Physics Commons^™

Motor-Driven Dynamics Of Cytoskeletal Filaments In Motility Assays, Shiladitya Banerjee, M. Cristina Marchetti, Kristian Muller-Nedebock

Physics - All Scholarship

We model analytically the dynamics of a cytoskeletal filament in a motility assay. The filament is described as rigid rod free to slide in two dimensions. The motor proteins consist of polymeric tails tethered to the plane and modeled as linear springs and motor heads that bind to the filament. As in related models of rigid and soft two-state motors, the binding/unbinding dynamics of the motor heads and the dependence of the transition rates on the load exerted by the motor tails play a crucial role in controlling the filament's dynamics. Our work shows that the filament effectively behaves as …

Fluctuations And Pattern Formation In Self-Propelled Particles, Shradha Mishra, Aparna Baskaran, M. Cristina Marchetti

Physics - All Scholarship

We consider a coarse-grained description of a system of self-propelled particles given by hydrodynamic equations for the density and polarization fields. We find that the ordered moving or flocking state of the system is unstable to spatial fluctuations beyond a threshold set by the self-propulsion velocity of the individual units. In this region, the system organizes itself into an inhomogeneous state of well-defined propagating stripes of flocking particles interspersed with low density disordered regions. Further, we find that even in the regime where the homogeneous flocking state is stable, the system exhibits large fluctuations in both density and orientational order. …

Nonequilibrium Statistical Mechanics Of Self-Propelled Hard Rods, Aparna Baskaran, M. Cristina Marchetti

Physics - All Scholarship

Using tools of nonequilibirum mechanics, we study a model of self-propelled hard rods on a substrate in two dimensions to quantify the interplay of self-propulsion and excluded-volume effects. We derive of a Smoluchowski equation for the configurational probability density of self-propelled rods that contains several modifications as compared to the familiar Smoluchowski equation for thermal rods. As a side-product of out work, we also present a purely dynamical derivation of the Onsager form of the mean field excluded volume interaction among thermal hard rods.

Mode-Locking In Driven Disordered Systems As A Boundary-Value Problem, William Kung, M. Cristina Marchetti

Physics - All Scholarship

We study mode-locking in disordered media as a boundary-value problem. Focusing on the simplest class of mode-locking models which consists of a single driven overdamped degree-of-freedom, we develop an analytical method to obtain the shape of the Arnol'd tongues in the regime of low ac-driving amplitude or high ac-driving frequency. The method is exact for a scalloped pinning potential and easily adapted to other pinning potentials. It is complementary to the analysis based on the well-known Shapiro's argument that holds in the perturbative regime of large driving amplitudes or low driving frequency, where the effect of pinning is weak.

Hydrodynamics Of Polar Liquid Crystals, William Kung, M. Cristina Marchetti, Karl Saunders

Physics - All Scholarship

Starting from a microscopic definition of an alignment vector proportional to the polarization, we discuss the hydrodynamics of polar liquid crystals with local

C1v-symmetry. The free energy for polar liquid crystals differs from that of nematic liquid crystals (D1h) in that it contains terms violating the n −n symmetry. First we show that these Z2-odd terms induce a general splay instability of a uniform polarized state in a range of parameters. Next we use the general Poissonbracket formalism to derive the hydrodynamic equations of the system in the polarized state. The structure of the linear hydrodynamic modes confirms the existence …

Hydrodynamics Of Self-Propelled Hard Rods, Aparna Baskaran, M. Cristina Marchetti

Physics - All Scholarship

Motivated by recent simulations and by experiments on aggregation of gliding bacteria, we study a model of the collective dynamics of self-propelled hard rods on a substrate in two dimensions. The rods have finite size, interact via excluded volume and their dynamics is overdamped by the interaction with the substrate. Starting from a microscopic model with non-thermal noise sources, a continuum description of the system is derived. The hydrodynamic equations are then used to characterize the possible steady states of the systems and their stability as a function of the particles packing fraction and the speed of self propulsion.

Viscoelasticity From A Microscopic Model Of Dislocation Dynamics, M. Cristina Marchetti, Karl Saunders

Physics - All Scholarship

It is shown that the dynamics of a two-dimensional crystal with a finite concentration of dislocations, as well as vacancy and interstitial defects, is governed by the hydrodynamic equations of a viscoelastic medium. At the longest length scales the viscoelasticity is described by the simplest Maxwell model, whose shear and compressional relaxation times are obtained in terms of microscopic quantities, including the density of free dislocations. At short length scales, bond orientational order effects become important and lead to wavevector dependent corrections to the relaxation times.

Interstitials, Vacancies And Dislocations In Flux-Line Lattices: A Theory Of Vortex Crystals, Supersolids And Liquids, M. Cristina Marchetti, Leo Radzihovsky

Physics - All Scholarship

We study a three dimensional Abrikosov vortex lattice in the presence of an equilibrium concentration of vacancy, interstitial and dislocation loops. Vacancies and interstitials renormalize the long-wavelength bulk and tilt elastic moduli. Dislocation loops lead to the vanishing of the long-wavelength shear modulus. The coupling to vacancies and interstitials - which are always present in the liquid state - allows dislocations to relax stresses by climbing out of their glide plane. Surprisingly, this mechanism does not yield any further independent renormalization of the tilt and compressional moduli at long wavelengths. The long wavelength properties of the resulting state are formally …