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1

Esposito, Massimiliano. "Kinetic theory for quantum nanosystems." Doctoral thesis, Universite Libre de Bruxelles, 2004. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211088.

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In this thesis, we investigate the emergence of kinetic processes in finite quantum systems. We first generalize the Redfield theory to describe the dynamics of a small quantum system weakly interacting with an environment of finite heat capacity. We then study in detail the spin-GORM model, a model made of a two-level system interacting with a random matrix environment. By doing this, we verify our new theory and find a critical size of the environment over which kinetic processes occur. We finally study the emergence of a diffusive transport process, on a finite tight-binding subsystem interacting with a fast environment, when the size of subsystem exceeds a critical value.
Doctorat en sciences, Spécialisation chimie
info:eu-repo/semantics/nonPublished
2

Sze, Pui King Ivy. "Conservation laws in recombination kinetic theory." Thesis, University of British Columbia, 1986. http://hdl.handle.net/2429/26089.

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The hydrodynamic equations of change for a reacting gas mixture of monomers and dimers are studied. The gas is considered to be dilute and described by the kinetic theory of Lowry and Snider (J. Chem. Phys. 61, 2320 (1974)). From the kinetic equations for the density operators representing the monomer and dimer, the equations of change for one-molecule observables are obtained. Since the energy operator involves the intermolecular potential energy, it is necessary to derive the energy balance equation from the von Neumann equation, since this includes molecule-molecule correlations. As well, the kinetic theory formulated by Lowry and Snider is rewritten so that rearrangement collisions are emphasized. A collisional sum rule is derived involving the commutation properties of channel projectors and their respective potentials. A known property of the optical theorem is that it identifies the reactive loss terms as part of the non-reactive transition superoperators. The sum rule is applied to rewrite the non-reactive transition superoperators so as to display the reactive loss terms. This aids in establishing conservation laws for the physical observables of mass, linear momentum, angular momentum and energy. A form of the optical theorem in which kinetic energy off-diagonality is allowed for is also derived. Both the optical theorem and the sum rule are based on the strong orthogonality hypothesis, which plays a fundamental role in the Lowry-Snider theory. On localising the physical attributes at the centres of mass of the molecules, the contributions to the equations of change from collisional transfer (due to the forces and torques between the collision partners) and from the transfer of the physical attributes from the reactants to the products are identified. The transformation of dimer internal degrees of freedom into monomer translational degrees of freedom or vice versa when a dimer Is dissociated or formed is found to contribute to the equations of change by virtue of the differing locality of the collision partners. The decomposition of the kinetic energy operator into its components for radial and rotational motions allows the kinetic energy flux contributions associated with the pressure tensor and the molecular angular momentum flux to be identified.
Science, Faculty of
Chemistry, Department of
Graduate
3

Valougeorgis, Dimitris V. "The Fn method in kinetic theory." Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/49949.

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A complete formulation of the recently developed. FN method in kinetic theory is presented and the accuracy of this advanced semi-analytical-numerical technique is demonstrated by testing the method to several classical problems in rarefied gas dynamics. The method is based on the existing analysis for the vector transport equation arising from the decomposition of the linearized BGK equation. Using full-range orthogonality, a system of singular integral equations for the distribution functions at the boundaries is established. The unknown distribution functions are then approximated by a finite expansion in terms of a set of basis functions and the coefficients of the expansion are found by requiring the set of the reduced algebraic equations to be satisfied at certain collocation points. By studying the half-space heat transfer and weak evaporation problems and the problem of heat transfer between two parallel plates it is demonstrated that the FN method is a viable solution technique yielding results of benchmark accuracy. Two different sets of basis functions are provided for half-space and finite media problems, respectively. In all cases, highly accurate numerical results are computed and compared to existing exact solutions. The obtained numerical results help in judging the accuracy to expect of the method and indicate that the FN method may be applied with confidence to problems for which, more exact methods of analysis do not appear possible. Then, the cylindrical Poiseuille flow and thermal creep problems, which are not amenable to exact treatment, are solved. The FN method is formulated and tested successfully for the first time in cylindrical geometry in kinetic theory. The complete solution of the two aforementioned problems is presented with the numerical results quoted as converged being of reference-quality good for benchmark accuracy.
Ph. D.
incomplete_metadata
4

Windfäll, Åsa. "Some Problems in Kinetic Theory and Applications." Doctoral thesis, Karlstads universitet, Avdelningen för matematik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-8498.

