Generalized Linear Boltzmann Equations for Particle Transport in Polycrystals

J. Marklof, Andreas Strombergsson
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引用次数: 9

Abstract

The linear Boltzmann equation describes the macroscopic transport of a gas of non-interacting point particles in low-density matter. It has wide-ranging applications, including neutron transport, radiative transfer, semiconductors, and ocean wave scattering. Recent research shows that the equation fails in highly correlated media, where the distribution of free path lengths is non-exponential. We investigate this phenomenon in the case of polycrystals whose typical grain size is comparable with the mean free path length. Our principal result is a new generalized linear Boltzmann equation that captures the long-range memory effects in this setting. A key feature is that the distribution of free path lengths has an exponential decay rate, as opposed to a power-law distribution observed in a single crystal.
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多晶体中粒子输运的广义线性玻尔兹曼方程
线性玻尔兹曼方程描述了低密度物质中不相互作用的点粒子气体的宏观输运。它具有广泛的应用,包括中子输运、辐射传输、半导体和海浪散射。最近的研究表明,该方程在高度相关介质中失效,其中自由路径长度的分布是非指数的。我们在典型晶粒尺寸与平均自由程长度相当的多晶的情况下研究了这种现象。我们的主要结果是一个新的广义线性玻尔兹曼方程,它捕获了这种情况下的长期记忆效应。一个关键特征是自由路径长度的分布具有指数衰减率,而不是在单晶中观察到的幂律分布。
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