subject:(Mean Field Theory)

Princeton University

1. Wang, Peiqi. Finite State Mean Field Games .

Degree: PhD, 2019, Princeton University

URL: http://arks.princeton.edu/ark:/88435/dsp01zw12z808g

► Mean field game is a powerful framework for studying the strategic interactions within a large population of rational agents. Although existing research has predominantly relied… (more)

▼ Mean field game is a powerful framework for studying the strategic interactions within a large population of rational agents. Although existing research has predominantly relied on diffusion models to depict agents’ states, numerous applications, such as epidemic control and botnet defense, can best be modeled by systems of particles in discrete state space. This thesis tackles finite state mean field games. In the first part of the thesis, we develop a probabilistic approach for finite state mean field games. Based on the weak formulation of optimal control, the approach accommodates the interactions through the players’ strategies and flexible information structures. The second part of the thesis is devoted to finite state mean field games involving a player possessing dominating influence. Two different mechanisms are explored. We first study a form of Stackelberg games, in which the dominating player, referred to as principal, moves first and chooses its strategy which impacts the dynamics and ob- jective functions of every remaining player, referred to as agent. Having observed the principal’s strategy, the agents reach a Nash equilibrium. We seek optimal strategies of the principal, whose objective function depends on the statistical distribution of the agents’ states in equilibrium. Using the weak formulation of finite state mean field games developed previously in the thesis, we transform the principal’s optimization problem into a McKean-Vlasov control problem, and provide a semi-explicit solution under the assumptions of linear transition rate, quadratic cost and risk-neutral utility. In the second model, we assume that all players move simultaneously and we study Nash equilibria formed jointly by major and minor players. We introduce finite player games and derive mean field game formulation in the limit of infinitely many minor players. In this limit, we characterize the best responses of major and minor players via viscosity solutions of HJB equations, and we prove existence of Nash equilibria under reasonable assumptions. We also derive approximate Nash equilibria for the finite player game from the solution of the mean field game. Advisors/Committee Members: Carmona, René (advisor).

Subjects/Keywords: Contract Theory; Mean Field Games; Nash Equilibrium

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APA (6^th Edition):

Wang, P. (2019). Finite State Mean Field Games . (Doctoral Dissertation). Princeton University. Retrieved from http://arks.princeton.edu/ark:/88435/dsp01zw12z808g

Chicago Manual of Style (16^th Edition):

Wang, Peiqi. “Finite State Mean Field Games .” 2019. Doctoral Dissertation, Princeton University. Accessed January 21, 2021. http://arks.princeton.edu/ark:/88435/dsp01zw12z808g.

MLA Handbook (7^th Edition):

Wang, Peiqi. “Finite State Mean Field Games .” 2019. Web. 21 Jan 2021.

Vancouver:

Wang P. Finite State Mean Field Games . [Internet] [Doctoral dissertation]. Princeton University; 2019. [cited 2021 Jan 21]. Available from: http://arks.princeton.edu/ark:/88435/dsp01zw12z808g.

Council of Science Editors:

Wang P. Finite State Mean Field Games . [Doctoral Dissertation]. Princeton University; 2019. Available from: http://arks.princeton.edu/ark:/88435/dsp01zw12z808g

Rutgers University

2. Xu, Wenhu, 1984-. Transport and magnetic properties of correlated electron systems.

Degree: PhD, Physics and Astronomy, 2014, Rutgers University

URL: https://rucore.libraries.rutgers.edu/rutgers-lib/45579/

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This thesis investigates the transport and magnetic properties of correlated electron systems in the framework of dynamical mean field theory. In Chapter 2, the bad… (more)

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This thesis investigates the transport and magnetic properties of correlated electron systems in the framework of dynamical mean field theory. In Chapter 2, the bad metallic transport in a doped Mott insulator is described by the Boltzmann theory of a hidden Fermi liquid, in which the quasiparticle scattering rate follows quadratic temperature and energy dependence far beyond the canonical Fermi liquid scale TFL. The quasiparticle renormalization is strongly dependent on temperature and energy, giving rise to the non-Fermi liquid transport, such as linear-in-T resistivity. Chapter 3 focuses on the thermoelectric power of correlated metals. The thermoelectric power in the high-frequency limit S* and in the Kelvin formula SK are compared with the transport limit S0. S* and SK can be computed with much less effort than S0. SK captures the contribution from renormalized density of states and is a better approximation of S0 for a strongly correlated metal, while for a weakly correlated metal, when S0 is dominated by the band velocity contribution, S* is a better indicator of S0. In Chapter 4, the phase diagram of a periodic Anderson model with the hybridization strength V as the tuning parameter is studied. The vanishing of the heavy Fermi liquid phase, characterized by a diminishing Fermi liquid scale TFL, is accompanied by the emergence of antiferromagnetic ordering. The dynamic spin susceptibility in the vicinity of magnetic instability indicates a momentum-independent, or localized picture of critical spin fluctuations. Chapter 5 discusses the the colossal Nernst effect and anomalies of the magnetoresistance in correlated semiconductor FeSb2. A phenomenological analysis based on Boltzmann theory suggests that a highly dispersive quasiparticle relaxation time is the key to understand the anomalous transport in FeSb2.

Advisors/Committee Members: Kotliar, Gabriel (chair), Haule, Kristjan (internal member), Wu, Weida (internal member), Moore, Gregory (internal member), Aron, Camille (outside member).

Subjects/Keywords: Mean field theory; Fermi liquids; Thermoelectricity

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APA (6^th Edition):

Xu, Wenhu, 1. (2014). Transport and magnetic properties of correlated electron systems. (Doctoral Dissertation). Rutgers University. Retrieved from https://rucore.libraries.rutgers.edu/rutgers-lib/45579/

Chicago Manual of Style (16^th Edition):

Xu, Wenhu, 1984-. “Transport and magnetic properties of correlated electron systems.” 2014. Doctoral Dissertation, Rutgers University. Accessed January 21, 2021. https://rucore.libraries.rutgers.edu/rutgers-lib/45579/.

MLA Handbook (7^th Edition):

Xu, Wenhu, 1984-. “Transport and magnetic properties of correlated electron systems.” 2014. Web. 21 Jan 2021.

Vancouver:

Xu, Wenhu 1. Transport and magnetic properties of correlated electron systems. [Internet] [Doctoral dissertation]. Rutgers University; 2014. [cited 2021 Jan 21]. Available from: https://rucore.libraries.rutgers.edu/rutgers-lib/45579/.

Council of Science Editors:

Xu, Wenhu 1. Transport and magnetic properties of correlated electron systems. [Doctoral Dissertation]. Rutgers University; 2014. Available from: https://rucore.libraries.rutgers.edu/rutgers-lib/45579/

University of Cambridge

3. Valeria Shumaylova, Valeria. Scale selection in hydromagnetic dynamos.

Degree: PhD, 2019, University of Cambridge

URL: https://www.repository.cam.ac.uk/handle/1810/290138

► One of the extraordinary properties of the Sun is the observed range of motion scales from the convection granules to the cyclic variation of magnetic… (more)

▼ One of the extraordinary properties of the Sun is the observed range of motion scales from the convection granules to the cyclic variation of magnetic activity. The Sun’s magnetic field exhibits coherence in space and time on much larger scales than the turbulent convection that ultimately powers the dynamo. Motivated by the scale separation considerations, in this thesis we study the parametric scale selection of dynamo action. Although helioseismology has made a lot of progress in the study of the solar interior, the precise motions of plasma are still unknown. In this work, we assume that the model flow is forced with helical viscous body forces acting on different characteristic scales and weak and strong large-scale shear flows that are believed to be present near the base of the convection zone. In this thesis, we look for numerical evidence of a large-scale magnetic field relative to the characteristic scale of the model flow. The investigation is based on the simulations of incompressible MHD equations in elongated triply-periodic domains. To commence the investigation, a linear stability analysis of the coarsening instability in a one-dimensional periodic system is performed to study the stability threshold in the mean-field limit that assumes large scale separation in the system. The simulations are used to discriminate between different forms of the mean-field α -effect and domain aspect ratio. The notion of scale selection refers to methods for estimating characteristic scales. We define the dynamo scale through the characteristic scales of the underlying model flow, forcing and the realised magnetic field. The aspect ratio of the elongated domains plays a crucial role in all considered cases. In Part II, we examine the dynamo generated by the imposed model flows. The transition from large-scale dynamo at the onset to small-scale dynamo as we increase Rm is smooth and takes place in two stages: a fast transition into a predominantly small-scale magnetic energy state and a slower transition into even smaller scales. The long wavelength perturbation imposed on the ABC flow in the modulated case is not preserved in the eigenmodes of the magnetic field. In the presence of the linear (semi-linear shearing-box approximation) and the sinusoidal shearing motions, the field again undergoes a smooth transition at the slow non-sheared rate, which is associated with the balance of the advection and diffusion terms in the induction equation. Part III considers the nonlinear extension of the analysis in Part II, where the incompressible cellular and sheared flows interact with the exponentially growing magnetic field via the Lorentz force in the dynamical regime. Both sheared and non-sheared helical cellular flows become unstable to large-scale perturbations even in the limit of high viscosity. Due to the helical properties of the imposed forcing, the inverse cascade of helicity leads to energy accumulation in the largest scales of the domain, albeit the characteristic lengthscale exhibits the transitional nature at a…

Subjects/Keywords: Dynamo theory; MHD; ABC flow; Mean-field theory

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

APA (6^th Edition):

Valeria Shumaylova, V. (2019). Scale selection in hydromagnetic dynamos. (Doctoral Dissertation). University of Cambridge. Retrieved from https://www.repository.cam.ac.uk/handle/1810/290138

Chicago Manual of Style (16^th Edition):

Valeria Shumaylova, Valeria. “Scale selection in hydromagnetic dynamos.” 2019. Doctoral Dissertation, University of Cambridge. Accessed January 21, 2021. https://www.repository.cam.ac.uk/handle/1810/290138.

MLA Handbook (7^th Edition):

Valeria Shumaylova, Valeria. “Scale selection in hydromagnetic dynamos.” 2019. Web. 21 Jan 2021.

Vancouver:

Valeria Shumaylova V. Scale selection in hydromagnetic dynamos. [Internet] [Doctoral dissertation]. University of Cambridge; 2019. [cited 2021 Jan 21]. Available from: https://www.repository.cam.ac.uk/handle/1810/290138.

