相关论文: First direct determination of the Boltzmann consta…
We prove an inequality on the Kantorovich-Rubinstein distance --which can be seen as a particular case of a Wasserstein metric-- between two solutions of the spatially homogeneous Boltzmann equation without angular cutoff, but with a…
Using a long-range polarization potential for HeH$^{+}$, we can obtain an empirical value for the Boltzmann constant $k_{B}$ with an order of magnitude greater precision than the previous best experimental value based on the dipole…
Measurements of fluctuations in the Cosmic Microwave Background Radiation (CMBR) is one of the most promising methods for measuring the fundamental cosmological parameters. However, in order to infer parameters from precision measurements…
We present it ab-initio calculations of the non-resonant Raman spectra of zigzag and armchair BN nanotubes. In comparison, we implement a generalized bond-polarizability model where the parameters are extracted from first-principles…
Room-temperature optical constants of crystalline Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ were determined using data extracted from Brillouin light scattering spectra. Optical extinction coefficient-to-refractive index ratios at a wavelength of…
We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres (with constant restitution coefficient $\alpha \in (0,1)$) under the thermalization induced by a host medium with a fixed Maxwellian distribution. We prove…
The Boltzmann equation has been a driving force behind significant mathematical research over the years. Its challenging theoretical complexity, combined with a wide variety of current scientific and technological problems that require…
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 $\Phi(x)$…
The frequency dependent phonon Boltzmann equation is transformed to an integral equation over the irreducible part of the Brillouin zone. Simultaneous diagonalization of the collision kernel of that equation and a symmetry crystal class…
The dependence of the bulk viscosity with the relativistic parameter $z=kT/mc^{2}$, obtained through the complete Boltzmann equation [1,2], is thoroughly analyzed. A complete and rigorous examination of the relevant non-relativistic and…
Within the framework of the post-Newtonian $2\frac12$ approximation theory, a kinetic theory for relativistic gases in the presence of gravitational fields is developed. The Boltzmann equation and the equilibrium Maxwell-J\"uttner…
Precision measurements are performed on highly excited vibrational quantum states of molecular hydrogen. The $v=12, J=0-3$ rovibrational levels of H$_2$ ($X^1\Sigma_g^+$), lying only $2000$ cm$^{-1}$ below the first dissociation limit, were…
We present a robust scheme for solving the electrokinetic equations. This goal is achieved by combining the lattice-Boltzmann method (LB) with a discrete solution of the convection-diffusion equation for the different charged and neutral…
We use Bloch oscillations in a horizontal moving standing wave to transfer a large number of photon recoils to atoms with a high efficiency (99.5% per cycle). By measuring the photon recoil of $^{87}Rb$, using velocity selective Raman…
The inverse power potential $U(r)=r^{-1/s}, 0<s<1$, generates the Boltzmann kernel $B^{s}=|v-v_*|^{1-4s} b_s(\theta)$ with an angular singularity as $\theta\to 0$. Jang-Kepka-Nota-Vel\'azquez (2023) proved the limit $B^{s}\to…
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…
Within the framework of the homogeneous non-linear Boltzmann equation, we present a new analytic method, without the intrinsic limitations of existing methods, for obtaining asymptotic solutions. This method permits extension of existing…
A rigorous derivation of the incompressible Euler equations with the no-penetration boundary condition from the Boltzmann equation with the diffuse reflection boundary condition has been a challenging open problem. We settle this open…
Lattice Boltzmann Method (LBM) is used to simulate and analyze the sedimentation of small ($15-80 \,\mu m$) columnar ice particles in the atmosphere. We are specially interested in evaluating the terminal falling velocity of columnar ice…
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…