Related papers: Emergent continuous symmetry in anisotropic flexib…
Lattice {\em Kirigami}, ultra-light metamaterials, poly-disperse aggregates, ceramic nano-lattices, and two-dimensional (2-D) atomic materials share an inherent structural discreteness, and their material properties evolve with their shape.…
Using dynamical-mean-field theory for clusters, we study the two-dimensional Hubbard model in which electrons are coupled with the orthorhombic lattice distortions through the modulation in the hopping matrix. Instability towards…
It is shown that the Goldstone modes associated with a broken continuous symmetry lead to anomalously large fluctuations of the zero field order parameter at any temperature below T_c. In dimensions 2<d<4, the variance of the extensive…
The jamming transition, generally manifested by a rapid increase of rigidity under compression (i.e., compression hardening), is ubiquitous in amorphous materials. Here we study shear hardening in deeply annealed frictionless packings…
We demonstrate the existence of sudden, finite-time, singularities, with constant scale factor, expansion rate and density, in expanding Bianchi type IX universes with free anisotropic pressures. A new type of non-simultaneous anisotropic…
We study a discrete model of an heterogeneous elastic line with internal disorder, submitted to thermal fluctuations. The monomers are connected through random springs with independent and identically distributed elastic constants drawn…
Nanophotonics enables unprecedented control over light-matter interactions, yet conventional isotropic materials limit the spectral range and mode response in subwavelength structures. Anisotropic nanoparticles -- ubiquitous in natural and…
We are concerned with supersonic vortex sheets for the Euler equations of compressible inviscid fluids in two space dimensions. For the problem with constant coefficients, in [10] the authors have derived a pseudo-differential equation…
While topological phases have been extensively studied in amorphous systems in recent years, it remains unclear whether the random nature of amorphous materials can give rise to higher-order topological phases that have no crystalline…
We show that nonlinear continuum elasticity can be effective in modeling plastic flows in crystals if it is viewed as Landau theory with an infinite number of equivalent energy wells whose configuration is dictated by the symmetry group…
Continuum elasticity is a powerful tool applicable in a broad range of physical systems and phenomena. Yet, understanding how and on what scales material disorder may lead to the breakdown of continuum elasticity is not fully understood. We…
The propagation of acoustic or elastic waves in artificial crystals, including the case of phononic and sonic crystals, is inherently anisotropic. As is known from the theory of periodic composites, anisotropy is directly dictated by the…
We study homogeneous cosmological models featuring shift-symmetric scalar fields (or, superfluids) in relative motion. In the presence of anisotropy this universe generally features rotation, in the sense that the principal axes of…
We revise the statistical properties of the primordial cosmological density anisotropies that, at the time of matter radiation equality, seeded the gravitational development of large scale structures in the, otherwise, homogeneous and…
Pattern formation induced by wrinkling is a very common phenomenon exhibited in soft-matter substrates. In all these systems wrinkles develop in presence of compressively stressed thin films lying on compliant substrates. Here we…
The main result of this work is a homogenization theorem via variational convergence for elastic materials with stiff checkerboard-type heterogeneities under the assumptions of physical growth and non-self-interpenetration. While the…
The fact that a disordered material is not constrained in its properties in the same way as a crystal presents significant and yet largely untapped potential for novel material design. However, unlike their crystalline counterparts,…
In this paper we explore the theory of the anisotropic porous medium equation in the slow diffusion range. After revising the basic theory, we prove the existence of self-similar fundamental solutions (SSFS) of the equation posed in the…
Universal displacements are those displacements that can be maintained for any member of a specific class of linear elastic materials in the absence of body forces, solely by applying boundary tractions. For linear hyperelastic (Green…
Nanoscale molecular transport plays a crucial role in regulating mass diffusion and responsiveness in condensed matter systems. In soft porous crystals, in particular, adsorption of guest molecules induces host framework deformation and…