Related papers: Atomistic origins of continuum dislocation dynamic…
Traditional deterministic subgrid-scale (SGS) models are often dissipative and unstable, especially in regions of chaotic and turbulent flow. Ongoing work in climate science and ocean modeling motivates the use of stochastic SGS models for…
The mean square displacement and instantaneous diffusion coefficient for different configurations of charged particles in stochastic motion are calculated by numerically solving the associated equations of motion. The method is suitable for…
Stochastic differential equations (SDEs) are a fundamental tool for modelling dynamic processes, including gene regulatory networks (GRNs), contaminant transport, financial markets, and image generation. However, learning the underlying SDE…
The interplay of screw dislocations with carbon atoms is investigated in tungsten at high temperature using in situ straining experiments in a transmission electron microscope (TEM) and through ab initio calculations. When the temperature…
Starting from a prototypical model of elasto-plasticity in the small-strain and quasi-static setting, where the evolution of the plastic distortion is driven exclusively by the motion of discrete dislocations, this work performs a rigorous…
We formulate a variational model for a geometrically necessary screw dislocation in an anti-plane lattice model at zero temperature. Invariance of the energy functional under lattice symmetries renders the problem non-coercive.…
The question of whether biological populations survive or are eventually driven to extinction has long been examined using mathematical models. In this work we study population survival or extinction using a stochastic, discrete…
Dispersive shock waves (DSWs), which connect states of different amplitude via a modulated wave train, form generically in nonlinear dispersive media subjected to abrupt changes in state. The primary tool for the analytical study of DSWs is…
Continuum dislocation dynamics models of mesoscale plasticity consist of dislocation transport-reaction equations coupled with crystal mechanics equations. The coupling between these two sets of equations is such that dislocation transport…
The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to…
We develop data-driven models to predict the dynamics of a freely settling sphere in a quiescent Newtonian fluid using experimentally obtained trajectories. Particle tracking velocimetry was used to obtain a comprehensive dataset of…
The role of memory and cognition in the movement of individuals (e.g. animals) within a population, is thought to play an important role in population dispersal. In response, there has been increasing interest in incorporating spatial…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…
We extend the work of Tanase-Nicola and Kurchan on the structure of diffusion processes and the associated supersymmetry algebra by examining the responses of a simple statistical system to external disturbances of various kinds. We…
The thermodynamic description of dislocation glide in crystals depends crucially on the shape of the Peierls barrier that the dislocation has to overcome when moving in the lattice. While the height of this barrier can be obtained…
Stochastic diffusion is the noisy and uncertain process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. Understanding these processes is becoming increasingly important as we attempt to…
Calculations and mechanistic explanations for the probabilistic movement of objects at the highly relevant cm length scales has been lacking and overlooked due to the complexity of current techniques. Predicting the final-configuration…
The elastic energy functional of a system of discrete dislocation lines is well known from dislocation theory. In this paper we demonstrate how the discrete functional can be used to systematically derive approximations which express the…
Timeseries generated from a dynamical source can often be modeled as sample paths of a stochastic differential equation (SDE). The timeseries thus reflects the motion of a particle which flows along the direction provided by a drift /…
The diffusive transport of particles in anisotropic media is a fundamental phenomenon in computational, medical and biological disciplines. While deterministic models (partial differential equations) of such processes are well established,…