou gyrocinétiques dont les hypothèses sont parfois contestables. Nous exposerons ensuite l’approche hamiltonienne choisie pour simuler la trajectoire exacte d’une particule et introduirons les différents outils dont nous aurons besoin. Dans la seconde partie, nous présenterons brièvement l’outil numérique développé qu mettra en évidence des différences de comportements importantes entre ligne de champ et trajectoire de particule. Dans un premier temps, nous exhiberons du chaos de trajectoire en présence de ligne de champ intégrable en ajoutant au champ magnétique idéal une perturbation. Un même résultat sera démontré dans le cas d’un champ magnétique idéal axisymétrique. Ce résultat entrainera des questions importantes autour de l’invariance du moment magnétique μ. Enfin, la dernière partie de ce manuscrit portera sur le comportement des particules tests en présence d’un champ magnétique potentiellement chaotique.

We will work on the study of the exact trajectory of a charged particle within a magnetic field of the tokamak type. We will consider test particles immerged into a timeindependent magnetic field. They don’t interact with each other and have no effect on the magnetic field. The objective of our study will be to prove major behaviour differences between the particles’ trajectories and the magnetic field lines. We will start in part one by making our motivations explicit and especially see that the technics used nowadays to simulate the dynamic of fusion plasma are based on magnetohydrodynamic or gyrokinetic models which hypotheses are sometimes debatable. We will then present the Hamiltonian approach chosen to simulate the exact trajectory of a particle, and will introduce the various tools we will later need, including the characterizationof chaotic phenomena. we will briefly the developed digital tool which will highlight behaviour differences between field line and particle trajectory. Initially, we will exhibit trajectory chaos in the presence of integrable field lines by adding a perturbation to the ideal magnetic field. In a second phase, we will show that a similar result can be proven in the case of an asymmetrical ideal magnetic field. This result will lead to substantial questions regarding the invariance of the μ. The last part of this manuscript will finally focus on the behaviour…

Advisors/Committee Members: Leoncini, Xavier (thesis director).

Subjects/Keywords: Fusion; Plasma; Chaos; Integrabilité; Itb; Trajectoires; Hamiltonien; Dynamique; Fusion; Plasma; Chaos; Integrability; Itb; Trajectory; Hamiltonian; Dynamics; 530

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Cambon, B. (2015). Chaos hamiltonien dans les plasmas de fusion : Hamiltonian chaos into fusion plasmas. (Doctoral Dissertation). Aix Marseille Université. Retrieved from http://www.theses.fr/2015AIXM4035

Chicago Manual of Style (16^th Edition):

Cambon, Benjamin. “Chaos hamiltonien dans les plasmas de fusion : Hamiltonian chaos into fusion plasmas.” 2015. Doctoral Dissertation, Aix Marseille Université. Accessed March 07, 2021. http://www.theses.fr/2015AIXM4035.

MLA Handbook (7^th Edition):

Cambon, Benjamin. “Chaos hamiltonien dans les plasmas de fusion : Hamiltonian chaos into fusion plasmas.” 2015. Web. 07 Mar 2021.

Vancouver:

Cambon B. Chaos hamiltonien dans les plasmas de fusion : Hamiltonian chaos into fusion plasmas. [Internet] [Doctoral dissertation]. Aix Marseille Université 2015. [cited 2021 Mar 07]. Available from: http://www.theses.fr/2015AIXM4035.

Council of Science Editors:

Cambon B. Chaos hamiltonien dans les plasmas de fusion : Hamiltonian chaos into fusion plasmas. [Doctoral Dissertation]. Aix Marseille Université 2015. Available from: http://www.theses.fr/2015AIXM4035

Vrije Universiteit Amsterdam

18. Schoonderwoerd, N.C.J. Light-front Hamiltonian field theory. Towards a relativistic description of bound states .

Degree: 1999, Vrije Universiteit Amsterdam

URL: http://hdl.handle.net/1871/10317

Subjects/Keywords: Light-front Hamiltonian Dynamics; Hamilton vergelijkingen; Veldtheorie; Hadronen

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APA (6^th Edition):

Schoonderwoerd, N. C. J. (1999). Light-front Hamiltonian field theory. Towards a relativistic description of bound states . (Doctoral Dissertation). Vrije Universiteit Amsterdam. Retrieved from http://hdl.handle.net/1871/10317

Chicago Manual of Style (16^th Edition):

Schoonderwoerd, N C J. “Light-front Hamiltonian field theory. Towards a relativistic description of bound states .” 1999. Doctoral Dissertation, Vrije Universiteit Amsterdam. Accessed March 07, 2021. http://hdl.handle.net/1871/10317.

MLA Handbook (7^th Edition):

Schoonderwoerd, N C J. “Light-front Hamiltonian field theory. Towards a relativistic description of bound states .” 1999. Web. 07 Mar 2021.

Vancouver:

Schoonderwoerd NCJ. Light-front Hamiltonian field theory. Towards a relativistic description of bound states . [Internet] [Doctoral dissertation]. Vrije Universiteit Amsterdam; 1999. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/1871/10317.

