subject:(Hamiltonian dynamics)

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

Degree: PhD, Mathematics, 2016, University of Georgia

URL: http://purl.galileo.usg.edu/uga_etd/zhang_jun_201608_phd

► 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 dynamics problems. 1.2 Review of Poltervoch-Shelukhin’s method Now back to Theorem… …x29; . Moreover, our Hamiltonian dynamics comes from a family of shear flow φtλ (highly… …have been successfully used to solve many problems on Hamiltonian dynamics (see, [… …the set of autonomous Hamiltonian diffeomorphisms and a timedependent Hamiltonian… …by Ham(X, ω) the set of all the Hamiltonian diffeomorphisms. Not only can we…

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APA (6^th Edition):

Zhang, J. (2016). Hamiltonian dynamics and persistent homology. (Doctoral Dissertation). University of Georgia. Retrieved from http://purl.galileo.usg.edu/uga_etd/zhang_jun_201608_phd

Chicago Manual of Style (16^th Edition):

Zhang, Jun. “Hamiltonian dynamics and persistent homology.” 2016. Doctoral Dissertation, University of Georgia. Accessed December 16, 2019. http://purl.galileo.usg.edu/uga_etd/zhang_jun_201608_phd.

MLA Handbook (7^th Edition):

Zhang, Jun. “Hamiltonian dynamics and persistent homology.” 2016. Web. 16 Dec 2019.

Vancouver:

Zhang J. Hamiltonian dynamics and persistent homology. [Internet] [Doctoral dissertation]. University of Georgia; 2016. [cited 2019 Dec 16]. Available from: http://purl.galileo.usg.edu/uga_etd/zhang_jun_201608_phd.

Council of Science Editors:

Zhang J. Hamiltonian dynamics and persistent homology. [Doctoral Dissertation]. University of Georgia; 2016. Available from: http://purl.galileo.usg.edu/uga_etd/zhang_jun_201608_phd

Georgia Tech

2. Berman, Simon Abraham. Classical Mechanisms of Recollision and High Harmonic Generation.

Degree: PhD, Physics, 2019, Georgia Tech

URL: http://hdl.handle.net/1853/61214

► 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 December 16, 2019. http://hdl.handle.net/1853/61214.

MLA Handbook (7^th Edition):

Berman, Simon Abraham. “Classical Mechanisms of Recollision and High Harmonic Generation.” 2019. Web. 16 Dec 2019.

Vancouver:

Berman SA. Classical Mechanisms of Recollision and High Harmonic Generation. [Internet] [Doctoral dissertation]. Georgia Tech; 2019. [cited 2019 Dec 16]. 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

University of Michigan

3. 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 December 16, 2019. 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. 16 Dec 2019.

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 2019 Dec 16]. 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

New Jersey Institute of Technology

4. 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 December 16, 2019. https://digitalcommons.njit.edu/dissertations/87.

MLA Handbook (7^th Edition):

Basarab, Casayndra H. “Hamiltonian bifurcations in Schrodinger trimers.” 2016. Web. 16 Dec 2019.

Vancouver:

Basarab CH. Hamiltonian bifurcations in Schrodinger trimers. [Internet] [Doctoral dissertation]. New Jersey Institute of Technology; 2016. [cited 2019 Dec 16]. 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

University of Colorado

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

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

URL: http://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 http://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 December 16, 2019. http://scholar.colorado.edu/appm_gradetds/57.

MLA Handbook (7^th Edition):

Mosovsky, Brock Alan. “Finite-Time Transport in Aperiodic Dynamical Systems.” 2013. Web. 16 Dec 2019.

Vancouver:

Mosovsky BA. Finite-Time Transport in Aperiodic Dynamical Systems. [Internet] [Doctoral dissertation]. University of Colorado; 2013. [cited 2019 Dec 16]. Available from: http://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: http://scholar.colorado.edu/appm_gradetds/57

6. 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 December 16, 2019. 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. 16 Dec 2019.

Vancouver:

Korepanov A. Small Perturbations In Hard Balls Dynamics. [Internet] [Thesis]. University of Alabama – Birmingham; 2013. [cited 2019 Dec 16]. 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

7. 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 December 16, 2019. 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. 16 Dec 2019.