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This thesis consists of four papers. the first is devoted to discrete velocity models, the second to hydrodynamic equation beyond Navier-Stokes level, the third to a multi-linear Maxwell model for economic or social dynamics and the fourth is devoted to a function related to the Riemann zeta-function. In Paper 1, we consider the general problem of construction and classification of normal, i.e. without spurious invariants, discrete velocity models (DVM) of the classical Boltzman equation. We explain in detail how this problem can be solved and present a complete classification of normal plane DVMs with relatively small number n of velocities (n≤10). Some results for models with larger number of velocities are also presented. In Paper 2, we discuss hydrodynamics at the Burnett level. Since the Burnett equations are ill-posed, we describe how to make a regularization of these. We derive the well-posed generalized Burnett equations (GBEs) and discuss briefly an optimal choice of free parameters and consider a specific version of these equations. Finally we prove linear stability for GBE and present some numerical result on the sound propagationbased on GBEs. In Paper 3, we study a Maxwell kinetic model of socio-economic behavior. The model can predict a time dependent distribution of wealth among the participants in economic games with an arbitrary, but sufficiently large, number of players. The model depends on three different positive parameters {γ,q,s} where s and q are fixed by market conditions and γ is a control parameter. In particular, we investigate the efficiency of control. Some exact solutions and numerical examples are presented. In Paper 4, we study a special function u(s,x), closely connected to the Riemann zeta-function ζ(s), where s is a complex number. We study in detail the properties of u(s,x) and in particular the location of its zeros s(x), for various x≥0. For x=0 the zeros s(0) coincide with non-trivial zeros of ζ(s). We perform a detailed numerical study of trajectories of various zeros s(x) of u(s,x).
5

SAMUDRA, SAMEER D. "KINETIC THEORY APPROACH TO PLASMA HEAT TRANSFER." University of Cincinnati / OhioLINK, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=ucin990028080.

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6

Lee, Koun-Ken. "Kinetic theory of strongly coupled electron-phonon systems." Thesis, University of Cambridge, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.615952.

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7

Vardulakis, George. "Superconducting kinetic inductance detectors : theory, simulations & experiments." Thesis, University of Cambridge, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.613121.

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8

Zhang, Ziji. "Theoretical and computational study of coupling of soot, gas kinetics and radiation in diffusion flames using reduced mechanisms /." Digital version accessible at:, 1998. http://wwwlib.umi.com/cr/utexas/main.

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9

Tronci, Cesare. "Geometric dynamics of Vlasov kinetic theory and its moments." Thesis, Imperial College London, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.486660.

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The Vlasov equation of kinetic theory is introduced and the Hamiltonian structure of its moments is presented. Then we focus on the geodesic evolution of the Vlasov moments [1.2]. As a first step, these moment equations generalize the Camassa-Holm equation [3] to its multi-component version [4]. Subsequently, adding electrostatic forces to the geodesic moment equations relates them to the Benney equations [5] and to the equations for beam dynamics in particle accelerators. Next, we develop a kinetic theory for self assembly in nano-particles. The Darcy law [6] is introduced as a general principle for aggregation dynamics in friction dominated systems (at different scales). Then, a kinetic equation is introduced [7,8] for the dissipative motion of isotropic nano-particles. The zeroth-moment dynamics of this equation recovers the classical Darcy law at the macroscopic level [7]. A kinetic-theory description for oriented nano-particles is also presented [9]. At the macroscopic level, the zeroth moments of this kinetic equation recover the magnetization dynamics of the Landau-Lifshitz-Gilbert equation [10]. The moment equations exhibit the spontaneous emergence of singular solutions (clumpons) that finally merge in one singularity. This behaviour represents aggregation and alignment of oriented nano-particles. Finally, the Smoluchowsky description is derived from the dissipative Vlasov equation for anisotropic interactions. Various levels of approximate Smoluchowsky descriptions are proposed as special cases of the general treatment. As a result, the macroscopic momentum emerges as an additional dynamical variable that in general cannot be neglected.
10

Geist, Wolfgang. "Kinetic theory of evaporative cooling of trapped atomic gases." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/29394.

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11

Kim, Hyeon-Deuk. "Local nonequilibrium effects in kinetic theory : The Boltzmann equation." Kyoto University, 2004. http://hdl.handle.net/2433/64954.

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Abstract:
Kyoto University (京都大学)
0048
新制・課程博士
博士(人間・環境学)
甲第10956号
人博第243号
15||198(吉田南総合図書館)
新制||人||60(附属図書館)
UT51-2004-G803
京都大学大学院人間・環境学研究科人間・環境学専攻
(主査)教授 冨田 博之, 助教授 早川 尚男, 助教授 阪上 雅昭
学位規則第4条第1項該当
12

Strain, Robert Mills. "Some applications of an energy method in collisional kinetic theory /." View online version; access limited to Brown University users, 2005. http://wwwlib.umi.com/dissertations/fullcit/3174679.

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13

Imamovi´c-Tomasovi´c, Milena. "Kadanoff-Baym kinetic theory for a trapped Bose-condensed gas." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ63751.pdf.

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14

Dai, Rongqing. "Granular flow studies through kinetic theory and numerical simulation approaches." Thesis, McGill University, 1993. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=41566.

