Related papers: Step Bunching In Conserved Systems: Scaling And Un…
By carrying out Monte Carlo simulations,we study step bunching during solution growth. For simplicity, we consider a square lattice, which represents a diffusion field in a solution, and express the diffusion of atoms as the hopping of…
Electromigration-induced step bunching in the presence of sublimation or deposition is studied theoretically in the attachment-limited regime. We predict a phase transition as a function of the relative strength of kinetic asymmetry and…
We model an apparent instability seen in recent experiments on current induced step bunching on Si(111) surfaces using a generalized 2D BCF model, where adatoms have a diffusion bias parallel to the step edges and there is an attachment…
Concerted experimental and numerical studies of step bunching on vicinal crystal surfaces resulting from step-down electromigration of partially charged adatoms, confirmed the theoretical prediction of scaling dependence of the minimal…
A scheme for stabilizing stochastic approximation iterates by adaptively scaling the step sizes is proposed and analyzed. This scheme leads to the same limiting differential equation as the original scheme and therefore has the same…
Uncovering the mechanism behind the scaling law in human trajectories is of fundamental significance in understanding many spatio-temporal phenomena. In combination of the exploration and the preferential returns, we propose a simple…
The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently a stationary stochastic process (time…
In this paper we study coordinated multipath routing at the flow-level in networks with routes of length one. As a first step the static case is considered, in which the number of flows is fixed. A clustering pattern in the rate allocation…
We approach the old-standing problem of vicinal crystal surfaces destabilized by step-down and step step-up currents from a unified modelling viewpoint with focus on both the initial and the intermediate stages of the instability. We…
Recent theoretical progress using multiscale asymptotic analysis has revealed various possible regimes of stratified turbulence. Notably, buoyancy transport can either be dominated by advection or diffusion, depending on the effective…
We explore an explicit link between stochastic gradient descent using common batching strategies and splitting methods for ordinary differential equations. From this perspective, we introduce a new minibatching strategy (called Symmetric…
Analytic scaling relations are derived for a phenomenological model of the plasmoid instability in an evolving current sheet, including the effects of reconnection outflow. Two scenarios are considered, where the plasmoid instability can be…
Constructing a conceptual model as an abstract representation of a portion of the real world involves capturing the (1) static (things/objects and trajectories of flow), (2) the dynamic (event identification), and (3) the behavior (e.g.,…
The decay of a crystalline cone below the roughening transition is studied. We consider local mass transport through surface diffusion, focusing on the two cases of diffusion limited and attachment-detachment limited step kinetics. In both…
On a Si(111) vicinal face near the structural transition temperature, the $1 \times 1$ structure and the $7 \times 7$ structure coexist in a terrace: the $1 \times 1$ structure is in the lower side of the step edge and the $7 \times 7$…
Given a family of systems, identifying stabilizing switching signals in terms of infinite walks constructed by concatenating cycles on the underlying directed graph of a switched system that satisfy certain conditions, is a well-known…
Mesoscopic models in the reaction-diffusion framework have gained recognition as a viable approach to describing chemical processes in cell biology. The resulting computational problem is a continuous-time Markov chain on a discrete and…
We propose a one-dimensional model based on the Burton-Cabrera-Frank equations to describe the electromigration-induced step bunching instability on vicinal surfaces. The step drift resulting from atomic evaporation and/or deposition is…
From a simple path integral involving a variable volatility in the velocity differences, we obtain velocity probability density functions with exponential tails, resembling those observed in fully developed turbulence. The model yields…
Bunching and meandering instability of steps at the 4H-SiC(0001) surface is studied by the kinetic Monte Carlo simulation method. Change in the character of step instability is analyzed for different rates of particle jumps towards step. In…