Vancouver:

Chin P. Gauge field induced spin dynamics and spin conductivity in the Luttinger semiconductor system. [Internet] [Thesis]. NSYSU; 2015. [cited 2019 Dec 16]. 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

Delft University of Technology

8. Driessen D.M. 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):

D.M., D. (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):

D.M., Driessen. “Large Deviations for Markov Jump Processes and Hamiltonian Trajectories:.” 2015. Masters Thesis, Delft University of Technology. Accessed December 16, 2019. http://resolver.tudelft.nl/uuid:3762ee57-0e0e-4012-bb35-157bd14961bf.

MLA Handbook (7^th Edition):

D.M., Driessen. “Large Deviations for Markov Jump Processes and Hamiltonian Trajectories:.” 2015. Web. 16 Dec 2019.

Vancouver:

D.M. D. Large Deviations for Markov Jump Processes and Hamiltonian Trajectories:. [Internet] [Masters thesis]. Delft University of Technology; 2015. [cited 2019 Dec 16]. Available from: http://resolver.tudelft.nl/uuid:3762ee57-0e0e-4012-bb35-157bd14961bf.

Council of Science Editors:

D.M. D. 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

Georgia Tech

9. Grigo, Alexander. Billiards and statistical mechanics.

Degree: PhD, Mathematics, 2009, Georgia Tech

URL: http://hdl.handle.net/1853/29610

► In this thesis we consider mathematical problems related to different aspects of hard sphere systems. In the first part we study planar billiards, which arise… (more)

Subjects/Keywords: Billiards; Boltzmann equation; Hamiltonian systems; Statistical mechanics; Ergodic theory; Dynamics; Transport theory

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APA (6^th Edition):

Grigo, A. (2009). Billiards and statistical mechanics. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/29610

Chicago Manual of Style (16^th Edition):

Grigo, Alexander. “Billiards and statistical mechanics.” 2009. Doctoral Dissertation, Georgia Tech. Accessed December 16, 2019. http://hdl.handle.net/1853/29610.

MLA Handbook (7^th Edition):

Grigo, Alexander. “Billiards and statistical mechanics.” 2009. Web. 16 Dec 2019.

Vancouver:

Grigo A. Billiards and statistical mechanics. [Internet] [Doctoral dissertation]. Georgia Tech; 2009. [cited 2019 Dec 16]. Available from: http://hdl.handle.net/1853/29610.

Council of Science Editors:

Grigo A. Billiards and statistical mechanics. [Doctoral Dissertation]. Georgia Tech; 2009. Available from: http://hdl.handle.net/1853/29610

University of California – Santa Cruz

10. Martins, Gabriel. The Hamiltonian Dynamics of Magnetic Confinement and Instances of Quantum Tunneling.

Degree: Mathematics, 2018, University of California – Santa Cruz

URL: http://www.escholarship.org/uc/item/90b3g9vt

► We consider a class of magnetic fields defined over the interior of a manifold M which go to infinity at its boundary and whose direction… (more)

Subjects/Keywords: Mathematics; Electromagnetics; Quantum physics; Differential Geometry; Hamiltonian Dynamics; Magnetic Confinement; Mathematical Physics; Quantum Mechanics

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APA (6^th Edition):

Martins, G. (2018). The Hamiltonian Dynamics of Magnetic Confinement and Instances of Quantum Tunneling. (Thesis). University of California – Santa Cruz. Retrieved from http://www.escholarship.org/uc/item/90b3g9vt

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):

Martins, Gabriel. “The Hamiltonian Dynamics of Magnetic Confinement and Instances of Quantum Tunneling.” 2018. Thesis, University of California – Santa Cruz. Accessed December 16, 2019. http://www.escholarship.org/uc/item/90b3g9vt.

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

MLA Handbook (7^th Edition):

Martins, Gabriel. “The Hamiltonian Dynamics of Magnetic Confinement and Instances of Quantum Tunneling.” 2018. Web. 16 Dec 2019.