Council of Science Editors:

Schoonderwoerd NCJ. Light-front Hamiltonian field theory. Towards a relativistic description of bound states . [Doctoral Dissertation]. Vrije Universiteit Amsterdam; 1999. Available from: http://hdl.handle.net/1871/10317

Vrije Universiteit Amsterdam

19. Wisniewska, J.J. Rabinowitz Floer Homology for Tentacular Hamiltonians .

Degree: 2017, Vrije Universiteit Amsterdam

URL: http://hdl.handle.net/1871/55254

Subjects/Keywords: symplectic geometry; Floer homology; Rabinowitz action functional; Hamiltonian dynamics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Wisniewska, J. J. (2017). Rabinowitz Floer Homology for Tentacular Hamiltonians . (Doctoral Dissertation). Vrije Universiteit Amsterdam. Retrieved from http://hdl.handle.net/1871/55254

Chicago Manual of Style (16^th Edition):

Wisniewska, J J. “Rabinowitz Floer Homology for Tentacular Hamiltonians .” 2017. Doctoral Dissertation, Vrije Universiteit Amsterdam. Accessed March 07, 2021. http://hdl.handle.net/1871/55254.

MLA Handbook (7^th Edition):

Wisniewska, J J. “Rabinowitz Floer Homology for Tentacular Hamiltonians .” 2017. Web. 07 Mar 2021.

Vancouver:

Wisniewska JJ. Rabinowitz Floer Homology for Tentacular Hamiltonians . [Internet] [Doctoral dissertation]. Vrije Universiteit Amsterdam; 2017. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/1871/55254.

Council of Science Editors:

Wisniewska JJ. Rabinowitz Floer Homology for Tentacular Hamiltonians . [Doctoral Dissertation]. Vrije Universiteit Amsterdam; 2017. Available from: http://hdl.handle.net/1871/55254

University of Colorado

20. Sen, Amrik. A Tale of Waves and Eddies in a Sea of Rotating Turbulence.

Degree: PhD, Applied Mathematics, 2014, University of Colorado

URL: https://scholar.colorado.edu/appm_gradetds/46

► In this thesis, we investigate several properties of rotating turbulent flows. First, we ran several computer simulations of rotating turbulent flows and performed statistical… (more)

Subjects/Keywords: Hamiltonian Dynamics; Nonlinear waves; perturbation Theory; Rotating Turbulence; Symmetries and reduction; Applied Mathematics; Geophysics and Seismology; Physics

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APA (6^th Edition):

Sen, A. (2014). A Tale of Waves and Eddies in a Sea of Rotating Turbulence. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/46

Chicago Manual of Style (16^th Edition):

Sen, Amrik. “A Tale of Waves and Eddies in a Sea of Rotating Turbulence.” 2014. Doctoral Dissertation, University of Colorado. Accessed March 07, 2021. https://scholar.colorado.edu/appm_gradetds/46.

MLA Handbook (7^th Edition):

Sen, Amrik. “A Tale of Waves and Eddies in a Sea of Rotating Turbulence.” 2014. Web. 07 Mar 2021.

Vancouver:

Sen A. A Tale of Waves and Eddies in a Sea of Rotating Turbulence. [Internet] [Doctoral dissertation]. University of Colorado; 2014. [cited 2021 Mar 07]. Available from: https://scholar.colorado.edu/appm_gradetds/46.

Council of Science Editors:

Sen A. A Tale of Waves and Eddies in a Sea of Rotating Turbulence. [Doctoral Dissertation]. University of Colorado; 2014. Available from: https://scholar.colorado.edu/appm_gradetds/46

University of Manchester

21. Fullerton, Christopher James. An investigation into growing correlation lengths in glassy systems.

Degree: PhD, 2011, University of Manchester

URL: https://www.research.manchester.ac.uk/portal/en/theses/an-investigation-into-growing-correlation-lengths-in-glassy-systems(ff3d3d77-7034-4c0a-9591-0378005f0da1).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.549052

► In this thesis Moore and Yeo's proposed mapping of the structural glass to the Ising spin glass in a random field is presented. In contrast… (more)

Subjects/Keywords: 666; Glass; Glassy Systems; Disordered Systems; Soft Matter; Spin Glass; Molecular Dynamics; Effective Hamiltonian; Statistical Mechanics

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APA (6^th Edition):

Fullerton, C. J. (2011). An investigation into growing correlation lengths in glassy systems. (Doctoral Dissertation). University of Manchester. Retrieved from https://www.research.manchester.ac.uk/portal/en/theses/an-investigation-into-growing-correlation-lengths-in-glassy-systems(ff3d3d77-7034-4c0a-9591-0378005f0da1).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.549052

Chicago Manual of Style (16^th Edition):

Fullerton, Christopher James. “An investigation into growing correlation lengths in glassy systems.” 2011. Doctoral Dissertation, University of Manchester. Accessed March 07, 2021. https://www.research.manchester.ac.uk/portal/en/theses/an-investigation-into-growing-correlation-lengths-in-glassy-systems(ff3d3d77-7034-4c0a-9591-0378005f0da1).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.549052.

MLA Handbook (7^th Edition):

Fullerton, Christopher James. “An investigation into growing correlation lengths in glassy systems.” 2011. Web. 07 Mar 2021.

Vancouver:

Fullerton CJ. An investigation into growing correlation lengths in glassy systems. [Internet] [Doctoral dissertation]. University of Manchester; 2011. [cited 2021 Mar 07]. Available from: https://www.research.manchester.ac.uk/portal/en/theses/an-investigation-into-growing-correlation-lengths-in-glassy-systems(ff3d3d77-7034-4c0a-9591-0378005f0da1).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.549052.

