Related papers: Modeling grain boundaries in solids using a combin…
Coupled Ginzburg-Landau equations appear in a variety of contexts involving instabilities in oscillatory media. When the relevant unstable mode is of vectorial character (a common situation in nonlinear optics), the pair of coupled…
The Drude-Lorentz model for the motion of electrons in a solid is a classical model in statistical mechanics, where electrons are represented as point particles bouncing on a fixed system of obstacles (the atoms in the solid). Under some…
A basic problem in the science of realistic granular matter is the plethora of heuristic models of the stress field in the absence of a first-principles theory. Such a theory is formulated here, based on the idea that static granular…
Numerous elliptic and parabolic variational problems arising in physics and geometry (Ginzburg-Landau equations, harmonic maps, Yang-Mills fields, Omega-instantons, Yamabe equations, geometric flows in general...) possess a critical…
Nanostructured materials consist of crystalline and grain boundary components. In the simplest case, both components are chemically identical. Here, we present the results of a study of a system consisting of a crystalline component built…
These lectures address the dynamics of phase ordering out of equilibrium in condensed matter and in quantum field theory in cosmological settings, emphasizing their similarities and differences. In condensed matter we describe the…
Symmetry provides important insight in understanding the nature of phase transitions. In the presence of crystalline symmetries, new phenomena in phase transition can emerge, such as intertwined orders and emergent symmetries. In this work,…
We propose a new type of symmetry breaking mechanism that takes boundaries into account, and show how it can detect surface modes by interpreting them as the order parameter associated with a generalized symmetry breaking. We argue that…
A phase field theory of polycrystalline solidification is presented that is able to describe the nucleation and growth of anisotropic particles with different crystallographic orientation in three dimensions. As opposed with the…
Using the recently developed theory of rigorously validated numerics, we address the Phase-Field-Crystal (PFC) model at the microscopic (atomistic) level. We show the existence of critical points and local minimizers associated with…
The evolution of occupied volume under progressive fragmentation of granular matter is studied using a purely geometric model. Rather than modelling disorder directly, properties are investigated by analysing highly ordered reference…
Grain boundaries (GBs) are planar lattice defects that govern the properties of many types of polycrystalline materials. Hence, their structures have been investigated in great detail. However, much less is known about their chemical…
This paper presents an overview of recent computer simulations of grain boundary (GB) diffusion focusing on atomistic understanding of diffusion mechanisms. At low temperatures when GB structure is ordered, diffusion is mediated by point…
Dijkgraaf-Witten theories are extended three-dimensional topological field theories of Turaev-Viro type. They can be constructed geometrically from categories of bundles via linearization. Boundaries and surface defects or interfaces in…
Obtaining microscopic structure-property relationships for grain boundaries are challenging because of the complex atomic structures that underlie their behavior. This has led to recent efforts to obtain these relationships with machine…
Machine learning has proven to be a valuable tool to approximate functions in high-dimensional spaces. Unfortunately, analysis of these models to extract the relevant physics is never as easy as applying machine learning to a large dataset…
Atomistic computer simulations are applied to investigate the atomic structure, thermal stability, and diffusion processes in Al-Si interphase boundaries as a prototype of metal-ceramic interfaces in composite materials. Some of the most…
Nanocrystalline (NC) materials are intrinsically unstable against grain growth. Significant research efforts have been dedicated to suppressing the grain growth by solute segregation, including the pursuit of a special NC structure that…
Advanced phase-field techniques have been applied to address various aspects of polycrystalline solidification including different modes of crystal nucleation. The height of the nucleation barrier has been determined by solving the…
We introduce a field theoretic formalism enabling the direct study of dislocation and interstitial dynamics. Explicit expressions for the energies of such defects are given. We provide links to earlier numerical, discrete elastic, time…