Vancouver:

Martins G. The Hamiltonian Dynamics of Magnetic Confinement and Instances of Quantum Tunneling. [Internet] [Thesis]. University of California – Santa Cruz; 2018. [cited 2019 Dec 16]. Available from: http://www.escholarship.org/uc/item/90b3g9vt.

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

Council of Science Editors:

Martins G. The Hamiltonian Dynamics of Magnetic Confinement and Instances of Quantum Tunneling. [Thesis]. University of California – Santa Cruz; 2018. Available from: http://www.escholarship.org/uc/item/90b3g9vt

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

11. 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 December 16, 2019. 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. 16 Dec 2019.

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 2019 Dec 16]. 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 North Texas

12. 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 December 16, 2019. 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. 16 Dec 2019.

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 2019 Dec 16]. 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 Colorado

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

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

URL: http://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 http://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 December 16, 2019. http://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. 16 Dec 2019.

Vancouver:

Sen A. A Tale of Waves and Eddies in a Sea of Rotating Turbulence. [Internet] [Doctoral dissertation]. University of Colorado; 2014. [cited 2019 Dec 16]. Available from: http://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: http://scholar.colorado.edu/appm_gradetds/46

14. 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 December 16, 2019. 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. 16 Dec 2019.

Vancouver:

A. RN. Chaotic dynamics in model hamiltonian and dissipative systems;. [Internet] [Thesis]. University of Calicut; 2015. [cited 2019 Dec 16]. 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

University of Manchester

15. 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 December 16, 2019. 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. 16 Dec 2019.

Vancouver:

Fullerton CJ. An investigation into growing correlation lengths in glassy systems. [Internet] [Doctoral dissertation]. University of Manchester; 2011. [cited 2019 Dec 16]. 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

Duke University

16. 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 December 16, 2019. 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. 16 Dec 2019.

Vancouver:

Nishimura A. General and Efficient Bayesian Computation through Hamiltonian Monte Carlo Extensions . [Internet] [Thesis]. Duke University; 2017. [cited 2019 Dec 16]. 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

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 (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 December 16, 2019. 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. 16 Dec 2019.

Vancouver:

Cambon B. Chaos hamiltonien dans les plasmas de fusion : Hamiltonian chaos into fusion plasmas. [Internet] [Doctoral dissertation]. Aix Marseille Université 2015. [cited 2019 Dec 16]. 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 December 16, 2019. 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. 16 Dec 2019.

Vancouver:

Schoonderwoerd NCJ. Light-front Hamiltonian field theory. Towards a relativistic description of bound states . [Internet] [Doctoral dissertation]. Vrije Universiteit Amsterdam; 1999. [cited 2019 Dec 16]. 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 December 16, 2019. http://hdl.handle.net/1871/55254.

MLA Handbook (7^th Edition):

Wisniewska, J J. “Rabinowitz Floer Homology for Tentacular Hamiltonians .” 2017. Web. 16 Dec 2019.

Vancouver:

Wisniewska JJ. Rabinowitz Floer Homology for Tentacular Hamiltonians . [Internet] [Doctoral dissertation]. Vrije Universiteit Amsterdam; 2017. [cited 2019 Dec 16]. 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 New Mexico

20. Merkel, Seth. Quantum control of d-dimensional quantum systems with application to alkali atomic spins.

Degree: Physics & Astronomy, 2009, University of New Mexico

URL: http://hdl.handle.net/1928/9831

► In this dissertation I analyze Hamiltonian control of d-dimensional quantum systems as realized in alkali atomic spins. Alkali atoms provide an ideal platform for studies… (more)

