相关论文: Wulff Construction for Deformable Media

We show that for elliptic parametric functionals whose Wulff shape is smooth and has strictly positive curvature, any surface with constant anisotropic mean curvature which is a topological sphere is a rescaling of the Wulff shape.

In this article we study the fields generated by the Fourier coefficients of modular forms at arbitrary cusps. We prove that these fields are contained in certain cyclotomic extensions of the field generated by the Fourier coefficients at…

Material functionality can be strongly determined by structure extending only over nanoscale distances. The pair distribution function presents an opportunity to shift structural studies beyond idealized crystal models and investigate…

Aim of this article is the construction of a spanning set for the space of super cusp forms on a complex bounded symmetric super domain B of rank 1 with respect to a lattice. The main ingredients are a generalization of the Anosov closing…

Properties in crystalline and ordered materials tend to be anisotropic, with their orientation affecting the macroscopic behavior and functionality of materials. The ability to image the orientation of anisotropic material properties in…

In charged colloidal suspensions, the competition between square-well attraction and long-range Yukawa repulsion leads to various stable domains and Wigner supercrystals. Using a continuum model and symmetry arguments, a phase diagram of…

We consider a model with two real scalar fields which admits phantom domain wall solutions. We investigate the structure and evolution of these phantom domain walls in an expanding homogeneous and isotropic universe. In particular, we show…

The main objective of this work is to numerically investigate the effect of geometric imperfections on the macroscopic response and domain formation in soft biological composites that exhibit plasticity in the stiff (fiber) phase.This work…

A fluid of domain walls has an effective equation of state $p_w = - {2/3}\rho_w$. This equation of state is qualitativelly in agreement with the supernova type Ia observations. We exploit a cosmological model where the matter content is…

We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectral dimensions, focussing on a flat background analogous to Minkowski spacetime. After reviewing the properties of fractional spaces with…

Solid materials are commonly classified as crystalline or amorphous based on the presence or absence of long-range order.Metal-organic frameworks (MOFs), like other solids,also display markedly different properties and functions in these…

Let W be a projective variety of dimension n+1, L a free line bundle on W, X in $H^0(L^d)$ a hypersurface of degree d which is generic among those given by sums of monomials from $L$, and let $f : Y \to X$ be a generically finite map from a…

The effective Nambu-Goto description of $(2+1)$-dimensional domain walls predicts singular behavior of its worldsheet resulting in swallowtail bifurcations. This phenomenon is intimately related to the formation of cusps, which emerge in…

This work deals with the Landau equation in a bounded domain with the Maxwell reflection condition on the boundary for any (possibly smoothly position dependent) accommodation coefficient and for the full range of interaction potentials,…

We establish an estimate on sums of shifted products of Fourier coefficients coming from holomorphic or Maass cusp forms of arbitrary level and nebentypus. These sums are analogous to the binary additive divisor sum which has been studied…

We have studied a two dimensional lattice model of Coulomb glass for a wide range of disorders at $T\sim 0$. The system was first annealed using Monte Carlo simulation. Further minimization of the total energy of the system was done using…

Perturbing the external control parameters of nonlinear systems leads to dramatic changes of its bifurcations. A branch of singular theory, the catastrophe theory, analyses the generating function that depends on state and control…

We introduce a geometric condition of Bloch type which guarantees that a subset of a bounded convex domain in several complex variables is degenerate with respect to every iterated function system. Furthermore we discuss the relations of…

Domain wall networks have attracted renewed interest, particularly in relation to the dynamics of network collapse. Accurately describing this process is challenging and typically requires large scale numerical simulations. Here we adopt a…

We study the effect of dipolar interactions on a magnetic striped monolayer with a microscopic unit cell of square symmetry, and of size $(N_x\times N_y)$ spins. Even if the aspect ratio $r=N_x/N_y$ is very large, an in-plane shape…