Related papers: Boltzmann Equation Solver for Thermalization
The particles model, the collision model, the polynomial development used for the equilibrium distribution, the time discretization and the velocity discretization are factors that let the lattice Boltzmann framework (LBM) far away from its…
Two-particle momentum correlations of $N$ identical bosons are studied in the quantum canonical ensemble. We define the latter as a properly selected subensemble of events associated with the grand canonical ensemble which is characterized…
We describe the implementation of a new approach to the numerical evaluation of the effects of non-cold relics on the evolution of cosmological perturbations. The Boltzmann hierarchies used to compute the contributions of these relics to…
This paper provides an initial description of the Method of Simultaneous Solutions, a Monte Carlo approach that simultaneously solves multiple Boltzmann-transport-like phenomena. Here, it is used to simultaneously solve the neutron…
We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The…
Accurate path integral Monte Carlo or molecular dynamics calculations of isotope effects have until recently been expensive because of the necessity to reduce three types of errors present in such calculations: statistical errors due to…
This paper reviews results on the scalar Boltzmann equation for a single-component polyatomic gas with continuous internal energy. For the space homogeneous problem, $L^1$-theory is established, for solutions with initial strictly positive…
We numerically solve the Boltzmann equation for trapped fermions in the normal phase using the test-particle method. After discussing a couple of tests in order to estimate the reliability of the method, we apply it to the description of…
In this paper, explicit method of constructing approximations (the Triangle Entropy Method) is developed for nonequilibrium problems. This method enables one to treat any complicated nonlinear functionals that fit best the physics of a…
The most rigorous physical description of non-equilibrium gas dynamics is rooted in the numerical solution of the Boltzmann equation. Yet, the large number of degrees of freedom and the wide range of both spatial and temporal scales render…
This paper considers a system of Boltzmann equations modelling the mixture of monatomic and polyatomic gases in an $L^{2}-L^{\infty}$ perturbation theory around global modified Maxwellians accounting for the internal energy of the mixture…
In this work, we develop a novel Monte Carlo method for solving the electromagnetic scattering problem. The method is based on a formal solution of the scattering problem as a modified Born series whose coefficients are found by a conformal…
We introduce a general technique to compute finite temperature electronic properties by a novel covariant formulation of the electronic partition function. By using a rigorous variational upper bound to the free energy we are led to the…
In this paper we develop a direct simulation Monte Carlo (DSMC) method for simulating highly nonequilibrium dynamics of nearly degenerate ultra-cold gases. We show that our method can simulate the high-energy collision of two thermal clouds…
The Boltzmann equation is a powerful theoretical tool for modeling the collective dynamics of quantum many-body systems subject to external perturbations. Analysis of the equation gives access to linear response properties including…
We present new results building on the conservative deterministic spectral method for the space inhomogeneous Boltzmann equation developed by Gamba and Tharkabhushaman. This approach is a two-step process that acts on the weak form of the…
We construct a novel class of exact solutions to the Boltzmann equation, in both its classical and quantum formulation, for arbitrary collision laws. When the system is subjected to a specific external forcing, the precise form of which is…
The Boltzmann equation describes the evolution of the phase-space probability distribution of classical particles under binary collisions. Approximations to it underlie the basis for several scholarly fields, including aerodynamics and…
The Poisson-Boltzmann equation is a widely used model to study the electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate…
Kinetic theories constitute one of the most promising tools to decipher the characteristic spatio-temporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides…