Kranz W T, Sperl M, Zippelius A
Georg-August-Universität Göttingen, Institut für Theoretische Physik, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Feb;87(2):022207. doi: 10.1103/PhysRevE.87.022207. Epub 2013 Feb 22.
We consider the stationary state of a fluid comprised of inelastic hard spheres or disks under the influence of a random, momentum-conserving external force. Starting from the microscopic description of the dynamics, we derive a nonlinear equation of motion for the coherent scattering function in two and three space dimensions. A glass transition is observed for all coefficients of restitution, ε, at a critical packing fraction φ(c)(ε) below random close packing. The divergence of timescales at the glass transition implies a dependence on compression rate upon further increase of the density-similar to the cooling-rate dependence of a thermal glass. The critical dynamics for coherent motion as well as tagged particle dynamics is analyzed and shown to be nonuniversal with exponents depending on space dimension and degree of dissipation.
我们考虑由非弹性硬球或硬圆盘组成的流体在随机、动量守恒外力影响下的稳态。从动力学的微观描述出发，我们推导了二维和三维空间中相干散射函数的非线性运动方程。对于所有恢复系数ε，在低于随机密堆积的临界堆积分数φ(c)(ε)处观察到玻璃化转变。玻璃化转变时时间尺度的发散意味着在密度进一步增加时对压缩率的依赖——类似于热玻璃对冷却速率的依赖。分析了相干运动以及标记粒子动力学的临界动力学，结果表明其是非普适的，指数取决于空间维度和耗散程度。
