Related papers: Counterexamples of Boltzmann's equation
This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…
We describe in detail a recently proposed lattice-Boltzmann model for simulating flows with multiple phases and components. In particular, the focus is on the modeling of one-component fluid systems which obey non-ideal gas equations of…
In this paper, we present an energy method for the system of Boltzmann equations in the multicomponent mixture case, based on a micro-macro decomposition. More precisely, the perturbation of a solution to the Boltzmann equation around a…
The stationary Boltzmann equation for hard and soft forces in the context of a two component gas is considered in the slab when the molecular masses of the 2 component are different. An $L^{1}$ existence theorem is proved when one component…
Interband effects such as coherence/tunneling have recently been shown to give an important contribution to the charge and heat transport properties under certain conditions. These can be captured by adding corrective terms to the…
The linear stability analysis of the Boltzmann kinetic equation has recently garnered research interest due to its potential applications in space exploration, where rarefaction effects can render the Navier Stokes equations invalid. Since…
A challenging problem in solving the Boltzmann equation numerically is that the velocity space is approximated by a finite region. Therefore, most methods are based on a truncation technique and the computational cost is then very high if…
An alternative approach - nonequilibrium evolution thermodynamics, is compared with classical Landau approach. A statistical justification of the approach is carried out with help of probability distribution function on an example of a…
Starting from the recently proposed energy-based deviational formulation for solving the Boltzmann equation [J.-P. Peraud and N. G. Hadjiconstantinou, Phys. Rev. B 84, 2011], which provides significant computational speedup compared to…
The Boltzmann equation describes the detailed microscopic behaviour of a dilute gas, and represents the basis of the kinetic theory of gases. In order to reduce the difficulties in solving the Boltzmann equation, simple expressions of a…
We present a framework for the solution of Boltzmann's equation in the swarm limit for arbitrary mass ratio, allowing for solutions of electron or ion transport. An arbitrary basis set can be used in the framework, which is achieved by…
The inversion problem for rational B\'ezier curves is addressed by using resultant matrices for polynomials expressed in the Bernstein basis. The aim of the work is not to construct an inversion formula but finding the corresponding value…
We study the path-integral formalism in the imaginary-time to show its validity in a case with a metastable ground state. The well-known method based on the bounce solution leads to the imaginary part of the energy even for a state that is…
The non-linear Poisson-Boltzmann equation for a circular, uniformly charged platelet, confined together with co- and counter-ions to a cylindrical cell, is solved semi-analytically by transforming it into an integral equation and solving…
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 worldline path integral approach to the Bern-Kosower formalism is reviewed, which offers an alternative to Feynman diagram calculations in quantum field theory. Recent progress in constructing a multiloop generalization of this…
We consider an inverse problem for the Boltzmann equation with nonlinear collision operator in dimensions $n\geq 2$. We show that the kinetic collision kernel can be uniquely determined from the incoming-to-outgoing mappings on the boundary…
Path integral solutions with kinetic coupling potentials $\propto p_1p_2$ are evaluated. As examples I give a Morse oscillator, i.e., a model in molecular physics, and the double pendulum in the harmonic approximation. The former is solved…
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…
Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While…