Related papers: Partial Localization, Lipid Bilayers, and the Elas…
Localized deformation patterns are a common motif in morphogenesis and are increasingly finding widespread applications in materials science, for instance as memory devices. Here we describe the emergence of spatially localized deformations…
The investigation of collective behaviour in dense assemblies of self-propelled active particles has been motivated by a wide range of biological phenomena. Of particular interest are dynamical transitions of cellular and sub-cellular…
In this paper we study the homogenization effects on the model of elastic plate in the bending regime, under the assumption that the energy density (material) oscillates in the direction of thickness. We study two different cases. First, we…
Signatures of the vulcanization transition--amorphous solidification induced by the random crosslinking of macromolecules--include the random localization of a fraction of the particles and the emergence of a nonzero static shear modulus. A…
Motivated by a model for lipid bilayer cell membranes, we study the minimization of the Willmore functional in the class of oriented closed surfaces with prescribed total mean curvature, prescribed area, and prescribed genus. Adapting…
The impact of confinement on self-assembly of particles interacting with short-range attraction and long-range repulsion (SALR) potential is studied for thermodynamic states corresponding to local ordering of clusters or layers in the bulk.…
Randomly crosslinked macromolecules undergo a liquid-to-amorphous solid phase transition at a critical crosslink concentration. This transition has two main signatures: the random localization of a fraction of the monomers and the emergence…
Plasma membranes appear as deformable systems wherein molecules are free to move and diffuse giving rise to condensed microdomains (composed of ordered lipids, transmembrane proteins and cholesterol) surrounded by disordered lipid…
We investigate the formation of polycrystalline structures in a class of particle systems. The atomistic energy is modeled as a sum of particle energies that favor atoms being locally isometric to a reference lattice. The discrete frame…
To characterize a destruction of Anderson localization by nonlinearity, we study the spreading behavior of initially localized states in disordered, strongly nonlinear lattices. Due to chaotic nonlinear interaction of localized linear or…
We consider a class of models motivated by previous numerical studies of wrinkling in highly stretched, thin rectangular elastomer sheets. The model used is characterized by a finite-strain hyperelastic membrane energy perturbed by small…
We devise a soft, solvent-free, coarse-grained model for lipid bilayer membranes. The non-bonded interactions take the form of a weighted-density functional which allows us to describe the thermodynamics of self-assembly and packing effects…
Nonlinear stiffening is a ubiquitous property of major types of biopolymers that make up the extracellular matrices (ECM) including collagen, fibrin and basement membrane. Within the ECM, many types of cells such as fibroblasts and cancer…
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the…
A typical feature of spontaneous collapse models which aim at localizing wavefunctions in space is the violation of the principle of energy conservation. In the models proposed in the literature the stochastic field which is responsible for…
In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, $\mathbb{R}^k$. We prove the $\Gamma$-convergence of elastic energies for configurations of a converging…
Understanding how electric fields destabilize biological membranes is important for electroporation-based technologies and bioelectronic interfaces. However, theoretical descriptions of this phenomenon remain fragmented. Existing theories…
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 many-body wave-function of an interacting one-dimensional electron system is probed, focusing on the low-density, strong interaction regime. The properties of the wave-function are determined using tunneling between two long, clean,…
The electron localization function (ELF) is a universal measure of electron localization that allows for, e.g., an effective characterization of physical bonds in molecular and solid state systems. In the context of the widely used…