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The investigations of three different topics of granular flows are reported in this thesis. (i) Second order solutions for granular simple shear flows are derived in the framework of granular kinetic theory. Compared to the first order solutions and the inconsistent second order solutions, the second order solutions of the present study provide better predictions of the numerical simulation results. (ii) Granular shear flows within narrow gaps and unbounded fields are studied by a molecular dynamics type discrete element simulation method. The effects of inelasticity and mean solids fraction on the distributions of granular temperatures, solids fractions and number densities of particle centers, and local mean velocities are examined. The slip velocities of bounded shear flows are calculated and the results are compared with the predictions of existing theories. (iii) Granular self-diffusion is investigated through both a kinetic theory and numerical simulation approaches by employing the time correlation function expression to determine the diffusion coefficient. The theoretical predictions agree very well with the simulation results for smooth particles at low concentrations, but at high concentrations the kinetic theory diffusion coefficients are lower than those determined in the computer simulations. The surface friction effect is examined numerically, and it is found that rough particles are less diffusive than smooth ones.
15

Haran, Joshi C. "Kinetic theory approach for the determination of rate of evaporation." Thesis, University of Huddersfield, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.430292.

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The problem of liquid evaporating/condensing from/to its surface is of importance in a wide variety of engineering applications. These can be classified into naturally occurring processes and those that came out of technological advancement. Of the naturally occurring processes the important problems are loss of water due to evaporation in dams, evaporation from moist material to dry it, condensation in droplets required for cloud formation etc. The processes which became important due to technological advancement are evaporation in freeze drying processes, evaporation and condensation required to produce thin films using vacuum coating techniques, drying processes required at ordinary temperatures and pressure to prevent chemical degradation at high temperature and the evaporation process which produce the cooling effect in evaporative cooling towers. The problem in which continuum concepts are valid are analysed using the Fick's Diffusion model. It involves the experimental determination of the diffusion coefficient in each case. Cases where evaporation took place under free molecular regime could not be analysed using the Fick's model. In the present study a Kinetic Theory approach is made to analyse the problem. The analysis is made in two stages. In the first stage, the evaporation from a free liquid surface to its own vapour is studied. In the second stage the study is extended to the case where noncondensable gas is also present along with the vapour. The analysis is carried out using the Boltzmann transport equation. The collision terms in the equation are obtained using the model suggested by Bhatnagar Gross and Krook and now known as the BGK equation. The numerical schemes are developed for both the cases and solutions are obtained for the net rate of evaporation. The distribution of temperature, pressure and molecular number density are also plotted for the region close to the interface. The evaporation coefficient introduced in the theoretical model is obtained by comparison with experimental data. Experiments are conducted with water as the fluid and nitrogen as the inert gas. The correlations are made and the results are presented. The evaporation coefficient was found to be in the range 0.0005 to 0.0007 for the single component case and for the twocomponent case it is found to be in the range 0.0009 to 0.00135. These values can be used for engineering design applications
16

Gräns, Samuelsson Linnéa. "Conservation laws in kinetic theory for spin-1/2 particles." Thesis, Umeå universitet, Institutionen för fysik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-110967.

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In this thesis a kinetic theory for spin-1/2 particles is given a brief overview, focusing on the derivation of an evolution equation for the quasiprobability distribution function used in the theory to describe certain types of quantum plasma. The current theory is expanded upon by exploring conservation laws. A local conservation law for momentum is derived using two different expressions for electromagnetic momentum, given by Abraham and Minkowski respectively. There has been some controversy over which of these expressions should be used; in the case considered here the expression given by Minkowski seems to be more suitable. Based on the conservation law for momentum, a conservation law for angular momentum is also derived.
17

Al-Naseri, Haidar. "Quantum kinetic relativistic theory of linearized waves in magnetized plasmas." Thesis, Umeå universitet, Institutionen för fysik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-150292.

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In this work we have studied linear wave propagation in magnetized plasmas using a fully relativistic kinetic equation of spin-1/2 particles in the long scale approximation. The linearized kinetic equation is very long and complicated, hence we worked with restricted geometries in order to simplify the calculations. The dispersion relation of the relativistic model was calculated and compared with a dispersion relation from a previous work at the semi-relativistic limit. Moreover, a new mode was discovered that survives in the zero temperature limit. The origin of the mode in the kinetic equation was discussed and derived from a non-relativistic kinetic equation from a previous work.
18

Mulzet, Alfred Kenric. "Exponential Stability for a Diffusion Equation in Polymer Kinetic Theory." Diss., Virginia Tech, 1997. http://hdl.handle.net/10919/30473.

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In this paper we present an exponential stability result for a diffusion equation arising from dumbbell models for polymer flow. Using the methods of semigroup theory, we show that the semigroup U(t) associated with the diffusion equation is well defined and that all solutions converge exponentially to an equilibrium solution. Both finitely and infinitely extensible dumbbell models are considered. The main tool in establishing stability is the proof of compactness of the semigroup.
Ph. D.
19

Molloy, Charles T. Whitham G. B. "Contributions to the kinetic theory of traffic flow with queuing /." Diss., Pasadena, Calif. : California Institute of Technology, 1985. http://resolver.caltech.edu/CaltechETD:etd-03262008-101545.

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20

Lun, Cliff Ki Keung. "Kinetic theories of granular flow." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=73989.

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21

Vinerean, Mirela Christina. "Classification of Normal Discrete Kinetic Models." Licentiate thesis, Karlstad University, Division for Engineering Sciences, Physics and Mathematics, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-2431.

