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Register a new userKinetic Theory of Drag on Objects in Nearly Free Molecular Flow
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Using an analogy between the density expansion of the transport coefficients of moderately dense gases and the inverse-Knudsen-number expansion of the drag on objects in nearly free molecular flows, we formulate the collision integrals that determine the first correction term to the free-molecular drag limit. We then show how the procedure can be applied to calculate the drag coefficients of an oriented disc and a sphere as a function of the speed ratio.
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We show that the kinetic theory of quantum and classical Calogero particles reduces to the free-particle Boltzmann equation. We reconcile this simple emergent behaviour with the strongly interacting character of the model by developing a Bethe-Lax correspondence in the classical case. This demonstrates explicitly that the freely propagating degrees of freedom are not bare particles, but rather quasiparticles corresponding to eigenvectors of the Lax matrix. We apply the resulting kinetic theory to classical Calogero particles in external trapping potentials and find excellent agreement with numerical simulations in all cases, both for harmonic traps that preserve integrability and exhibit perfect revivals, and for anharmonic traps that break microscopic integrability. Our framework also yields a simple description of multi-soliton solutions in a harmonic trap, with solitons corresponding to sharp peaks in the quasiparticle density. Extensions to quantum systems of Calogero particles are discussed.
In this work, we introduce an effective model for both ideal and viscous fluid dynamics within the framework of kinetic field theory (KFT). The main application we have in mind is cosmic structure formation where gaseous components need to be gravitationally coupled to dark matter. However, we expect that the fluid model is much more widely applicable. The idea behind the effective model is similar to that of smoothed particle hydrodynamics. By introducing mesoscopic particles equipped with a position, a momentum, and an enthalpy, we construct a free theory for such particles and derive suitable interaction operators. We then show that the model indeed leads to the correct macroscopic evolution equations, namely the continuity, Euler, Navier-Stokes, and energy conservation equations of both ideal and viscous hydrodynamics.
We obtain a kinetic description of spatially averaged dynamics of particle systems. Spatial averaging is one of the three types of averaging relevant within the Irwing-Kirkwood procedure (IKP), a general method for deriving macroscopic equations from molecular models. The other two types, ensemble averaging and time averaging, have been extensively studied, while spatial averaging is relatively less understood. We show that the average density, linear momentum, and kinetic energy used in IKP can be obtained from a single average quantity, called the generating function. A kinetic equation for the generating function is obtained and tested numerically on Lennard-Jones oscillator chains.
An explicit solution of the stationary one dimensional half-space boundary value problem for the linear Boltzmann equation is presented in the presence of an arbitrarily high constant external field. The collision kernel is assumed to be separable, which is also known as relaxation time approximation; the relaxation time may depend on the electron velocity. Our method consists in a transformation of the half-space problem into a nonnormal singular integral equation, which has an explicit solution.
The Navier--Stokes transport coefficients of multicomponent granular suspensions at moderate densities are obtained in the context of the (inelastic) Enskog kinetic theory. The suspension is modeled as an ensemble of solid particles where the influence of the interstitial gas on grains is via a viscous drag force plus a stochastic Langevin-like term defined in terms of a background temperature. In the absence of spatial gradients, it is shown first that the system reaches a homogeneous steady state where the energy lost by inelastic collisions and viscous friction is compensated for by the energy injected by the stochastic force. Once the homogeneous steady state is characterized, a emph{normal} solution to the set of Enskog equations is obtained by means of the Chapman--Enskog expansion around the emph{local} version of the homogeneous state. To first-order in spatial gradients, the Chapman--Enskog solution allows us to identify the Navier--Stokes transport coefficients associated with the mass, momentum, and heat fluxes. In addition, the first-order contributions to the partial temperatures and the cooling rate are also calculated. Explicit forms for the diffusion coefficients, the shear and bulk viscosities, and the first-order contributions to the partial temperatures and the cooling rate are obtained in steady-state conditions by retaining the leading terms in a Sonine polynomial expansion. The results show that the dependence of the transport coefficients on inelasticity is clearly different from that found in its granular counterpart (no gas phase). The present work extends previous theoretical results for emph{dilute} multicomponent granular suspensions [Khalil and Garzo, Phys. Rev. E textbf{88}, 052201 (2013)] to higher densities.
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