Council of Science Editors:

Fullerton CJ. An investigation into growing correlation lengths in glassy systems. [Doctoral Dissertation]. University of Manchester; 2011. Available from: https://www.research.manchester.ac.uk/portal/en/theses/an-investigation-into-growing-correlation-lengths-in-glassy-systems(ff3d3d77-7034-4c0a-9591-0378005f0da1).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.549052

22. Mietka, Colin. Ondes périodiques dans des systèmes d’ÉDP hamiltoniens : stabilité, modulations et chocs dispersifs : Periodic waves in some Hamiltonian PDEs : stability, modulations and dispersive shocks.

Degree: Docteur es, Mathématiques, 2017, Lyon

URL: http://www.theses.fr/2017LYSE1031

►

La première partie de cette thèse concerne l'étude du problème de Cauchy pour l'équation de KdV quasi-linéaire.On établit un théorème d'existence locale obtenu grâce à… (more)

▼

La première partie de cette thèse concerne l'étude du problème de Cauchy pour l'équation de KdV quasi-linéaire.On établit un théorème d'existence locale obtenu grâce à des propriétés structurelles et des techniques de jauge qui permettent de compenser les pertes de dérivées apparentes dans les estimations a priori.Dans la seconde partie, les propriétés de stabilité orbitale co-périodique et modulationnelle sont explorées numériquement en exploitant des critères algébriques tous établis à partir d'une même intégrale d'action et de ses dérivées secondes. Notre méthode utilise des quadratures numériques suivies de différences finies afin de calculer la matrice hessienne de l'intégrale d'action. Le comportement asymptotique de cette matrice nous pousse à prêter beaucoup d'attention à l'étude des ondes de grande période ou de faible amplitude. Les résultats numériquesprésentés fournissent de nombreuses informations en lien avec des questions ouvertes.On effectue également des simulations directes sur le système d' ÉDP original pour étudier à la fois le comportement des ondes périodiques sous différents types de perturbations, et les solutions de problèmes de Cauchy avec donnée initiale discontinue. Pour ces derniers, on s'attend à observer des chocs dispersifs, dont la compréhension est basée sur le problème de Gurevich-Pitaevskii, où les équations modulées à la Whitham sont utilisées pour approcher la zone oscillante des chocs. On compare des simulations directes aux solutions idéales du problème de Gurevich-Pitaevskii, en commençant par la célèbre équation de KdV

The first part of this manuscript presents a well-posedness result for a quasilinear version of the KdV equation.The proof takes advantage of structural properties and gauge techniques to deal with apparent loss of derivativesin a priori estimates.In the second part, we investigate the modulational and orbital coperiodic stability of periodic waves by computingalgebraic criteria involving the same abbreviated action integral and its second order derivatives. Our methoduses numerical integrations followed by finite differences to compute the Hessian matrix of the action integral.We pay attention to the asymptotic behavior of this matrix in the large period and small amplitude limits. Thenumerical results about stability give some new insight on several analytical open questions.Finally, direct numerical computations are done on the original system of PDEs to study the behavior of periodictraveling waves under various kinds of perturbations and the solutions of Cauchy problem with discontinuousinitial data. For the latter, we expect dispersive shock waves to arise. The building block for understandingdispersive shocks is known as the Gurevich-Pitaevskii problem, in which modulated equations 'a la Whitham'are used as an approximate model for the oscillatory zone. We compare direct numerical simulations to idealizedsolutions of Gurevich-Pitaevskii problems, starting with the famous KdV equation

Advisors/Committee Members: Benzoni-Gavage, Sylvie (thesis director), Rodrigues, Luis Miguel (thesis director).

Subjects/Keywords: Onde périodique; Dynamique hamiltonienne; Dispersion; Stabilité; Modulation; Choc dispersif; Periodic wave; Hamiltonian dynamics; Dispersion; Stability; Modulation; Dispersive shocks; 510

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APA (6^th Edition):

Mietka, C. (2017). Ondes périodiques dans des systèmes d’ÉDP hamiltoniens : stabilité, modulations et chocs dispersifs : Periodic waves in some Hamiltonian PDEs : stability, modulations and dispersive shocks. (Doctoral Dissertation). Lyon. Retrieved from http://www.theses.fr/2017LYSE1031

Chicago Manual of Style (16^th Edition):

Mietka, Colin. “Ondes périodiques dans des systèmes d’ÉDP hamiltoniens : stabilité, modulations et chocs dispersifs : Periodic waves in some Hamiltonian PDEs : stability, modulations and dispersive shocks.” 2017. Doctoral Dissertation, Lyon. Accessed March 07, 2021. http://www.theses.fr/2017LYSE1031.

MLA Handbook (7^th Edition):

Mietka, Colin. “Ondes périodiques dans des systèmes d’ÉDP hamiltoniens : stabilité, modulations et chocs dispersifs : Periodic waves in some Hamiltonian PDEs : stability, modulations and dispersive shocks.” 2017. Web. 07 Mar 2021.

Vancouver:

Mietka C. Ondes périodiques dans des systèmes d’ÉDP hamiltoniens : stabilité, modulations et chocs dispersifs : Periodic waves in some Hamiltonian PDEs : stability, modulations and dispersive shocks. [Internet] [Doctoral dissertation]. Lyon; 2017. [cited 2021 Mar 07]. Available from: http://www.theses.fr/2017LYSE1031.

