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We consider a model of interface growth in two dimensions, given by a height function on the sites of the one--dimensional integer lattice. According to the discrete time update rule, the height above the site $x$ increases to the height…
I consider how cell shape and environmental geometry affect the rate of nutrient capture and the consequent maximum growth rate of a cell, focusing on rod-like species like \textit{E.\ coli}. Simple modeling immediately implies that it is…
Using Molecular Dynamics (MD) and Monte Carlo (MC) simulations interfacial properties of crystal-fluid interfaces are investigated for the hard sphere system and the one-component metallic system Ni (the latter modeled by a potential of the…
Ordered phases on curved substrates experience a complex interplay of ordering and intrinsic curvature, commonly producing frustration and singularities. This is an especially important issue in crystals as ever-smaller scale materials are…
We study the spatial evolutionary dynamics of solid tumors as they obtain additional driver mutations. We start with a cancer clone that expands uniformly in three dimensions giving rise to a spherical shape. We assume that cell division…
We present a robust computational framework for Hele-Shaw tumor growth with necrotic cores, a problem identified as the incompressible limit of the Porous Media Equation. Simulating this system presents a fundamental challenge: while the…
We present a unified variational treatment of evolving configurations in crystalline solids with microstructure. The crux of our treatment lies in the introduction of a vector configurational field. This field lies in the material, or…
A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…
We study a quasi-two-dimensional macroscopic system of magnetic spherical particles settled on a shallow concave dish under a temporally oscillating magnetic field. The system reaches a stationary state where the energy losses from…
Modeling the spontaneous evolution of morphology in natural systems and its preservation by proportionate growth remains a major scientific challenge. Yet, it is conceivable that if the basic mechanisms of growth and the coupled kinetic…
Geometrical constructions, such as the tangent construction on the molar free energy for determining whether a particular composition of a solution, is stable, are related to similar tangent constructions on the orientation-dependent…
Nucleation and growth is the dominant relaxation mechanism driving first order phase transitions. In two-dimensional at systems nucleation has been applied to a wide range of problems in physics, chemistry and biology. Here we study…
We discuss shape profiles emerging in inhomogeneous growth of squeezed tissues. Two approaches are used simultaneously: i) conformal embedding of two-dimensional domain with hyperbolic metrics into the plane, and ii) a pure energetic…
We study the dynamics of a growing crystalline facet where the growth mechanism is controlled by the geometry of the local curvature. A continuum model, in (2+1) dimensions, is developed in analogy with the Kardar-Parisi-Zhang (KPZ) model…
The study of the internal structure of star clusters provides important clues concerning their formation mechanism and dynamical evolution. There are both observational and numerical evidences indicating that open clusters evolve from an…
The solidification of metallic droplets into powder particles involves a complex interplay between heat diffusion, surface tension, and geometric constraints. In confined, curved systems -- such as those encountered in atomisation,…
The dynamics of fluctuating radially growing interfaces is approached using the formalism of stochastic growth equations on growing domains. This framework reveals a number of dynamic features arising during surface growth. For fast growth,…
The devil's staircase is a term used to describe surface or an equilibrium phase diagram in which various ordered facets or phases are infinitely closely packed as a function of some model parameter. A classic example is a 1-D Ising model…
The growth of stochastic interfaces in the vicinity of a boundary and the non-trivial crossover towards the behaviour deep in the bulk is analysed. The causal interactions of the interface with the boundary lead to a roughness larger near…
In the present work, evolution of gas-filled pore inside spherical nanoshells is considered. On the supposition that diffusion fluxes are quasistationary, the nonlinear equation system is obtained analytically, that describes completely the…