Council of Science Editors:

Valeria Shumaylova V. Scale selection in hydromagnetic dynamos. [Doctoral Dissertation]. University of Cambridge; 2019. Available from: https://www.repository.cam.ac.uk/handle/1810/290138

University of Cambridge

4. Valeria Shumaylova, Valeria. Scale selection in hydromagnetic dynamos.

Degree: PhD, 2019, University of Cambridge

URL: https://doi.org/10.17863/CAM.37367 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.767874

► One of the extraordinary properties of the Sun is the observed range of motion scales from the convection granules to the cyclic variation of magnetic… (more)

▼ One of the extraordinary properties of the Sun is the observed range of motion scales from the convection granules to the cyclic variation of magnetic activity. The Sun's magnetic field exhibits coherence in space and time on much larger scales than the turbulent convection that ultimately powers the dynamo. Motivated by the scale separation considerations, in this thesis we study the parametric scale selection of dynamo action. Although helioseismology has made a lot of progress in the study of the solar interior, the precise motions of plasma are still unknown. In this work, we assume that the model flow is forced with helical viscous body forces acting on different characteristic scales and weak and strong large-scale shear flows that are believed to be present near the base of the convection zone. In this thesis, we look for numerical evidence of a large-scale magnetic field relative to the characteristic scale of the model flow. The investigation is based on the simulations of incompressible MHD equations in elongated triply-periodic domains. To commence the investigation, a linear stability analysis of the coarsening instability in a one-dimensional periodic system is performed to study the stability threshold in the mean-field limit that assumes large scale separation in the system. The simulations are used to discriminate between different forms of the mean-field α -effect and domain aspect ratio. The notion of scale selection refers to methods for estimating characteristic scales. We define the dynamo scale through the characteristic scales of the underlying model flow, forcing and the realised magnetic field. The aspect ratio of the elongated domains plays a crucial role in all considered cases. In Part II, we examine the dynamo generated by the imposed model flows. The transition from large-scale dynamo at the onset to small-scale dynamo as we increase Rm is smooth and takes place in two stages: a fast transition into a predominantly small-scale magnetic energy state and a slower transition into even smaller scales. The long wavelength perturbation imposed on the ABC flow in the modulated case is not preserved in the eigenmodes of the magnetic field. In the presence of the linear (semi-linear shearing-box approximation) and the sinusoidal shearing motions, the field again undergoes a smooth transition at the slow non-sheared rate, which is associated with the balance of the advection and diffusion terms in the induction equation. Part III considers the nonlinear extension of the analysis in Part II, where the incompressible cellular and sheared flows interact with the exponentially growing magnetic field via the Lorentz force in the dynamical regime. Both sheared and non-sheared helical cellular flows become unstable to large-scale perturbations even in the limit of high viscosity. Due to the helical properties of the imposed forcing, the inverse cascade of helicity leads to energy accumulation in the largest scales of the domain, albeit the characteristic lengthscale exhibits the transitional nature at a…

Subjects/Keywords: Dynamo theory; MHD; ABC flow; Mean-field theory

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

APA (6^th Edition):

Valeria Shumaylova, V. (2019). Scale selection in hydromagnetic dynamos. (Doctoral Dissertation). University of Cambridge. Retrieved from https://doi.org/10.17863/CAM.37367 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.767874

Chicago Manual of Style (16^th Edition):

Valeria Shumaylova, Valeria. “Scale selection in hydromagnetic dynamos.” 2019. Doctoral Dissertation, University of Cambridge. Accessed January 21, 2021. https://doi.org/10.17863/CAM.37367 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.767874.

MLA Handbook (7^th Edition):

Valeria Shumaylova, Valeria. “Scale selection in hydromagnetic dynamos.” 2019. Web. 21 Jan 2021.

Vancouver:

Valeria Shumaylova V. Scale selection in hydromagnetic dynamos. [Internet] [Doctoral dissertation]. University of Cambridge; 2019. [cited 2021 Jan 21]. Available from: https://doi.org/10.17863/CAM.37367 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.767874.

Council of Science Editors:

Valeria Shumaylova V. Scale selection in hydromagnetic dynamos. [Doctoral Dissertation]. University of Cambridge; 2019. Available from: https://doi.org/10.17863/CAM.37367 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.767874

University of Hong Kong

5. Yao, Cheong-chuen. Properties of neutron stars in the relativistic mean field theory.

Degree: 1996, University of Hong Kong

URL: http://hdl.handle.net/10722/52365

Subjects/Keywords: Mean field theory.; Neutron stars.

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APA (6^th Edition):

Yao, C. (1996). Properties of neutron stars in the relativistic mean field theory. (Thesis). University of Hong Kong. Retrieved from http://hdl.handle.net/10722/52365

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):

Yao, Cheong-chuen. “Properties of neutron stars in the relativistic mean field theory.” 1996. Thesis, University of Hong Kong. Accessed January 21, 2021. http://hdl.handle.net/10722/52365.

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

MLA Handbook (7^th Edition):

Yao, Cheong-chuen. “Properties of neutron stars in the relativistic mean field theory.” 1996. Web. 21 Jan 2021.

Vancouver:

Yao C. Properties of neutron stars in the relativistic mean field theory. [Internet] [Thesis]. University of Hong Kong; 1996. [cited 2021 Jan 21]. Available from: http://hdl.handle.net/10722/52365.

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

Council of Science Editors:

Yao C. Properties of neutron stars in the relativistic mean field theory. [Thesis]. University of Hong Kong; 1996. Available from: http://hdl.handle.net/10722/52365

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

McMaster University

6. Jackel, Benjamin. Magnetic Dynamos: How Do They Even Work?.

Degree: PhD, 2015, McMaster University

URL: http://hdl.handle.net/11375/18299

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The origin of cosmic magnetic fields is a important area of astrophysics. The process by which they are created falls under the heading of dynamo… (more)

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The origin of cosmic magnetic fields is a important area of astrophysics. The process by which they are created falls under the heading of dynamo theory, and is the topic of this thesis. Our focus for the location of where these magnetic fields operate is one the most ubiquitous objects in the universe, the accretion disk. By studying the accretion disk and the dynamo process that occurs there we wish to better understand both the accretion process and the dynamo process in stars and galaxies as well. We analyse the output from a stratified zero net flux shearing box simulation performed using the ATHENA MHD code in collaboration with Shane Davis. The simulation has turbulence which is naturally forced by the presence of a linear instability called the magnetorotational instability (MRI). We utilise Fourier filtering and the tools of mean field dynamo theory to establish a connection between the calculated EMF and the model predictions of the dynamically quenched alpha model. We find a positive correlation for both components parallel to the large scale magnetic field and the azimuthal components. We have explored many aspects of the theory including additional contributions from magnetic buoyancy and an effect arising from the large scale shear and the current density. We also directly measure the turbulent correlation time for the velocity and magnetic fields both large scale and small. We can also observe the effects of the dynamo cycle, with the azimuthal component of the large scale magnetic field flipping sign in this analysis. We find a positive correlation between the divergence of the eddy scale magnetic helicity flux and the component of the electromotive force parallel to the large scale magnetic field. This correlation directly links the transfer of magnetic helicity to the dynamo process in a system with naturally driven turbulence. This highlights the importance of magnetic helicity and its conservation even in a system with triply periodic boundary conditions.

Thesis

Doctor of Philosophy (PhD)

Advisors/Committee Members: Vishniac, Ethan, Physics and Astronomy.

Subjects/Keywords: Accretion Disk; Magnetic Dynamo; magnetohydrodynamics; Mean Field Theory

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APA (6^th Edition):

Jackel, B. (2015). Magnetic Dynamos: How Do They Even Work?. (Doctoral Dissertation). McMaster University. Retrieved from http://hdl.handle.net/11375/18299

Chicago Manual of Style (16^th Edition):

Jackel, Benjamin. “Magnetic Dynamos: How Do They Even Work?.” 2015. Doctoral Dissertation, McMaster University. Accessed January 21, 2021. http://hdl.handle.net/11375/18299.

MLA Handbook (7^th Edition):

Jackel, Benjamin. “Magnetic Dynamos: How Do They Even Work?.” 2015. Web. 21 Jan 2021.

Vancouver:

Jackel B. Magnetic Dynamos: How Do They Even Work?. [Internet] [Doctoral dissertation]. McMaster University; 2015. [cited 2021 Jan 21]. Available from: http://hdl.handle.net/11375/18299.

Council of Science Editors:

Jackel B. Magnetic Dynamos: How Do They Even Work?. [Doctoral Dissertation]. McMaster University; 2015. Available from: http://hdl.handle.net/11375/18299

7. Liard, Quentin. Dérivation des équations de Schrödinger non linéaires par une méthode des caractéristiques en dimension infinie : Derivation of the non linear Schrödinger equations by the characteristics method in a infinite dimensional space.

Degree: Docteur es, Mathématiques et applications, 2015, Rennes 1

URL: http://www.theses.fr/2015REN1S126

►

Dans cette thèse, nous aborderons l'approximation de champ moyen pour des particules bosoniques. Pour un certain nombre d'états quantiques, la dérivation de la limite de… (more)

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Dans cette thèse, nous aborderons l'approximation de champ moyen pour des particules bosoniques. Pour un certain nombre d'états quantiques, la dérivation de la limite de champ moyen est connue, et il semble naturel d'étendre ces travaux à un cadre général d'états quantiques quelconques. L'approximation de champ moyen consiste à remplacer le problème à N corps quantique par un problème non linéaire, dit de Hartree, quand le nombre de particules est grand. Nous prouverons un résultat général pour un système de particules, confinées ou non, interagissant au travers d'un potentiel singulier. La méthode utilisée repose sur les mesures de Wigner. Notre contribution consiste en l'extension de la méthode des caractéristiques au cadre de champ de vitesse singulier associé à l'équation de Hartree. Cela complète les travaux d'Ammari et Nier et permet de prouver des résultats pour des potentiels critiques pour les équations de Hartree. En particulier, on s'intéressera à un système de bosons interagissant au travers d'un potentiel à plusieurs corps et nous démontrerons l'approximation de champ moyen sous une hypothèse de compacité forte sur ce dernier. Les résultats s’appuient en grande partie sur la flexibilité des mesures de Wigner, ce qui permet également de proposer une preuve alternative à l'approximation de champ moyen dans un cadre variationnel.

In this thesis, we justify the mean field approximation in a general framework for bosonic systems. The derivation of mean field dynamics is known for some specific quantum states. Therefore it is natural to expect the extension of these results for a general family of normal states. The mean field approximation for bosons consists in replacing the many-body quantum problem by a non linear one, so-called Hartree problem, when the number of particles tends to infinity. We establish a general result for bosons confined or not, interacting through a singular potential. The method used is based on Wigner measures. Our contribution consists in extending the characteristics method when the velocity field associated to the Hartree equation is subcritical or critical. It complements the work of Ammari and Nier and provides a result for critical potential for the Hartree equation. We also focus on bosonic systems interacting through a multi-body potential and we prove the mean field approximation under a strong assumption on this potential. All these results essentially rely on the flexibility of Wigner measures and we can give an alternative proof of the variational mean field approximation.

Advisors/Committee Members: Ammari, Zied (thesis director), Nier, Francis (thesis director).

Subjects/Keywords: Théorie du champ moyen; Mean-Field theory; Non linear Schrödinger equations

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APA (6^th Edition):

Liard, Q. (2015). Dérivation des équations de Schrödinger non linéaires par une méthode des caractéristiques en dimension infinie : Derivation of the non linear Schrödinger equations by the characteristics method in a infinite dimensional space. (Doctoral Dissertation). Rennes 1. Retrieved from http://www.theses.fr/2015REN1S126

Chicago Manual of Style (16^th Edition):

Liard, Quentin. “Dérivation des équations de Schrödinger non linéaires par une méthode des caractéristiques en dimension infinie : Derivation of the non linear Schrödinger equations by the characteristics method in a infinite dimensional space.” 2015. Doctoral Dissertation, Rennes 1. Accessed January 21, 2021. http://www.theses.fr/2015REN1S126.

MLA Handbook (7^th Edition):

Liard, Quentin. “Dérivation des équations de Schrödinger non linéaires par une méthode des caractéristiques en dimension infinie : Derivation of the non linear Schrödinger equations by the characteristics method in a infinite dimensional space.” 2015. Web. 21 Jan 2021.