▼ In this dissertation I analyze Hamiltonian control of d-dimensional quantum systems as realized in alkali atomic spins. Alkali atoms provide an ideal platform for studies of quantum control due to the extreme precision with which the control fields are characterized as well as their isolation from their environment. In many cases, studies into the control of atomic spins restrict attention to a 2-dimesional subspace in order to consider qubit control. The geometry of quantum 2-level systems is much simpler than for any larger dimensional Hilbert space, and so control techniques for qubits often are not applicable to larger systems. In reality, atoms have many internal levels. It seems a shame to throw away most of our Hilbert space when it could in principle be used for encoding information and performing error correction. This work develops some of the tools necessary to control these large atomic spins. Quantum control theory has some very generic properties that have previously been explored in the literature, notably in the work from the Rabitz group. I provide a review of this literature, showing that while the landscape topology of quantum control problems is relatively independent of physical platform, different optimization techniques are required to find optimal controls depending on the particular control task. To this end I have developed two optimal control algorithms for finding unitary maps for the problems of: "state preparation" where we require only that a single fiducial state us taken to a particular target state and "unitary construction" where the entire map is specified. State mapping turns out to be a simple problem to solve and is amenable to a gradient search method. This protocol is not feasible for the task of finding full unitary maps, but I show how we can weave state mappings together to form full unitary maps. This construction of unitary maps is efficient in the dimension of the Hilbert space. The particular system I have used for demonstrating these control techniques is that of alkali atoms, specifically {133}Cs. The state preparation algorithm was used to create a broad range of target states in the 7-dimension F=3 hyperfine manifold in an experiment using a combination of time-dependent magnetic fields and a static tensor light shift. The yields from this experiment were in the range of 0.8-0.9. I have developed another control system for the full hyperfine manifold in the ground-electronic state of {133}Cs, a 16-dimensional Hilbert space, based on applied radio frequency and microwave fields. Numerical studies of the state preparation algorithm find good operating points commensurate with modest laboratory requirements. This system of microwave and rf control also admits a Hamiltonian structure than can be used by my protocol for unitary construction. I demonstrate the performance of this algorithm by creating a standard set of qudit gates using physically realistic control fields, as well as by implementing a simple form of error correction. Advisors/Committee Members: Deutsch, Ivan, Caves, Carlton, Jessen, Poul, Landahl, Andrew.

Subjects/Keywords: Quantum theory; Control theory; Hamiltonian systems; Quantum computers; Feedback control systems – Dynamics; Nuclear spin; Alkali metals.

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APA (6^th Edition):

Merkel, S. (2009). Quantum control of d-dimensional quantum systems with application to alkali atomic spins. (Doctoral Dissertation). University of New Mexico. Retrieved from http://hdl.handle.net/1928/9831

Chicago Manual of Style (16^th Edition):

Merkel, Seth. “Quantum control of d-dimensional quantum systems with application to alkali atomic spins.” 2009. Doctoral Dissertation, University of New Mexico. Accessed December 16, 2019. http://hdl.handle.net/1928/9831.

MLA Handbook (7^th Edition):

Merkel, Seth. “Quantum control of d-dimensional quantum systems with application to alkali atomic spins.” 2009. Web. 16 Dec 2019.

Vancouver:

Merkel S. Quantum control of d-dimensional quantum systems with application to alkali atomic spins. [Internet] [Doctoral dissertation]. University of New Mexico; 2009. [cited 2019 Dec 16]. Available from: http://hdl.handle.net/1928/9831.

Council of Science Editors:

Merkel S. Quantum control of d-dimensional quantum systems with application to alkali atomic spins. [Doctoral Dissertation]. University of New Mexico; 2009. Available from: http://hdl.handle.net/1928/9831

University of Notre Dame

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

Degree: PhD, 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>. (Doctoral Dissertation). University of Notre Dame. Retrieved from https://curate.nd.edu/show/41687h1664c

Chicago Manual of Style (16^th Edition):

Hampton, Scott S. “An Analysis of Shadow Hybrid Monte Carlo Methods</h1>.” 2007. Doctoral Dissertation, University of Notre Dame. Accessed December 16, 2019. https://curate.nd.edu/show/41687h1664c.

MLA Handbook (7^th Edition):

Hampton, Scott S. “An Analysis of Shadow Hybrid Monte Carlo Methods</h1>.” 2007. Web. 16 Dec 2019.

Vancouver:

Hampton SS. An Analysis of Shadow Hybrid Monte Carlo Methods</h1>. [Internet] [Doctoral dissertation]. University of Notre Dame; 2007. [cited 2019 Dec 16]. Available from: https://curate.nd.edu/show/41687h1664c.

