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A unified method for extracting geometric shape features from binary image data using a steady state partial differential equation (PDE) system as a boundary value problem is presented in this paper. The PDE and functions are formulated to…
This paper develops a geometrical model of dislocations and disclinations in single crystals at the mesoscopic scale. In the continuation of previous work the distribution theory is used to represent concentrated effects in the defect lines…
Using the orbital-free density functional theory as a model theory, we present an analysis of the field theoretic approach to quasi-continuum method. In particular, by perturbation method and multiple scale analysis, we provide a formal…
Using a strategy that may be applied in theory or in experiments, we identify the regime in which a model binary soft matter mixture forms quasicrystals. The system is described using classical density functional theory combined with…
To overcome the brittleness limitation of ceramics, various toughening mechanisms have been proposed. Some of the most remarkable, especially for oxides, include the tetragonal-to-monoclinic phase transformation leading to crack shielding…
A theoretical model supported by experimental results explains the dependence of the Raman scattering signal on the evolution of structural parameters along the amorphization trajectory of polycrystalline graphene systems. Four parameters…
We describe experimental investigations of the structure of two-dimensional spherical crystals. The crystals, formed by beads self-assembled on water droplets in oil, serve as model systems for exploring very general theories about the…
We address an unusual problem in the theory of elasticity motivated by the problem of reconstructing the strain field from partial information obtained using X-ray diffraction. Referred to as either high-energy X-ray diffraction…
Strength, ductility, and failure properties of metals are tailored by plastic deformation routes. Predicting these properties requires modeling of the structural dynamics and stress evolution taking place on several length scales. Progress…
Granular materials are heterogenous grains in contact, which are ubiquitous in many scientific and engineering applications such as chemical engineering, fluid mechanics, geomechanics, pharmaceutics, and so on. Granular materials pose a…
We propose a highly coarse-grained simulation model for crystalline polymer solids with crystalline lamellar structures. The mechanical properties of a crystalline polymer solid are mainly determined by the crystalline lamellar structures.…
Atomistic simulations have now established themselves as an indispensable tool in understanding deformation mechanisms of materials at the atomic scale. Large scale simulations are regularly used to study the behavior of polycrystalline…
A field theory is presented for predicting damage and fracture in quasi-brittle materials. The approach taken here is new and blends a non-local constitutive law with a two-point phase field. In this formulation, the material displacement…
Effective methods are introduced for testing zero-dimensionality of varieties at a point. The motivation of this paper is to compute and analyze deformations of isolated hypersurface singularities. As an application, methods for computing…
Grain growth competition during solidification determines microstructural features, such as dendritic arm spacings, segregation pattern, and grain texture, which have a key impact on the final mechanical properties. During metal additive…
Dust grains play a significant role in several astrophysical processes, including gas/dust dynamics, chemical reactions, and radiative transfer. Replenishment of small-grain populations is mainly governed by fragmentation during pair-wise…
Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the…
Organic molecular crystals encompass a vast range of materials from pharmaceuticals to organic optoelectronics and proteins to waxes in biological and industrial settings. Crystal defects from grain boundaries to dislocations are known to…
Deformation heterogeneities within microstructures of polycrystalline shape memory alloys (SMAs) during superelastic stressing are studied using both experiments and simulations. In situ X-ray diffraction, specifically the far-field high…
The calculation of the transfer matrix for a large non-periodic multilayered system may become unstable in the presence of absorption. We discuss the origin of this instability and we explore two methods to overcome it: the use of a total…