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摘要翻译：
研究了粒子在膨胀球体中进行布朗运动的问题，该球体的表面是粒子的吸收边界。这个问题类似于多晶材料晶粒长大时杂质在晶粒中扩散的问题。我们求解了粒子在D维膨胀球中的时间相关扩散方程，得到了粒子的密度函数（空间和时间的函数）。存活率或作为时间函数的单位体积颗粒总数被评估。对于d=3且球面呈抛物增长的情形，我们得到了精确的特解。导出了当球体生长速率相对于粒子扩散系数较小时，反之亦然时，粒子密度的渐近解。
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英文标题：
《Diffusion of particles in an expanding sphere with an absorbing boundary》
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作者：
Karl Forsberg and Ali R. Massih
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最新提交年份：
2008
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
We study the problem of particles undergoing Brownian motion in an expanding sphere whose surface is an absorbing boundary for the particles. The problem is akin to that of the diffusion of impurities in a grain of polycrystalline material undergoing grain growth. We solve the time dependent diffusion equation for particles in a d-dimensional expanding sphere to obtain the particle density function (function of space and time). The survival rate or the total number of particles per unit volume as a function of time is evaluated. We have obtained particular solutions exactly for the case where d=3 and a parabolic growth of the sphere. Asymptotic solutions for the particle density when the sphere growth rate is small relative to particle diffusivity and vice versa are derived.
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PDF链接：
https://arxiv.org/pdf/801.2032
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