arXiv subjects

Sumithra Sankararaman

Publications and source records attributed to Sumithra Sankararaman.

6 recordsLinked to original sources

arXiv2009

Instabilities and waves in thin films of living fluids

We formulate the thin-film hydrodynamics of a suspension of polar self-driven particles and show that it is prone to several instabilities through the interplay of activity, polarity and the existence of a free surface. Our approach extends, to self-propelling systems, the work of Ben Amar and Cummings [Phys Fluids 13 (2001) 1160] on thin-film nematics. Based on our estimates the instabilities should be seen in bacterial suspensions and the lamellipodium, and are potentially relevant to the morphology of biofilms. We suggest several experimental tests of our theory.

cond-mat.soft↗

arXiv2003

Asters, Spirals and Vortices in Mixtures of Motors and Microtubules: The Effects of Confining Geometries on Pattern Formation

We model the effects of confinement on the stable self-organized patterns obtained in the non-equilibrium steady states of mixtures of molecular motors and microtubules. In experiments [Nedelec et al. Nature, 389, 305 (1997); Surrey et al., Science, 292, 1167 (2001)] performed in a quasi-two-dimensional confined geometry, microtubules are oriented by complexes of motor proteins. This interaction yields a variety of patterns, including arangements of asters, vortices and disordered configurations. We model this system via a two-dimensional vector field describing the local coarse-grained microtubule orientation and two scalar density fields associated to molecular motors. These scalar fields describe motors which either attach to and move along microtubules or diffuse freely within the solvent. Transitions between single aster, spiral and vortex states are obtained as a consequence of confinement, as parameters in our model are varied. We also obtain other novel states, including ``outward asters'', distorted vortices and lattices of asters on confined systems. We calculate the steady state distribution of bound and free motors in aster and vortex configurations of microtubules and compare these to our simulation results, providing qualitative arguments for the stability of different patterns in various regimes of parameter space. We also study the role of crowding or ``saturation'' effects on the density profiles of motors in asters, discussing the role of such effects in stabilizing single asters.

cond-mat.stat-mech↗

arXiv2003

Self-organized Pattern Formation in Motor-Microtubule Mixtures

We propose and study a hydrodynamic model for pattern formation in mixtures of molecular motors and microtubules. The steady state patterns we obtain in different regimes of parameter space include arrangements of vortices and asters separately as well as aster-vortex mixtures and fully disordered states. Such stable steady states are observed in experiments in vitro. The sequence of patterns obtained in the experiments can be associated with smooth trajectories in a non-equilibrium phase diagram for our model.

cond-mat.stat-mech↗

arXiv2003

Quantum Hall Skyrmion Lattices at $g \approx 0$

We investigate the classical ground state configurations of a collection of skyrmions in the limit of vanishing Lánde $g$ factor. We show that in this limit, the skyrmions which are large and overlapping, behave qualitatively differently from small skyrmions. We investigate the system in various regimes of spin stiffness. We find that in all regimes, at $g=0$, the ground state configuration is a rectangular skyrmion lattice with Néel orientational ordering. The charge distribution has a higher symmetry of a face-centered rectangular lattice and the $z$-component of the spin polarization is zero. We also present general argument for the vanishing of spin polarization at $g=0$ at finite temperature and in the presence of disorder and discuss some experimental consequences of our results.

cond-mat.mes-hall↗

arXiv2002

Two-Component Fluid Membranes Near Repulsive Walls: Linearized Hydrodynamics of Equilibrium and Non-equilibrium States

We study the linearized hydrodynamics of a two-component fluid membrane near a repulsive wall, via a model which incorporates curvature- concentration coupling as well as hydrodynamic interactions. This model is a simplified version of a recently proposed one [J.-B. Manneville et al. Phys. Rev. E, 64, 021908 (2001)] for non-equilibrium force-centres embedded in fluid membranes, such as light-activated bacteriorhodopsin pumps incorporated in phospholipid (EPC) bilayers. The pump/membrane system is modeled as an impermeable, two-component bilayer fluid membrane in the presence of an ambient solvent, in which one component, representing active pumps, is described in terms of force dipoles displaced with respect to the bilayer midpoint. We first discuss the case in which such pumps are rendered inactive, computing the mode structure in the bulk as well as the modification of hydrodynamic properties by the presence of a nearby wall. We then discuss the fluctuations and mode structure in steady state of active two-component membranes near a repulsive wall. We find that proximity to the wall smoothens membrane height fluctuations in the stable regime, resulting in a logarithmic scaling of the roughness even for initially tensionless membranes. This explicitly non-equilibrium result, a consequence of the incorporation of curvature-concentration coupling in our treatment, also indicates that earlier scaling arguments which obtained an increase in the roughness of active membranes near repulsive walls may need to be reevaluated.

cond-mat.soft↗

arXiv2002

Spiral orientational order in quantum Hall skyrmion lattices

We investigate the existence of spiral ordering in the planar spin orientation of skyrmions localised on a face centered rectangular lattice (FCRL). We use the non-linear sigma model (NLSM) to numerically calculate the minimum energy configurations of this lattice around the $ν=1$ quantum Hall ground state. Our variational ansatz contains an angle $θ$, characterising the FCRL and an angle $q$, characterising the orientational order. As $ν$ is increased towards one, there is a smooth transition from the triangular lattice (TL) characterised by $(θ,q) = (120^o,120^o)$ to FCRLs with spiral orientational order. The novel feature we find is that these phases are characterised by $θ, q)$ values such that $θ+q = 240^o$ (same as the TL phase). As $ν$ incresaes further towards one, there is a sharp transition from the FCRLs to the square lattice (SL), characterised by $(θ,q)=(90^o,180^o)$. Consequently, the parameter $θ+q$ jumps sharply at the FCRL-SL transition and can serve as an order parameter to characterise it.

cond-mat.mes-hall↗