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Active matter such as swarming bacteria and motile colloids exhibits exotic properties different from conventional equilibrium materials. Among these properties, the enhanced diffusion of tracer particles is generally deemed as a hallmark of active matter. Here, rather than spherical tracers, we investigate the diffusion of isolated ellipsoids in quasi-two-dimensional bacterial bath. Our study reveals a nonlinear enhancement of both translational and rotational diffusions. More importantly, we uncover an anomalous coupling between translation and rotation that is strictly prohibited in the classic Brownian diffusion. Combining experiments with theoretical modeling, we show that such an anomaly arises from generic stretching flows induced by swimming bacteria. Our work illustrates a universal organizing principle of active matter and sheds new light on fundamental transport processes in microbiological systems., Comment: 13 pages, 4 figures

The macroscopic properties, the properties of individual components and how those components interact with each other are three important aspects of a composited structure. An understanding of the interplay between them is essential in the study of complex systems. Using axonal cytoskeleton as an example system, here we perform a theoretical study of slender structures that can be coarse-grained as a simple smooth 3-dimensional curve. We first present a generic model for such systems based on the fundamental theorem of curves. We use this generic model to demonstrate the applicability of the well-known worm-like chain (WLC) model to the network level and investigate the situation when the system is stretched by strong forces (weakly bending limit). We specifically studied recent experimental observations that revealed the hitherto unknown periodic cytoskeleton structure of axons and measured the longitudinal fluctuations. Instead of focusing on single molecules, we apply analytical results from the WLC model to both single molecule and network levels and focus on the relations between extensions and fluctuations. We show how this approach introduces constraints to possible local dynamics of the spectrin tetramers in the axonal cytoskeleton and finally suggests simple but self-consistent dynamics of spectrins in which the spectrins in one spatial period of axons fluctuate in-sync., Comment: 18 pages, 4 figures

The presence of slight azimuthal asymmetry in the initial shape of an underwater bubble entirely alters the final breakup dynamics. Here I examine the influence of initial asymmetry on the final breakup by simulating the bubble surface evolution as a Hamiltonian evolution corresponding to an inviscid, two-dimensional, planar implosion. I find two types of breakups: a previously reported coalescence mode in which distant regions along the air-water surface curve inwards and eventually collide with finite speed, and a hitherto unknown cusp-like mode in which the surface develops sharp tips whose radii of curvature are much smaller than the average neck radius. I present three sets of results that characterize the nature of this cusp mode. First, I show that the cusp mode corresponds to a saddle-node. In other words, an evolution towards a cross-section shape with sharp tips invariably later evolves away from it. In phase space, this saddle-node separates coalescence modes whose coalescence planes lie along different spatial orientations. Second, I show that the formation of the sharp tips can be interpreted as a weakly first-order transition which becomes second-order, corresponding to the formation of a finite-time curvature singularity, in the limit that the initial perturbation amplitude approaches zero. Third I show that, as the curvature singularity is approached, the maximum surface curvature diverges approximately as $(t_c - t)^{-0.8}$, where $t_c$ is the onset time of the singularity and the maximum velocity diverges approximately as $(t_c-t)^{-0.4}$. In practice, these divergences imply that viscous drag and compressibility of the gas flow, two effects not included in my analysis, become significant as the interface evolves towards the curvature singularity., 34 pages, 11 figures, submitted to Physics of Fluids

The disconnection of an underwater bubble illustrates how slight initial asymmetries can prevent the formation of a finite-time singularity. Creating a singularity by focusing a finite amount of energy dynamically into a vanishingly small amount of material requires that the initial condition be perfectly symmetric. In reality, imperfections are always present. We show a slight azimuthal asymmetry in the initial shape of the bubble neck excites vibrations that persist over time. As a result, the focusing singularity is generically preempted by a smooth contact.