Colloidal particles with active boundary layers -regions surrounding the particles where nonequilibrium processes produce large velocity gradients -are common in many physical, chemical and biological contexts. The velocity or stress at the edge of the boundary layer determines the exterior fluid flow and, hence, the many-body interparticle hydrodynamic interaction. Here, we present a method to compute the many-body hydrodynamic interaction between N spherical active particles induced by their exterior microhydrodynamic flow. First, we use a boundary integral representation of the Stokes equation to eliminate bulk fluid degrees of freedom. Then, we expand the boundary velocities and tractions of the integral representation in an infinite-dimensional basis of tensorial spherical harmonics and, on enforcing boundary conditions in a weak sense on the surface of each particle, obtain a system of linear algebraic equations for the unknown expansion coefficients. The truncation of the infinite series, fixed by the degree of accuracy required, yields a finite linear system that can be solved accurately and efficiently by iterative methods. The solution linearly relates the unknown rigid body motion to the known values of the expansion coefficients, motivating the introduction of propulsion matrices. These matrices completely characterize hydrodynamic interactions in active suspensions just as mobility matrices completely characterize hydrodynamic interactions in passive suspensions. The reduction in the dimensionality of the problem, from a three-dimensional partial differential equation to a two-dimensional integral equation, allows for dynamic simulations of hundreds of thousands of active particles on multi-core computational architectures. In our simulation of 10 4 active colloidal particle in a harmonic trap, we find that the necessary and sufficient ingredients to obtain steady-state convective currents, the so-called "selfassembled pump", are (a) one-body self-propulsion and (b) two-body rotation from the vorticity of the Stokeslet induced in the trap.

We simulate the nonlocal Stokesian hydrodynamics of an elastic filament which is active due to a permanent distribution of stresslets along its contour. A bending instability of an initially straight filament spontaneously breaks flow symmetry and leads to autonomous filament motion which, depending on conformational symmetry can be translational or rotational. At high ratios of activity to elasticity, the linear instability develops into nonlinear fluctuating states with large amplitude deformations. The dynamics of these states can be qualitatively understood as a superposition of translational and rotational motion associated with filament conformational modes of opposite symmetry. Our results can be tested in molecular-motor filament mixtures, synthetic chains of autocatalytic particles or other linearly connected systems where chemical energy is converted to mechanical energy in a fluid environment. , their collective behavior tends to be universal and can be understood by appealing to symmetries and conservation laws [5]. This realization has led to many studies of the collective properties of suspensions of hydrodynamically interacting autonomously motile particles [6].There are ample instances in biology, however, where the conversion of chemical to mechanical energy is not confined to a particle-like element but is, instead, distributed over a line-like element. Such a situation arises, for example, in a microtubule with a row of molecular motors converting energy while walking on it. The mechanical energy thus obtained not only produces motion of the motors but also generates reaction forces on the microtubule, which can deform elastically in response. Hydrodynamic interactions between the motors and between segments of the microtubule must be taken into account since both are surrounded by a fluid. This combination of elasticity, autonomous motility through energy conversion and hydrodynamics is found in biomimetic contexts as well. A recent example is provided by mixtures of motors which crosslink and walk on polymer bundles. A remarkable cilia-like beating phenomenon is observed in these systems [7]. A polymer in which the monomeric units are autocatalytic nanorods provides a nonbiological example of energy conversion on linear elastic elements.Though such elements are yet to be realized in the laboratory, active elements coupled to passive components through covalent bonds have been synthesized [2] and may lead to new kinds of nanomachines [3].Motivated by these biological and biomimetic examples, we study, in this Letter, a semiflexible elastic filament immersed in a viscous fluid with energy converting "active" elements distributed along its length. We present an equation of motion for the filament that incorporates the effects of nonlinear elastic deformation, active processes and nonlocal Stokesian hydrodynamic interactions. We use the lattice Boltzmann (LB) method to numerically solve the active filament equation of motion. Our simulations show that a straight active filament is linearly unsta...

Recent experiments imaging fluid flow around swimming microorganisms have revealed complex time-dependent velocity fields that differ qualitatively from the stresslet flow commonly employed in theoretical descriptions of active matter. Here we obtain the most general flow around a finite sized active particle by expanding the surface stress in irreducible Cartesian tensors. This expansion, whose first term is the stresslet, must include, respectively, third-rank polar and axial tensors to minimally capture crucial features of the active oscillatory flow around translating Chlamydomonas and the active swirling flow around rotating Volvox. The representation provides explicit expressions for the irreducible symmetric, antisymmetric, and isotropic parts of the continuum active stress. Antisymmetric active stresses do not conserve orbital angular momentum and our work thus shows that spin angular momentum is necessary to restore angular momentum conservation in continuum hydrodynamic descriptions of active soft matter.

Non-equilibrium processes which convert chemical energy into mechanical motion enable the motility of organisms. Bundles of inextensible filaments driven by energy transduction of molecular motors form essential components of micron-scale motility engines like cilia and flagella. The mimicry of cilia-like motion in recent experiments on synthetic active filaments supports the idea that generic physical mechanisms may be sufficient to generate such motion. Here we show, theoretically, that the competition between the destabilising effect of hydrodynamic interactions induced by force-free and torque-free chemomechanically active flows, and the stabilising effect of nonlinear elasticity, provides a generic route to spontaneous oscillations in active filaments. These oscillations, reminiscent of prokaryotic and eukaryotic flagellar motion, are obtained without having to invoke structural complexity or biochemical regulation. This minimality implies that biomimetic oscillations, previously observed only in complex bundles of active filaments, can be replicated in simple chains of generic chemomechanically active beads.

Recent fluorescence spectroscopy measurements of single-enzyme kinetics have shown that enzymatic turnovers form a renewal stochastic process in which the inverse of the mean waiting time between turnovers follows the Michaelis-Menten equation. We study enzyme kinetics at physiologically relevant mesoscopic concentrations using a master equation. From the exact solution of the master equation we find that the waiting times are neither independent nor identically distributed, implying that enzymatic turnovers form a nonrenewal stochastic process. The inverse of the mean waiting time shows strong departure from the Michaelis-Menten equation. The waiting times between consecutive turnovers are anticorrelated, where short intervals are more likely to be followed by long intervals and vice versa. Correlations persist beyond consecutive turnovers indicating that multiscale fluctuations govern enzyme kinetics.