Reduced Persistence Length and Fluctuation-Induced Interactions of Directed Semiflexible Polymers on Fluctuating surfaces

We consider directed semiflexible polymers embedded in a fluctuating surface which is governed by either surface tension or bending rigidity. The attractive interactions induced by the fluctuations of the surface reduce the rigidity of the polymers. In particular, it is shown that for arbitrarily stiff parallel polymers, there is a characteristic separation below which they prefer to bend rather than stay linear. The out-of plane fluctuations of the polymer, screen out the long-range fluctuation-induced forces, resulting in only a short-ranged effective attraction.Comment: REVTEX, one postscript figur

Distribution of Interacting Ionic Particles in Disordered Media

Equilibrium distribution of interacting ionic particles in a charged disordered background is studied using the nonlinear Poisson-Boltzmann equation. For an arbitrarily given realization of the disorder, an exact solution of the equation is obtained in one dimension using a mapping of the nonlinear Poisson-Boltzmann equation to a self-consistent Schrodinger equation. The resulting density profile shows that the ions are delocalized, despite what the equivalent Schrodinger formulation in one dimension would suggest. It is shown that the ions are not distributed so as to locally neutralize the background, presumably due to their mutual interactions

Emergent Run-and-Tumble Behavior in a Simple Model of Chlamydomonas with Intrinsic Noise

Recent experiments on the green alga Chlamydomonas that swims using synchronized beating of a pair of flagella have revealed that it exhibits a run-and-tumble behavior similar to that of bacteria such as E. Coli. Using a simple purely hydrodynamic model that incorporates a stroke cycle and an intrinsic Gaussian white noise, we show that a stochastic run-and-tumble behavior could emerge, due to the nonlinearity of the combined synchronization-rotation-translation dynamics. This suggests the intriguing possibility that the alga might exploit nonlinear mechanics---as opposed to sophisticated biochemical circuitry as used by bacteria---to control its behavior.Comment: 5 pages, 2 composite figures (made of 12 separate EPS files

Anomalous Diffusion of Symmetric and Asymmetric Active Colloids

The stochastic dynamics of colloidal particles with surface activity—in the form of catalytic reaction or particle release—and self-phoretic effects are studied analytically. Three different time scales corresponding to inertial effects, solute redistribution, and rotational diffusion are identified and shown to lead to a plethora of different regimes involving inertial, propulsive, anomalous, and diffusive behaviors. For symmetric active colloids, a regime is found where the mean-squared displacement has a superdiffusive t 3 / 2 behavior. At the longest time scales, an effective diffusion coefficient is found which has a nonmonotonic dependence on the size of the colloid

Fluctuation-Induced Interactions between Rods on Membranes and Interfaces

We consider the interaction between two rods embedded in a fluctuating surface which is governed by either surface tension or rigidity. The modification of fluctuations by the rods leads to an attractive long-range interaction that falls off as $1/R^4$ with their separation. The orientational dependence of the resulting interaction is non-trivial and may lead to interesting patterns of rod-like objects on such surfaces.Comment: Revtex, 10 pages, one figur

Casimir Dispersion Forces and Orientational Pairwise Additivity

A path integral formulation is used to study the fluctuation-induced interactions between manifolds of arbitrary shape at large separations. It is shown that the form of the interactions crucially depends on the choice of the boundary condition. In particular, whether or not the Casimir interaction is pairwise additive is shown to depend on whether the ``metallic'' boundary condition corresponds to a ``grounded'' or an ``isolated'' manifold.Comment: 6 pages, RevTe

Path Integral Approach to the Dynamic Casimir Effect with Fluctuating Boundaries

A path integral formulation is developed for the dynamic Casimir effect. It allows us to study arbitrary deformations in space and time of the perfectly reflecting (conducting) boundaries of a cavity. The mechanical response of the intervening vacuum is calculated to linear order in the frequency-wavevector plane, using which a plethora of interesting phenomena can be studied. For a single corrugated plate we find a correction to mass at low frequencies, and an effective shear viscosity at high frequencies that are both anisotropic. The anisotropy is set by the wavevector of the corrugation. For two plates, the mass renormalization is modified by a function of the ratio between the separation of the plates and the wave-length of corrugations. The dissipation rate is not modified for frequencies below the lowest optical mode of the cavity, and there is a resonant dissipation for all frequencies greater than that. In this regime, a divergence in the response function implies that such high frequency deformation modes of the cavity can not be excited by any macroscopic external forces. This phenomenon is intimately related to resonant particle creation. For particular examples of two corrugated plates that are stationary, or moving uniformly in the lateral directions, Josephson-like effects are observed. For capillary waves on the surface of mercury a renormalization to surface tension, and sound velocity is obtained

Coherent Hydrodynamic Coupling for Stochastic Swimmers

A recently developed theory of stochastic swimming is used to study the notion of coherence in active systems that couple via hydrodynamic interactions. It is shown that correlations between various modes of deformation in stochastic systems play the same role as the relative internal phase in deterministic systems. An example is presented where a simple swimmer can use these correlations to hunt a non-swimmer by forming a hydrodynamic bound state of tunable velocity and equilibrium separation. These results highlight the significance of coherence in the collective behavior of nano-scale stochastic swimmers.Comment: 6 pages, 3 figure

Small object limit of Casimir effect and the sign of the Casimir force

We show a simple way of deriving the Casimir Polder interaction, present some general arguments on the finiteness and sign of mutual Casimir interactions and finally we derive a simple expression for Casimir radiation from small accelerated objects.Comment: 13 pages, late

Phase Dependent Forcing and Synchronization in the three-sphere model of Chlamydomonas

The green alga {\it Chlamydomonas} swims with synchronized beating of its two flagella, and is experimentally observed to exhibit run-and-tumble behaviour similar to bacteria. Recently we studied a simple hydrodynamic three-sphere model of {\it Chlamydomonas} with a phase dependent driving force which can produce run-and-tumble behaviour when intrinsic noise is added, due to the non-linear mechanics of the system. Here, we consider the noiseless case and explore numerically the parameter space in the driving force profiles, which determine whether or not the synchronized state evolves from a given initial condition, as well as the stability of the synchronized state. We find that phase dependent forcing, or a beat pattern, is necessary for stable synchronization in the geometry we work with.Comment: 17 pages, 10 composite figures (made of 32 separate files