Related papers: Coupling Diffusion and Finite Deformation in Phase…
During phase transitions certain properties of a material change, such as composition field and lattice-symmetry distortions. These changes are typically coupled, and affect the microstructures that form in materials. Here, we propose a 2D…
We develop a theoretical framework for the diffusion of a single unconstrained species of atoms on a crystal lattice that provides a generalization of the classical theories of atomic diffusion and diffusion-induced phase separation to…
At high temperature and pressure, solid diffusion and chemical reactions between rock minerals lead to phase transformations. Chemical transport during uphill diffusion causes phase separation, that is, spinodal decomposition. Thus, to…
Topological insulating phases are usually found in periodic lattices stemming from collective resonant effects, and it may thus be expected that similar features may be prohibited in thermal diffusion, given its purely dissipative and…
We present a comprehensive theoretical and computational model that explores the behavior of a thin hydrated film bonded to a non-hydrated / impermeable soft substrate in the context of surface and bulk elasticity coupled with surface…
Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical…
In this paper a geometric field theory of dislocation dynamics and finite plasticity in single crystals is formulated. Starting from the multiplicative decomposition of the deformation gradient into elastic and plastic parts, we use…
We study in detail a one-dimensional lattice model of a continuum, conserved field (mass) that is transferred deterministically between neighbouring random sites. The model falls in a wider class of lattice models capturing the joint effect…
Various unusual behaviors of artificial materials are governed by their topological properties, among which the edge state at the boundary of a photonic or phononic lattice has been captivated as a popular notion. However, this remarkable…
We study gradient field models on an integer lattice with non-convex interactions. These models emerge in distinct branches of physics and mathematics under various names. In particular, as zero-mass lattice (Euclidean) quantum field…
This article examines the dynamic phase transitions and pattern formations attributed to binary systems modeled by the Cahn-Hilliard equation. In particular, we consider a two-dimensional lattice structure and determine how different…
We precisely and rigorously characterise the decay of elastic fields generated by dislocations in crystalline materials, focusing specifically on the role of multilattices. Concretely, we establish that the elastic field generated by a…
This work presents a general thermodynamic approach to describe particle diffusion on a lattice, a model used to study transport processes in solids and on surfaces. By treating each lattice site as an open thermodynamic system, the effects…
High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce.…
Grain boundary migration is driven by the boundary's curvature and external loads such as temperature and stress. In intercalation electrodes an additional driving force results from Li-diffusion. That is, Li-intercalation induces volume…
Using an interface displacement model derived from a microscopic density functional theory we investigate thin liquidlike wetting layers adsorbed on flat substrates with an embedded chemical heterogeneity forming a stripe. For a wide range…
Discontinuous transitions into absorbing states require an effective mechanism that prevents the stabilization of low density states. They can be found in different systems, such as lattice models or stochastic differential equations (e.g.…
We present the detailed analysis of the diffusive transport of spatially inhomogeneous fluid mixtures and the interplay between structural and dynamical properties varying on the atomic scale. The present treatment is based on different…
The influence of nearest-neighbor diffusion on the decay of a metastable low-coverage phase (monolayer adsorption) in a square lattice-gas model of electrochemical metal deposition is investigated by kinetic Monte Carlo simulations. The…
This paper presents a modeling framework---mathematical model and computational framework---to study the response of a plastic material due to the presence and transport of a chemical species in the host material. Such a modeling framework…