Council of Science Editors:

Mietka C. Ondes périodiques dans des systèmes d’ÉDP hamiltoniens : stabilité, modulations et chocs dispersifs : Periodic waves in some Hamiltonian PDEs : stability, modulations and dispersive shocks. [Doctoral Dissertation]. Lyon; 2017. Available from: http://www.theses.fr/2017LYSE1031

University of Notre Dame

23. Scott S Hampton. An Analysis of Shadow Hybrid Monte Carlo Methods</h1>.

Degree: Computer Science and Engineering, 2007, University of Notre Dame

URL: https://curate.nd.edu/show/41687h1664c

► Hybrid Monte Carlo (HMC) is a rigorous sampling method that uses molecular dynamics (MD) as a global Monte Carlo move to search the phase… (more)

▼ Hybrid Monte Carlo (HMC) is a rigorous sampling method that uses molecular dynamics (MD) as a global Monte Carlo move to search the phase space of molecules. However, the acceptance rate of HMC, and thus the efficiency of the method, decays exponentially with increased system size or timestep. The Shadow Hybrid Monte Carlo (SHMC) method was previously introduced to overcome this performance degradation by sampling from the shadow Hamiltonian in lieu of the actual Hamiltonian. A numerical integrator for a Hamiltonian system of ordinary differential equations exactly solves a shadow Hamiltonian if and only if the integrator is symplectic. High order approximations to the shadow Hamiltonian are efficiently computed, thus, allowing significant acceptance of the MD step in SHMC. In order to remove the bias of sampling from the shadow Hamiltonian, a reweighting step is performed on the collected data. The increase in efficiency of SHMC comes at the expense of the variance of reweighted observables. In this dissertation, I discuss the development of an analytical framework for the analysis of shadow hybrid Monte Carlo methods. From this analysis, I show that the performance of SHMC is limited by the need to generate momenta for the MD step from a non-separable shadow Hamiltonian. In addition, I present a method for determining the optimal parameterization of SHMC. This includes the ability to ascertain the timestep which will allow for maximum efficiency of the method. The reweighting step usually causes an increase in the variance of observed data, but it is now possible to ascertain the magnitude of the variance beforehand. Finally, I introduce a new algorithm, Separable Shadow Hybrid Monte Carlo (S2HMC), which is based on a separable formulation of the shadow Hamiltonian. S2HMC is able to quickly generate momenta from the correct distribution, thereby overcoming a limitation of SHMC. S2HMC has the added advantage that no additional parameters are required. Through analysis and numerical experiments I show that S2HMC is at least twice more efficient than HMC for all systems larger than a few thousand atoms. Advisors/Committee Members: Kathie Newman, Committee Chair, Amitabh Chaudhary, Committee Member, J. Daniel Gezelter, Committee Member, Jesus Izaguirre, Committee Member, Patrick Flynn, Committee Member.

Subjects/Keywords: Hybrid Monte Carlo; Molecular Dynamics; Shadow Hamiltonian; Simulation

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APA (6^th Edition):

Hampton, S. S. (2007). An Analysis of Shadow Hybrid Monte Carlo Methods</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/41687h1664c

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Hampton, Scott S. “An Analysis of Shadow Hybrid Monte Carlo Methods</h1>.” 2007. Thesis, University of Notre Dame. Accessed March 07, 2021. https://curate.nd.edu/show/41687h1664c.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Hampton, Scott S. “An Analysis of Shadow Hybrid Monte Carlo Methods</h1>.” 2007. Web. 07 Mar 2021.

Vancouver:

Hampton SS. An Analysis of Shadow Hybrid Monte Carlo Methods</h1>. [Internet] [Thesis]. University of Notre Dame; 2007. [cited 2021 Mar 07]. Available from: https://curate.nd.edu/show/41687h1664c.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Hampton SS. An Analysis of Shadow Hybrid Monte Carlo Methods</h1>. [Thesis]. University of Notre Dame; 2007. Available from: https://curate.nd.edu/show/41687h1664c

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Duke University

24. Nishimura, Akihiko. General and Efficient Bayesian Computation through Hamiltonian Monte Carlo Extensions .

Degree: 2017, Duke University

URL: http://hdl.handle.net/10161/16309

► Hamiltonian Monte Carlo (HMC) is a state-of-the-art sampling algorithm for Bayesian computation. Popular probabilistic programming languages Stan and PyMC rely on HMC’s generality and… (more)

▼ Hamiltonian Monte Carlo (HMC) is a state-of-the-art sampling algorithm for Bayesian computation. Popular probabilistic programming languages Stan and PyMC rely on HMC’s generality and efficiency to provide automatic Bayesian inference platforms for practitioners. Despite its wide-spread use and numerous success stories, HMC has several well known pitfalls. This thesis presents extensions of HMC that overcome its two most prominent weaknesses: inability to handle discrete parameters and slow mixing on multi-modal target distributions. Discontinuous HMC (DHMC) presented in Chapter 2 extends HMC to discontinuous target distributions – and hence to discrete parameter distributions through embedding them into continuous spaces — using an idea of event-driven Monte Carlo from the computational physics literature. DHMC is guaranteed to outperform a Metropolis-within-Gibbs algorithm since, as it turns out, the two algorithms coincide under a specific (and sub-optimal) implementation of DHMC. The theoretical justification of DHMC extends an existing theory of non-smooth Hamiltonian mechanics and of measure-valued differential inclusions. Geometrically tempered HMC (GTHMC) presented in Chapter 3 improves HMC’s performance on multi-modal target distributions. The efficiency improvement is achieved through differential geometric techniques, relating a target distribution to another distribution with less severe multi-modality. We establish a geometric theory behind Riemannian manifold HMC to motivate our geometric tempering methods. We then develop an explicit variable stepsize reversible integrator for simulating Hamiltonian dynamics to overcome a stability issue of the usual Stormer-Verlet integrator. The integrator is of independent interest, being the first of its kind designed specifically for HMC variants. In addition to the two extensions described above, Chapter 4 describes a variable trajectory length algorithm that generalizes the acceptance and rejection procedure of HMC — and in fact of any reversible dynamics based samplers — to allow for more flexible choices of trajectory lengths. The algorithm in particular enables an effective application of a variable stepsize integrator to HMC extensions, including GTHMC. The algorithm is widely applicable and provides a recipe for constructing valid dynamics based samplers beyond the known HMC variants. Chapter 5 concludes the thesis with a simple and practical algorithm to improve computational efficiencies of HMC and related algorithms over their traditional implementations. Advisors/Committee Members: Dunson, David (advisor).

