On the Maxwell-Stefan diffusion limit for a reactive mixture of polyatomic gases in non-isothermal setting

The term "detonability" with respect to fuel-air mixtures (FAMs) implies the ability of a reactive mixture of a given composition to support the propagation of a stationary detonation wave in various thermodynamic and gasdynamic conditions. The detonability of FAMs, on the one hand, determines their explosion hazards during storage, transportation, and use in various sectors of the economy and, on the other hand, the possibility of their practical application in advanced energy-converting devices operating on detonative pressure gain combustion.

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Steady-State Analysis of the Join-the-Shortest-Queue Model in the Halfin–Whitt Regime

Mathematics of Operations Research ◽

10.1287/moor.2019.1023 ◽

2020 ◽

Vol 45 (3) ◽

pp. 1069-1103

Author(s):

Anton Braverman

Keyword(s):

Steady State ◽

Diffusion Limit ◽

Fluid Limit ◽

Time Intervals ◽

Dimensional Diffusion ◽

Queue Model ◽

Join The Shortest Queue ◽

Shortest Queue ◽

Process Level ◽

General Tool

This paper studies the steady-state properties of the join-the-shortest-queue model in the Halfin–Whitt regime. We focus on the process tracking the number of idle servers and the number of servers with nonempty buffers. Recently, Eschenfeldt and Gamarnik proved that a scaled version of this process converges, over finite time intervals, to a two-dimensional diffusion limit as the number of servers goes to infinity. In this paper, we prove that the diffusion limit is exponentially ergodic and that the diffusion scaled sequence of the steady-state number of idle servers and nonempty buffers is tight. Combined with the process-level convergence proved by Eschenfeldt and Gamarnik, our results imply convergence of steady-state distributions. The methodology used is the generator expansion framework based on Stein’s method, also referred to as the drift-based fluid limit Lyapunov function approach in Stolyar. One technical contribution to the framework is to show how it can be used as a general tool to establish exponential ergodicity.

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The Asymptotic Diffusion Limit of Numerical Schemes for the SN Transport Equation

Nuclear Science and Engineering ◽

10.1080/00295639.2019.1638660 ◽

2019 ◽

Vol 193 (12) ◽

pp. 1339-1354

Author(s):

Dean Wang

Keyword(s):

Transport Equation ◽

Diffusion Limit ◽

Numerical Schemes

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Generalized fractional Poisson process and related stochastic dynamics

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2020-0034 ◽

2020 ◽

Vol 23 (3) ◽

pp. 656-693 ◽

Cited By ~ 2

Author(s):

Thomas M. Michelitsch ◽

Alejandro P. Riascos

Keyword(s):

Poisson Process ◽

Continuous Time ◽

Counting Process ◽

Stochastic Dynamics ◽

Waiting Times ◽

Fractional Diffusion ◽

Diffusion Limit ◽

Fractional Operators ◽

Fractional Poisson Process ◽

Erlang Process

AbstractWe survey the ‘generalized fractional Poisson process’ (GFPP). The GFPP is a renewal process generalizing Laskin’s fractional Poisson counting process and was first introduced by Cahoy and Polito. The GFPP contains two index parameters with admissible ranges 0 < β ≤ 1, α > 0 and a parameter characterizing the time scale. The GFPP involves Prabhakar generalized Mittag-Leffler functions and contains for special choices of the parameters the Laskin fractional Poisson process, the Erlang process and the standard Poisson process. We demonstrate this by means of explicit formulas. We develop the Montroll-Weiss continuous-time random walk (CTRW) for the GFPP on undirected networks which has Prabhakar distributed waiting times between the jumps of the walker. For this walk, we derive a generalized fractional Kolmogorov-Feller equation which involves Prabhakar generalized fractional operators governing the stochastic motions on the network. We analyze in d dimensions the ‘well-scaled’ diffusion limit and obtain a fractional diffusion equation which is of the same type as for a walk with Mittag-Leffler distributed waiting times. The GFPP has the potential to capture various aspects in the dynamics of certain complex systems.

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Diffusion limit of a Boltzmann–Poisson system with nonlinear equilibrium state

Journal of Hyperbolic Differential Equations ◽

10.1142/s021989161950005x ◽

2019 ◽

Vol 16 (01) ◽

pp. 131-156

Author(s):

Lanoir Addala ◽

Mohamed Lazhar Tayeb

Keyword(s):

Nonlinear Diffusion ◽

Collision Operator ◽

Nonlinear Diffusion Equation ◽

One Dimension ◽

Diffusion Limit ◽

Poisson System ◽

Nonlinear Relaxation ◽

Contraction Property ◽

Hilbert Expansion ◽

Nonlinear Equilibrium

The diffusion approximation for a Boltzmann–Poisson system is studied. Nonlinear relaxation type collision operator is considered. A relative entropy is used to prove useful [Formula: see text]-estimates for the weak solutions of the scaled Boltzmann equation (coupled to Poisson) and to prove the convergence of the solution toward the solution of a nonlinear diffusion equation coupled to Poisson. In one dimension, a hybrid Hilbert expansion and the contraction property of the operator allow to exhibit a convergence rate.

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