The formation of shock waves by a moving piston and the thermal disturbance of a fixed wall by sudden temperature change are studied according to the kinetic theory of gases. The Ellipsoidal Statistical model which gives the correct Prandtl number for a monatomic gas has been solved numerically. Also, the perturbation method proposed by Chu is also applied. Velocity, density, temperature and pressure distributions have been calculated at each time step for various piston speeds for the piston problem. A comparison between the Bhatnager-Gross-Krook model solution and the Ellipsoidal Statistical model solution has been made. The thermal disturbances of velocity, density and temperature have I also been calculated at each time step for various wall temperatures. A comparison between the Kovitz-Hellman solutions and the Ellipsoidal model has been made. / Ph. D.

Call number: LD2668 .T4 1962 H37

Call number: LD2668 .T4 1984 L56 / Master of Science

<p align="justify">Ce travail consiste à étudier des systèmes constitués par un grand nombre de grains, auxquels de l’énergie cinétique est fournie, et à étudier leurs similarités et leurs différences avec des fluides traditionnels. Je me concentre principalement sur la nature de non-équilibre de ces fluides granulaires, en montrant que, même si les méthodes de méchanique statistique y sont applicables, leurs propriétés sont très différentes de celles de systèmes à l’équilibre ou proches de l’équilibre :</p> <ul><li>Les fluides granulaires présentent des phénomènes de transport qui n’ont pas d’équivalent dans des fluides moléculaires, tels qu’un couplage spécifique entre flux de chaleur et gradient de densité. <li>Leur distribution de vitesse est en général différente de la distribution de Maxwell-Boltzmann, et présente une surpopulation pour les grandes vitesses. <li>Dans le cas de mélanges, différentes espèces de grains sont en général caractérisées par des énergies cinétiques différentes, i.e. ces systèmes sont sujet à une non-equipartition de leur énergie. <li>Ces fluides ont tendance à former des inhomogénéités spatiales spontanément. Cette propriété est illustrée en étudiant l’expérience du Demon de Maxwell appliquée aux systèmes granulaires.</ul> <p align="justify">Chacune de ces particularités est discutée en détail dans des chapitres distincts, où l’on applique différentes méthodes de méchanique statistique (équation de Boltzmann, transition de phase, mean field models…) et où l’on vérifie les prédictions théoriques par simulations numériques (MD, Monte Carlo…).</p>

Modelling of laminar multiphase flow is extremely important in a wide range of engineering and scientific applications. The particle phases are often difficult to model, especially when particles display a range of sizes and velocities at each location in space. Lagrangian methods can be too expensive and many Eulerian methods, though often computationally more affordable, suffer from model deficiencies and mathematical artifacts that lead to non-physical results. For example, efficient Eulerian models that can accurately predict the crossing of multiple streams of non-interacting particles in laminar flow have traditionally been lacking. The predictive capabilities of modern techniques from the kinetic theory of gases to the treatment of disperse multiphase flows are investigated. In particular, several moment-methods, including a recently proposed fourteen-moment approximation to the underlying kinetic equation describing particle motion, are considered and their abilities to predict particle-stream crossing are assessed. Furthermore, a new polydisperse model has been proposed for treatment of flows that display a range of particles sizes. The proposed model is an extension of the well-known maximum-entropy ten-moment model from rarefied gas dynamics with an addition for the treatment of a range of particle diameters. This model allows for anisotropic variance of particle velocities in phase space and directly treats correlations between particle diameter and velocity. The derivation and mathematical structure, of the proposed models are presented. A fine-volume discretization solution procedure for the resulting moment equations is described and used for performing numerical experiments. Results for flow problems that are designed to demonstrate the fundamental behaviour of each model are presented. It is shown that the new models offer clear advantages in terms of accuracy as compared to traditional Eulerian models for multiphase flows.

Nesta tese, estudamos cosmologias com criação de matéria como alternativa ao modelo $\\Lambda$CDM. Generalizamos a equação de Boltzmann relativística com um termo de produção de partículas fenomenológico, de tal forma que a equação resultante seja capaz de reobter os resultados da termodinâmica de não-equilíbrio das equações de balanço e evolução de temperatura. Após obter o termo correto para a equação generalizada de Boltzmann, investigamos como o formalismo proposto altera a equação de evolução de relíquias cósmicas na presença de criação gravitacional de partículas. / In this thesis, we study matter creation cosmologies as an alternative to the $\\Lambda$CDM model. We generalize the relativistic Boltzmann equation with a phenomenological particle production term, in such a way that the resulting equation will be able to reproduce the non-equilibrium thermodynamics results of the balance equations and temperature evolution law. After obtaining the correct term to the generalized Boltzmann equation, we investigate how the proposed formalism changes the cosmic relic evolution equation in the presence of gravitational particle creation.

No description available.

<p>“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).”</p>

Benjamin Lax, W.P. Allis, Sanborn C. Brown. / "June 30, 1950." / Bibliography: p. 16. / Army Signal Corps Contract No. W36-039-sc-32037 Project No. 102B Dept. of the Army Project No. 3-99-10-022

“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).”