Subjects/Keywords: Applied mathematics; Statistics; Bayesian statistics; Geometric integration; Hamiltonian dynamics; Markov chain monte carlo; Probabilistic programming; Riemannian geometry

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APA (6^th Edition):

Nishimura, A. (2017). General and Efficient Bayesian Computation through Hamiltonian Monte Carlo Extensions . (Thesis). Duke University. Retrieved from http://hdl.handle.net/10161/16309

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Nishimura, Akihiko. “General and Efficient Bayesian Computation through Hamiltonian Monte Carlo Extensions .” 2017. Thesis, Duke University. Accessed March 07, 2021. http://hdl.handle.net/10161/16309.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Nishimura, Akihiko. “General and Efficient Bayesian Computation through Hamiltonian Monte Carlo Extensions .” 2017. Web. 07 Mar 2021.

Vancouver:

Nishimura A. General and Efficient Bayesian Computation through Hamiltonian Monte Carlo Extensions . [Internet] [Thesis]. Duke University; 2017. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/10161/16309.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Nishimura A. General and Efficient Bayesian Computation through Hamiltonian Monte Carlo Extensions . [Thesis]. Duke University; 2017. Available from: http://hdl.handle.net/10161/16309

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Texas – Austin

25. -9896-1704. Hamiltonian description of Hall and sub-electron scales in collisionless plasmas with reduced fluid models.

Degree: PhD, Physics, 2018, University of Texas – Austin

URL: http://hdl.handle.net/2152/68628

► In MHD magnetic helicity has been shown to represent Gauss linking numbers of magnetic field lines by Moffatt and others; thus it is endowed with… (more)

▼ In MHD magnetic helicity has been shown to represent Gauss linking numbers of magnetic field lines by Moffatt and others; thus it is endowed with topological meaning. The noncanonical Hamiltonian formulation of extended MHD models (that take two-fluid effects into account) has been used to arrive at their common mathematical structure, which manifests itself via the existence of two generalized helicities and two Lie-dragged 2-forms. The helicity invariants play an important role in the second part of thesis dedicated to understanding the directionality of turbulent cascades. Generally speaking, invariants (such as energy) can flow in two directions in a turbulent cascade: forward (towards small scales, leading to dissipation) and inverse (towards large scales), leading to the formation of a condensate. This directionality in extended MHD models is estimated using analytical considerations as well as tests involving 2D numerical simulations. The cascade reversal (transition) of the square magnetic vector potential is found, viz. when the forcing wavenumber exceeds the inverse electron skin depth the square magnetic vector potential starts to flow towards large wavenumbers, as opposed to the typical MHD behavior. In addition, the numerics suggest a simultaneous transition to the inverse cascade of energy in this inertial MHD regime. This is accompanied by the appearance of large scale structures in the velocity field, as opposed to the magnetic field as in the MHD case. Final chapters of the thesis are devoted to devising the action principle for the relativistic extended MHD. First the special relativistic version is discussed, where the covariant noncanonical Poisson bracket is found. This is followed by a short recourse towards describing relativistic collisionless reconnection mediated by the electron thermal inertia (purely relativistic effect). Next, 3+1 splitting inside the Poisson bracket is performed, while only non-relativistic terms are retained. Thus one arrives at nonrelativistic extended MHD bracket with arbitrary ion to electron mass ratio. In conclusion, it is outlined how the Hamiltonian 3+1 formalism can be developed for general relativistic Hall MHD using canonical Clebsch parametrization and some comments are added on possible issues regarding the quasi-neutrality assumption in the model that is used throughout the chapter. Advisors/Committee Members: Morrison, Philip J. (advisor), Hazeltine, Richard (committee member), Breizman, Boris (committee member), Fitzpatrick, Richard (committee member), Gamba, Irene M (committee member).

Subjects/Keywords: MHD; Magnetohydrodynamics; XMHD; Inertial MHD; Hall MHD; Turbulence; Reconnection; Hamiltonian dynamics; Casimir invariants; Poisson bracket; Noncanonical

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APA (6^th Edition):

-9896-1704. (2018). Hamiltonian description of Hall and sub-electron scales in collisionless plasmas with reduced fluid models. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/68628

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Chicago Manual of Style (16^th Edition):

-9896-1704. “Hamiltonian description of Hall and sub-electron scales in collisionless plasmas with reduced fluid models.” 2018. Doctoral Dissertation, University of Texas – Austin. Accessed March 07, 2021. http://hdl.handle.net/2152/68628.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-9896-1704. “Hamiltonian description of Hall and sub-electron scales in collisionless plasmas with reduced fluid models.” 2018. Web. 07 Mar 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-9896-1704. Hamiltonian description of Hall and sub-electron scales in collisionless plasmas with reduced fluid models. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2018. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/2152/68628.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-9896-1704. Hamiltonian description of Hall and sub-electron scales in collisionless plasmas with reduced fluid models. [Doctoral Dissertation]. University of Texas – Austin; 2018. Available from: http://hdl.handle.net/2152/68628

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

University of Texas – Austin

26. Padhye, Nikhil Subhash, 1970-. Topics in Lagrangian and Hamiltonian fluid dynamics : relabeling symmetry and ion-acoustic wave stability.