Council of Science Editors:

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

22. 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

Record Details Similar Records Cite « Share

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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 December 16, 2019. 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. 16 Dec 2019.

Vancouver:

Wisniewska JJ. Rabinowitz Floer Homology for Tentacular Hamiltonians. [Internet] [Doctoral dissertation]. NARCIS; 2017. [cited 2019 Dec 16]. 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

23. 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

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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)

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

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 December 16, 2019. 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. 16 Dec 2019.

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 2019 Dec 16]. 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 Texas – Austin

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

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 December 16, 2019. 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. 16 Dec 2019.

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 2019 Dec 16]. 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

University of Texas – Austin

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

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 December 16, 2019. 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. 16 Dec 2019.

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 2019 Dec 16]. 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

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

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 December 16, 2019. 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. 16 Dec 2019.

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 2019 Dec 16]. 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

University of Florida

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

Degree: PhD, Physics, 2013, University of Florida

URL: http://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 http://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 December 16, 2019. http://ufdc.ufl.edu/UFE0045878.

MLA Handbook (7^th Edition):

Sabri Dashti, Danial. “Developing and Optimizing the Replica Exchange-Based Free Energy Methods.” 2013. Web. 16 Dec 2019.

Vancouver:

Sabri Dashti D. Developing and Optimizing the Replica Exchange-Based Free Energy Methods. [Internet] [Doctoral dissertation]. University of Florida; 2013. [cited 2019 Dec 16]. Available from: http://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: http://ufdc.ufl.edu/UFE0045878

28. Turchi, Alessio. Dynamics and statistics of systems with long range interactions : application to 1-dimensional toy-models : Dinamica e statistica di sistemi con interazione a lungo raggio : applicazioni a modelli giocattolo 1-dimensionali.

Degree: Docteur es, Physique Théorique et Mathématique, 2012, Aix Marseille Université

URL: http://www.theses.fr/2012AIXM4810

►

L'objectif de ce thèse est l'étude des systèmes dynamiques avec interaction à longue portée. La complexité de leur dynamique met en évidence des propriétés contre-intuitives… (more)

▼

L'objectif de ce thèse est l'étude des systèmes dynamiques avec interaction à longue portée. La complexité de leur dynamique met en évidence des propriétés contre-intuitives et inattendues, comme l'existence d'états stationnaires hors-équilibre (QSS). Dans le QSS on peut observer des propriétés particulières: chaleur spécifique négative, inéquivalence des ensembles statistiques et phénomènes d'auto-organisation. Les théories des interactions LR ont été appliquées pour décrire la dynamique des systèmes auto-gravitants, de tourbillons bidimensionnels, de systèmes avec interactions onde-particule et des plasmas chargés. Mon travail s'est tout d'abord consacré à l'extension de la solution de Lynden-Bell pour le modèle HMF, en généralisant l'analyse à des conditions initiales de «water-bag" à plusieurs niveaux, qui approchent des conditions initiales continues. En suite je me suis intéressé à la caractérisation formelle de la thermodynamique des QSS dans l'ensemble statistique canonique. En appliquant la théorie standard, il est possible de mesurer une chaleur spécifique "cinétique'' négative. Cette propriété inattendue amène à la violation du second principe de la thermodynamique. Un tel résultat nous pousse à reconsidérer l'applicabilité de la théorie thermodynamique actuelle aux systèmes LR. En suite j'ai étudié, pour le modèle α-HMF, la persistance des caractéristiques typiques du régime LR, dans le limite dynamique à courte portée. Les résultats suggèrent une généralisation de la définition des systèmes LR. Le dernier chapitre est consacré à la caractérisation d'un nouveau modèle LR, extension naturelle du précédent α-HMF et d'intérêt potentiel applicatif.

