精确可解的主动流体模型中的压力
Pressure in an exactly solvable model of active fluid
摘要：
本文研究了三种具有自推进和持续运动特性的随机模型，即主动布朗粒子（ABP）模型、高斯色噪声（GCN）模型和统一色噪声模型（UCNA）的稳态压强。而在短但有限的持续时间的限制下，UCNA模型中的压力可以通过不同的方法获得，这些方法在平衡系统中具有类似性，在其余两个模型中，只有维里路径通常是可能的。根据这种方法，尽管每个模型都遵循其特定的微观演化规律，但压力表现出某种普遍的行为。对于一般的粒子间和封闭的潜力，我们推导出一个公式，建立了GCN和UCNA压力之间的对应关系。为了提供明确的公式和例子，我们专门讨论的情况下，一个组件的弹性哑铃局限于一个抛物线井。通过使用UCNA，我们发现，对于这个模型，由热力学方法确定的压力与由维里和力学方法获得的压力一致。当应用于GCN时，这三种方法给出的压力与通过UCNA获得的压力相同。最后，我们发现ABP维里压与UCNA和GCN的结果完全一致。
英文摘要：
We consider the pressure in the steady-state regime of three stochastic models characterized by self-propulsion and persistent motion and widely employed to describe the behavior of active particles, namely the Active Brownian particle (ABP) model, the Gaussian colored noise (GCN) model and the unified colored noise model (UCNA). Whereas in the limit of short but finite persistence time the pressure in the UCNA model can be obtained by different methods which have an analog in equilibrium systems, in the remaining two models only the virial route is, in general, possible. According to this method, notwithstanding each model obeys its own specific microscopic law of evolution, the pressure displays a certain universal behavior. For generic interparticle and confining potentials, we derive a formula which establishes a correspondence between the GCN and the UCNA pressures. In order to provide explicit formulas and examples, we specialize the discussion to the case of an assembly of elastic dumbbells confined to a parabolic well. By employing the UCNA we find that, for this model, the pressure determined by the thermodynamic method coincides with the pressures obtained by the virial and mechanical methods. The three methods when applied to the GCN give a pressure identical to that obtained via the UCNA. Finally, we find that the ABP virial pressure exactly agrees with the UCNA and GCN result.
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