Vancouver:

Liard Q. Dérivation des équations de Schrödinger non linéaires par une méthode des caractéristiques en dimension infinie : Derivation of the non linear Schrödinger equations by the characteristics method in a infinite dimensional space. [Internet] [Doctoral dissertation]. Rennes 1; 2015. [cited 2021 Jan 21]. Available from: http://www.theses.fr/2015REN1S126.

Council of Science Editors:

Liard Q. Dérivation des équations de Schrödinger non linéaires par une méthode des caractéristiques en dimension infinie : Derivation of the non linear Schrödinger equations by the characteristics method in a infinite dimensional space. [Doctoral Dissertation]. Rennes 1; 2015. Available from: http://www.theses.fr/2015REN1S126

Columbia University

8. He, Zhuoran. Computational Studies and Algorithmic Research of Strongly Correlated Materials.

Degree: 2019, Columbia University

URL: https://doi.org/10.7916/d8-246b-xs86

► Strongly correlated materials are an important class of materials for research in condensed matter physics. Other than ordinary solid-state physical systems, which can be well… (more)

▼ Strongly correlated materials are an important class of materials for research in condensed matter physics. Other than ordinary solid-state physical systems, which can be well described and analyzed by the energy band theory, the electron-electron correlation effects in strongly correlated materials are far more significant. So it is necessary to develop theories and methods that are beyond the energy band theory to describe their rich and varied behaviors. Not only are there electron-electron correlations, typically the multiple degrees of freedom in strongly correlated materials, such as charge distribution, orbital occupancies, spin orientations, and lattice structure exhibit cooperative or competitive behaviors, giving rise to rich phase diagrams and sensitive or non-perturbative responses to changes in external parameters such as temperature, strain, electromagnetic fields, etc. This thesis is divided into two parts. In the first part, we use the density functional theory (DFT) plus U correction, i.e., the DFT+U method, to calculate the equilibrium and nonequilibrium phase transitions of LuNiO3 and VO2. The effect of adding U is manifested in both materials as the change of band structure in response to the change of orbital occupancies of electrons, i.e., the soft band effect. This effect bring about competitions of electrons between different orbitals by lowering the occupied orbitals and raising the empty orbitals in energy, giving rise to multiple metastable states. In the second part, we study the dynamic mean field theory (DMFT) as a beyond band-theory method. This is a Green's function based theory for open quantum systems. By selecting one lattice site of an interacting lattice model as an open system, the other lattice sites as the environment are equivalently replaced by a set of non-interaction orbitals according to the hybridization function, so the whole system is transformed into an Anderson impurity model. We studied how to use the density matrix renormalization group (DMRG) method to perform real-time evolutions of the Anderson impurity model to study the non-equilibrium dynamics of a strongly correlated lattice system. We begin in Chapter 1 with an introduction to strongly correlated materials, density functional theory (DFT) and dynamical mean-field theory (DMFT). The Kohn-Sham density functional theory and its plus U correction are discussed in detail. We also demonstrate how the DMFT reduces the lattice sites other than the impurity site as a set of non-interacting bath orbitals. Then in Chapters 2 and 3, we show material-related studies of LuNiO3 as an example of rare-earth nickelates under substrate strain, and VO2 as an example of a narrow-gap Mott insulator in a pump-probe experiment. These are two types of strongly correlated materials with localized 3d orbitals (for Ni and V). We use the DFT+U method to calculate their band structures and study the structural phase transitions in LuNiO3 and metal-insulator transitions in both materials. The competition between the…

Subjects/Keywords: Condensed matter; Materials; Physics; Density functionals; Mean field theory

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

APA (6^th Edition):

He, Z. (2019). Computational Studies and Algorithmic Research of Strongly Correlated Materials. (Doctoral Dissertation). Columbia University. Retrieved from https://doi.org/10.7916/d8-246b-xs86

Chicago Manual of Style (16^th Edition):

He, Zhuoran. “Computational Studies and Algorithmic Research of Strongly Correlated Materials.” 2019. Doctoral Dissertation, Columbia University. Accessed January 21, 2021. https://doi.org/10.7916/d8-246b-xs86.

MLA Handbook (7^th Edition):

He, Zhuoran. “Computational Studies and Algorithmic Research of Strongly Correlated Materials.” 2019. Web. 21 Jan 2021.

Vancouver:

He Z. Computational Studies and Algorithmic Research of Strongly Correlated Materials. [Internet] [Doctoral dissertation]. Columbia University; 2019. [cited 2021 Jan 21]. Available from: https://doi.org/10.7916/d8-246b-xs86.

Council of Science Editors:

He Z. Computational Studies and Algorithmic Research of Strongly Correlated Materials. [Doctoral Dissertation]. Columbia University; 2019. Available from: https://doi.org/10.7916/d8-246b-xs86

9. Briggs, A. J. Numerical solutions of Hamilton-Jacobi equations.

Degree: PhD, 1999, University of Sussex

URL: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.298668

Subjects/Keywords: 519; Superconductivity; Mean field theory

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

APA (6^th Edition):

Briggs, A. J. (1999). Numerical solutions of Hamilton-Jacobi equations. (Doctoral Dissertation). University of Sussex. Retrieved from https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.298668

Chicago Manual of Style (16^th Edition):

Briggs, A J. “Numerical solutions of Hamilton-Jacobi equations.” 1999. Doctoral Dissertation, University of Sussex. Accessed January 21, 2021. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.298668.

MLA Handbook (7^th Edition):

Briggs, A J. “Numerical solutions of Hamilton-Jacobi equations.” 1999. Web. 21 Jan 2021.

Vancouver:

Briggs AJ. Numerical solutions of Hamilton-Jacobi equations. [Internet] [Doctoral dissertation]. University of Sussex; 1999. [cited 2021 Jan 21]. Available from: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.298668.

Council of Science Editors:

Briggs AJ. Numerical solutions of Hamilton-Jacobi equations. [Doctoral Dissertation]. University of Sussex; 1999. Available from: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.298668

Hong Kong University of Science and Technology

10. Wong, Ming-Wai. Studying the mutual interaction between ferromagnet and antiferromagnet planes by using the Schwinger-Boson mean field theory.

Degree: 2002, Hong Kong University of Science and Technology

URL: http://repository.ust.hk/ir/Record/1783.1-5425 ; https://doi.org/10.14711/thesis-b779389 ; http://repository.ust.hk/ir/bitstream/1783.1-5425/1/th_redirect.html

► We study the magnetic properties of a system which is composed of 2 layers of ferromagnetic and antiferromagnetic materials in the presence of applied magnetic… (more)

Subjects/Keywords: Ferromagnetism ; Antiferromagnetism ; Mean field theory

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APA (6^th Edition):

Wong, M. (2002). Studying the mutual interaction between ferromagnet and antiferromagnet planes by using the Schwinger-Boson mean field theory. (Thesis). Hong Kong University of Science and Technology. Retrieved from http://repository.ust.hk/ir/Record/1783.1-5425 ; https://doi.org/10.14711/thesis-b779389 ; http://repository.ust.hk/ir/bitstream/1783.1-5425/1/th_redirect.html

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

Chicago Manual of Style (16^th Edition):

Wong, Ming-Wai. “Studying the mutual interaction between ferromagnet and antiferromagnet planes by using the Schwinger-Boson mean field theory.” 2002. Thesis, Hong Kong University of Science and Technology. Accessed January 21, 2021. http://repository.ust.hk/ir/Record/1783.1-5425 ; https://doi.org/10.14711/thesis-b779389 ; http://repository.ust.hk/ir/bitstream/1783.1-5425/1/th_redirect.html.

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

MLA Handbook (7^th Edition):

Wong, Ming-Wai. “Studying the mutual interaction between ferromagnet and antiferromagnet planes by using the Schwinger-Boson mean field theory.” 2002. Web. 21 Jan 2021.

Vancouver:

Wong M. Studying the mutual interaction between ferromagnet and antiferromagnet planes by using the Schwinger-Boson mean field theory. [Internet] [Thesis]. Hong Kong University of Science and Technology; 2002. [cited 2021 Jan 21]. Available from: http://repository.ust.hk/ir/Record/1783.1-5425 ; https://doi.org/10.14711/thesis-b779389 ; http://repository.ust.hk/ir/bitstream/1783.1-5425/1/th_redirect.html.

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

Council of Science Editors:

Wong M. Studying the mutual interaction between ferromagnet and antiferromagnet planes by using the Schwinger-Boson mean field theory. [Thesis]. Hong Kong University of Science and Technology; 2002. Available from: http://repository.ust.hk/ir/Record/1783.1-5425 ; https://doi.org/10.14711/thesis-b779389 ; http://repository.ust.hk/ir/bitstream/1783.1-5425/1/th_redirect.html

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

University of Washington

11. Ashrafi, Seyed Shwan. Random Access over Multi-Packet Reception Channels: A Mean-Field Approach.

Degree: PhD, 2016, University of Washington

URL: http://hdl.handle.net/1773/37106

► This thesis addresses the problem of Multi-Packet Reception (MPR) for random access scenarios in Wireless LAN type infrastructure network. Our results builds on a recently… (more)

▼ This thesis addresses the problem of Multi-Packet Reception (MPR) for random access scenarios in Wireless LAN type infrastructure network. Our results builds on a recently proposed physical-layer network coding mechanism – Compute-and-Forward (C&F); we embed this within slotted ALOHA and Carrier Sense Multiple Access (CSMA) protocols for operational scenarios where multiple simultaneous transmissions are likely to occur. A mean-field approach is used to understand the impact of multi-packet reception in random access networks. By focusing on a special family of MPR channels – the all-or-nothing model, stability conditions are derived for slotted ALOHA and CSMA systems under the above assumption. Interestingly, a number of physical-layer network coding schemes such as compute-and-forward, successive compute-and-forward (SCF) and successive interference cancellation can be viewed as special cases of all-or-nothing symmetric MPR model. In addition, the problem is analyzed under the general symmetric MPR channels which turns out not to be fundamentally different from the all-or-nothing MPR. The primary outcome is a deeper understanding of the behavior of random access schemes over general symmetric MPR channels. Due to the interaction among users and the challenges emanating from such interactions, random access can be more readily analyzed if the state of users are assumed decoupled and an approximate stability region obtained for the system. Nonetheless, the approximate stability region computation based on the decoupling assumption is still complicated for even small (few clients) networks. By a mean-field approach, the random access problem is studied in the large number of clients regime. As a result, the evolution of the system state in the limit can be well approximated by a deterministic dynamical system. The stability conditions for the limiting system then paves the way for a better understanding of a known/observed phenomenon called meta-stability whereby (finite) random-access networks undergo a phase transition: from stability to meta-stability. In the thesis, we first present results for slotted ALOHA with all-or-nothing MPR model. An approximate stability region is characterized which is then used for system performance evaluation in terms of throughput and delay. These results are then extended to the case of general symmetric MPR channels. Next, the stability of persistent CSMA systems is analyzed similar to slotted ALOHA analysis and throughput and delay results are obtained. Meta-stability is discussed for CSMA systems and system design guidelines are outlined to guarantee certain quality-of-service requirements, i.e., avoidance of meta-stable behavior. By adding a back-off mechanism, the stationary behavior of a saturated system is studied, again through mean-field analysis. Finally, we propose a novel extension to the cooperating multiple AP scenario for dense networks, where we present new algorithms for MPR-capable systems and present some initial analysis. Advisors/Committee Members: Roy, Sumit (advisor).

