Related papers: $\Gamma$-limit for a sharp interface model related…
We consider a one-dimensional version of a variational model for pattern formation in biological membranes. The driving term in the energy is a coupling between the order parameter and the local curvature of the membrane. We derive scaling…
The Ohta-Kawasaki model for diblock-copolymers is well known to the scientific community of diffuse-interface methods. To accurately capture the long-time evolution of the moving interfaces, we present a derivation of the corresponding…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…
We consider the problem of sampling from the Ising model when the underlying interaction matrix has eigenvalues lying within an interval of length $\gamma$. Recent work in this setting has shown various algorithmic results that apply…
The envelope-function method with generalized boundary conditions is applied to the description of localized and resonant interface states. A complete set of phenomenological conditions which restrict the form of connection rules for…
In this paper, we introduce a nonlocal, variational model for thin films. We consider convolution-type functionals defined on a thin domain whose thickness is of order $\gamma$, where the effective interactions range between points is of…
We use the reduced relaxed micromorphic model (RRMM) to capture the effective "bulk" dynamical response of finite size metamaterial specimens made out of a Labyrinthine unit cell. We show that for small finite-size specimens, boundary…
he inhomogeneous structure of a fluid at a wall can be characterized in several ways. Within a thermodynamic description the surface free energy $\gamma$ and the excess adsorption $\Gamma$ are of central importance. For theoretical studies…
We propose models in nonlinear elasticity for nonsimple materials that include surface energy terms. Additionally, we also discuss living surface loads on the boundary. We establish corresponding linearized models and show their…
Galactic-scale structure is of particular interest since it provides important clues to dark matter properties and its observation is improving. Weakly interacting massive particles (WIMPs) behave as cold dark matter on galactic scales,…
This paper presents a systematic and accurate treatment of the evolution of cosmological perturbations in self-interacting dark matter models, for particles which decoupled from the primordial plasma while relativistic. We provide a…
We study fermionic conformal field theories on surfaces with spin structure in the presence of boundaries, defects, and interfaces. We obtain the relevant crossing relations, taking particular care with parity signs and signs arising from…
Interfaces play critical roles in materials, and are usually both structurally and compositionally complex microstructural features. The precise characterization of their nature in three-dimensions at the atomic-scale is one of the grand…
We use the technique developed in [32]-[33] to construct the upper and the lower bounds for classes of problems containing non-local terms, including problems in micromagnetics and problems arising in the variational study of the Method of…
The geometric state of a flat boundary is frequently described using the so-called macroscopic parameters. They are a principal tool for dealing with interfaces at the continuous scale. The paper describes a new method for macroscopic…
We present the first of two articles on the small volume fraction limit of a nonlocal Cahn-Hilliard functional introduced to model microphase separation of diblock copolymers. Here we focus attention on the sharp-interface version of the…
Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors, the dynamics of a border connecting a stripe pattern and a uniform state is studied. Numerical simulations of a prototype isotropic model, the subcritical…
Complex natural or engineered systems comprise multiple characteristic scales, multiple spatiotemporal domains, and even multiple physical closure laws. To address such challenges, we introduce an interface learning paradigm and put forth a…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…
We consider the Bernoulli bond percolation process (with parameter $p$) on infinite graphs and we give a general criterion for bounded degree graphs to exhibit a non-trivial percolation threshold based either on a single isoperimetric…