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“In many interesting papers on discrete velocity models (DVMs), authors postulate from the beginning that the finite velocity space with "good" properties is given and only after this step they study the Discrete Boltzmann Equation. Contrary to this approach, our aim is not to study the equation, but to discuss all possible choices of finite phase spaces (sets) satisfying this type of "good" restrictions. Due to the velocity discretization it is well known that it is possible to have DVMs with "spurious" summational invariants (conservation laws which are not linear combinations of physical invariants). Our purpose is to give a method for constructing normal models (without spurious invariants) and to classify all normal plane models with small number of velocities (which usually appear in applications). On the first step we describe DKMs as algebraic systems. We introduce for this an abstract discrete model (ADM) which is defined by a matrix of reactions (the same as for the concrete model). This matrix contains as rows all vectors of reactions describing the "jump" from a pre-reaction state to a new reaction state. The conservation laws corresponding to the many-particle system are uniquely determined by the ADM and do not depend on the concrete realization. We find the restrictions on ADM and then we give a general method of constructing concrete normal models (using the results on ADMs). Having the general algorithm, we consider in more detail, the particular cases of models with mass and momentum conservation (inelastic lattice gases with pair collisions) and models with mass, momentum and energy conservation (elastic lattice gases with pair collisions).”

22

Vinerean, Mirela Cristina. "Discrete Kinetic Models and Conservation Laws." Doctoral thesis, Karlstads universitet, Institutionen för ingenjörsvetenskap, fysik och matematik, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-2407.

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Classical kinetic theory of gases is based on the Boltzmann equation (BE) which describes the evolution of a system of particles undergoing collisions preserving mass, momentum and energy. Discretization methods have been developed on the idea of replacing the original BE by a finite set of nonlinear hyperbolic PDEs corresponding to the densities linked to a suitable finite set of velocities. One open problem related to the discrete BE is the construction of normal (fulfilling only physical conservation laws) discrete velocity models (DVMs). In many papers on DVMs, authors postulate from the beginning that a finite velocity space with such "good" properties is given, and after this step, they study the discrete BE. Our aim is not to study the equations for DVMs, but to discuss all possible choices of finite phase spaces (sets) satisfying this type of "good" restrictions. We start by introducing the most general class of discrete kinetic models (DKMs) and then, develop a general method for the construction and classification of normal DKMs. We apply this method in the particular cases of DVMs of the inelastic BE (where we show that all normal models can be explicitly described) and elastic BE (where we give a complete classification of normal models up to 9 velocities). Using our general approach to DKMs and our results on normal DVMs for a single gas, we develop a method for the construction of the most natural (from physical point of view) subclass of normal DVMs for binary gas mixtures. We call such models supernormal models (SNMs). We apply this method and obtain SNMs with up to 20 velocities and their spectrum of mass ratio. Finally, we develop a new method that can lead, by symmetric transformations, from a given normal DVM to extended normal DVMs. Many new normal models can be constructed in this way, and we give some examples to illustrate this.
23

Liu, Hongwei. "Gas-kinetic methods for viscous fluid flows /." View abstract or full-text, 2007. http://library.ust.hk/cgi/db/thesis.pl?MATH%202007%20LIU.

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24

Merino, Aceituno Sara. "Contributions in fractional diffusive limit and wave turbulence in kinetic theory." Thesis, University of Cambridge, 2015. https://www.repository.cam.ac.uk/handle/1810/256994.

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This thesis is split in two different topics. Firstly, we study anomalous transport from kinetic models. Secondly, we consider the equations coming from weak wave turbulence theory and we study them via mean-field limits of finite stochastic particle systems. $\textbf{Anomalous transport from kinetic models.}$ The goal is to understand how fractional diffusion arises from kinetic equations. We explain how fractional diffusion corresponds to anomalous transport and its relation to the classical diffusion equation. In previous works it has been seen that particles systems undergoing free transport and scattering with the media can give rise to fractional phenomena in two cases: firstly, if in the dynamics of the particles there is a heavy-tail equilibrium distribution; and secondly, if the scattering rate is degenerate for small velocities. We use these known results in the literature to study the emergence of fractional phenomena for some particular kinetic equations. Firstly, we study BGK-type equations conserving not only mass (as in previous results), but also momentum and energy. In the hydrodynamic limit we obtain a fractional diffusion equation for the temperature and density making use of the Boussinesq relation and we also demonstrate that with the same rescaling fractional diffusion cannot be derived additionally for the momentum. But considering the case of conservation of mass and momentum only, we do obtain the incompressible Stokes equation with fractional diffusion in the hydrodynamic limit for heavy-tailed equilibria. Secondly, we will study diffusion phenomena arising from transport of energy in an anharmonic chain. More precisely, we will consider the so-called FPU-$\beta$ chain, which is a very simple model for a one-dimensional crystal in which atoms are coupled to their nearest neighbours by a harmonic potential, weakly perturbed by a nonlinear quartic potential. The starting point of our mathematical analysis is a kinetic equation; lattice vibrations, responsible for heat transport, are modelled by an interacting gas of phonons whose evolution is described by the Boltzmann Phonon Equation. Our main result is the derivation of an anomalous diffusion equation for the temperature. $\textbf{Weak wave turbulence theory and mean-field limits for stochastic particle systems.}$ The isotropic 4-wave kinetic equation is considered in its weak formulation using model homogeneous kernels. Existence and uniqueness of solutions is proven in a particular setting. We also consider finite stochastic particle systems undergoing instantaneous coagulation-fragmentation phenomena and give conditions in which this system approximates the solution of the equation (mean-field limit).
25

Ben, Dhia Zakaria. "Novel Treatments for Multi-phase Flow Prediction Inspired By Kinetic Theory." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/34924.