Subjects/Keywords: Mean Field Analysis; Queueing Theory; Random Access; Electrical engineering; electrical engineering

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APA (6^th Edition):

Ashrafi, S. S. (2016). Random Access over Multi-Packet Reception Channels: A Mean-Field Approach. (Doctoral Dissertation). University of Washington. Retrieved from http://hdl.handle.net/1773/37106

Chicago Manual of Style (16^th Edition):

Ashrafi, Seyed Shwan. “Random Access over Multi-Packet Reception Channels: A Mean-Field Approach.” 2016. Doctoral Dissertation, University of Washington. Accessed January 21, 2021. http://hdl.handle.net/1773/37106.

MLA Handbook (7^th Edition):

Ashrafi, Seyed Shwan. “Random Access over Multi-Packet Reception Channels: A Mean-Field Approach.” 2016. Web. 21 Jan 2021.

Vancouver:

Ashrafi SS. Random Access over Multi-Packet Reception Channels: A Mean-Field Approach. [Internet] [Doctoral dissertation]. University of Washington; 2016. [cited 2021 Jan 21]. Available from: http://hdl.handle.net/1773/37106.

Council of Science Editors:

Ashrafi SS. Random Access over Multi-Packet Reception Channels: A Mean-Field Approach. [Doctoral Dissertation]. University of Washington; 2016. Available from: http://hdl.handle.net/1773/37106

University of Florida

12. Zhang, Long. Density Functional Theory plus Dynamical Mean Field Theory Calculation for Transition Metal Oxides.

Degree: PhD, Physics, 2017, University of Florida

URL: https://ufdc.ufl.edu/UFE0051525

Subjects/Keywords: dynamical; field; mean; theory

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APA (6^th Edition):

Zhang, L. (2017). Density Functional Theory plus Dynamical Mean Field Theory Calculation for Transition Metal Oxides. (Doctoral Dissertation). University of Florida. Retrieved from https://ufdc.ufl.edu/UFE0051525

Chicago Manual of Style (16^th Edition):

Zhang, Long. “Density Functional Theory plus Dynamical Mean Field Theory Calculation for Transition Metal Oxides.” 2017. Doctoral Dissertation, University of Florida. Accessed January 21, 2021. https://ufdc.ufl.edu/UFE0051525.

MLA Handbook (7^th Edition):

Zhang, Long. “Density Functional Theory plus Dynamical Mean Field Theory Calculation for Transition Metal Oxides.” 2017. Web. 21 Jan 2021.

Vancouver:

Zhang L. Density Functional Theory plus Dynamical Mean Field Theory Calculation for Transition Metal Oxides. [Internet] [Doctoral dissertation]. University of Florida; 2017. [cited 2021 Jan 21]. Available from: https://ufdc.ufl.edu/UFE0051525.

Council of Science Editors:

Zhang L. Density Functional Theory plus Dynamical Mean Field Theory Calculation for Transition Metal Oxides. [Doctoral Dissertation]. University of Florida; 2017. Available from: https://ufdc.ufl.edu/UFE0051525

University of Tennessee – Knoxville

13. Brown, Ellen. Examination of 4He droplets and droplets containing impurities at zero Kelvin using a density functional approach.

Degree: MS, Chemistry, 2011, University of Tennessee – Knoxville

URL: https://trace.tennessee.edu/utk_gradthes/951

► Abstract Detailed in this manuscript is a methodology to model ground state properties of ⁴He droplets at zero pressure and zero Kelvin using a… (more)

Subjects/Keywords: superfluidity; mean field; density functional theory; liquid helium; Physical Chemistry

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APA (6^th Edition):

Brown, E. (2011). Examination of 4He droplets and droplets containing impurities at zero Kelvin using a density functional approach. (Thesis). University of Tennessee – Knoxville. Retrieved from https://trace.tennessee.edu/utk_gradthes/951

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):

Brown, Ellen. “Examination of 4He droplets and droplets containing impurities at zero Kelvin using a density functional approach.” 2011. Thesis, University of Tennessee – Knoxville. Accessed January 21, 2021. https://trace.tennessee.edu/utk_gradthes/951.

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

MLA Handbook (7^th Edition):

Brown, Ellen. “Examination of 4He droplets and droplets containing impurities at zero Kelvin using a density functional approach.” 2011. Web. 21 Jan 2021.

Vancouver:

Brown E. Examination of 4He droplets and droplets containing impurities at zero Kelvin using a density functional approach. [Internet] [Thesis]. University of Tennessee – Knoxville; 2011. [cited 2021 Jan 21]. Available from: https://trace.tennessee.edu/utk_gradthes/951.

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

Council of Science Editors:

Brown E. Examination of 4He droplets and droplets containing impurities at zero Kelvin using a density functional approach. [Thesis]. University of Tennessee – Knoxville; 2011. Available from: https://trace.tennessee.edu/utk_gradthes/951

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

Laurentian University

14. Rodger, Clifford John. Bond mean field theory for electron spin resonance frequency shift analysis .

Degree: 2015, Laurentian University

URL: https://zone.biblio.laurentian.ca/dspace/handle/10219/2325

► Electron spin resonance (ESR) is an important experimental technique. A comprehensive theory of ESR has been di cult to establish, and as such several di… (more)

Subjects/Keywords: ESR; spin lattices; bond-mean-field theory; solid state

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APA (6^th Edition):

Rodger, C. J. (2015). Bond mean field theory for electron spin resonance frequency shift analysis . (Thesis). Laurentian University. Retrieved from https://zone.biblio.laurentian.ca/dspace/handle/10219/2325

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):

Rodger, Clifford John. “Bond mean field theory for electron spin resonance frequency shift analysis .” 2015. Thesis, Laurentian University. Accessed January 21, 2021. https://zone.biblio.laurentian.ca/dspace/handle/10219/2325.

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

MLA Handbook (7^th Edition):

Rodger, Clifford John. “Bond mean field theory for electron spin resonance frequency shift analysis .” 2015. Web. 21 Jan 2021.

Vancouver:

Rodger CJ. Bond mean field theory for electron spin resonance frequency shift analysis . [Internet] [Thesis]. Laurentian University; 2015. [cited 2021 Jan 21]. Available from: https://zone.biblio.laurentian.ca/dspace/handle/10219/2325.

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

Council of Science Editors:

Rodger CJ. Bond mean field theory for electron spin resonance frequency shift analysis . [Thesis]. Laurentian University; 2015. Available from: https://zone.biblio.laurentian.ca/dspace/handle/10219/2325

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

15. Lee, Juho, 1987-. Methodological study of computational approaches to address the problem of strong correlations.

Degree: PhD, Physics and Astronomy, 2017, Rutgers University

URL: https://rucore.libraries.rutgers.edu/rutgers-lib/52226/

► The main focus of this thesis is the detailed investigation of computational methods to tackle strongly correlated materials in which a rich variety of exotic… (more)

▼ The main focus of this thesis is the detailed investigation of computational methods to tackle strongly correlated materials in which a rich variety of exotic phenomena are found. A many-body problem with sizable electronic correlations can no longer be explained by independent-particle approximations such as density functional theory (DFT) or tight-binding approaches. The influence of an electron to the others is too strong for each electron to be treated as an independent quasiparticle and consequently those standard band-structure methods fail even at a qualitative level. One of the most powerful approaches for strong correlations is the dynamical mean-field theory (DMFT), which has enlightened the understanding of the Mott transition based on the Hubbard model. For realistic applications, the dynamical mean-field theory is combined with various independent-particles approaches. The most widely used one is the DMFT combined with the DFT in the local density approximation (LDA), so-called LDA+DMFT. In this approach, the electrons in the weakly correlated orbitals are calculated by LDA while others in the strongly correlated orbitals are treated by DMFT. Recently, the method combining DMFT with Hedin's GW approximation was also developed, in which the momentum-dependent self-energy is also added. In this thesis, we discuss the application of those methodologies based on DMFT. First, we apply the dynamical mean-field theory to solve the 3-dimensional Hubbard model in Chap. 3. In this application, we model the interface between the thermodynamically coexisting metal and Mott insulator. We show how to model the required slab geometry and extract the electronic spectra. We construct an effective Landau free energy and compute the variation of its parameters across the phase diagram. Finally, using a linear mixture of the density and double-occupancy, we identify a natural Ising order parameter which unifies the treatment of the bandwidth and filling controlled Mott transitions. Secondly, we study the double-counting problem, a subtle issue that arises in LDA+DMFT. We propose a highly precise double-counting functional, in which the intersection of LDA and DMFT is calculated exactly, and implement a parameter-free version of the LDA+DMFT that is tested on one of the simplest strongly correlated systems, the H2 molecule. We show that the exact double-counting treatment along with a good DMFT projector leads to very accurate and total energy and excitation spectrum of H₂ molecule. Finally, we implement various versions of GW+DMFT, in its fully self-consistent way, one shot GW approximation, and quasiparticle self-consistent scheme, and studied how well these combined methods perform on H₂ molecule as compared to more established methods such as LDA+DMFT. We found that most flavors of GW+DMFT break down in strongly correlated regime due to causality violation. Among GW+DMFT methods, only the self-consistent quasiparticle GW+DMFT with static double-counting, and a new method with causal… Advisors/Committee Members: Haule, Kristjan (chair), Kotliar, Gabriel (internal member), Shapiro, Joel (internal member), Gershenson, Michael (internal member), Park, Hyowon (outside member).

Subjects/Keywords: Mean field theory

…deal with strongly correlated systems, the dynamical mean-field theory (DMFT) [… …theory and its applications. In Chapter 2, the main idea of dynamical mean-field theory (… …Chapter 2 Dynamical Mean-Field Theory This chapter is devoted to dynamical mean-field theory… …mean-field theory. It allowed theorists to develop and solve a wide range of models on the… …In this chapter, we will explore the basic construction of the dynamical mean-field theory…

7 more images…

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APA (6^th Edition):

Lee, Juho, 1. (2017). Methodological study of computational approaches to address the problem of strong correlations. (Doctoral Dissertation). Rutgers University. Retrieved from https://rucore.libraries.rutgers.edu/rutgers-lib/52226/

Chicago Manual of Style (16^th Edition):

Lee, Juho, 1987-. “Methodological study of computational approaches to address the problem of strong correlations.” 2017. Doctoral Dissertation, Rutgers University. Accessed January 21, 2021. https://rucore.libraries.rutgers.edu/rutgers-lib/52226/.

MLA Handbook (7^th Edition):

Lee, Juho, 1987-. “Methodological study of computational approaches to address the problem of strong correlations.” 2017. Web. 21 Jan 2021.

Vancouver:

Lee, Juho 1. Methodological study of computational approaches to address the problem of strong correlations. [Internet] [Doctoral dissertation]. Rutgers University; 2017. [cited 2021 Jan 21]. Available from: https://rucore.libraries.rutgers.edu/rutgers-lib/52226/.

Council of Science Editors:

Lee, Juho 1. Methodological study of computational approaches to address the problem of strong correlations. [Doctoral Dissertation]. Rutgers University; 2017. Available from: https://rucore.libraries.rutgers.edu/rutgers-lib/52226/

16. Giera, Brian. Primitive Model Simulations and Mean-Field Studies of Electric Double Layers.

Degree: 2014, University of California – eScholarship, University of California

URL: http://www.escholarship.org/uc/item/16m3449t

► When a charged surface, such as an electrode, colloid, or protein, is submerged into an electrolyte or ionic liquid, ions within the fluid rearrange into… (more)

Subjects/Keywords: Chemical engineering; Dissertation; Electric Double Layer; Mean-Field Theory; Molecular Dynamics; Primitive Model; Theory

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APA (6^th Edition):

Giera, B. (2014). Primitive Model Simulations and Mean-Field Studies of Electric Double Layers. (Thesis). University of California – eScholarship, University of California. Retrieved from http://www.escholarship.org/uc/item/16m3449t

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):

Giera, Brian. “Primitive Model Simulations and Mean-Field Studies of Electric Double Layers.” 2014. Thesis, University of California – eScholarship, University of California. Accessed January 21, 2021. http://www.escholarship.org/uc/item/16m3449t.

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

MLA Handbook (7^th Edition):

Giera, Brian. “Primitive Model Simulations and Mean-Field Studies of Electric Double Layers.” 2014. Web. 21 Jan 2021.

Vancouver:

Giera B. Primitive Model Simulations and Mean-Field Studies of Electric Double Layers. [Internet] [Thesis]. University of California – eScholarship, University of California; 2014. [cited 2021 Jan 21]. Available from: http://www.escholarship.org/uc/item/16m3449t.

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

Council of Science Editors:

Giera B. Primitive Model Simulations and Mean-Field Studies of Electric Double Layers. [Thesis]. University of California – eScholarship, University of California; 2014. Available from: http://www.escholarship.org/uc/item/16m3449t

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

Columbia University

17. Cheng, Zhengqian. Variational Discrete Action Theory.

Degree: 2021, Columbia University

URL: https://doi.org/10.7916/d8-94wt-r702

► This thesis focuses on developing new approaches to solving the ground state properties of quantum many-body Hamiltonians, and the goal is to develop a systematic… (more)

▼ This thesis focuses on developing new approaches to solving the ground state properties of quantum many-body Hamiltonians, and the goal is to develop a systematic approach which properly balances efficiency and accuracy. Two new formalisms are proposed in this thesis: the Variational Discrete Action Theory (VDAT) and the Off-Shell Effective Energy Theory (OET). The VDAT exploits the advantages of both variational wavefunctions and many-body Green's functions for solving quantum Hamiltonians. VDAT consists of two central components: the Sequential Product Density matrix (SPD) and the Discrete Action associated with the SPD. The SPD is a variational ansatz inspired by the Trotter decomposition and characterized by an integer N, and N controls the balance of accuracy and cost; monotonically converging to the exact solution for N → ∞. The Discrete Action emerges by treating the each projector in the SPD as an effective discrete time evolution. We generalize the path integral to our discrete formalism, which converts a dynamic correlation function to a static correlation function in a compound space. We also generalize the usual many-body Green's function formalism, which results in analogous but distinct mathematical structures due to the non-abelian nature of the SPD, yielding discrete versions of the generating functional, Dyson equation, and Bethe-Salpeter equation. We apply VDAT to two canonical models of interacting electrons: the Anderson impurity model (AIM) and the Hubbard model. We prove that the SPD can be exactly evaluated in the AIM, and demonstrate that N=3 provides a robust description of the exact results with a relatively negligible cost. For the Hubbard model, we introduce the local self-consistent approximation (LSA), which is the analogue of the dynamical mean-field theory, and prove that LSA exactly evaluates VDAT for d=∞. Furthermore, VDAT within the LSA at N=2 exactly recovers the Gutzwiller approximation (GA), and therefore N>2 provides a new class of theories which balance efficiency and accuracy. For the d=∞ Hubbard model, we evaluate N=2-4 and show that N=3 provides a truly minimal yet precise description of Mott physics with a cost similar to the GA. VDAT provides a flexible scheme for studying quantum Hamiltonians, competing both with state-of-the-art methods and simple, efficient approaches all within a single framework. VDAT will have broad applications in condensed matter and materials physics. In the second part of the thesis, we propose a different formalism, off-shell effective energy theory (OET), which combines the variational principle and effective energy theory, providing a ground state description of a quantum many-body Hamiltonian. The OET is based on a partitioning of the Hamiltonian and a corresponding density matrix ansatz constructed from an off-shell extension of the equilibrium density matrix; and there are dual realizations based on a given partitioning. To approximate OET, we introduce the central point expansion (CPE), which is an expansion of the density matrix…

Subjects/Keywords: Physics; Materials science; Hamiltonian systems; Hubbard model; Quantum theory; Mean field theory; Bethe-Salpeter equation

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APA (6^th Edition):

Cheng, Z. (2021). Variational Discrete Action Theory. (Doctoral Dissertation). Columbia University. Retrieved from https://doi.org/10.7916/d8-94wt-r702

Chicago Manual of Style (16^th Edition):

Cheng, Zhengqian. “Variational Discrete Action Theory.” 2021. Doctoral Dissertation, Columbia University. Accessed January 21, 2021. https://doi.org/10.7916/d8-94wt-r702.

MLA Handbook (7^th Edition):

Cheng, Zhengqian. “Variational Discrete Action Theory.” 2021. Web. 21 Jan 2021.

Vancouver:

Cheng Z. Variational Discrete Action Theory. [Internet] [Doctoral dissertation]. Columbia University; 2021. [cited 2021 Jan 21]. Available from: https://doi.org/10.7916/d8-94wt-r702.

Council of Science Editors:

Cheng Z. Variational Discrete Action Theory. [Doctoral Dissertation]. Columbia University; 2021. Available from: https://doi.org/10.7916/d8-94wt-r702

University of Pennsylvania

18. Chao, Huikuan. Equilibrium Field Theoretic And Dynamic Mean Field Simulations Of Inhomogeneous Polymeric Materials.

Degree: 2017, University of Pennsylvania

URL: https://repository.upenn.edu/edissertations/3068

► Inhomogeneous polymeric materials is a large family of promising materials including but limited to block copolymers (BCPs), polymer nanocomposites (PNCs) and microscopically confined polymer films.… (more)

▼ Inhomogeneous polymeric materials is a large family of promising materials including but limited to block copolymers (BCPs), polymer nanocomposites (PNCs) and microscopically confined polymer films. The promising application of the materials originates from the materials' unique microstructures, which offer enhanced mechanical, thermal, optical and electrical properties to the materials. Due to the complex interactions and the large parameter space, behaviors of the microstructures formed by grafted nanoparticles and nanorods in PNCs are difficult to understand. Separately, because of relatively weak interactions, the microstructures are typically achieved through rapid processing that are kinetically controlled and beyond equilibrium. However, efficient simulation framework to study nonequilbrium dynamics of the materials is currently not available. To attack the first difficulty, I extended an efficient simulation framework, polymer nanocomposite field theory (PNC-FT), to incorporate grafted nanoparticles and nanorods. This extended framework is demonstrated against existing experimental studies and implemented to study how the nanoparticle design affects the nanoparticle distribution in binary homopolymer blends. The grafted nanoparticle model is also used as a platform to adopt an advanced optimization method to inversely design nanoparticles which are able to self-assemble into targeted two dimensional lattices. The nanorod model under PNC-FT framework is used to investigate the design of nanorod and block copolymer thin films to control the nanorod distribution. To attack the second difficulty, I established an efficient framework (SCMF-LD) based on a recently proposed dynamic mean field theory and used SCMF-LD to study how to kinetically control the nanoparticle distribution at the end of solvent annealing block copolymer thin films. The framework is then extended to incorporate hydrodynamics (SCMF-DPD) and the extended framework is implemented to study morphology development in phase inversion processing polymer thin films, where hydrodynamic effects play an important role. By exploring both equilibrium and nonequilibrium properties in a spectrum of inhomogeneous polymeric material systems, I successfully extended PNC-FT and established SCMF-LD and SCMF-DPD frameworks, which are expected to be efficient and powerful tools in studies of inhomogeneous polymeric material design and processing.

Subjects/Keywords: Dynamic Mean Field Theory; Inverse Material Design; Polymer Field Theory; Polymer Nanocomposites; Polymer Thin Films; Chemical Engineering; Physical Chemistry; Physics

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APA (6^th Edition):

Chao, H. (2017). Equilibrium Field Theoretic And Dynamic Mean Field Simulations Of Inhomogeneous Polymeric Materials. (Thesis). University of Pennsylvania. Retrieved from https://repository.upenn.edu/edissertations/3068

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):

Chao, Huikuan. “Equilibrium Field Theoretic And Dynamic Mean Field Simulations Of Inhomogeneous Polymeric Materials.” 2017. Thesis, University of Pennsylvania. Accessed January 21, 2021. https://repository.upenn.edu/edissertations/3068.

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

MLA Handbook (7^th Edition):

Chao, Huikuan. “Equilibrium Field Theoretic And Dynamic Mean Field Simulations Of Inhomogeneous Polymeric Materials.” 2017. Web. 21 Jan 2021.

Vancouver:

Chao H. Equilibrium Field Theoretic And Dynamic Mean Field Simulations Of Inhomogeneous Polymeric Materials. [Internet] [Thesis]. University of Pennsylvania; 2017. [cited 2021 Jan 21]. Available from: https://repository.upenn.edu/edissertations/3068.

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

Council of Science Editors:

Chao H. Equilibrium Field Theoretic And Dynamic Mean Field Simulations Of Inhomogeneous Polymeric Materials. [Thesis]. University of Pennsylvania; 2017. Available from: https://repository.upenn.edu/edissertations/3068

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

Indian Institute of Science

19. Bag, Soumen Kumar. Effects of Strong Electron-Electron Correlations on Band Insulators in Equilibrium and Non-Equilibrium.

Degree: PhD, Faculty of Science, 2020, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/4343

► In this thesis, several aspects of correlation effects in band insulators that were hitherto not addressed, both in equilibrium and non-equilibrium, are studied using the… (more)

▼ In this thesis, several aspects of correlation effects in band insulators that were hitherto not addressed, both in equilibrium and non-equilibrium, are studied using the Ionic Hubbard model (IHM) at half-filling and Dynamical mean-field theory (DMFT). The IHM is an extension of the Hubbard model on a bipartite lattice with a staggered on-site “ionic" potential Δ added in. The Hubbard model by itself is a tight-binding model of electrons hopping between (orbitals localized on) lattice sites, with amplitudes t and t’ for first neighbor and second neighbor hopping respectively, together with a coulomb repulsion energy cost of U for double occupancy (i.e., with both up and down spin electrons) at any lattice site. The studies in this thesis address strong correlation effects in this model using DMFT techniques which map the lattice problem to a self consistently embedded quantum impurity problem. The impurity problem itself is solved using state of the art continuous time quantum monte-carlo (CTQMC) techniques (Ch.s 3 and 4) as well as the somewhat simpler Iterated Perturbation Theory (IPT) (Ch.s 3, 5 and 6). Chapter 3 of the thesis is devoted to a detailed analysis of the properties of the half-filled t-U-Δ IHM (i.e., with t’=0) on a Bethe lattice of infinite connectivity. It is shown conclusively here that for a finite Δ and at zero temperature (T=0), the IHM has a first order transition from the Band Insulator (BI) phase to an antiferromagnetic insulating (AFI) phase at a threshold U = UAF (which increases with Δ) such that the BI to AFI transition preempts the transition from the BI to the correlation induced paramagnetic metallic (PM) phase. Evidence is also presented for a quantum transition to a sliver of half-metal (HM) phase just after the AF order turns on, followed by a return to the AFI phase on further increasing U. With increasing T, the AF order is lost via a first-order transition for weak to intermediate U/t. In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, the transition from the AFI to the paramagnetic Mott insulating phase (adiabatically connected to the BI phase) is of second order. As T increases, the range of U over which the AF order is stable shrinks, collapsing eventually to a line of tricritical points that separates the surfaces of first- and second-order phase transitions in the T-U-Δ space. In Chapter 4 of the thesis the t-t’-U-Δ IHM on a square lattice is studied using DMFT+CTQMC. It is shown here that the presence of t’ frustrates the AF order for weak to intermediate correlations, resulting in the stabilization of the correlation induced PM phase over a broad region of the parameter space, although the AFI is always the stable phase for large enough U. In the intermediate coupling regimes, two other interesting phases show up as a result of the competition among U, Δ and t’ : a Ferrimagnetic metallic (FM) phase which has non-zero values of the uniform as well as staggered magnetization; and even more interesting, an… Advisors/Committee Members: Krishnamurthy, H R (advisor), Jain, Manish (advisor).

