摘要翻译：
考虑非弹性Maxwell模型的Boltzmann方程来确定简单剪切流动状态下的四阶速度矩。首先，用还原系数α和折合剪切速率α精确地评价了材料的流变特性（与二次速度矩有关）。对于给定的$\α$值，上述输运性质随剪切速率的增大而减小。而且，如预期的那样，当三度矩和非对称四度矩与热速度成比例时，它们在长时间内消失。另一方面，与弹性碰撞的情况一样，我们的结果表明，对于给定的αα值，当剪切速率大于某一临界值a_c^*(α)$时，标度对称四次矩随时间发散，随着耗散的增加而减小。在此临界值以下的四次弯矩也得到了显式的剪切速率依赖关系。
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英文标题：
《Simple shear flow in inelastic Maxwell models》
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作者：
Andres Santos, Vicente Garzo
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Soft Condensed Matter        软凝聚态物质
分类描述：Membranes, polymers, liquid crystals, glasses, colloids, granular matter
膜，聚合物，液晶，玻璃，胶体，颗粒物质
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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：
  The Boltzmann equation for inelastic Maxwell models is considered to determine the velocity moments through fourth degree in the simple shear flow state. First, the rheological properties (which are related to the second-degree velocity moments) are {\em exactly} evaluated in terms of the coefficient of restitution $\alpha$ and the (reduced) shear rate $a^*$. For a given value of $\alpha$, the above transport properties decrease with increasing shear rate. Moreover, as expected, the third-degree and the asymmetric fourth-degree moments vanish in the long time limit when they are scaled with the thermal speed. On the other hand, as in the case of elastic collisions, our results show that, for a given value of $\alpha$, the scaled symmetric fourth-degree moments diverge in time for shear rates larger than a certain critical value $a_c^*(\alpha)$ which decreases with increasing dissipation. The explicit shear-rate dependence of the fourth-degree moments below this critical value is also obtained.
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PDF链接：
https://arxiv.org/pdf/706.0475