Related papers: Configurational Continuum modelling of crystalline…
We present simulations of the relaxation towards equilibrium of one dimensional steps and sinusoidal grooves imprinted on a surface below its roughening transition. We use a generalization of the hypercube stacking model of Forrest and…
ESFEM is a method introduced in order to solve a linear advection-diffusion equation on an evolving two-dimensional surface with finite elements by using a moving grid with nodes sitting on and evolving with the surface. The evolution of…
We investigate the structure of crystalline particle arrays on constant mean curvature (CMC) surfaces of revolution. Such curved crystals have been realized physically by creating charge-stabilized colloidal arrays on liquid capillary…
We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence.…
Freestanding tubular crystals offer a general description of crystalline order on deformable surfaces with cylindrical topology, such as single-walled carbon nanotubes, microtubules, and recently reported colloidal assemblies. These systems…
We fully generalize a previously-developed computational geometry tool [1] to perform large-scale simulations of arbitrary two-dimensional faceted surfaces $z = h(x,y)$. Our method uses a three-component facet/edge/junction storage model,…
This is a review of recent theoretical work on complex dynamical behavior of steps on crystal surfaces. The first part of the article is devoted to the electromigration-driven motion of islands and voids, and the second part addresses step…
Fourth order curvature driven interface evolution equations frequently appear in the natural sciences. Often axisymmetric geometries are of interest, and in this situation numerical computations are much more efficient. We will introduce…
We consider the quasi-static evolution of a brittle layer on a stiff substrate; adhesion between layers is assumed to be elastic. Employing a phase-field approach we obtain the quasi-static evolution as the limit of time-discrete evolutions…
The Burton-Cabrera-Frank (BCF) model for the flow of line defects (steps) on crystal surfaces has offered useful insights into nanostructure evolution. This model has rested on phenomenological grounds. Our goal is to show via scaling…
Crystal growth processes produce a diverse array of surface formations, primarily distinguished by their geometric shapes. While some structures strictly adhere to the underlying crystal symmetry, others exhibit universal circular or oval…
Software engineers frequently face the challenge of developing systems whose requirements are likely to change in order to adapt to organizational reconfigurations or other external pressures. Evolving requirements present difficulties,…
The growth of a crystal is usually determined by its surface. Many factors influence the growth dynamics. Energy barriers associated with the presence of steps most often decide about the emerging pattern. The height and type of…
The distinction between absolute and convective instabilities is well known in the context of hydrodynamics and plasma physics. In this Letter, we examine an epitaxial crystal growth model from this point of view and show that a…
In two papers we proposed a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities and discussed some of its properties. The model aims to be analogous to a discrete algorithm…
Phase field crystal (PFC) models constitute a field theoretical approach to solidification, melting and related phenomena at atomic length and diffusive time scales. One of the advantages of these models is that they naturally contain…
In this paper we focus on the finite-dimensional approximation of quasi-static evolutions of critical points of the phase-field model of brittle fracture. In a space discretized setting, we first discuss an alternating minimization scheme…
Solid modeling is a technique underlying CAD software as we see it today, and its theories and algorithms are among the most fundamental milestones in the historical development of CAD. Basically, it has answered the question of what…
The potential flow of two-dimensional ideal incompressible fluid with a free surface is studied. Using the theory of conformal mappings and Hamiltonian formalism allows us to derive exact equations of surface evolution. Simple form of the…
We investigate the dynamical evolution of a thermodynamically unstable crystal surface into a hill-and-valley structure. We demonstrate that, for quasi one-dimensional ordering, the equation of motion maps exactly to the modified…