Related papers: Unified continuum approach to crystal surface morp…
Point-like topological defects are singular configurations that occur in a variety of in and out of equilibrium systems with two-dimensional orientational order. As they are associated with a nonzero circuitation condition, the presence of…
A continuum theory based on thermodynamics has been developed for modeling diffusional creep of polycrystalline solids. It consists of a coupled problem of vacancy diffusion and mechanics where the vacancy generation/absorption at grain…
This paper provides an elementary introduction to the basic concepts used in describing epitaxial crystal growth in terms of the thermodynamics and kinetics of atomic steps. Selected applications to morphological instabilities of stepped…
As a point of departure it is suggested that Quantum Cosmology is a topological concept independent from metrical constraints. Methods of continuous topological evolution and topological thermodynamics are used to construct a cosmological…
A different perspective on the long-standing problem of amorphous solidification is offered, based on an alternative definition of a solid as a porous medium. General, model-free results are obtained concerning the growing dynamic length…
A unification of characteristic mode decomposition for all method-of-moment formulations of field integral equations describing free-space scattering is derived. The work is based on an algebraic link between impedance and transition…
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…
Driven surface diffusion occurs, for example, in molecular beam epitaxy when particles are deposited under an oblique angle. Elastic phase transitions happen when normal modes in crystals become soft due to the vanishing of certain elastic…
Modeling the spontaneous evolution of morphology in natural systems and its preservation by proportionate growth remains a major scientific challenge. Yet, it is conceivable that if the basic mechanisms of growth and the coupled kinetic…
We investigate the application of conformable derivatives to model critical phenomena near continuous phase transitions. By incorporating a deformation parameter into the differential structure, we derive unified expressions for…
A unifying moving mesh method is developed for general $m$-dimensional geometric objects in $d$-dimensions ($d \ge 1$ and $1\le m \le d$) including curves, surfaces, and domains. The method is based on mesh equidistribution and alignment…
Optical tweezers setup is often used to probe the motion of individual tracer particle, which promotes the study of relaxation dynamics of a generic process confined in a harmonic potential. We uncover the dependence of ensemble- and…
Parallel Molecular Dynamics simulations are conducted for describing growth on surfaces with different kind of roughness: a perfect ordered crystalline flat graphite surface, a disordered rough graphite surface and flat surface with an…
A new phase field crystal (PFC) type theory is presented, which accounts for the full spectrum of solid-liquid-vapor phase transitions within the framework of a single density order parameter. Its equilibrium properties show the most…
We theoretically and numerically investigate the steady flow of two-dimensional granular materials in a rotating drum using the discrete element method and a continuum model with the $\mu(I)$-rheology. The velocity fields obtained from both…
We introduce a dislocation density tensor and derive its kinematic evolution law from a phase field description of crystal deformations in three dimensions. The phase field crystal (PFC) model is used to define the lattice distortion,…
We study the adsorption-desorption of fluid molecules on a solid substrate by introducing a schematic model in which the adsorption/desorption transition probabilities are given by irreversible kinetic constraints with a tunable violation…
How topological defects affect the dynamics of particles hopping between lattice sites of a distorted, two-dimensional crystal is addressed. Perturbation theory and numerical simulations show that weak, short-ranged topological disorder…
Morphological properties of strained epitaxial films are examined through a mesoscopic approach developed to incorporate both the film crystalline structure and standard continuum theory. Film surface profiles and properties, such as…
The phase field crystal (PFC) model captures the elastic and topological properties of crystals with a single scalar field at small undercooling. At large undercooling, new foam-like behavior emerges. We characterize this foam phase of the…