Related papers: $\Gamma$-limit for a sharp interface model related…
The dynamics of a rigid particle above a fluid-fluid interface in shear flow is studied here numerically and analytically as a function of the downward force applied on the particle. It is found here that the particle goes below the…
We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…
The criteria for strong correlations on surfaces of three-dimensional topological insulators are discussed. Usually, the Coulomb repulsion at such surfaces is too weak for driving a phase transition to a strongly correlated regime. I…
Explicit representations of complex structures on closed manifolds are valuable, but relatively rare in the literature. Using isoparametric theory, we construct complex structures on isoparametric hypersurfaces with $g=4, m=1$ in the unit…
We establish the $\Gamma$-convergence of some energy functionals describing nonlocal attractive interactions in bounded domains. The interaction potential solves an elliptic equation (local or nonlocal) in the bounded domain and the primary…
An atomistic to continuum model for a graphene sheet undergoing bending is presented. Under the assumption that the atomic interactions are governed by a harmonic approximation of the 2nd-generation Brenner REBO (reactive empirical…
This paper studies the effect of anisotropy on sharp or diffuse interfaces models. When the surface tension is a convex function of the normal to the interface, the anisotropy is said to be weak. This usually ensures the lower…
We investigate the multi-order parameter phase field model of Steinbach and Pezzolla [I. Steinbach, F. Pezzolla, A generalized field method for multiphase transformations using interface fields, Physica D 134 (1999) 385-393] concerning its…
We investigate the systematic design of compliant morphing structures composed of materials reacting to an external stimulus. We add a perimeter penalty term to ensure existence of solutions. We propose a phase-field approximation of this…
The subject of this paper is the rigorous derivation of reduced models for a thin plate by means of {\Gamma}-convergence, in the framework of finite plasticity. Denoting by {\epsilon} the thickness of the plate, we analyse the case where…
The effective transport properties of heterogeneous nanoscale materials and structures are affected by several geometrical and physical factors. Among them the presence of imperfect interfaces plays a central role being often at the origin…
We calculate statistical properties of amorphous polymer chains between crystalline lamellae by self-consistent field model simulations. In our model, an amorphous subchain is modelled as a polymer chain of which ends are grafted onto the…
We consider a continuum mechanical model of cell invasion through thin membranes. The model consists of a transmission problem for cell volume fraction complemented with continuity of stresses and mass flux across the surfaces of the…
The architecture of mechanical metamaterialsis designed to harness geometry, non-linearity and topology to obtain advanced functionalities such as shape morphing, programmability and one-way propagation. While a purely geometric framework…
The membrane model is a Gaussian interface model with a Hamiltonian involving second derivatives of the interface height. We consider the model in dimension $\mathsf{d}\ge4$ under the influence of $\delta$-pinning of strength $\varepsilon$.…
The motion of microstructural interfaces is important in modeling materials that undergo twinning and structural phase transformations. Continuum models fall into two classes: sharp-interface models, where interfaces are singular surfaces;…
We predict the structural interaction of crystalline solid-melt interfaces using amplitude equations which are derived from classical density functional theory or phase-field-crystal modeling. The solid ordering decays exponentially on the…
When two surfaces are brought into contact and slide against each other, junctions are formed at the interface. The dynamics of formation, rupture and evolution of these junctions governs the tribological response of the macro-contact.…
We explore a chameleon type of interacting dark matter-dark energy scenario in which a scalar field adiabatically traces the minimum of an effective potential sourced by the dark matter density. We discuss extensively the effect of this…
We formulate a theoretical model of the shear failure of a thin film tethered to a rigid substrate. The interface between film and substrate is modeled as a cohesive layer with randomly fluctuating shear strength/fracture energy. We…