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This study entails an investigation of a novel moment closure, originally constructed for rarefied-gas prediction, to the modelling of inert, dilute, disperse, particle flows. Such flows are important in many engineering situations. As one example, in internal-combustion engines, fuel is often injected as a spray of tiny droplets and, during combustion, a cloud of tiny soot particles can be formed. These particle phases are often difficult to model, especially when particles display a range of velocities at each location in space. Lagrangian methods are often too costly and many Eulerian field-based methods suffer from model deficiencies and mathematical artifacts. Often, Eulerian formulations assume that all particles at a location and time have the same velocity. This assumption leads to nonphysical results, including an inability to predict particle paths crossing and a limited number of boundary conditions that can be applied. The typical multi-phase situation of many particles is, in many ways, similar to that of a gas compressed of a huge number of atoms or molecules. It is therefore expected that powerful techniques from the kinetic theory of gases could be applied. This work explores the advantages of using a modern fourteen-moment model, originally derived for rarefied gases, to predict multi-phase flows. Details regarding the derivation, the mathematical structure, and physical behaviour of the resulting model are explained. Finally, a numerical implementation is presented and results for several flow problems that are designed to demonstrate the fundamental behaviour of the models are presented. Comparisons are made with other classical models.
26

Napier, Duncan George. "Far-from-equilibrium gas kinetic theory : reactive systems and sound propagation." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq25127.pdf.

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27

Khambekar, Jayant Vijay. "Kinetic Theory for Anisotropic Thermalization and Transport of Vibrated Granular Material." Digital WPI, 2007. https://digitalcommons.wpi.edu/etd-dissertations/246.

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The purpose of this work is to develop a continuum theory that may be used to predict the effects of anisotropic boundary vibrations on loose granular assemblies. In order to do so, we extend statistical averaging techniques employed in the kinetic theory to derive an anisotropic flow theory for rapid, dense flows of identical, inelastic spheres. The theory is anisotropic in the sense that it treats the full second moment of velocity fluctuations, rather than only its isotropic piece, as a mean field to be determined. In this manner, the theory can, for example, predict granular temperatures that are different in different directions. The flow theory consists of balance equations for mass, momentum, and full second moment of velocity fluctuations, as well as constitutive relations for the pressure tensor, the flux of second moment, and the source of second moment. The averaging procedure employed in deriving the constitutive relations is based on a Maxwellian that is perturbed due to the presence of a deviatoric second and full third moment of velocity fluctuations. Because the theory is anisotropic, it can predict the normal stress differences observed in granular shear flows, as well as the evolution to isotropy in an assembly with granular temperatures that are initially highly anisotropic. In order to complement the theory, we employ similar statistical techniques to derive boundary conditions that ensure that the flux of momentum as well as the flux of second moment are balanced at the vibrating boundary. The bumps are hemispheres arranged in regular arrays, and the fluctuating boundary motion is described by an anisotropic Maxwellian distribution function. The bumpiness of the surface may be adjusted by changing the size of the hemispheres, the spacing between the hemispheres in two separate array-directions, and the angle between the two directions. Statistical averaging consistent with the constitutive theory yields the rates at which momentum and full second moment are transferred to the flow. In order to present results in a form that is easy to interpret physically, the statistical parameters that describe the boundary fluctuations are related in a plausible manner to amplitudes and frequencies of sinusoidal vibrations that may differ in three mutually perpendicular directions, and to phase angles that may be adjusted between the three directions of vibration. The focus of the results presented here is on the steady response of unconfined granular assemblies that are thermalized and driven by horizontal bumpy vibrating boundaries. In a first detailed study of the effects of the boundary geometry and boundary motion on the overall response of the assemblies, the anisotropic theory is reduced to a more familiar isotropic form. The resulting theory predicts the manner in which the profiles of isotropic granular temperature and solid volume fraction as well as the uniform velocity and corresponding flow rate vary with spacings between the bumps, angle of the bump-array, energy of vibration, direction of vibration, and phase angles of the vibration. In a second study, we solve the corresponding, but more elaborate, boundary value problem for anisotropic flows induced by anisotropic boundary vibrations. The main focus in presenting these results is on the differences between granular temperatures in three perpendicular directions normal and tangential to the vibrating surface, and how each is affected by the bumpiness of the boundary and the direction of the vibration. In each case, we calculate the corresponding nonuniform velocity profile, solid volume fraction profile, and mass flow rate.
28

Matsui, Tatsuki. "Kinetic theory and simulation of collisionless tearing in bifurcated current sheets." Diss., University of Iowa, 2008. http://ir.uiowa.edu/etd/38.

