Related papers: Determination of Boltzmann constant by gas expansi…
Given an obstacle in $\mathbb{R}^3$ and a non-zero velocity with small amplitude at the infinity, we construct the unique steady Boltzmann solution flowing around such an obstacle with the prescribed velocity as $|x|\to \infty$, which…
Based on the concept of a nonequilibrium steady state, we present a novel method to experimentally determine energy landscapes acting on colloidal systems. By measuring the stationary probability distribution and the current in the system,…
We use a careful treatment of time-dependent wave-mechanical scattering to determine the conditions under which a dilute, non-degenerate quantum gas can obey a Boltzmann equation. If the gas possesses weak long-range coherence, such as may…
We study the effect of dissipation on the density profile of a one dimensional gas that is subject to gravity. The gas is in thermal equilibrium at temperature T with a heat reservoir at the bottom wall. Perturbative analysis of the…
We apply the method of invariant manifolds to derive equations of generalized hydrodynamics from the linearized Boltzmann equation and determine exact transport coefficients, obeying Green-Kubo formulas. Numerical calculations are performed…
We present the perturbative solution of the multicomponent Boltzmann kinetic equation based on the set of observables including the hydrodynamic velocity and temperature for each component. The solution is obtained by modifying the formal…
We study uncertainty quantification for a Boltzmann-Poisson system that models electron transport in semiconductors and the physical collision mechanisms over the charges. We use the stochastic Galerkin method in order to handle the…
We study freely evolving and forced inelastic gases using the Boltzmann equation. We consider uniform collision rates and obtain analytical results valid for arbitrary spatial dimension d and arbitrary dissipation coefficient epsilon. In…
We solve the one-dimensional boost-invariant kinetic equation for a relativistic massive system with the collision term treated in the relaxation time approximation. The result is an exact integral equation which can be solved numerically…
We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that: (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square…
Researchers at the National Institute of Standards and Technology have been using a watt balance, NIST-3, to measure the Planck constant $h$ for over ten years. Two recently published values disagree by more than one standard uncertainty.…
Lattice Boltzmann methods are numerical schemes derived as a kinetic approximation of an underlying lattice gas. A numerical convergence theory for nonlinear convective-diffusive lattice Boltzmann methods is established. Convergence,…
In the weakly non-ideal gas model [1], the Bose-Einstein condensation at constant pressure is considered. The temperature of transition to the state with condensate is found. Temperature dependences of the total density and condensate…
Several consecutive experiments with specifically built set-up are described. Performing of the consecutive experimental tasks enables possibility to determine Boltzmann's constant $k_\mathrm{_B}$. The fluctuations of the voltage $U(t)$ of…
For a massless gas with constant cross section in a homogeneous, isotropically expanding spacetime we reformulate the relativistic Boltzmann equation as a set of non-linear coupled moment equations. For a particular initial condition this…
We demonstrate operation of a constant-pressure flowmeter capable of generating and accurately measuring flows as low as $2\times10^{-13}$ mol/s. Generation of such small flows is accomplished by using a small conductance element with…
We report a study of the homogeneous isotropic Boltzmann equation for an open system. We seek for nonequilibrium steady solutions in presence of forcing and dissipation. Using the language of weak turbulence theory, we analyze the…
We perform a calculation of the first and second order infinitesimal variations, with respect to energy, of the Boltzmann entropy of constant energy hypersurfaces of a system with a finite number of degrees of freedom. We comment on the…
We present a new approach to find accurate solutions to the Poisson equation, as obtained from the steady-state limit of a diffusion equation with strong source terms. For this purpose, we start from Boltzmann's kinetic theory and…
The Boltzmann equation is a fundamental equation in kinetic theory that describes the motion of rarefied gases. In this study, we examine the Boltzmann equation within a $C^1$ bounded domain, subject to a large external potential $\Phi(x)$…