Subjects/Keywords: Band Insulator; Non-Equilibrium Physics; Strongly Correlated System; Half Metal; Dynamical Mean Field Theory; Dynamical mean-field Theory (DMFT); Condensed Matter Physics

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APA (6^th Edition):

Bag, S. K. (2020). Effects of Strong Electron-Electron Correlations on Band Insulators in Equilibrium and Non-Equilibrium. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/4343

Chicago Manual of Style (16^th Edition):

Bag, Soumen Kumar. “Effects of Strong Electron-Electron Correlations on Band Insulators in Equilibrium and Non-Equilibrium.” 2020. Doctoral Dissertation, Indian Institute of Science. Accessed January 21, 2021. http://etd.iisc.ac.in/handle/2005/4343.

MLA Handbook (7^th Edition):

Bag, Soumen Kumar. “Effects of Strong Electron-Electron Correlations on Band Insulators in Equilibrium and Non-Equilibrium.” 2020. Web. 21 Jan 2021.

Vancouver:

Bag SK. Effects of Strong Electron-Electron Correlations on Band Insulators in Equilibrium and Non-Equilibrium. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2020. [cited 2021 Jan 21]. Available from: http://etd.iisc.ac.in/handle/2005/4343.

Council of Science Editors:

Bag SK. Effects of Strong Electron-Electron Correlations on Band Insulators in Equilibrium and Non-Equilibrium. [Doctoral Dissertation]. Indian Institute of Science; 2020. Available from: http://etd.iisc.ac.in/handle/2005/4343

University of Alberta

20. Bach, Giang Huong. Dynamical mean field theory for the Dynamic Hubbard model.

Degree: PhD, Department of Physics, 2011, University of Alberta

URL: https://era.library.ualberta.ca/files/cw0892996r

► Dynamical mean field theory is applied to the Dynamic Hubbard model. The Dynamic Hubbard model describes the orbital relaxation that occurs when two electrons occupy… (more)

Subjects/Keywords: Dynamic Hubbard model; hole superconductivity; Dynamical mean field theory; electron-hole asymmetry

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APA (6^th Edition):

Bach, G. H. (2011). Dynamical mean field theory for the Dynamic Hubbard model. (Doctoral Dissertation). University of Alberta. Retrieved from https://era.library.ualberta.ca/files/cw0892996r

Chicago Manual of Style (16^th Edition):

Bach, Giang Huong. “Dynamical mean field theory for the Dynamic Hubbard model.” 2011. Doctoral Dissertation, University of Alberta. Accessed January 21, 2021. https://era.library.ualberta.ca/files/cw0892996r.

MLA Handbook (7^th Edition):

Bach, Giang Huong. “Dynamical mean field theory for the Dynamic Hubbard model.” 2011. Web. 21 Jan 2021.

Vancouver:

Bach GH. Dynamical mean field theory for the Dynamic Hubbard model. [Internet] [Doctoral dissertation]. University of Alberta; 2011. [cited 2021 Jan 21]. Available from: https://era.library.ualberta.ca/files/cw0892996r.

Council of Science Editors:

Bach GH. Dynamical mean field theory for the Dynamic Hubbard model. [Doctoral Dissertation]. University of Alberta; 2011. Available from: https://era.library.ualberta.ca/files/cw0892996r

Texas A&M University

21. Eren, Ezgi. Stochastic Modeling and Analysis of Plant Microtubule System Characteristics.

Degree: PhD, Industrial Engineering, 2012, Texas A&M University

URL: http://hdl.handle.net/1969.1/ETD-TAMU-2012-05-11085

► In this dissertation, we consider a complex biological system known as cortical microtubule (CMT) system, where stochastic dynamics of the components (i.e., the CMTs) are… (more)

▼ In this dissertation, we consider a complex biological system known as cortical microtubule (CMT) system, where stochastic dynamics of the components (i.e., the CMTs) are defined in both space and time. CMTs have an inherent spatial dimension of their own, as their length changes over time in addition to their location. As a result of their dynamics in a confined space, they run into and interact with each other according to simple stochastic rules. Over time, CMTs acquire an ordered structure that is achieved without any centralized control beginning with a completely disorganized system. It is also observed that this organization might be distorted, when parameters of dynamicity and interactions change due to genetic mutation or environmental conditions. The main question of interest is to explore the characteristics of this system and the drivers of its self-organization, which is not feasible relying solely on biological experiments. For this, we replicate the system dynamics and interactions using computer simulations. As the simulations successfully mimic the organization seen in plant cells, we conduct an extensive analysis to discover the effects of dynamics and interactions on system characteristics by experimenting with different input parameters. To compare simulation results, we characterize system properties and quantify organization level using metrics based on entropy, average length and number of CMTs in the system. Based on our findings and conjectures from simulations, we develop analytical models for more generalized conclusions and efficient computation of system metrics. As a fist step, we formulate a mean-field model, which we use to derive sufficient conditions for organization to occur in terms of input parameters. Next, considering the parameter ranges that satisfy these conditions, we develop predictive methodologies for estimation of expected average length and number of CMTs over time, using a fluid model, transient analysis, and approximation algorithms tailored to our problem. Overall, we build a comprehensive framework for analysis and control of microtubule organization in plant cells using a wide range of models and methodologies in conjunction. This research also has broader impacts related to the fields of bio-energy, healthcare, and nanotechnology; in addition to its methodological contribution to stochastic modeling of systems with high-level spatial and temporal complexity. Advisors/Committee Members: Gautam, Natarajan (advisor), Curry, Guy L. (committee member), Feldman, Richard M. (committee member), Yurttas, Salih (committee member), Dixit, Ram (committee member).

Subjects/Keywords: fluid queues; mean-field theory; simulation; spatio-temporal bio-processes; plant cell cortical microtubules

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APA (6^th Edition):

Eren, E. (2012). Stochastic Modeling and Analysis of Plant Microtubule System Characteristics. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/ETD-TAMU-2012-05-11085

Chicago Manual of Style (16^th Edition):

Eren, Ezgi. “Stochastic Modeling and Analysis of Plant Microtubule System Characteristics.” 2012. Doctoral Dissertation, Texas A&M University. Accessed January 21, 2021. http://hdl.handle.net/1969.1/ETD-TAMU-2012-05-11085.

MLA Handbook (7^th Edition):

Eren, Ezgi. “Stochastic Modeling and Analysis of Plant Microtubule System Characteristics.” 2012. Web. 21 Jan 2021.

Vancouver:

Eren E. Stochastic Modeling and Analysis of Plant Microtubule System Characteristics. [Internet] [Doctoral dissertation]. Texas A&M University; 2012. [cited 2021 Jan 21]. Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2012-05-11085.

Council of Science Editors:

Eren E. Stochastic Modeling and Analysis of Plant Microtubule System Characteristics. [Doctoral Dissertation]. Texas A&M University; 2012. Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2012-05-11085

22. Champion, Maxime. Mécanique statistique des systèmes auto-gravitants : Statistical mechanics of self-gravitating systems.

Degree: Docteur es, Physique, 2015, Lyon, École normale supérieure

URL: http://www.theses.fr/2015ENSL0997

►

L’étude des systèmes avec interactions gravitationnelles à l’aide des outils de la mécanique statistique repose jusqu’à présent sur l’utilisation d’une approximation de type champ moyen,… (more)

▼

L’étude des systèmes avec interactions gravitationnelles à l’aide des outils de la mécanique statistique repose jusqu’à présent sur l’utilisation d’une approximation de type champ moyen, qui néglige par construction les effets à courte portée de l’interaction. Pour commencer, je décris cette approximation dans son contexte historique, à savoir le modèle de la sphère isotherme. Puis, dans le cadre de la mécanique statistique du problème à N -corps, j’introduis un système de sphères dures massives, qui permet de s’affranchir de l’effondrement du système de points matériels. La validité de l’approche hydrostatique est discutée dans l’ensemble microcanonique, en introduisant une limite d’échelle adéquate.Cette étude permet de mettre en avant les critères de validité pour l’approche hydrostatique, et de constater qu’ils peuvent être mis en défaut dans les systèmes astrophysiques de type amas globulaire. Pour mieux les comprendre et les illustrer, je me concentre ensuite sur l’étude d’un modèle de bâtonnets durs massifs à une dimension, dont l’avantage est de permettre tous les calculs analytiques des différentes grandeurs statistiques. Ainsi, je mets en évidence comment l’approche de type champ moyen est mise en défaut pour certains états effondrés.Enfin, dans le but de tenter de décrire des amas globulaires, je développe un modèle comprenant des étoiles célibataires et des étoiles binaires. Ce modèle reproduit bien les effets qualitatifs attendus, et il constitue une première correction satisfaisante au modèle historique de la sphère isotherme. Je met aussi en évidence l’absence d’équilibre thermodynamique au sens strict pour les systèmes considérés. En conclusion, je réalise une discussion succincte de certains éléments dynamiques du problème.

The study of systems with gravitational interactions with the tools of mechanics statistics was based so far on the use of a mean-field approximation, which neglect by construction effects of the short-range interaction. To begin, I describe this approximation in its historical context, namely the model of isothermal sphere. Then, as part of statistical mechanics of many-body problem, I introduce a system of massive hard spheres, which overcomes the collapse of the point partcile system. The validity of the hydrostatic approach is discussed in the microcanonical ensemble, by introducing an appropriate scaling limit.This study helps to highlight conditions of validity of the the hydrostatic approach and show that those conditions may prove defective in astrophysical systems such globular clusters. To better understand and illustrate this point, I focus on the study of a model of massive hard sticks in one dimension, which has the advantage of allowing all analytical calculations of various statistical quantities. Thus, I highlight how the mean field type approach can be wrong for some collapsed states.Finally, in an attempt to describe globular clusters, I develop a model consisting of single stars and binaries stars systems. This model reproduces the expected qualitative…

Advisors/Committee Members: Alastuey, Angel (thesis director).

Subjects/Keywords: Physique statistique; Gravitation; Théorie du champ moyen; Statistical mechanics; Gravitation; Mean-field Theory

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APA (6^th Edition):

Champion, M. (2015). Mécanique statistique des systèmes auto-gravitants : Statistical mechanics of self-gravitating systems. (Doctoral Dissertation). Lyon, École normale supérieure. Retrieved from http://www.theses.fr/2015ENSL0997

Chicago Manual of Style (16^th Edition):

Champion, Maxime. “Mécanique statistique des systèmes auto-gravitants : Statistical mechanics of self-gravitating systems.” 2015. Doctoral Dissertation, Lyon, École normale supérieure. Accessed January 21, 2021. http://www.theses.fr/2015ENSL0997.

