标题： 无热惯性游走-翻转粒子在剪切增稠介质中的速度分布和扩散 显示英文标题

标题： Velocity Distribution and Diffusion of an Athermal Inertial Run-and-Tumble Particle in a Shear-Thickening Medium

摘要： 我们研究了在$d=1$中运动的无热惯性跑停粒子的动力学行为。 介质的粘度由非线性函数$f(v)\sim\tan(v)$表示，而强度为$\Sigma$且翻转速率为$\lambda$的对称二元噪声模拟了粒子的活动性。 从粒子速度 $v$ 在时间 $t$ 的时间依赖概率分布 $W_{\pm\Sigma}(v, t)$ 的福克-普朗克~(FP) 方程出发，且主动力为 $\pm\Sigma$，我们解析地推导出稳态速度分布函数 $W_s(v)$ 和有效扩散系数 $D_{\rm eff}$ 的求积表达式。 对于固定的$\Sigma$，$W_s(v)$在不同的$\lambda$下经历多次转变，并且我们已经确定了相应的转变点。然后我们数值计算了$W_s(v)$，均方速度$\langle v^2\rangle(t)$和扩散系数$D_{\rm eff}$，所有这些结果都与稳态下的分析结果高度一致。 最后，我们通过考虑一个替代的$f(v)$函数来测试$W_s(v)$的鲁棒性，该函数也能捕捉介质的剪切增稠行为。 显示英文摘要

摘要： We study the dynamics of an athermal inertial run-and-tumble particle moving in a shear-thickening medium in $d=1$. The viscosity of the medium is represented by a nonlinear function $f(v)\sim\tan(v)$, while a symmetric dichotomous noise of strength $\Sigma$ and flipping rate $\lambda$ models the activity of the particle. Starting from the Fokker-Planck~(FP) equation for the time-dependent probability distribution $W_{\pm\Sigma}(v, t)$ of the particle's velocity $v$ at time $t$ and the active force is $\pm\Sigma$, we analytically derive the steady-state velocity distribution function $W_s(v)$ and a quadrature expression for the effective diffusion coefficient $D_{\rm eff}$. For a fixed $\Sigma$, $W_s(v)$ undergoes multiple transitions with varying $\lambda$, and we have identified the corresponding transition points. We then numerically compute $W_s(v)$, the mean-squared velocity $\langle v^2\rangle(t)$, and the diffusion coefficient $D_{\rm eff}$, all of which show excellent agreement with the analytical results in the steady-state. Finally, we test the robustness of the transitions in $W_s(v)$ by considering an alternative $f(v)$ function that also capture the shear-thickening behavior of the medium.