Related papers: An Exploration of the Limits of the Maxwell-Boltzm…
Despite its importance, in the introductory disciplines of exact science courses, the demonstration of the Maxwell-Boltzmann velocity distribution law is not explained, only its final equation is shown. In order to fill this deficiency, in…
We investigate the fractional diffusion limit of a Linear Boltzmann equation with heavy-tailed velocity equilibrium in a half-space with Maxwell boundary conditions. We derive a new confined version of the fractional Laplacian and show…
For the whole range of cutoff intermolecular interactions, we give a rigorous mathematical justification of the limit from the Vlasov-Maxwell-Boltzmann system to the Vlasov-Poisson-Boltzmann system as the light speed tends to infinity.Such…
Some problems relevant to the relativistic generalization of Maxwell's velocity distribution are discussed.
High energy infers high velocity and high velocity is a concept of special relativity. The Maxwellian velocity distribution is corrected to be consistent with special relativity. The corrected velocity distribution reduces to the Maxwellian…
This article contains a digest of the theory of electromagnetism and a review of the transformation between inertial frames, especially under low speed limits. The covariant nature of the Maxwell's equations is explained using the…
We study the Boltzmann equation near a global Maxwellian in the case of bounded domains. We consider the boundary conditions to be either specular reflections or Maxwellian diffusion. Starting from the reference work of Guo in…
The Maxwell-Boltzmann (MB) distribution for velocities in ideal gases is usually defined between zero and infinity. A double truncated MB distribution is here introduced and the probability density function, the distribution function, the…
We study the velocity distribution function for inelastic Maxwell models, characterized by a Boltzmann equation with constant collision rate, independent of the energy of the colliding particles. By means of a nonlinear analysis of the…
For the spatially homogeneous Boltzmann equation with cutoff hard potentials it is shown that solutions remain bounded from above, uniformly in time, by a Maxwellian distribution, provided the initial data have a Maxwellian upper bound. The…
This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise…
Quantum speed limits are relations yielding lower bounds on the evolution time of quantum systems. These results have been generalized in some ways, in particular by including evolutions to non-orthogonal states. However, there was a gap in…
Multi-species Boltzmann equations for gaseous mixtures, with analytic cross sections and under Grad's angular cutoff assumption, are considered under diffusive scaling. In the limit, we formally obtain an explicit expression for the binary…
This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fields of science, the mathematics of the underlying model of…
Consider the initial-boundary value problem for the 2-speed Carleman model of the Boltzmann equation of the kinetic theory of gases set in some bounded interval with boundary conditions prescribing the density of particles entering the…
The paper is concerned with the asymptotic analysis of a family of Boltzmann (multiplicative) distributions over the set $\check{\varLambda}^{q}$ of strict integer partitions (i.e., with unequal parts) into perfect $q$-th powers. A…
A typical introductory treatment of electromagnetism culminates with the investigation of Maxwell's equations, showing the beautiful connection between the concepts covered in the many prior weeks. The lab described here is an experimental…
Problems associated with the Boltzmann collisional operator are unveiled and discussed. By careful investigation it is shown that collective effects of molecular collisions in the six-dimensional position and velocity space are more…
Limitations to the speed of evolution of quantum systems, typically referred to as quantum speed limits (QSLs), have important consequences for quantum control problems. However, in its standard formulation, is not straightforward to obtain…
The Euler and Navier-Stokes fluid mechanics equations are derived using a modified statistical mechanical approach using theory taken from the Chapman-Enskog perturbation analysis used to support the lattice Boltzmann method. Additional…