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29

Que, Yin Tik. "BGK kinetic scheme for the shallow-water equations /." View Abstract or Full-Text, 2003. http://library.ust.hk/cgi/db/thesis.pl?MATH%202003%20QUE.

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Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003.
Includes bibliographical references (leaves 108-109). Also available in electronic version. Access restricted to campus users.
30

Walus, Wlodzimierz Ignacy. "Stationary solutions of abstract kinetic equations." Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/53613.

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The abstract kinetic equation Tψ’=-Aψ is studied with partial range boundary conditions in two geometries, in the half space x≥0 and on a finite interval [0, r]. T and A are abstract self-adjoint operators in a complex Hilbert space. In the case of the half space problem it is assumed that T is a (possibly) unbounded injection and A is a positive compact perturbation of the identity satisfying a regularity condition, while in the case of slab geometry T is a bounded injection and A is a bounded Fredholm operator with a finite dimensional negative part. Existence and uniqueness theory is developed for both models. Results are illustrated on relevant physical examples.
Ph. D.
31

Jin, Changqiu. "Gas-kinetic moving mesh methods for viscous flow simulations /." View abstract or full-text, 2006. http://library.ust.hk/cgi/db/thesis.pl?MATH%202006%20JIN.

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32

Perkyns, John Stephen. "The solution to the reference hypernetted-chain approximation for fluids of hard spheres with dipoles and quadrupoles with application to liquid ammonia." Thesis, University of British Columbia, 1985. http://hdl.handle.net/2429/24897.

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Abstract:
This thesis is divided into two parts. In Part A the reference hypernetted-chain (RHNC) approximation is solved for a fluid of hard spheres with embedded point dipoles and linear quadrupoles. The thermodynamic properties, the dielectric constant, ∈, and the pair correlation function are compared with previously calculated Monte Carlo data as well as with results from other integral equation methods. The RHNC is found to closely approximate the Monte Carlo results and is shown to improve on the other methods. In Part B a self-consistent mean field theory for molecular polarizability is used, together with the RHNC approximation used in Part A, for a polarizable dipole-linear quadrupole fluid with ammonia-like parameters. The dielectric constant is calculated at three sub-critical temperatures and it is found to be quite sensitive to the quadrupole moment. Experimental results for ∈ are shown to be well within the uncertainty, set by the quadrupole moment, in the calculated ∈ values. These calculated ∈ values are shown to be significantly larger than the dielectric constants for the equivalent non-polarizable system.
Science, Faculty of
Chemistry, Department of
Graduate
33

Eppard, William M. "Kinetic algorithms for non-equilibrium gas dynamics." Diss., This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-06062008-165605/.

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34

Funagane, Hitoshi. "Studies on internal rarefied gas flows on the basis of kinetic theory." 京都大学 (Kyoto University), 2012. http://hdl.handle.net/2433/157525.

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35

Hüser, Julian [Verfasser], and Tilmann [Akademischer Betreuer] Kuhn. "Kinetic theory of magnon Bose-Einstein condensation / Julian Hüser ; Betreuer: Tilmann Kuhn." Münster : Universitäts- und Landesbibliothek Münster, 2016. http://d-nb.info/1141683075/34.

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36

Mao, Kefei. "Kinetic theory of irreversible processes in a system of radiation and matter." Thesis, McGill University, 1993. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=41706.

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Thermodynamics of irreversible processes in a radiation field is formulated, based on kinetic theory, by treating nonequilibrium radiation as a nonequilibrium photon gas interacting with matter. The generalized hydrodynamic equations for macroscopic variables necessary for describing temporal and spatial evolution of irreversible processes in the system of matter and radiation are derived from kinetic equations by using the modified moment method. The method rigorously yields the conclusion that entropy differential is not an exact differential when the system is away from equilibrium. Therefore, an extended Gibbs relation for the entropy density does not hold valid. However, an extended Gibbs relation-like equation holds for the compensation differential which has been shown to be an exact differential. The entropy balance equation is cast into an equivalent form in terms of a new function called the Boltzmann function. In the context of the present formalism the light-induced viscous flow is theoretically explained for the entire range of pressure. The modified moment method has been extended to the covariant Boltzmann equation in order to formulate a theory of relativistic irreversible thermodynamics. Furthermore, the kinetic theory foundations for relativistic irreversible thermodynamics for the system of radiation and matter are provided. The statistical mechanical formulas are obtained for various material and radiative transport coefficients. The radiative transport coefficients stand in simple ratios independent of material parameters. The ratios calculated are in agreement with those used in the phenomenological theory using the Rosseland mean.
37

Ortiz, Ruben Santamaria. "Density functional theory of kinetic and exchange energies of atoms and molecules." Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.276885.

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38

Jeffery, Helen B. (Helen Barbara). "The kinetic paradox of objects : a working theory for designing architectural fabric." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/12260.