MLA Handbook (7^th Edition):

Champion, Maxime. “Mécanique statistique des systèmes auto-gravitants : Statistical mechanics of self-gravitating systems.” 2015. Web. 21 Jan 2021.

Vancouver:

Champion M. Mécanique statistique des systèmes auto-gravitants : Statistical mechanics of self-gravitating systems. [Internet] [Doctoral dissertation]. Lyon, École normale supérieure; 2015. [cited 2021 Jan 21]. Available from: http://www.theses.fr/2015ENSL0997.

Council of Science Editors:

Champion M. Mécanique statistique des systèmes auto-gravitants : Statistical mechanics of self-gravitating systems. [Doctoral Dissertation]. Lyon, École normale supérieure; 2015. Available from: http://www.theses.fr/2015ENSL0997

Universitat Rovira i Virgili

23. Daful, Asfaw Gezae. Microscopic modeling of the self assembly of surfactants: shape transitions and critical micelle concentrations.

Degree: Departament de Química Física i Inorgànica, 2011, Universitat Rovira i Virgili

URL: http://hdl.handle.net/10803/33596

► El CMC, tamaño y forma de micelas son características importantes en la determinación de sus principales propiedades y campos de aplicación. Esta tesis tiene dos… (more)

Subjects/Keywords: Micelles; Surfuctants; Monte Carlo simulation; Single Chain mean field Theory; 53; 544; 62

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APA (6^th Edition):

Daful, A. G. (2011). Microscopic modeling of the self assembly of surfactants: shape transitions and critical micelle concentrations. (Thesis). Universitat Rovira i Virgili. Retrieved from http://hdl.handle.net/10803/33596

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):

Daful, Asfaw Gezae. “Microscopic modeling of the self assembly of surfactants: shape transitions and critical micelle concentrations.” 2011. Thesis, Universitat Rovira i Virgili. Accessed January 21, 2021. http://hdl.handle.net/10803/33596.

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

MLA Handbook (7^th Edition):

Daful, Asfaw Gezae. “Microscopic modeling of the self assembly of surfactants: shape transitions and critical micelle concentrations.” 2011. Web. 21 Jan 2021.

Vancouver:

Daful AG. Microscopic modeling of the self assembly of surfactants: shape transitions and critical micelle concentrations. [Internet] [Thesis]. Universitat Rovira i Virgili; 2011. [cited 2021 Jan 21]. Available from: http://hdl.handle.net/10803/33596.

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

Council of Science Editors:

Daful AG. Microscopic modeling of the self assembly of surfactants: shape transitions and critical micelle concentrations. [Thesis]. Universitat Rovira i Virgili; 2011. Available from: http://hdl.handle.net/10803/33596

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

University of Toronto

24. Huang, Xuancheng. Mean-Field Games and Ambiguity Aversion.

Degree: PhD, 2017, University of Toronto

URL: http://hdl.handle.net/1807/80975

► This thesis focuses on incorporating the idea of ambiguity aversion into mean-field games. Intuitively, mean-field games describes the dynamics of a system with an infinite… (more)

▼ This thesis focuses on incorporating the idea of ambiguity aversion into mean-field games. Intuitively, mean-field games describes the dynamics of a system with an infinite population. It is useful in approximating systems with a large population, for which an exact result is computationally intractable. By adding in ambiguity aversion, the mean-field game reflects how players in the population should act if they wish to protect themselves from model misspecification. Two applications of mean-field games are considered through two distinct approaches. The broker execution problem is investigated in a multi-agent framework containing (i) a major agent who is liquidating a large number of shares, (ii) a number of minor agents (high-frequency traders (HFTs)) who search for statistical arbitrage strategies, and (iii) noise traders who buy and sell for exogenous reasons. All optimizing agents (the broker and HFTs) trade against noise traders as well as one another. We use a mean-field game approach to solve the problem and obtain a set of decentralized feedback trading strategies for the major and minor agents. Furthermore, the mean-field game strategies have an ε_N-Nash equilibrium property where ε_N\to0 as N → ∞. The second application focuses on interbank borrowing and lending, which may induce systemic risk into financial markets. A simple model of this is to assume that log-monetary reserves are coupled, and that banks can also borrow/lend from/to a central bank. When all banks optimize their cost of borrowing and lending, this leads to a stochastic game. We account for model uncertainty by recasting the problem as a robust stochastic game and succeed in providing a strategy which leads to a Nash equilibria for both the finite game and the mean-field game limit. We prove that an ε-Nash equilibrium exists and show that when firms are ambiguity-averse, default probabilities can be reduced relative to their ambiguity-neutral counterparts. Finally, this thesis develops a modified stochastic maximum principle for min-max problems, and derives new existence and uniqueness results for a mean-field game with ambiguity averse players. An ε-Nash equilibrium is shown to exist for this class of mean-field games, and the mean-field game equations are explicitly derived in the linear-quadratic framework. Advisors/Committee Members: Jaimungal, Sebastian, Statistics.

Subjects/Keywords: ambiguity aversion; game theory; high frequency trading; mathematical finance; mean-field games; stochastic games; 0463

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APA (6^th Edition):

Huang, X. (2017). Mean-Field Games and Ambiguity Aversion. (Doctoral Dissertation). University of Toronto. Retrieved from http://hdl.handle.net/1807/80975

Chicago Manual of Style (16^th Edition):

Huang, Xuancheng. “Mean-Field Games and Ambiguity Aversion.” 2017. Doctoral Dissertation, University of Toronto. Accessed January 21, 2021. http://hdl.handle.net/1807/80975.

MLA Handbook (7^th Edition):

Huang, Xuancheng. “Mean-Field Games and Ambiguity Aversion.” 2017. Web. 21 Jan 2021.

Vancouver:

Huang X. Mean-Field Games and Ambiguity Aversion. [Internet] [Doctoral dissertation]. University of Toronto; 2017. [cited 2021 Jan 21]. Available from: http://hdl.handle.net/1807/80975.

Council of Science Editors:

Huang X. Mean-Field Games and Ambiguity Aversion. [Doctoral Dissertation]. University of Toronto; 2017. Available from: http://hdl.handle.net/1807/80975

University of Toronto

25. Casgrain, Philippe. Algorithmic Trading with Latent Models and Mean-Field Games.

Degree: PhD, 2019, University of Toronto

URL: http://hdl.handle.net/1807/95757

► This thesis explores how agents should optimally trade in electronic markets when they account for latent factors and the optimal actions of other traders. It… (more)

▼ This thesis explores how agents should optimally trade in electronic markets when they account for latent factors and the optimal actions of other traders. It investigates the problem from the perspective of large-scale stochastic games with incomplete information and populations composed of heterogeneous agents, to which it provides closed form and model-agnostic solutions. The thesis contains two main parts. In the first part, we study the single agent optimal control problem when an agent has incomplete market information. Using the dynamic programming principle and filtration projection techniques we obtain closed-form formulae for the optimal trading strategy for a wide class of latent Markov models. We generalize this problem to an economy where the agent simultaneously trades multiple assets and tracks a stochastic benchmark. Using a novel method based on infinite-dimensional convex analysis we solve the agent’s optimization problem by representing it as the solution to a system of forward-backward stochastic differential equations. This allows both the extension to very general models for asset prices and implicitly provides the existence and uniqueness of solutions to the optimal control problem. In addition, we consider the practical implementation of these latent models and provide algorithms for the estimation of model parameters using expectation-maximization algorithm. In the second part, we consider the case of large populations of heterogeneous agents competing amongst one another on an exchange. We model these as stochastic games with partial and asymmetric information driven by latent semi-martingale price processes. By taking the limit as the population size tends to infinity, we obtain a mean-field game for which we can solve the Nash equilibrium in closed form by generalizing the convex analysis methods developed earlier. We further extend these models to incorporate disagreement amongst agents, represented by their beliefs on the probability measure driving asset prices. Although solutions to the extended model cannot be computed explicitly, we provide a least-square Monte-Carlo based algorithm to approximate the Nash equilibrium. In both cases, we show that the optimal solutions we obtain satisfy an ε-Nash equilibrium property in finite population games. Advisors/Committee Members: Jaimungal, Sebastian, Mathematical Finance.

Subjects/Keywords: Algorithmic Trading; Game Theory; Mathematical Finance; Mean-Field Games; Probability; Stochastic Control; 0364

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

APA (6^th Edition):

Casgrain, P. (2019). Algorithmic Trading with Latent Models and Mean-Field Games. (Doctoral Dissertation). University of Toronto. Retrieved from http://hdl.handle.net/1807/95757

Chicago Manual of Style (16^th Edition):

Casgrain, Philippe. “Algorithmic Trading with Latent Models and Mean-Field Games.” 2019. Doctoral Dissertation, University of Toronto. Accessed January 21, 2021. http://hdl.handle.net/1807/95757.

MLA Handbook (7^th Edition):

Casgrain, Philippe. “Algorithmic Trading with Latent Models and Mean-Field Games.” 2019. Web. 21 Jan 2021.

Vancouver:

Casgrain P. Algorithmic Trading with Latent Models and Mean-Field Games. [Internet] [Doctoral dissertation]. University of Toronto; 2019. [cited 2021 Jan 21]. Available from: http://hdl.handle.net/1807/95757.

Council of Science Editors:

Casgrain P. Algorithmic Trading with Latent Models and Mean-Field Games. [Doctoral Dissertation]. University of Toronto; 2019. Available from: http://hdl.handle.net/1807/95757

26. Yee, Chuck-Hou, 1982-. Towards an ab initio description of correlated materials.

Degree: Physics and Astronomy, 2012, Rutgers University

URL: http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000067031

Subjects/Keywords: Mean field theory; Density functionals

…bosons for the Anderson Impurity Model . . . . . . 129 C.1. Review of Mean-field theory… …dynamical mean-field theory (DMFT). Historically, the formulation was taken in two steps… …heavy fermions, nickelates, and cuprates. 10 Chapter 2 Dynamical Mean-Field Theory The… …dynamical mean-field theory (DMFT) approach to treating strongly-correlated systems… …consistently determined effective medium [7, 8]. It is a mean-field theory in that inter…

10 more images…

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APA (6^th Edition):

Yee, Chuck-Hou, 1. (2012). Towards an ab initio description of correlated materials. (Thesis). Rutgers University. Retrieved from http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000067031

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):

Yee, Chuck-Hou, 1982-. “Towards an ab initio description of correlated materials.” 2012. Thesis, Rutgers University. Accessed January 21, 2021. http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000067031.

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

MLA Handbook (7^th Edition):

Yee, Chuck-Hou, 1982-. “Towards an ab initio description of correlated materials.” 2012. Web. 21 Jan 2021.

Vancouver:

Yee, Chuck-Hou 1. Towards an ab initio description of correlated materials. [Internet] [Thesis]. Rutgers University; 2012. [cited 2021 Jan 21]. Available from: http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000067031.