The scope of this thesis is the study of systems with long-range interactions (LR). The complexity of their dynamics evidences counter-intuitive and unexpected properties, as for instance the existence of out-of-equilibrium stationary states (QSS). Considering a system in the QSS, one may observe peculiar properties, as negative specific heat, statistical ensemble inequivalence and phenomena of self-organizations. The main theories of long-range interactions have been applied to describing self-gravitating systems, two-dimensional vortices, systems with wave-particle interactions and charged plasmas. My work has been initially dedicated to extending the Lynden-Bell solution for the HMF model, generalizing the analysis to multi-level water-bag initial condition that could approximate continuous distributions. Then I concentrated to the formal characterization of the thermodynamics of QSS in the canonical statistical ensemble. By applying the standard theory, it is possible to measure negative “kinetic” specific heat. This latter unexpected property leads to a violation of the second principle of thermodynamics. Such result forces us to reconsider the applicability of the accepted thermodynamic theory to LR systems. Afterwards I studied, in the context of the α-HMF model, the persistence of the typical characteristics of the LR regime in the limit of short-range…

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

Subjects/Keywords: Longue portée; Mécanique statistique; Thermodynamique; Dynamique; Systèmes complexes; Systèmes hamiltonien; Hors-équilibre; Équation de Vlasov; Long range; Statistical mechanics; Thermodynamics; Dynamics; Complex systems; Hamiltonian systems; Out-of-equilibrium; Vlasov equation

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

APA (6^th Edition):

Turchi, A. (2012). Dynamics and statistics of systems with long range interactions : application to 1-dimensional toy-models : Dinamica e statistica di sistemi con interazione a lungo raggio : applicazioni a modelli giocattolo 1-dimensionali. (Doctoral Dissertation). Aix Marseille Université. Retrieved from http://www.theses.fr/2012AIXM4810

Chicago Manual of Style (16^th Edition):

Turchi, Alessio. “Dynamics and statistics of systems with long range interactions : application to 1-dimensional toy-models : Dinamica e statistica di sistemi con interazione a lungo raggio : applicazioni a modelli giocattolo 1-dimensionali.” 2012. Doctoral Dissertation, Aix Marseille Université. Accessed December 16, 2019. http://www.theses.fr/2012AIXM4810.

MLA Handbook (7^th Edition):

Turchi, Alessio. “Dynamics and statistics of systems with long range interactions : application to 1-dimensional toy-models : Dinamica e statistica di sistemi con interazione a lungo raggio : applicazioni a modelli giocattolo 1-dimensionali.” 2012. Web. 16 Dec 2019.

Vancouver:

Turchi A. Dynamics and statistics of systems with long range interactions : application to 1-dimensional toy-models : Dinamica e statistica di sistemi con interazione a lungo raggio : applicazioni a modelli giocattolo 1-dimensionali. [Internet] [Doctoral dissertation]. Aix Marseille Université 2012. [cited 2019 Dec 16]. Available from: http://www.theses.fr/2012AIXM4810.

Council of Science Editors:

Turchi A. Dynamics and statistics of systems with long range interactions : application to 1-dimensional toy-models : Dinamica e statistica di sistemi con interazione a lungo raggio : applicazioni a modelli giocattolo 1-dimensionali. [Doctoral Dissertation]. Aix Marseille Université 2012. Available from: http://www.theses.fr/2012AIXM4810

University of Oxford

29. Warneford, Emma S. The thermal shallow water equations, their quasi-geostrophic limit, and equatorial super-rotation in Jovian atmospheres.

Degree: PhD, 2014, University of Oxford

URL: http://ora.ox.ac.uk/objects/uuid:6604fcac-afe6-4abe-8a6f-6a09de4f933f ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.618532

► Observations of Jupiter show a super-rotating (prograde) equatorial jet that has persisted for decades. Shallow water simulations run in the Jovian parameter regime reproduce the… (more)