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Thesis (M. Arch.)--Massachusetts Institute of Technology, Dept. of Architecture, 1994.
Includes bibliographical references (p. 49-51).
If all architectural form could be simplistically grouped into only two categories, these might be "object" and "partial enclosure," where objects are in dialogue with the space around them while partial enclosures articulate the space within them. In contemporary architectural discourse, "object" is in disfavor. Particularly in the sphere of urban planning, and in reaction to city-hating International-style buildings, architectural objects are to be avoided in favor of continuing the weave of existing urban fabric. Such objection is based on a figure-ground understanding of urbanism that values the figure of public space over th at of architectural element. This white-and-black construct has been used in architectural theory to sometimes prefer space and sometimes object, but this paper takes the position that hierarchy is not necessarily the appropriate relationship. This paper describes an object-space dialogue that is not based on figure-ground. It starts from the assumption that space is potential movement. By studying existing masterworks, the relationship between object and movement space that was discovered is interesting because it is paradoxic: objects articulate space to suggest movement often while simultaneously acting as obstructions. Architecture that takes advantage or such ambiguities, such as Michelangelo's reconstruction of the Capitoline Hill, " .. .force[s] the observer into a personal solution of [the] paradox [thus endowing] movement ... with aesthetic overtones." [Ackerman 1970, 156.] This paper called this object-space relationship the kinetic paradox, and used it as the basis for a design method to resolve a problematic innercity site.
by Helen B. Jeffery.
M.Arch.
39

Bhave, Aparna Vasant. "Kinetic theory for dilute and concentrated polymer solution study of nonhomogeneous effects." Thesis, Massachusetts Institute of Technology, 1992. http://hdl.handle.net/1721.1/12553.

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40

Wolfson, Michael Aaron. "Kinetic theory of waves in random media and amelioration of classical chaos." Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186895.

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The approach to the classical limit of wave mechanics is investigated where, in the classical limit, the dynamical system is nonintegrable and the motion in phase space is chaotic. The problem is cast in the setting of wave propagation in random media, and the fundamental starting point is an idealized stochastic parabolic wave equation (SPE) in two space dimensions with plane wave initial data. The potential is taken to have mean zero, strength ε ≪ 1 fluctuations which are homogeneous, isotropic, and have a single scale. The formal classical limit of the SPE, the parabolic ray equations are inherently non-integrable for any given realization of the potential. For the relative motion of two particles, an advection-diffusion Fokker-Planck equation is derived and shown for small initial separations to exhibit chaotic behavior, characterized by the existence of a positive Lyapunov exponent. It is shown that this physically relates to the exponential proliferation of caustics, or tendrils in phase space. A generalized wave kinetic equation (GWKE) is derived for the evolution in a relative phase space of a mean, two-particle Wigner function which corresponds classically to the advection-diffusion Fokker-Planck equation. The GWKE is analytically examined semi-classically by a novel boundary layer method (called the "extended quantum notch method") which enable the derivation of several important results: First, the "log time" (range) is obtained where semi-classical theory breaks down due to the saturation of caustics, then it is shown that this range is where the normalized intensity fluctuations (scintillation index) approaches unity. Finally, a wave (quantum) manifestation of classical chaos is seen to be the exponential decay of the scintillation index beyond its peak while on approach to saturation.
41

Tian, Chun-Lin. "Compressible convection simulation by the gas-kinetic BGK scheme /." View abstract or full-text, 2005. http://library.ust.hk/cgi/db/thesis.pl?MATH%202005%20TIAN.

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42

Pihnastyi, O. M., and K. V. Likhno. "About the kinetic models of controlled production processes." Thesis, Національний технічний університет "Харківський політехнічний інститут", 2017. http://repository.kpi.kharkov.ua/handle/KhPI-Press/42512.

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43

Tzanakopoulos, Antonios. "On the kinetic theory of test-particles weakly-coupled to large equilibrium systems." Doctoral thesis, Universite Libre de Bruxelles, 1987. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/213446.

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44

Yao, Aixiang. "Kinetic theory and global existence in Lp1s for a dense square-well fluid." Diss., Virginia Tech, 1995. http://hdl.handle.net/10919/39600.

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In this paper, we consider the kinetic equation for a dense square-well fluid and the geometric factor Y _ 1, provide the related kinetic theory, and prove a global existence theorem in L1 for the kinetic equation under rather general initial value condition. An analogue of the classical H-theorem is verified.
Ph. D.
45

Mossberg, Eva. "Some numerical and analytical methods for equations of wave propagation and kinetic theory." Doctoral thesis, Karlstad : Fakulty of Technology and Science, Mathematics, Karlstads universitet, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-1848.

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46

Yao, Aixiang. "Kinetic theory and global existence in L¹ for a dense square-well fluid /." This resource online, 1995. http://scholar.lib.vt.edu/theses/available/etd-10042006-143850/.

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47

Taguchi, Satoshi. "Kinetic-Theory Study of Vapor Flows in the Presence of a Noncondensable Gas." 京都大学 (Kyoto University), 2004. http://hdl.handle.net/2433/147621.

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48

Shi, Feng. "Nucleation and Growth in Materials and on Surfaces:Kinetic Monte Carlo Simulation and Rate Equation Theory." University of Toledo / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1216839589.

