Related papers: Deterministic and stochastic models of dislocation…
Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental…
A central question in developmental biology is how size and position are determined. The genetic code carries instructions on how to control these properties in order to regulate the pattern and morphology of structures in the developing…
Near-term prediction of the structured spatio-temporal processes driving our climate is of profound importance to the safety and well-being of millions, but the prounced nonlinear convection of these processes make a complete mechanistic…
Based on symmetry consideration of migration and shape deformations, we formulate phenomenologically the dynamics of cell crawling in two dimensions. Forces are introduced to change the cell shape. The shape deformations induce migration of…
This paper studies spatial patterns formed by proximate population migration driven by real wage gradients and other idiosyncratic factors. The model consists of a tractable core-periphery model incorporating a quasi-linear log utility…
The spatial heterogeneity of cities -- the uneven distribution of population and activities -- is fundamental to urban dynamics and related to critical issues such as infrastructure overload, housing affordability, and social inequality.…
Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction--diffusion theory, which connects cellular signalling and transport…
We have developed a set of numerical tools for the quantitative analysis of defect dynamics in quasiperiodic structures. We have applied these tools to study dislocation motion in the dynamical equation of Lifshitz and Petrich [Phys. Rev.…
We study a one-dimensional model of a dislocation pileup driven by an external stress and interacting with random quenched disorder, focusing on predictability of the plastic deformation process. Upon quasistatically ramping up the…
Materials are often heterogeneous at various length scales, with variations in grain structure, defects, and composition which has a strong influence on the emergent macroscopic plastic behavior. In particular, heterogeneities lead to…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
We provide a comprehensive theoretical framework to study how crystal dislocations influence the functional properties of materials, based on the idea of quantized dislocation, namely a "dislon". In contrast to previous work on dislons…
Fatigue simulation requires accurate modeling of unloading and reloading. However, classical ductile damage models treat deformations after complete failure as irrecoverable -- which leads to unphysical behavior during unloading. This…
We consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model (among other things) biological transport and traffic flow. We begin with a broad overview of…
Theories of localised pattern formation are important to understand a broad range of natural patterns, but are less well-understood than more established mechanisms of domain-filling pattern formation. Here, we extend recent work on pattern…
In this paper, we study the traveling wave solutions to the density-suppressed motility model describing the ``self-trapping'' mechanism that induces spatio-temporal pattern formations observed in the experiment. We establish the existence…
Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical…
Intracellular transport processes driven by molecular motors can be described by stochastic lattice models of self-driven particles. Here we focus on bidirectional transport models excluding the exchange of particles on the same track. We…
Micro-plasticity theories and models are suitable to explain and predict mechanical response of devices on length scales where the influence of the carrier of plastic deformation - the dislocations - cannot be neglected or completely…
The continuum theory of dislocations, as developed predominantly by Kr\"oner and Kosevich, views each dislocation as a source of incompatibility of strains. We show that this concept can be employed efficiently in the Landau free energy…