Degree: PhD, Physics, 1998, University of Texas – Austin

URL: http://hdl.handle.net/2152/38684

► Relabeling symmetries of the Lagrangian action are found for the ideal, compressible fluid and magnetohydrodynamics (MHD). These give rise to conservation laws of potential vorticity… (more)

▼ Relabeling symmetries of the Lagrangian action are found for the ideal, compressible fluid and magnetohydrodynamics (MHD). These give rise to conservation laws of potential vorticity (Ertel's theorem) and helicity in the ideal fluid, cross helicity in MHD, and a conservation law for an ideal fluid with three thermodynamic variables. The symmetry that gives rise to Ertel's theorem is generated by an infinite parameter group, and leads to a generalized Bianchi identity. The existence of a more general symmetry is also shown, with dependence on time and space derivatives of the fields, and corresponds to a family of conservation laws associated with the potential vorticity. In the Hamiltonian formalism, Casimir invariants of the noncanonical formulation are directly constructed from the symmetries of the reduction map from Lagrangian to Eulerian variables. Casimir invariants of MHD include a gauge-dependent family of invariants that incorporates magnetic helicity as a special case. Novel examples of finite dimensional, noncanonical Hamiltonian dynamics are also presented: the equations for a magnetic field line flow with a symmetry direction, and Frenet formulas that describe a curve in 3-space. In the study of Lyapunov stability of ion-acoustic waves, existence of negative energy perturbations is found at short wavelengths. The effect of adiabatic, ionic pressure on ion-acoustic waves is investigated, leading to explicit solitary and nonlinear periodic wave solutions for the adiabatic exponent r = 3. In particular, solitary waves are found to exist at any wave speed above Mach number one, without an upper cutoff speed. Negative energy perturbations are found to exist despite the addition of pressure, which prevents the establishment of Lyapunov stability; however the stability of ion-acoustic waves is established in the KdV limit, in a manner far simpler than the proof of KdV soliton stability. It is also shown that the KdV free energy (Benjamin, 1972) is recovered upon evaluating (the negative of) the ion-acoustic free energy at the critical point, in the KdV approximation. Numerical study of an ion-acoustic solitary wave with a negative energy perturbation shows transients with increased perturbation amplitude. The localized perturbation moves to the left in the wave-frame, leaving the solitary wave peak intact, thus indicating that the wave may be stable. Advisors/Committee Members: Morrison, Philip J. (advisor).

Subjects/Keywords: Lagrange equations; Hamiltonian systems; Ion acoustic waves; Fluid dynamics

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APA (6^th Edition):

Padhye, Nikhil Subhash, 1. (1998). Topics in Lagrangian and Hamiltonian fluid dynamics : relabeling symmetry and ion-acoustic wave stability. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/38684

Chicago Manual of Style (16^th Edition):

Padhye, Nikhil Subhash, 1970-. “Topics in Lagrangian and Hamiltonian fluid dynamics : relabeling symmetry and ion-acoustic wave stability.” 1998. Doctoral Dissertation, University of Texas – Austin. Accessed March 07, 2021. http://hdl.handle.net/2152/38684.

MLA Handbook (7^th Edition):

Padhye, Nikhil Subhash, 1970-. “Topics in Lagrangian and Hamiltonian fluid dynamics : relabeling symmetry and ion-acoustic wave stability.” 1998. Web. 07 Mar 2021.

Vancouver:

Padhye, Nikhil Subhash 1. Topics in Lagrangian and Hamiltonian fluid dynamics : relabeling symmetry and ion-acoustic wave stability. [Internet] [Doctoral dissertation]. University of Texas – Austin; 1998. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/2152/38684.

Council of Science Editors:

Padhye, Nikhil Subhash 1. Topics in Lagrangian and Hamiltonian fluid dynamics : relabeling symmetry and ion-acoustic wave stability. [Doctoral Dissertation]. University of Texas – Austin; 1998. Available from: http://hdl.handle.net/2152/38684

University of Texas – Austin

27. Gaidashev, Denis Gennad'yevich. Renormalization of isoenergetically degenerate Hamiltonian flows, and instability of solitons in shear hydrodynamic flows.

Degree: PhD, Physics, 2003, University of Texas – Austin

URL: http://hdl.handle.net/2152/588

► Part I of this Thesis presents a study of the renormalization group transformation acting on an appropriate space of Hamiltonian functions in two angle and… (more)

Subjects/Keywords: Hamiltonian systems; Renormalization (Physics); Solitons; Fluid dynamics

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APA (6^th Edition):

Gaidashev, D. G. (2003). Renormalization of isoenergetically degenerate Hamiltonian flows, and instability of solitons in shear hydrodynamic flows. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/588

Chicago Manual of Style (16^th Edition):

Gaidashev, Denis Gennad'yevich. “Renormalization of isoenergetically degenerate Hamiltonian flows, and instability of solitons in shear hydrodynamic flows.” 2003. Doctoral Dissertation, University of Texas – Austin. Accessed March 07, 2021. http://hdl.handle.net/2152/588.

