Related papers: A variational model for dislocations at semi-coher…
We study the dynamics of elastic interfaces-membranes-immersed in thermally excited fluids. The work contains three components: the development of a numerical method, a purely theoretical approach, and numerical simulation. In developing a…
We consider a model for elastic dislocations in geophysics. We model a portion of the Earth's crust as a bounded, inhomogeneous elastic body with a buried fault surface, along which slip occurs. We prove well-posedness of the resulting…
We present a systematic derivation of the gradient flows associated to a broad class of interfacial energies, emphasizing the relation between intrinsic and extrinsic variations of the interface. We show that the intrinsic variables…
We describe a general phase-field model for hyperelastic multiphase materials. The model features an elastic energy functional that depends on the phase-field variable and a surface energy term that depends in turn on the elastic…
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 study the effective forces acting between colloidal particles trapped at a fluid interface which itself is exposed to a pressure field. To this end we apply what we call the ``force approach'', which relies solely on the condition of…
In the modeling of dislocations one is lead naturally to energies concentrated on lines, where the integrand depends on the orientation and on the Burgers vector of the dislocation, which belongs to a discrete lattice. The dislocations may…
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain…
We derive a connection between the intrinsic tribological properties and the electronic properties of a solid interface. In particular, we show that the adhesion and frictional forces are dictated by the electronic charge redistribution…
In this letter we propose a model that demonstrates the effect of free surface on the lattice resistance experienced by a moving dislocation in nanodimensional systems. This effect manifests in an enhanced velocity of dislocation due to the…
The evolution of the interface between two ideal dielectric liquids in a strong vertical electric field is studied. It is found that a particular flow regime, for which the velocity potential and the electric field potential are linearly…
Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…
In this paper we show the emergence of polycrystalline structures as a result of elastic energy minimisation. For this purpose, we introduce a variational model for two-dimensional systems of edge dislocations, within the so-called core…
Heterogeneous interfaces are central to many energy-related applications in the nanoscale. From the first-principles electronic structure perspective, one of the outstanding problems is accurately and efficiently calculating how the…
We introduce a class of stochastic weakly coupled map lattices, as models for studying heat conduction in solids. Each particle on the lattice evolves according to an internal dynamics that depends on its energy, and exchanges energy with…
Viscoelasticity and rate-dependent adhesion of soft matter lead to difficulties in modeling the 'relatively simple' problem of a rigid sphere in contact with a viscoelastic half-space. For this reason, approximations in describing surface…
We have performed small-angle light-scattering measurements of the static structure factor of a critical binary mixture undergoing diffusive partial remixing. An uncommon scattering geometry integrates the structure factor over the sample…
In this paper we consider the equilibrium problem in the relaxed linear model of micromorphic elastic materials. The basic kinematical fields of this extended continuum model are the displacement $u\in \mathbb{R}^3$ and the non-symmetric…
We study the interfaces between lattice Laughlin states at different fillings. We propose a class of model wavefunctions for such systems constructed using conformal field theory. We find a nontrivial form of charge conservation at the…
Nonequilibrium dynamics at interfaces is generally driven by a chemical potential. Here we demonstrate a generic technique to derive the basic equations of motion, boundary conditions and the chemical potential in a consistent way from…