▼ Observations of Jupiter show a super-rotating (prograde) equatorial jet that has persisted for decades. Shallow water simulations run in the Jovian parameter regime reproduce the mixture of robust vortices and alternating zonal jets observed on Jupiter, but the equatorial jet is invariably sub-rotating (retrograde). Recent work has obtained super-rotating equatorial jets by extending the standard shallow water equations to relax the height field towards its mean value. This Newtonian cooling-like term is intended to model radiative cooling to space, but its addition breaks key conservation properties for mass and momentum. In this thesis the radiatively damped thermal shallow water equations are proposed as an alternative model for Jovian atmospheres. They extend standard shallow water theory by permitting horizontal variations of the thermodynamic properties of the fluid. The additional temperature equation allows a Newtonian cooling term to be included while conserving mass and momentum. Simulations reproduce equatorial jets in the correct directions for both Jupiter and Neptune (which sub-rotates). Quasi-geostrophic theory filters out rapidly moving inertia-gravity waves. A local quasi-geostrophic theory of the radiatively damped thermal shallow water equations is derived, and then extended to cover whole planets. Simulations of this global thermal quasi-geostrophic theory show the same transition, from sub- to super-rotating equatorial jets, seen in simulations of the original thermal shallow water model as the radiative time scale is decreased. Thus the mechanism responsible for setting the direction of the equatorial jet must exist within quasi-geostrophic theory. Such a mechanism is developed by calculating the competing effects of Newtonian cooling and Rayleigh friction upon the zonal mean zonal acceleration induced by equatorially trapped Rossby waves. These waves transport no momentum in the absence of dissipation. Dissipation by Newtonian cooling creates an eastward zonal mean zonal acceleration, consistent with the formation of super-rotating equatorial jets in simulations, while the corresponding acceleration is westward for dissipation by Rayleigh friction.

Subjects/Keywords: 532; Mathematics; Fluid mechanics (mathematics); Geophysics (mathematics); geophysical fluid dynamics; computational applied mathematics; Hamiltonian mechanics; asymptotic analysis; thermal shallow water equations; Jupiter; zonal jets

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

APA (6^th Edition):

Warneford, E. S. (2014). The thermal shallow water equations, their quasi-geostrophic limit, and equatorial super-rotation in Jovian atmospheres. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:6604fcac-afe6-4abe-8a6f-6a09de4f933f ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.618532

Chicago Manual of Style (16^th Edition):

Warneford, Emma S. “The thermal shallow water equations, their quasi-geostrophic limit, and equatorial super-rotation in Jovian atmospheres.” 2014. Doctoral Dissertation, University of Oxford. Accessed December 16, 2019. http://ora.ox.ac.uk/objects/uuid:6604fcac-afe6-4abe-8a6f-6a09de4f933f ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.618532.

MLA Handbook (7^th Edition):

Warneford, Emma S. “The thermal shallow water equations, their quasi-geostrophic limit, and equatorial super-rotation in Jovian atmospheres.” 2014. Web. 16 Dec 2019.

Vancouver:

Warneford ES. The thermal shallow water equations, their quasi-geostrophic limit, and equatorial super-rotation in Jovian atmospheres. [Internet] [Doctoral dissertation]. University of Oxford; 2014. [cited 2019 Dec 16]. Available from: http://ora.ox.ac.uk/objects/uuid:6604fcac-afe6-4abe-8a6f-6a09de4f933f ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.618532.

Council of Science Editors:

Warneford ES. The thermal shallow water equations, their quasi-geostrophic limit, and equatorial super-rotation in Jovian atmospheres. [Doctoral Dissertation]. University of Oxford; 2014. Available from: http://ora.ox.ac.uk/objects/uuid:6604fcac-afe6-4abe-8a6f-6a09de4f933f ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.618532

30. Perin, Maxime. Hamiltonian fluid reductions of kinetic equations in plasma physics : Réductions fluides hamiltoniennes des équations cinétiques en physique des plasmas.

Degree: Docteur es, Physique Théorique et Mathématique, 2016, Aix Marseille Université

URL: http://www.theses.fr/2016AIXM4050

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La réduction fluide des équations cinétiques est un procédé couramment utilisé en physique des plasmas qui a pour objectif de remplacer la fonction de distribution… (more)

