Related papers: An energy method for averaging lemmas
We use the methods of commutator and fundamental solutions to establish averaging lemmas and hypoelliptic estimates for purely kinetic transport equations. Assuming certain amount of velocity regularity for solutions, we extend our analysis…
We obtain several averaging lemmas for transport operator with a force term. These lemmas improve the regularity yet known by not considering the force term as part of an arbitrary right-hand side. Two methods are used: local variable…
We develop a new approach to velocity averaging lemmas based on the dispersive properties of the kinetic transport operator. This method yields unprecedented sharp results, which display, in some cases, a gain of one full derivative.…
Multiple pendulums are investigated numerically and analytically to clarify the nonuniformity of average kinetic energies of particles. The nonuniformity is attributed to the system having constraints and it is consistent with the…
We prove new velocity averaging lemmas for multi-dimensional hyperbolic-parabolic partial differential equations. These theorems may be applied to establish several compactness results for both deterministic and stochastic…
The semiclassical description of the dynamics of wave packets in periodic potentials and subject to an applied force relies on the concepts of effective mass and anomalous transport. This picture is valid if the force changes slowly in time…
We argue that statistical mechanics of systems with relaxation implies breaking the energy function of systems into two having different transformation rules. With this duality the energy approach incorporates the generalized vortex forces.…
In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization…
In the relativistic uniform model for continuous medium the integral theorem of generalized virial is derived, in which generalized momenta are used as particles momenta. This allows us to find exact formulas for the radial component of the…
We consider two classes of linear kinetic equations: with constant collision frequency and constant mean free path of gas molecules (i.e., frequency of molecular collisions, proportional to the modulus molecular velocity). Based homogeneous…
A new kinetic model is proposed where the equilibrium distribution with bounded support has a range of velocities about two average velocities in 1D. In 2D, the equilibrium distribution function has a range of velocities about four average…
The concept of duality reflects a link between two seemingly different physical objects. An example in quantum mechanics is a situation where the spectra (or their parts) of two Hamiltonians go into each other under a certain…
This paper examines an averaging technique applied to the transport equations as an alternative to vanishing viscosity. Such techniques have been shown to be valid shock-regularizations of the Burgers equation and the Euler equations, but…
Many features of granular media can be modelled as a fluid of hard spheres with {\em inelastic} collisions. Under rapid flow conditions, the macroscopic behavior of grains can be described through hydrodynamic equations. At low-density, a…
A new kinetic theory Boltzmann-like collision term including correlations is proposed. In equilibrium it yields the one-particle distribution function in the form of a generalised-Lorentzian resembling but not being identical with the…
In recent years, machine learning methods have been widely used to study physical systems that are challenging to solve with governing equations. Physicists and engineers are framing the data-driven paradigm as an alternative approach to…
The granular gas is a paradigm for understanding the effects of inelastic interactions in granular materials. Kinetic theory provides a general theoretical framework for describing the granular gas. Its central result is that the tail of…
We investigate the kinetic theory of two-temperature plasmas for reactive polyatomic gas mixtures. The Knudsen number is taken proportional to the square root of the mass ratio between electrons and heavy-species, and thermal…
A Lie-group based similarity theory is developed for both momentum and energy distributions in a turbulent pipe flow, leading to asymptotic logarithmic profiles of mean velocity and turbulent kinetic energy. Both channel and pipe data over…
According to the general theory of relativity, kinetic energy contributes to gravitational mass. Surprisingly, the observational evidence for this prediction does not seem to be discussed in the literature. I reanalyze existing experimental…