标题： 由非弹性玻尔兹曼方程描述的稀薄颗粒气体的傅里叶态 显示英文标题

标题： The Fourier state of a dilute granular gas described by the inelastic Boltzmann equation

摘要： 非弹性硬球或圆盘的非线性玻尔兹曼方程存在两个定态解的情况被研究。它们既不限于弱耗散也不限于小梯度。假设单粒子分布函数具有标度性质，即所有的位置依赖性都通过密度和温度出现。在宏观层面，这两种状态的特点是均匀压力、无质量流动以及线性温度分布。此外，该状态表现出两个特殊特征。首先，碰撞的非弹性性、压力和温度梯度之间存在关系。其次，热流可以表示为温度梯度的线性函数，即遵循类似傅里叶定律的规律。其中一个解在弹性极限下是奇异的。从另一个解得出的理论预测与分子动力学模拟结果进行了比较，在傅里叶状态实际上可以在模拟中观察到的参数区域内获得了良好的一致性，即非弹性性不是太强。 显示英文摘要

摘要： The existence of two stationary solutions of the nonlinear Boltzmann equation for inelastic hard spheres or disks is investigated. They are restricted neither to weak dissipation nor to small gradients. The one-particle distribution functions are assumed to have an scaling property, namely that all the position dependence occurs through the density and the temperature. At the macroscopic level, the state corresponding to both is characterized by uniform pressure, no mass flow, and a linear temperature profile. Moreover, the state exhibits two peculiar features. First, there is a relationship between the inelasticity of collisions, the pressure, and the temperature gradient. Second, the heat flux can be expressed as being linear in the temperature gradient, i.e. a Fourier-like law is obeyed. One of the solutions is singular in the elastic limit. The theoretical predictions following from the other one are compared with molecular dynamics simulation results and a good agreement is obtained in the parameter region in which the Fourier state can be actually observed in the simulations, namely not too strong inelasticity.