自对准固体的活性弹性理论
Active elastic theory of self-aligning solids
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中文总结 AI 辅助
本文推导了自对准活性固体的闭合非线性位移场方程，揭示了由噪声与对准竞争驱动的二阶动力学相变，并预测了系统尺度振荡与活性弹性波，与人群和组织实验一致。
中文摘要 AI 辅助
活性无序固体，包括密集的人群和受限环境中的上皮细胞，表现出引人注目的系统尺度振荡时空模式。这些模式与一种局部反馈机制——自对准（self-alignment）——相关，该机制将粒子运动矢量的方向与总力对齐。由这类活性粒子构成的固体的模拟和实验显示了这些自发振荡模式。在理论上，这些模式已被关联到非线性分岔以及长波长简正模的选择。在此，我们推导了一个闭合的非线性方程，用于描述受角噪声影响的二维自对准活性固体的位移场。沿着固体的简正模，模式振幅的动力学对应于非线性阻尼且受随机驱动的谐振子。在线性阶，我们表明系统从活性布朗型相关运动转变为振荡运动，且振荡日益凝聚到固体的最低模式上。我们将模式谱的解析预测与模拟进行比较，发现从无序侧接近转变时具有极好的一致性。在强对准和小噪声下，振荡相深处表现出强非线性，这与先前的观察一致。在连续介质层面，我们推导出自对准固体的闭合形式非线性波动方程。向无阻尼振荡的转变是一个二阶动力学相变，由噪声与对准之间的竞争驱动。在线性层面，我们预测了行进的活性弹性波，以及受限系统中系统尺度振荡的出现，这与在组织和人群中的观察一致。我们的框架扩展了对自对准固体的理解，这类固体在跨多个尺度的人工和生物系统中普遍存在。
英文摘要
Active disordered solids including dense human crowds and epithelial cells under confinement exhibit striking system-scale oscillatory spatiotemporal patterns. These are linked to a local feedback mechanism, self-alignment, that aligns the direction of a particle's motility vector to the total force. Simulations and experiments of solids made of such agents show these spontaneous oscillation patterns. Theoretically, they have been linked to both a nonlinear bifurcation and to selection of long-wavelength normal modes. Here we derive a closed nonlinear equation for the displacement field of active self-aligning 2d solids subject to angular noise. Along the normal modes of the solid, the dynamics of the mode amplitudes correspond to nonlinearly damped and stochastically driven harmonic oscillators. To linear order, we show that the system transitions from Active Brownian type correlated motion to oscillatory motion that increasingly condenses onto the lowest modes of the solid. We compare the analytical predictions for the mode spectra with simulations, finding excellent agreement approaching the transition from the disordered side. Strong nonlinearities manifest deep in the oscillating phase at strong alignment and small noise, consistent with the previous observations. At the continuum level, we derive a closed-form nonlinear wave equation for self-aligning solids. The transition to undamped oscillations is a second order dynamical phase transition driven by the competition between noise and alignment. At the linear level, we predict travelling acto-elastic waves, together with the emergence of system-scale oscillations for confined systems, consistent with observations in tissues and crowds. Our framework extends the understanding of self-aligning solids, which are pervasive among artificial and biological systems across multiple scales.
发表机构
- Universiteit Leiden（莱顿大学）
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