We study a reaction diffusion model which describes the formation of patterns on surfaces having defects. Through this model, the primary goal is to study the growth process of Ge on Si surface. We consider a two species reaction diffusion process where the reacting species are assumed to diffuse on the two dimensional surface with first order interconversion reaction occuring at various defect sites which we call reaction centers. Two models of defects, namely a ring defect and a point defect are considered separately. As reaction centers are assumed to be strongly localized in space, the proposed reaction-diffusion model is found to be exactly solvable. We use Green's function method to study the dynamics of reaction diffusion processes. Further we explore this model through Monte Carlo (MC) simulations to study the growth processes in the presence of a large number of defects. The first passage time statistics has been studied numerically
We introduce a stochastic agent-based model for the flocking dynamics of self-propelled particles that exhibit velocity-alignment interactions with neighbours within their field of view. The stochasticity in the dynamics of the model arises purely from the uncertainties at the level of interactions. Despite the absence of attractive forces, this model gives rise to a wide array of emergent patterns that exhibit long-time spatial cohesion. In order to gain further insights into the dynamical nature of the resulting patterns, we investigate the system behaviour using an algorithm that identifies spatially distinct clusters of the flock and computes their corresponding angular momenta. Our results suggest that the choice of field of view is crucial in determining the resulting emergent dynamics of stochastically interacting particles. arXiv:1805.00755v2 [cond-mat.stat-mech]
Reaction-diffusion process with exclusion in the presence of traps has been studied. The asymptotic survival probability for the case of uniformly distributed random traps shows a stretched exponential behavior. We show that additional correction terms appear in the stretched exponent when exclusion is taken into account. Analytically it is shown to be ∼ t 1/6 which is verified by numerical simulations.
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