Arvind Baskaran

Mechanisms of Stranski-Krastanov growth

Stranski-Krastanov (SK) growth is reported experimentally as the growth mode that is responsible for the transition to three dimensional islands in heteroepitaxial growth. A kinetic Monte Carlo (KMC) model is proposed that can replicate many of the experimentally observed features of this growth mode. Simulations reveal that this model effectively captures the SK transition and subsequent growth. Annealing simulations demonstrate that the wetting layer formed during SK growth is stable, with entropy playing a key role in its stability. It is shown that this model also captures the apparent critical thickness that tends to occur at higher deposition rates and for alloy films (where intermixing is significant). This work shows that the wetting layer thickness increases with increasing temperature, whereas the apparent critical thickness decreases with increasing temperature. Both of which are in agreement with experiments.

Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation

In this paper we present two unconditionally energy stable finite difference schemes for the modified phase field crystal (MPFC) equation, a sixth-order nonlinear damped wave equation, of which the purely parabolic phase field crystal (PFC) model can be viewed as a special case. The first is a convex splitting scheme based on an appropriate decomposition of the discrete energy and is first order accurate in time and second order accurate in space. The second is a new, fully second-order scheme that also respects the convex splitting of the energy. Both schemes are nonlinear but may be formulated from the gradients of strictly convex, coercive functionals. Thus, both are uniquely solvable regardless of the time and space step sizes. The schemes are solved by efficient nonlinear multigrid methods. Numerical results are presented demonstrating the accuracy, energy stability, efficiency, and practical utility of the schemes. In particular, we show that our multigrid solvers enjoy optimal, or nearly optimal complexity in the solution of the nonlinear schemes.

Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation

In this paper we provide a detailed convergence analysis for an unconditionally energy stable, second order accurate convex splitting scheme for the modified phase field crystal equation, a generalized damped wave equation for which the usual phase field crystal equation is a special degenerate case. The fully discrete, fully second order finite difference scheme in question was derived in a recent work [A. Baskaran et al., J. Comput. Phys., 250 (2013), pp. 270--292]. An introduction of a new variable

Insensitivity of active nematic liquid crystal dynamics to topological constraints

\psi

Kinetic density functional theory of freezing

, corresponding to the temporal derivative of the phase variable

Energy Stable Multigrid Method for Local and Non-local Hydrodynamic Models for Freezing

\phi

Theory of Microphase separation in bidisperse Chiral membranes

, could bring an accuracy reduction in the formal consistency estimate, because of the hyperbolic nature of the equation. A higher order consistency analysis by an asymptotic expansion is performed to overcome this difficulty. In turn, second order convergence in both time and space is established in a discrete

Instabilities, defects, and defect ordering in an overdamped active nematic

L^\infty (0,T; H^3)

Theory of Raft Interactions in Ternary Colloidal Membranes

norm.

Dynamics of an active nematic under topologically incommensurate confinement

Confining a liquid crystal imposes topological constraints on the orientational order, allowing global control of equilibrium systems by manipulation of anchoring boundary conditions. In this article, we investigate whether a similar strategy allows control of active liquid crystals. We study a hydrodynamic model of an extensile active nematic confined in containers, with different anchoring conditions that impose different net topological charges on the nematic director. We show that the dynamics are controlled by a complex interplay between topological defects in the director and their induced vortical flows. We find three distinct states by varying confinement and the strength of the active stress: A topologically minimal state, a circulating defect state, and a turbulent state. In contrast to equilibrium systems, we find that anchoring conditions are screened by the active flow, preserving system behavior across different topological constraints. This observation identifies a fundamental difference between active and equilibrium materials.