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La réduction fluide des équations cinétiques est un procédé couramment utilisé en physique des plasmas qui a pour objectif de remplacer la fonction de distribution définie dans l'espace des phases par des grandeurs fluides comme la densité et la pression. Cette réduction diminue la complexité du système initial. En contrepartie, la réduction fluide s'accompagne de la nécessité d'effectuer une fermeture sur les moments d'ordre supérieur. Celle-ci est souvent construite ad hoc en se basant sur des arguments physiques (e.g., quantités conservées, existance d'un théorème H, ...). Dans ce manuscrit, on propose un procédé de réduction qui permet de préserver la structure hamiltonienne du modèle cinétique parent. Ceci est important pour assurer qu'aucune dissipation d'origine non physique est introduite dans le modèle fluide, le munissant ainsi d'une structure hamiltonienne dont l'origine peut être suivie jusqu'à celle de la dynamique microscopique des particules. On utilise cette méthode pour construire des modèles fluides non-adiabatiques pour les trois premiers moments de la fonction de distribution associée à l'équation de Vlasov-Poisson à une dimension, i.e., la densité, la vitesse fluide et la pression. Les résultats sont ensuite étendus pour inclure la dynamique du flux de chaleur en considérant des fermetures construites à partir de l'analyse dimensionnelle. On montre également, pour un nombre arbitraire de champs, la relation existant avec le modèle water-bags. L'extension à des dimensions supérieures est étudiée dans le cadre de l'équation drift-cinétique ainsi que de l'équation de Vlasov-Poisson à trois dimensions.

Fluid reduction of kinetic equations is a ubiquitous procedure in plasma physics which aims to replace the distribution function defined in phase space with more concrete fluid quantities defined solely in configuration space such as the density, the fluid velocity and the pressure. This reduction lowers the complexity of the initial system, leading to a gain of physical insight into the phenomena under investigation as well as a significant decrease of the cost of numerical simulations. On the other hand, in order for the fluid reduction to be complete, one needs to perform a closure on the higher order fluid moments. The choice of the closure usually relies on some ad hoc physical arguments (e.g., conserved quantities, existence of an H-theorem, ...). In this manuscript, we present a reduction procedure that preserves the Hamiltonian structure of the parent kinetic model. This is important in order to ensure that no non-physical dissipation is introduced in the resulting fluid model, providing it with a geometric structure that can be traced back to the microscopic dynamics of the particles. We use this procedure to derive non-adiabatic fluid models for the first three fluid moments of the distribution function of the one dimensional Vlasov-Poisson equation, namely the density, the fluid velocity and the pressure. The results are extended to include the dynamics of the heat-flux by considering a…

Advisors/Committee Members: Chandre, Cristel (thesis director), Tassi, Emanuele (thesis director).

Subjects/Keywords: Physique des plasmas; Réduction fluide; Système hamiltonien; Équation cinétique; Dynamique non linéaire; Plasma physics; Fluid reduction; Hamiltonian system; Kinetic equation; Nonlinear dynamics; 530

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

APA (6^th Edition):

Perin, M. (2016). Hamiltonian fluid reductions of kinetic equations in plasma physics : Réductions fluides hamiltoniennes des équations cinétiques en physique des plasmas. (Doctoral Dissertation). Aix Marseille Université. Retrieved from http://www.theses.fr/2016AIXM4050

Chicago Manual of Style (16^th Edition):

Perin, Maxime. “Hamiltonian fluid reductions of kinetic equations in plasma physics : Réductions fluides hamiltoniennes des équations cinétiques en physique des plasmas.” 2016. Doctoral Dissertation, Aix Marseille Université. Accessed December 16, 2019. http://www.theses.fr/2016AIXM4050.

MLA Handbook (7^th Edition):

Perin, Maxime. “Hamiltonian fluid reductions of kinetic equations in plasma physics : Réductions fluides hamiltoniennes des équations cinétiques en physique des plasmas.” 2016. Web. 16 Dec 2019.

Vancouver:

Perin M. Hamiltonian fluid reductions of kinetic equations in plasma physics : Réductions fluides hamiltoniennes des équations cinétiques en physique des plasmas. [Internet] [Doctoral dissertation]. Aix Marseille Université 2016. [cited 2019 Dec 16]. Available from: http://www.theses.fr/2016AIXM4050.

Council of Science Editors:

Perin M. Hamiltonian fluid reductions of kinetic equations in plasma physics : Réductions fluides hamiltoniennes des équations cinétiques en physique des plasmas. [Doctoral Dissertation]. Aix Marseille Université 2016. Available from: http://www.theses.fr/2016AIXM4050

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