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49

Garcia, Cantu Ros Anselmo. "Thermodynamic and kinetic aspects of interaction networks." Doctoral thesis, Universite Libre de Bruxelles, 2007. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210420.

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In view of the fact that a same complex phenomenon can be approached by different conceptual frameworks, it is natural to inquire on the possibility to find connections between different types of quantities, such as topological, dynamical, statistical or thermodynamical, characterizing the same system. The present work is built on the idea that this line of approach can provide interesting insights on possible universal principles governing complex phenomena. In Chapter I we introduce concepts and tools of dynamical systems and thermodynamics as applied in macroscopic scale description as well as, for a later use, a number of selected representative models. In Chapter II we briefly present the elements of the theory of Markov processes describing a large class of stochastic process and also introduce some important concepts on the probabilistic description of deterministic systems. This chapter ends with a thermodynamic formulation accounting for the evolution of the entropy under the effect of stochastic fluctuations. In Chapter III, after introducing the main concepts and recent advances in network theory, we provide a connection between dynamical systems and network theory, which shows how universal structural properties of evolving networks can arise from deterministic dynamics. More specifically, we show explicitly the relation between the connectivity patterns of these networks and the indicators of the underlying dynamics, such as the local Lyapunov exponents. Our analysis is applied to representative models of chaotic maps, chaotic flows and is finally extended to stochastic processes. In Chapter IV we address the inverse problem, namely, processes whose dynamics is determined, in part, by the structure of the network in which they are embedded. In particular, we focus on systems of particles diffusing on a lattice and reacting instantaneously upon encountering each other. We study the role of the topology, the degree of synchronicity of motion and the reaction mechanism on the efficiency of the process. This lead us to identify a common generic mechanism responsible for the behavior of the efficiency, as a function of the control parameters. Finally, in Chapter V we study the connection between the topology and the thermodynamic properties of reaction networks, with focus on the entropy production and the system’s efficiency at nonequilibrium steady states. We also explore the connection between dynamic and thermodynamic properties of nonlinear feedbacks, as well as the response properties of reaction networks against both deterministic and stochastic external perturbations. We address networks of varying topologies, from regular lattices to complex structures./Le présent travail s’inscrit dans le domaine de recherche sur les systèmes complexes. Différentes approches, basées des systèmes dynamiques, de la thermodynamique des systèmes hors d’équilibre, de la physique statistique et, plus récemment, de la théorie des réseaux, sont combinés afin d’explorer des liens entre différentes types de grandeurs qui caractérisent certaines classes de comportements complexes. Dans le Chapitre I nous introduisons les principaux concepts et outils de systèmes dynamiques et de thermodynamique. Dans le Chapitre II nous présentons premièrement des éléments de la théorie de processus de Markov, ainsi que les concepts à la base de la description probabiliste des systèmes déterministes. Nous finissons le chapitre en proposant une formulation thermodynamique qui décrit l’évolution de l’entropie hors d’équilibre, soumis à l’influence de fluctuations stochastiques. Dans le Chapitre III nous introduisons les concepts de base en théorie des réseaux, ainsi qu’un résumé générale des progrès récents dans le domaine. Nous établissons ensuite une connexion entre la théorie des systèmes dynamiques et la théorie de réseaux. Celle-ci permet d’approfondir la compréhension des mécanismes responsables de l’émergence des propriétés structurelles dans des réseaux crées par des lois dynamiques déterministes. En particulier, nous mettons en évidence la relation entre des motifs de connectivité de ce type de réseaux et des indicateurs de la dynamique sous-jacente, tel que des exposant de Lyapounov locaux. Notre analyse est illustrée par des applications et des flots chaotiques et étendue à des processus stochastiques. Dans le Chapitre IV nous étudions le problème complémentaire, à savoir, celui de processus dont la dynamique est déterminée, en partie, par la structure du réseau dans lequel elle se déroule. Plus précisément, nous nous concentrons sur le cas de systèmes de particules réactives, diffusent au travers d’un réseau et réagissant instantanément lorsqu’un rencontre se produit entre elles. Nous étudions le rôle de la topologie, du degré de synchronicité des mouvements et aussi celui du mécanisme de réaction sur l’efficacité du processus. Dans les différents modèles étudiés, nous identifions un mécanisme générique commun, responsable du comportement de l’efficacité comme fonction des paramètres de contrôle. Enfin, dans le Chapitre V nous abordons la connexion entre la topologie et les propriétés thermodynamiques des réseaux de réactions, en analysant le comportement local et global de la production d’entropie et l’efficacité du système dans des état stationnaires de non-équilibre. Nous explorons aussi la connexion entre la dynamique et les propriétés de boucles de rétroaction non linéaires, ainsi que les propriétés de réponse des réseaux de réaction à des perturbations stochastiques et déterministes externes. Nous considérons le cas de réseaux à caractère régulier aussi bien que celui de réseaux complexes.


Doctorat en Sciences
info:eu-repo/semantics/nonPublished

50

Pack, Jeong-Ki. "A wave-kinetic numerical method for the propagation of optical waves." Thesis, Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/104527.

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