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  1. 1. Combinatorial Considerations on Two Models from Statistical Mechanics

    Författare :Johan Thapper; Svante Linusson; Peter Jonsson; Jakob Jonsson; Linköpings universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; fully packed loop model; rhombus tilings; hard particle model; independence complex; discrete morse theory; Discrete mathematics; Diskret matematik;

    Sammanfattning : Interactions between combinatorics and statistical mechanics have provided many fruitful insights in both fields. A compelling example is Kuperberg’s solution to the alternating sign matrix conjecture, and its following generalisations. LÄS MER

  3. 2. Graphical representations of Ising and Potts models : Stochastic geometry of the quantum Ising model and the space-time Potts model

    Författare :Jakob Erik Björnberg; Anders Björner; Jeffrey Steif; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Quantum Ising model; Ising model; Potts model; random-cluster model; random-current representation; random-parity representation; differential inequality; phase transition; Discrete mathematics; Diskret matematik;

    Sammanfattning : HTML clipboard Statistical physics seeks to explain macroscopic properties of matter in terms of microscopic interactions. Of particular interest is the phenomenon of phase transition: the sudden changes in macroscopic properties as external conditions are varied. LÄS MER

  4. 3. Discrete Kinetic Models and Conservation Laws

    Författare :Mirela Cristina Vinerean; Alexander Bobylev; Giampiero Spiga; Karlstads universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Kinetic theory; discrete kinetic velocity models; conservation laws; MATHEMATICS; MATEMATIK; Matematik; Mathematics;

    Sammanfattning : 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. LÄS MER

  5. 4. Classification of Normal Discrete Kinetic Models

    Författare :Mirela Christina Vinerean; Alexander Bobylev; Mirela Vinerean-Bernhoff; Karlstads universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Kinetic theory; discrete kinetic velocity models; conservation laws; MATHEMATICS; MATEMATIK; Matematik; Mathematics;

    Sammanfattning : “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. LÄS MER

  7. 5. Discrete Velocity Models and Half-Space Problems

    Författare :Niclas Bernhoff; Karlstads universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Boltzmann equation; discrete velocity models; half-space problems; Matematik; Mathematics;

    Sammanfattning : We study some questions related to discrete velocity models (DVMs) of the Boltzmann equation. In the case of plane stationary problems the typical DVM reduces to a dynamical system (system of ODEs). Properties of such systems are studied in this paper in the most general case. LÄS MER