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We prove the uniform in space and time convergence of the scaled heights of large classes of deterministic growth models that are monotone and equivariant under translations by constants. The limits are characterized as the unique…
Urban expansion fronts display a robust local roughness exponent together with strongly dispersed growth and nonuniversal dynamic exponents. We show that this coexistence can arise from a disorder-controlled crossover in projected-front…
We present simple models for disk evolution based on two different approaches: a forward approach based on predictions generic to hierarchical models for structure formation (e.g., Mo, Mao, & White 1998) and a backwards approach based on…
In this paper we address some modelling issues related to biological growth. Our treatment is based on a recently-proposed, general formulation for growth within the context of Mixture Theory (Journal of the Mechanics and Physics of Solids,…
We demonstrate the large deviation principle in the small noise limit for the mild solution of stochastic evolution equations with monotone nonlinearity. A recently developed method, weak convergent method, has been employed in studying the…
We consider a congested aggregation model that describes the evolution of a density through the competing effects of nonlocal Newtonian attraction and a hard height constraint. This provides a counterpoint to existing literature on…
Equations for dislocation evolution bridge the gap between dislocation properties and continuum descriptions of plastic behavior of crystalline materials. Computer simulations can help us verify these evolution equations and find their…
This paper compares the continuum evolution for density equation modelling and the Gaussian mixture model on the 2D phase space long-term density propagation problem in the context of high-altitude and high area-to-mass ratio satellite…
This paper deals with the evolution equation of a curve obtained as the sharp interface limit of a non-linear system of two reaction-diffusion PDEs. This system was introduced as a phase-field model of (crawling) motion of eukaryotic cells…
We report three-dimensional particle mechanics static calculations that predict the microstructure evolution during die-compaction of elastic spherical particles up to relative densities close to one. We employ a nonlocal contact…
Clusters formed by fluctuations of two-dimensional (2D) directed interfaces around a threshold level have been extensively studied at equilibrium and in nonequilibrium steady states, but their coarsening dynamics remain poorly understood.…
A macroscopic theory for describing cellular states during steady-growth is presented, which is based on the consistency between cellular growth and molecular replication, as well as the robustness of phenotypes against perturbations.…
We study the depinning transition for models representative of each of the two universality classes of interface roughening with quenched disorder. For one of the universality classes, the roughness exponent changes value at the transition,…
We simulate competitive two-component growth on a one dimensional substrate of $L$ sites. One component is a Poisson-type deposition that generates Kardar-Parisi-Zhang (KPZ) correlations. The other is random deposition (RD). We derive the…
Plasticity is governed by the evolution of, in general anisotropic, systems of dislocations. We seek to faithfully represent this evolution in terms of density-like variables which average over the discrete dislocation microstructure.…
We discuss the behavior of bounded slope quenched noise invasion models in high dimensions. We first observe that the roughness of such a steady state interface is generated by the combination of the roughness of the invasion process…
For stationary interface growth, governed by the Kardar-Parisi-Zhang (KPZ) equation in 1 + 1 dimensions, typical fluctuations of the interface height at long times are described by the Baik-Rains distribution. Recently Chhita et al. [1]…
Based on dynamical renormalization group (RG) calculations to the one-loop order, the surface growth described by a nonlinear stochastic conserved growth equation, {\partial h \over \partial t} = \pm \nu_2 \nabla^2 h + \lambda\nabla \cdot…
The pinning-depinning phase transitions of interfaces for two classes of discrete elastic-string models are investigated numerically. In the (1+1)-dimensions, we revisit these two elastic-string models with slight modification to growth…
This paper advances an analytical incremental contact model for the purely elastic or elastic-perfectly plastic Gaussian rough surfaces. The contact is modelled by the accumulation of identical circular contacts with radius given by the…