MLA Handbook (7^th Edition):

Gaidashev, Denis Gennad'yevich. “Renormalization of isoenergetically degenerate Hamiltonian flows, and instability of solitons in shear hydrodynamic flows.” 2003. Web. 07 Mar 2021.

Vancouver:

Gaidashev DG. Renormalization of isoenergetically degenerate Hamiltonian flows, and instability of solitons in shear hydrodynamic flows. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2003. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/2152/588.

Council of Science Editors:

Gaidashev DG. Renormalization of isoenergetically degenerate Hamiltonian flows, and instability of solitons in shear hydrodynamic flows. [Doctoral Dissertation]. University of Texas – Austin; 2003. Available from: http://hdl.handle.net/2152/588

28. Wisniewska, J.J. Rabinowitz Floer Homology for Tentacular Hamiltonians.

Degree: Faculty of Sciences, 2017, NARCIS

URL: https://research.vu.nl/en/publications/e74baa79-5a39-4702-a23b-8420fcc85f05 ; urn:nbn:nl:ui:31-1871/55254 ; e74baa79-5a39-4702-a23b-8420fcc85f05 ; 1871/55254 ; urn:isbn:9789463321556 ; urn:nbn:nl:ui:31-1871/55254 ; https://research.vu.nl/en/publications/e74baa79-5a39-4702-a23b-8420fcc85f05

Subjects/Keywords: symplectic geometry; Floer homology; Rabinowitz action functional; Hamiltonian dynamics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Wisniewska, J. J. (2017). Rabinowitz Floer Homology for Tentacular Hamiltonians. (Doctoral Dissertation). NARCIS. Retrieved from https://research.vu.nl/en/publications/e74baa79-5a39-4702-a23b-8420fcc85f05 ; urn:nbn:nl:ui:31-1871/55254 ; e74baa79-5a39-4702-a23b-8420fcc85f05 ; 1871/55254 ; urn:isbn:9789463321556 ; urn:nbn:nl:ui:31-1871/55254 ; https://research.vu.nl/en/publications/e74baa79-5a39-4702-a23b-8420fcc85f05

Chicago Manual of Style (16^th Edition):

Wisniewska, J J. “Rabinowitz Floer Homology for Tentacular Hamiltonians.” 2017. Doctoral Dissertation, NARCIS. Accessed March 07, 2021. https://research.vu.nl/en/publications/e74baa79-5a39-4702-a23b-8420fcc85f05 ; urn:nbn:nl:ui:31-1871/55254 ; e74baa79-5a39-4702-a23b-8420fcc85f05 ; 1871/55254 ; urn:isbn:9789463321556 ; urn:nbn:nl:ui:31-1871/55254 ; https://research.vu.nl/en/publications/e74baa79-5a39-4702-a23b-8420fcc85f05.

MLA Handbook (7^th Edition):

Wisniewska, J J. “Rabinowitz Floer Homology for Tentacular Hamiltonians.” 2017. Web. 07 Mar 2021.

Vancouver:

Wisniewska JJ. Rabinowitz Floer Homology for Tentacular Hamiltonians. [Internet] [Doctoral dissertation]. NARCIS; 2017. [cited 2021 Mar 07]. Available from: https://research.vu.nl/en/publications/e74baa79-5a39-4702-a23b-8420fcc85f05 ; urn:nbn:nl:ui:31-1871/55254 ; e74baa79-5a39-4702-a23b-8420fcc85f05 ; 1871/55254 ; urn:isbn:9789463321556 ; urn:nbn:nl:ui:31-1871/55254 ; https://research.vu.nl/en/publications/e74baa79-5a39-4702-a23b-8420fcc85f05.

Council of Science Editors:

Wisniewska JJ. Rabinowitz Floer Homology for Tentacular Hamiltonians. [Doctoral Dissertation]. NARCIS; 2017. Available from: https://research.vu.nl/en/publications/e74baa79-5a39-4702-a23b-8420fcc85f05 ; urn:nbn:nl:ui:31-1871/55254 ; e74baa79-5a39-4702-a23b-8420fcc85f05 ; 1871/55254 ; urn:isbn:9789463321556 ; urn:nbn:nl:ui:31-1871/55254 ; https://research.vu.nl/en/publications/e74baa79-5a39-4702-a23b-8420fcc85f05

University of Florida

29. Sabri Dashti, Danial. Developing and Optimizing the Replica Exchange-Based Free Energy Methods.

Degree: PhD, Physics, 2013, University of Florida

URL: https://ufdc.ufl.edu/UFE0045878

► In recent decades, by increasing the power of computers’ hardware and developing efficient algorithms, the study of large biomolecular systems has been facilitated. During my… (more)

Subjects/Keywords: Algorithms; Chemicals; Copyrights; Fees; Free energy; Information standards; Molecular dynamics; Print media; Professional certification; United States government publications; carlo – dynamics – exchange – hamiltonian – metropolis – molecular – monte – optimization – replica

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Sabri Dashti, D. (2013). Developing and Optimizing the Replica Exchange-Based Free Energy Methods. (Doctoral Dissertation). University of Florida. Retrieved from https://ufdc.ufl.edu/UFE0045878

Chicago Manual of Style (16^th Edition):

Sabri Dashti, Danial. “Developing and Optimizing the Replica Exchange-Based Free Energy Methods.” 2013. Doctoral Dissertation, University of Florida. Accessed March 07, 2021. https://ufdc.ufl.edu/UFE0045878.

