Related papers: Analytic Materials
Exactly solvable models are interesting for science and education, since they help in scientific search and in understanding of phenomena. Some exact solutions for simple quantum-mechanical models are considered. The models include two…
This is a survey of recent progress in several areas of combinatorial algebra. We consider combinatorial problems about free groups, polynomial algebras, free associative and Lie algebras. Our main idea is to study automorphisms and, more…
We study homogenization by Gamma-convergence of periodic multiple integrals of the calculus of variations when the integrand can take infinite values outside of a convex set of matrices.
Metamaterials are nano-engineered media with designed properties beyond those available in nature with applications in all aspects of materials science. In particular, metamaterials have shown promise for next generation of optical…
Providing a sound appraisal of the nature of the relationship between flow $(Q)$ and pressure drop $(\Delta P)$ for porous media is a long-standing fundamental research challenge. A wide variety of environmental, societal and industrial…
A new future for metamaterials is suggested, involving the insertion of quantum degrees of freedom, under the guise of quantum dots or cold atoms, in an photonic matrix. It is argued that new emergent, quantum, properties could be obtained.
We find a new type of boundary layers that occur at the top and bottom surfaces of an inhomogeneous plate. The boundary layers of this type never occur in homogeneous plates or plates made of layers of homogeneous materials. The thickness…
Rigorous theories connecting physical properties of a heterogeneous material to its microstructure offer a promising avenue to guide the computational material design and optimization. We present here an efficient Fourier-space based…
The inclusion of rigid elements into elastic composites may lead to superior mechanical properties for the equivalent elastic continuum, such as, for instance, extreme auxeticity. To allow full exploitation of these properties, a tool for…
A wide variety of real random composites can be studied by means of prototypes of multiphase microstructures with a controllable spatial inhomogeneity. To create them, we propose a versatile model of randomly overlapping super-spheres of a…
A homogenization result for a family of integral energies is presented, where the fields are subjected to periodic first order oscillating differential constraints in divergence form. The work is based on the theory of A -quasiconvexity…
Two key types of inhomogeneous spatially dispersive media are described, both based on a spatially dispersive generalisation of the single resonance model of permittivity. The boundary conditions for two such media with different properties…
Adequate characterization of two-dimensional materials with low energy barriers for impurity adsorption is key for advancing applications based on catalysis, sensing, and surface functionalization. However, first-principles methods, such as…
For convex optimization problems Bregman divergences appear as regret functions. Such regret functions can be defined on any convex set but if a sufficiency condition is added the regret function must be proportional to information…
Many geologic materials have a composite structure, in which macroscopic mechanical behavior is determined by the properties, shape, and heterogeneous distribution of individual constituents. In particular, sedimentary rocks commonly…
Data comes in many forms. From a shallow perspective, they can be viewed as being either in structured (e.g., as a relation, as key-value pairs) or unstructured (e.g., text, image) formats. So far, machines have been fairly good at…
The homogenization of a composite material comprising three isotropic dielectric materials was investigated. The component materials were randomly distributed as spherical particles, with the particles of two of the component materials…
A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…
Metamaterials are artificial materials designed to exhibit effective material parameters that go beyond those found in nature. Composed of unit cells with rich designability that are assembled into multiscale systems, they hold great…
Two choices are possible for the refractive index of a linear, homogeneous, isotropic, active, dielectric material. Either of the choices is adequate for obtaining frequency-domain solutions for (i) scattering by slabs, spheres, and other…