论文标题
非线性阻力下分子气体的mpemba效应
Mpemba effect in molecular gases under nonlinear drag
论文作者
论文摘要
我们研究了MPEMBA效应 - 最初更热的样品在具有非线性粘性阻力的分子气中更快冷却。具体而言，气体颗粒通过弹性碰撞以及平衡的背景流体在它们之间相互作用。因此，在动力学理论的框架内，我们的气体由enskog- fokker-planck方程描述。分析是在第一个超声的近似中进行的，其中温度的演变与多余的峰度相结合。这种耦合导致MPEMBA效应的出现，这在放松的早期阶段就可以观察到，当两个样品的初始温度足够接近时。这允许发展一个简单的理论，使参考温度周围的温度演变线性化 - 即初始温度更接近渐近平衡值。线性理论提供了对效果的半定量描述，包括分频器时间和最大温度差的表达式。我们还讨论了线性化理论的局限性。
We look into the Mpemba effect---the initially hotter sample cools sooner---in a molecular gas with nonlinear viscous drag. Specifically, the gas particles interact among them via elastic collisions and also with a background fluid at equilibrium. Thus, within the framework of kinetic theory, our gas is described by an Enskog--Fokker--Planck equation. The analysis is carried out in the first Sonine approximation, in which the evolution of the temperature is coupled to that of the excess kurtosis. This coupling leads to the emergence of the Mpemba effect, which is observed in an early stage of the relaxation and when the initial temperatures of the two samples are close enough. This allows for the development of a simple theory, linearizing the temperature evolution around a reference temperature---namely the initial temperature closer to the asymptotic equilibrium value. The linear theory provides a semiquantitative description of the effect, including expressions for the crossover time and the maximum temperature difference. We also discuss the limitations of our linearized theory.