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

Council of Science Editors:

Yee, Chuck-Hou 1. Towards an ab initio description of correlated materials. [Thesis]. Rutgers University; 2012. Available from: http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000067031

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

Purdue University

27. Harrison, Aaron. Detailed Investigations of Capillary and van der Waals Forces in the Adhesion between Solids.

Degree: PhD, Chemical Engineering, 2015, Purdue University

URL: https://docs.lib.purdue.edu/open_access_dissertations/1114

► The primary focus of this dissertation is on characterizing two fundamental forces common to adhesion between solids: capillary and van der Waals forces. These two… (more)

Subjects/Keywords: Capillary Forces; Hamaker Constants; Kelvin Equation; mean-field density functional theory; Photothermal Induced Resonace

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APA (6^th Edition):

Harrison, A. (2015). Detailed Investigations of Capillary and van der Waals Forces in the Adhesion between Solids. (Doctoral Dissertation). Purdue University. Retrieved from https://docs.lib.purdue.edu/open_access_dissertations/1114

Chicago Manual of Style (16^th Edition):

Harrison, Aaron. “Detailed Investigations of Capillary and van der Waals Forces in the Adhesion between Solids.” 2015. Doctoral Dissertation, Purdue University. Accessed January 21, 2021. https://docs.lib.purdue.edu/open_access_dissertations/1114.

MLA Handbook (7^th Edition):

Harrison, Aaron. “Detailed Investigations of Capillary and van der Waals Forces in the Adhesion between Solids.” 2015. Web. 21 Jan 2021.

Vancouver:

Harrison A. Detailed Investigations of Capillary and van der Waals Forces in the Adhesion between Solids. [Internet] [Doctoral dissertation]. Purdue University; 2015. [cited 2021 Jan 21]. Available from: https://docs.lib.purdue.edu/open_access_dissertations/1114.

Council of Science Editors:

Harrison A. Detailed Investigations of Capillary and van der Waals Forces in the Adhesion between Solids. [Doctoral Dissertation]. Purdue University; 2015. Available from: https://docs.lib.purdue.edu/open_access_dissertations/1114

Delft University of Technology

28. Devriendt, Karel (author). Structure and dynamics of complex networks: Network epidemics and a geometric robustness measure.

Degree: 2017, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:00b2ef38-02d0-4bf2-90ef-bfc38f928da8

► As new technologies continue to find their way into everyday life, the world becomes more and more connected. Airplanes and other means of transportation provide… (more)

▼ As new technologies continue to find their way into everyday life, the world becomes more and more connected. Airplanes and other means of transportation provide global connections in the physical world, while the omnipresence of the Internet means that information is shared around the globe, easier than ever before. But not only these man-made systems are distinctly connected, other complex systems like the human brain, or metabolic networks are successfully being studied from the perspective of their constituting connections. The combining concept in all these examples is the structure of the problem at hand: each system consists of interacting elementary components at the lowest level, from which a network structure emerges at the global level. The study of such networked systems, their observed features and the wide range of related analysis tools is commonly referred to as Network Science. In this thesis, the specific problem of how diseases spread over networks is addressed. Better understanding this spreading behavior has significant practical importance, i.e. for the prediction and control of disease prevalence, and poses many interesting theoretical challenges. In the context of modeling epidemics on networks, we formulate the Universal Mean-Field Framework. This new and theoretically well-founded framework unifies and generalizes a number of existing approximate models, and brings forth new approaches to bound the approximations. Apart from the work on epidemics, some new insights are explored in the context of the connections between electrical circuits, networks and simplices (higher-dimensional triangles). These deep theoretical equivalences allow the tools and intuitions from electrical circuits and geometry to be used in the study of networks. A comprehensive introduction and discussion of the equivalent representations and their connections is given. Additionally, we derive a new formula for the volume of a hyperacute simplex and propose to use this volume as a network-robustness measure. Advisors/Committee Members: Van Mieghem, Piet (mentor), Delft University of Technology (degree granting institution).

Subjects/Keywords: complex networks; SIS epidemics; mean-field theory; network robustness; effective resistance; spectral graph theory; Laplacian matrix; graph theory

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APA (6^th Edition):

Devriendt, K. (. (2017). Structure and dynamics of complex networks: Network epidemics and a geometric robustness measure. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:00b2ef38-02d0-4bf2-90ef-bfc38f928da8

Chicago Manual of Style (16^th Edition):

Devriendt, Karel (author). “Structure and dynamics of complex networks: Network epidemics and a geometric robustness measure.” 2017. Masters Thesis, Delft University of Technology. Accessed January 21, 2021. http://resolver.tudelft.nl/uuid:00b2ef38-02d0-4bf2-90ef-bfc38f928da8.

MLA Handbook (7^th Edition):

Devriendt, Karel (author). “Structure and dynamics of complex networks: Network epidemics and a geometric robustness measure.” 2017. Web. 21 Jan 2021.

Vancouver:

Devriendt K(. Structure and dynamics of complex networks: Network epidemics and a geometric robustness measure. [Internet] [Masters thesis]. Delft University of Technology; 2017. [cited 2021 Jan 21]. Available from: http://resolver.tudelft.nl/uuid:00b2ef38-02d0-4bf2-90ef-bfc38f928da8.

Council of Science Editors:

Devriendt K(. Structure and dynamics of complex networks: Network epidemics and a geometric robustness measure. [Masters Thesis]. Delft University of Technology; 2017. Available from: http://resolver.tudelft.nl/uuid:00b2ef38-02d0-4bf2-90ef-bfc38f928da8

Princeton University

29. Cerenzia, Mark Joseph. Integrable models, Coulomb interactions, and mean field game theory .

Degree: PhD, 2019, Princeton University

URL: http://arks.princeton.edu/ark:/88435/dsp01rn3014305

► Random matrix statistics emerge in a broad class of strongly correlated systems, with evidence suggesting they can play a universal role comparable to the one… (more)

Subjects/Keywords: dynamic game theory; mathematical physics; mean field game theory; partial differential equations; probability; random matrix theory

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APA (6^th Edition):

Cerenzia, M. J. (2019). Integrable models, Coulomb interactions, and mean field game theory . (Doctoral Dissertation). Princeton University. Retrieved from http://arks.princeton.edu/ark:/88435/dsp01rn3014305

Chicago Manual of Style (16^th Edition):

Cerenzia, Mark Joseph. “Integrable models, Coulomb interactions, and mean field game theory .” 2019. Doctoral Dissertation, Princeton University. Accessed January 21, 2021. http://arks.princeton.edu/ark:/88435/dsp01rn3014305.

MLA Handbook (7^th Edition):

Cerenzia, Mark Joseph. “Integrable models, Coulomb interactions, and mean field game theory .” 2019. Web. 21 Jan 2021.

Vancouver:

Cerenzia MJ. Integrable models, Coulomb interactions, and mean field game theory . [Internet] [Doctoral dissertation]. Princeton University; 2019. [cited 2021 Jan 21]. Available from: http://arks.princeton.edu/ark:/88435/dsp01rn3014305.

Council of Science Editors:

Cerenzia MJ. Integrable models, Coulomb interactions, and mean field game theory . [Doctoral Dissertation]. Princeton University; 2019. Available from: http://arks.princeton.edu/ark:/88435/dsp01rn3014305

University of Oulu

30. Samarakoon, S. (Sumudu). Learning-based methods for resource allocation and interference management in energy-efficient small cell networks.

Degree: 2017, University of Oulu

URL: http://urn.fi/urn:isbn:9789526216874

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Abstract Resource allocation and interference management in wireless small cell networks have been areas of key research interest in the past few years. Although a… (more)

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Abstract Resource allocation and interference management in wireless small cell networks have been areas of key research interest in the past few years. Although a large number of research studies have been carried out, the needs for high capacity, reliability, and energy efficiency in the emerging fifth-generation (5G) networks warrants the development of methodologies focusing on ultra-dense and self-organizing small cell network (SCN) scenarios. In this regard, the prime motivation of this thesis is to propose an array of distributed methodologies to solve the problem of joint resource allocation and interference management in SCNs pertaining to different network architectures. The present dissertation proposes and investigates distributed control mechanisms for wireless SCNs mainly in three cases: a backhaul-aware interference management mechanism of the uplink of wireless SCNs, a dynamic cluster-based approach for maximizing the energy efficiency of dense wireless SCNs, and a joint power control and user scheduling mechanism for optimizing energy efficiency in ultra-dense SCNs. Optimizing SCNs, especially in the ultra-dense regime, is extremely challenging due to the severe coupling in interference and the dynamics of both queues and channel states. Moreover, due to the lack of inter-base station/cluster communications, smart distributed learning mechanisms are required to autonomously choose optimal transmission strategies based on local information. To overcome these challenges, an array of distributed algorithms are developed by combining the tools from machine learning, Lyapunov optimization and mean-field theory. For each of the above proposals, extensive sets of simulations have been carried out to validate the performance of the proposed methods compared to conventional models that fail to account for the limitations due to network scale, dynamics of queue and channel states, backhaul heterogeneity and capacity constraints, and the lack of coordination between network elements. The results of the proposed methods yield significant gains of the proposed methods in terms of energy savings, rate improvements, and delay reductions compared to the conventional models studied in the existing literature.

Tiivistelmä Langattomien piensoluverkkojen resurssien allokointi ja häiriön hallinta on ollut viime vuosina tärkeä tutkimuskohde. Tutkimuksia on tehty paljon, mutta uudet viidennen sukupolven (5G) verkot vaativat suurta kapasiteettia, luotettavuutta ja energiatehokkuutta. Sen vuoksi on kehitettävä menetelmiä, jotka keskittyy ultratiheisiin ja itseorganisoituviin piensoluverkkoihin. (SCN). Tämän väitöskirjan tärkein tavoite onkin esittää joukko hajautettuja menetelmiä piensoluverkkojen yhteisten resurssien allokointiin ja häiriön hallintaan, kun käytössä on erilaisia verkkoarkkitehtuureja. Tässä väitöskirjassa ehdotetaan ja tutkitaan hajautettuja menetelmiä langattomien piensoluverkkojen hallintaan kolmessa eri tilanteessa: välityskanavan huomioiva häiriönhallinta menetelmä langattomissa piensoluverkoissa,…

Advisors/Committee Members: Latva-aho, M. (Matti), Bennis, M. (Mehdi).

Subjects/Keywords: Lyapunov optimization; base station clustering; distributed learning algorithm; mean-field game theory; ultra-dense deployment; Lyapunovin optimointi; hajautettu oppimisalgoritmi; mean-field-peliteoria; tukiasemaklusterit; ultratiheä teknologia

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

APA (6^th Edition):

Samarakoon, S. (. (2017). Learning-based methods for resource allocation and interference management in energy-efficient small cell networks. (Doctoral Dissertation). University of Oulu. Retrieved from http://urn.fi/urn:isbn:9789526216874

Chicago Manual of Style (16^th Edition):

Samarakoon, S (Sumudu). “Learning-based methods for resource allocation and interference management in energy-efficient small cell networks.” 2017. Doctoral Dissertation, University of Oulu. Accessed January 21, 2021. http://urn.fi/urn:isbn:9789526216874.

MLA Handbook (7^th Edition):

Samarakoon, S (Sumudu). “Learning-based methods for resource allocation and interference management in energy-efficient small cell networks.” 2017. Web. 21 Jan 2021.

Vancouver:

Samarakoon S(. Learning-based methods for resource allocation and interference management in energy-efficient small cell networks. [Internet] [Doctoral dissertation]. University of Oulu; 2017. [cited 2021 Jan 21]. Available from: http://urn.fi/urn:isbn:9789526216874.

Council of Science Editors:

Samarakoon S(. Learning-based methods for resource allocation and interference management in energy-efficient small cell networks. [Doctoral Dissertation]. University of Oulu; 2017. Available from: http://urn.fi/urn:isbn:9789526216874

Open Access Theses and Dissertations