Related papers: Configurational Continuum modelling of crystalline…
For particles confined to two dimensions, any curvature of the surface affects the structural, kinetic and thermodynamic properties of the system. If the curvature is non-uniform, an even richer range of behaviours can emerge. Using a…
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…
Using a coarse molecular-dynamics (CMD) approach with an appropriate choice of coarse variable (order parameter), we map the underlying effective free-energy landscape for the melting of a crystalline solid. Implementation of this approach…
Accurate representation of interfaces and flux exchange is vital for coupled multiphysics simulations across a broad range of applications. Currently, coupling approaches are limited by the underlying discretization or to specific physical…
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…
It is proved that a generic simple, closed, piecewise regular curve in space can be the boundary of only finitely many developable surfaces with nonvanishing mean curvature. The relevance of this result in the context of the dynamics of…
We describe here in detail the recently introduced methodology for simulation of structural transitions in crystals. The applications of the new scheme are illustrated on various kinds of crystals and the advantages with respect to previous…
Mechanochemical processes on surfaces such as the cellular cortex or epithelial sheets, play a key role in determining patterns and shape changes of biological systems. To understand the complex interplay of hydrodynamics and material flows…
The evolution of interfaces is intrinsic to many physical processes ranging from cavitation in fluids to recrystallization in solids. Computational modeling of interface motion entails a number of challenges, many of which are related to…
An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow, powers of mean and inverse mean curvature flow, etc. Error estimates are proven for semi- and full…
Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic, or…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
Interfaces in a model with a single, real nonconserved order parameter and purely dissipative evolution equation are considered. We show that a systematic perturbative approach, called the expansion in width and developed for curved domain…
I discuss the so-called stochastic individual based model of adaptive dynamics and in particular how different scaling limits can be obtained by taking limits of large populations, small mutation rate, and small effect of single mutations…
The BCF theory of crystal growth has been successful in describing a wide range of phenomena in surface physics. Typical crystal surfaces are slightly misoriented with respect to a facet plane; thus, the BCF theory views such systems as…
Continuum equations are ubiquitous in physical modelling of elastic, viscous, and viscoelastic systems. The equations of continuum mechanics take nontrivial forms on curved surfaces. Although the curved surface formulation of the continuum…
We develop a stabilized cut finite element method for the convection problem on a surface based on continuous piecewise linear approximation and gradient jump stabilization terms. The discrete piecewise linear surface cuts through a…
Understanding and predicting microstructure evolution is fundamental to materials science, as it governs the resulting properties and performance of materials. Traditional simulation methods, such as phase-field models, offer high-fidelity…
A continuum (Mullins-type) model is formulated for the isotropic evolution of a solid surface on which the mass transport occurs by oscillatory surface diffusion. The time-space oscillations of diffusivity are assumed to be induced by…
Mathematical models are vital interpretive and predictive tools used to assist in the understanding of cell migration. There are typically two approaches to modelling cell migration: either micro-scale, discrete or macro-scale, continuum.…