相关论文: Functionally Graded Media

Let $X$ be a differentiable manifold endowed with a transitive action $\alpha:A\times X\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms…

This is the first paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In this paper, we lay the foundations for this study by introducing the…

In these lecture notes we will try to give an introduction to the use of the mathematics of fibre bundles in the understanding of some global aspects of gauge theories, such as monopoles and instantons. They are primarily aimed at beginning…

The physics of disordered media, from metallic glasses to colloidal suspensions, granular matter and biological tissues, offers difficult challenges because it often occurs far from equilibrium, in materials lacking symmetries and evolving…

We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense…

An approach to homogenization of high porosity metallic foams is explored. The emphasis is on the \Alporas{} foam and its representation by means of two-dimensional wire-frame models. The guaranteed upper and lower bounds on the effective…

This work presents a generalized physical interpretation of unconventional dispersion asymmetries associated moving elastic solids. By shifting the notion from systems with time-variant material fields to physically traveling materials, the…

In this paper, algebroid bundle associated to affine metrics provide an structure for unification of gravity and electromagnetism and, geometrization of matter.

We study affine maps between affine manifolds. Even when the fibers are compact and diffeomorphic, two of them can inherit different affine structures from the source space. This leads to a fixed linear holonomy deformation theory of the…

The homogenization of a metamaterial made of a collection of scatterers periodically disposed is studied from three different points of view. Specifically tools for multiple scattering theory, functional analysis, differential geometry and…

We investigate the effect of interstitial liquid on the physical properties of granular media by measuring the angle of repose as a function of the liquid content. The resultant adhesive forces lead to three distinct regimes in the observed…

Hyperuniform materials, characterized by their suppressed density fluctuations and vanishing structure factors as the wave number approaches zero, represent a unique state of matter that straddles the boundary between order and randomness.…

We investigate the behaviour of solutions of a fractional semilinear partial differential equation that models the evolution of an interface in a random medium. We show a pinning result and apply it to the related homogenizing process.

The paper is concerned with dynamics of multi-phase media consisting of a solid permeable material and a compressible Newtonian fluid. Governing macroscopic equations are derived starting from the space-averaged microscopic mass and…

Layered monoidal theories provide a categorical framework for studying scientific theories at different levels of abstraction, via string diagrammatic algebra. We introduce models for three closely related classes of layered monoidal…

We obtain analogues of classical results on automorphism groups of holomorphic fiber bundles, in the setting of group schemes. Also, we establish a lifting property of the connected automorphism group, for torsors under abelian varieties.…

Generalized geometry finds many applications in the mathematical description of some aspects of string theory. In a nutshell, it explores various structures on a generalized tangent bundle associated to a given manifold. In particular,…

A very useful result concerning flatness in Algebraic Geometry is EGA's ``fiber'' criterion. We propose similar fiber criteria to verify flatness of a module while avoiding ``finiteness'' assumptions. Motivated by a Tannakian viewpoint…

In this paper we study the asymptotic behaviour via Gamma-convergence of some integral functionals which model some multi-dimensional structures and depend explicitly on the linearized strain tensor. The functionals are defined in…

Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…