MLA Handbook (7^th Edition):

Sabri Dashti, Danial. “Developing and Optimizing the Replica Exchange-Based Free Energy Methods.” 2013. Web. 07 Mar 2021.

Vancouver:

Sabri Dashti D. Developing and Optimizing the Replica Exchange-Based Free Energy Methods. [Internet] [Doctoral dissertation]. University of Florida; 2013. [cited 2021 Mar 07]. Available from: https://ufdc.ufl.edu/UFE0045878.

Council of Science Editors:

Sabri Dashti D. Developing and Optimizing the Replica Exchange-Based Free Energy Methods. [Doctoral Dissertation]. University of Florida; 2013. Available from: https://ufdc.ufl.edu/UFE0045878

30. Κατσανίκας, Ματθαίος. Η δομή του φασικού χώρου σε περιστρεφόμενα χαμιλτονιανά συστήματα τριών βαθμών ελευθερίας γαλαξιακού τύπου.

Degree: 2012, National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ)

URL: http://hdl.handle.net/10442/hedi/26802

►

In this PhD thesis we studied the structure of the phase space in the neighborhood of periodic orbits of a 3D autonomous Hamiltonian system of… (more)

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In this PhD thesis we studied the structure of the phase space in the neighborhood of periodic orbits of a 3D autonomous Hamiltonian system of galactic type. A Basic problem was the visualization of the 4D surfaces of section. In order to overcome this problem we used the method of color and rotation (Patsis & Zachilas 1994). By this way, we studied and put in order the different dynamical behavior in the neighborhood of periodic orbits according to their stability (stable, simple unstable, double unstable, complex unstable). Furthermore, we studied the dynamical phenomena like the phenomenon of stickiness, the dynamics in the neighborhood of periodic orbits with high order multiplicity, the Arnold Diffusion, the topology of the invariant manifolds of unstable periodic orbits, the structure of (KAM) invariant tori and the Hamiltonian Hopf Bifurcation.

Στην παρούσα διδακτορική διατριβή, μελετήσαμε τη δομή του φασικού χώρου στην περιοχή των περιοδικών τροχιών ενός 3D αυτόνομου Χαμιλτονιανού συστήματος Γαλαξιακού τύπου. Ένα βασικό πρόβλημα που αντιμετωπίσαμε ήταν η οπτικοποίηση των 4D επιφανειών τομής. Για να ξεπεράσουμε αυτό το πρόβλημα χρησιμοποιήσαμε τη μέθοδο χρώματος και περιστροφής (Patsis & Zachilas 1994). Με αυτό τον τρόπο μελετήσαμε τη διαφορετική δυναμική συμπεριφορά στην περιοχή των περιοδικών τροχιών σύμφωνα με το είδος ευσταθειάς τους (ευσταθείς, απλά ασταθείς, διπλά ασταθείς, μιγαδικά ασταθείς). Επίσης μελετήσαμε δυναμικά φαινόμενα όπως το φαινόμενο κολλητικότητας, τη διάχυση Arnold, τη δυναμική στην περιοχή περιοδικών τροχιών πολλαπλής περιόδου, την τοπολογία των αναλλοίωτων πολλαπλοτήτων ασταθών περιοδικών τροχιών, τη δομή των (KAM) αναλλοίωτων τόρων και τη Χαμιλτονιανή διακλάδωση Hopf.

Subjects/Keywords: Χάος και δυναμικά συστήματα; Χαμιλτονιανά συστήματα; Μη γραμμική δυναμική; Δυναμική αστρονομία; Γαλαξιακή δυναμική; Chaos and dynamical systems; Hamiltonian systems; Nonlinear dynamics; Dynamical astronomy; Galactic dynamics

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APA (6^th Edition):

Κατσανίκας, . �. (2012). Η δομή του φασικού χώρου σε περιστρεφόμενα χαμιλτονιανά συστήματα τριών βαθμών ελευθερίας γαλαξιακού τύπου. (Thesis). National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ). Retrieved from http://hdl.handle.net/10442/hedi/26802

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Κατσανίκας, Ματθαίος. “Η δομή του φασικού χώρου σε περιστρεφόμενα χαμιλτονιανά συστήματα τριών βαθμών ελευθερίας γαλαξιακού τύπου.” 2012. Thesis, National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ). Accessed March 07, 2021. http://hdl.handle.net/10442/hedi/26802.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Κατσανίκας, Ματθαίος. “Η δομή του φασικού χώρου σε περιστρεφόμενα χαμιλτονιανά συστήματα τριών βαθμών ελευθερίας γαλαξιακού τύπου.” 2012. Web. 07 Mar 2021.

Vancouver:

Κατσανίκας �. Η δομή του φασικού χώρου σε περιστρεφόμενα χαμιλτονιανά συστήματα τριών βαθμών ελευθερίας γαλαξιακού τύπου. [Internet] [Thesis]. National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ); 2012. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/10442/hedi/26802.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Κατσανίκας �. Η δομή του φασικού χώρου σε περιστρεφόμενα χαμιλτονιανά συστήματα τριών βαθμών ελευθερίας γαλαξιακού τύπου. [Thesis]. National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ); 2012. Available from: http://hdl.handle.net/10442/hedi/26802

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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