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Steady structures originating from dynamic self-assembly have begun to show their advantages in new generation materials, and pose challenges to equilibrium self-assembly. In view of the important role of confinement in self-assembly, here,…
We study the dynamics of the boundary dilaton gravity coupled to N massles scalars. We rederive the boundary conditions of [1] and [3] in a way which makes the requirement of reparametrization invariance and role of conformal anomaly…
We study the excitation of harmonic waves in thin elastic samples by a single dislocation in arbitrary motion. We consider both screw and edge dislocations that move perpendicularly to the surfaces of the layer. In Fourier space the…
We investigate the effective friction encountered by a mass sliding on a granular layer as a function of bed thickness and boundary roughness conditions. The observed friction has minima for a small number of layers before it increases and…
We study the rheology of a granular material slowly driven in a confined geometry. The motion is characterized by a steady sliding with a resistance force increasing with the driving velocity and the surrounding relative humidity. For lower…
The possibility of treating boundary conditions in terms of a bilocal dynamical field is formalized in terms of a boundary action. This allows for a simple path-integral perturbation theory approach to physical effects such as radiation…
This paper focuses on an elastic dislocation problem that is motivated by applications in the geophysical and seismological communities. In our model, the displacement satisfies the Lam\'e system in a bounded domain with a mixed homogeneous…
We present a theoretical study of the interaction of vacancies with a tilt grain boundary in aluminum based on the density functional theory. The grain boundary volume expansion and vacancy induced contraction are calculated and compared…
Dislocation-interface interactions dictate the mechanical properties of polycrystalline materials through dislocation absorption, emission and reflection and interface sliding. We derive a mesoscale interface boundary condition to describe…
We investigate a model for the dynamics of a solid object, which moves over a randomly vibrating solid surface and is subject to a constant external force. The dry friction between the two solids is modeled phenomenologically as being…
The technique of distributed dislocations proved to be in the past an effective approach in studying crack problems within classical elasticity. The present work is intended to extend this technique in studying crack problems within…
This paper studies the boundary behaviour at mechanical equilibrium at the ends of a finite interval of a class of systems of interacting particles with monotone decreasing repulsive force. Our setting covers pile-ups of dislocations,…
We study mixtures of self-propelled and passive rod-like particles in two dimensions using Brownian dynamics simulations. The simulations demonstrate that the two species spontaneously segregate to generate a rich array of dynamical domain…
The semi-analytical wall boundary conditions present a mathematically rigorous framework to prescribe the influence of solid walls in SPH for fluid flows. In this paper they are investigated with respect to the skew-adjoint property which…
An abstract 2nd-order evolution equation or inclusion is discretised in time in such a way that the energy is conserved at least in qualified cases, typically in the cases when the governing energy is component-wise quadratic or…
We systematically investigated the impact of boundary confinement on the shear-thickening rheology of dense granular suspensions. Under highly confined conditions, dense suspensions were found to exhibit size-dependent or even rarely…
Biological membranes are host to proteins and molecules which may form domain-like structures resulting in spatially-varying material properties. Vesicles with such heterogeneous membranes can exhibit intricate shapes at equilibrium and…
We develop a continuum model for the dynamics of grain boundaries in three dimensions that incorporates the motion and reaction of the constituent dislocations. The continuum model is based on a simple representation of densities of curved…
The buckling of thin elastic sheets is a classic mechanical instability that occurs over a wide range of scales. In the extreme limit of atomically thin membranes like graphene, thermal fluctuations can dramatically modify such mechanical…
An inverse problem for the wave equation outside an obstacle with a {\it dissipative boundary condition} is considered. The observed data are given by a single solution of the wave equation generated by an initial data supported on an open…