Condensed Matter Theory

Abstract:

We present the phenomenology of the one-dimensional nonreciprocal Cahn-Hilliard model for varying nonreciprocity $\left(\alpha \right)$ and different boundary conditions. At small $\alpha$ , a perturbed uniform state evolves to a defect-laden configuration that lacks global polar order. Defects are the sources and sinks of traveling waves. For a given $\alpha$ , defects with a unique wave number that increases monotonically with $\alpha$ are selected. A critical threshold ${\alpha }_c$ marks the onset of a transition to states with finite global polar order. For periodic boundary conditions, above ${\alpha }_c$ , the system shows traveling waves that are completely ordered. In contrast, traveling waves are incompatible with the Neumann and Dirichlet boundary conditions. Instead, for $\alpha \gtrsim {\alpha }_c$ , we find fluctuating domains that show intermittent polar order, and at large $\alpha$ , the system partitions into two domains with opposite polar order.

Abstract:

We investigate the self-diffusiophoretic motion of a catalytically active spherical particle confined within a wedge-shaped domain. Using the Fourier-Kontorovich-Lebedev transform, we solve the Laplace equation for the concentration field in the diffusion-dominated regime. The method of images is employed to obtain the first and second reflections of the concentration field, accounting for both monopole and dipole contributions of the particle's surface activity. Based on these results, we derive leading-order expressions for the self-induced phoretic velocity in the far-field limit and examine how it varies with the wedge opening angle and the particle's position within the domain. We focus on the contributions to the phoretic velocities arising from phoretic interactions, without accounting for hydrodynamic effects. Our findings reveal that the wedge geometry significantly affects both the magnitude and direction of particle motion. Our study provides a systematic framework for calculating the contributions to the phoretic velocity arising from concentration disturbances near corners, with implications for microfluidic design and control of autophoretic particles in confined geometries.

Abstract:

Active matter—for example, bacteria, cells, tissues, and microtubule-motor suspensions—internally generates stresses and flows. How these are communicated to their environments remains an open question central to interpreting experimental observations and emergent dynamics. To investigate the impact of active systems on their surroundings, we introduce a model that couples an active nematic fluid to an isotropic substrate fluid via friction. We numerically show that as the active layer develops turbulence, the substrate inherits the chaotic behavior, exhibiting a novel form of turbulence driven by locally generated stochastic forcing from the active layer. In particular, the short-length-scale flow structures in the active layer are filtered out, so the system behaves as a de facto low-pass filter. We derive the transfer function between the two layers analytically and use it to predict the large-q decay of the substrate energy spectrum and to investigate how tensorial quantities, such as the strain rate and the active stresses, are transmitted between the active layer and the substrate. Our analysis agrees with recent experiments measuring velocity-velocity correlations in mixtures of active and passive microtubules, and it may have implications for traction force microscopy measurements in cellular layers.