相关论文: Classification of Material G-structures
The study of topology in solids is undergoing a renaissance following renewed interest in the properties of ferroic domain walls as well as recent discoveries regarding topological insulators and skyrmionic lattices. Each of these systems…
We consider several aspects of holomorphic brane configurations. We recently showed that an important part of the defining data of such a configuration is the gluing morphism, which specifies how the constituents of a configuration are…
Intrinsic nonlinear elasticity deals with the deformations of elastic bodies as isometric immersions of Riemannian manifolds into the Euclidean spaces (see Ciarlet [9,10]). In this paper, we study the rigidity and continuity properties of…
The robustness properties of bipartite entanglement in systems of N bosons distributed in M different modes are analyzed using a definition of separability based on commuting algebras of observables, a natural choice when dealing with…
The macroscopic mechanical properties of colloidal particle gels strongly depend on the local arrangement of the powder particles. Experiments have shown that more heterogeneous microstructures exhibit up to one order of magnitude higher…
Structures involving solid particles of nanometric dimensions play an increasingly important role in material sciences. These structures are often characterized through the vibrational properties of their constituent particles, which can be…
Mechanical metamaterials leverage geometric design to achieve unconventional properties, such as high strength at low density, efficient wave guiding, and complex shape morphing. The ability to control shape changes builds on the complex…
We give a geometric characterization of the quantitative non-integrability, introduced by Katz, of strong stable and unstable bundles of partially hyperbolic measures and sets in dimension 3. This is done via the use of higher order…
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…
The damage and fracture of materials are technologically of enormous interest due to their economic and human cost. They cover a wide range of phenomena like e.g. cracking of glass, aging of concrete, the failure of fiber networks in the…
A conception of inhomogeneous locally random distribution of microdefects in crystalline solids is proposed. A method to calculate some physical properties of solids, containing inhomogeneously distributed defects, is developed. A…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
In the homogenization of composite metamaterials the role played by the relative positions of the wires and resonators is not well understood, though essential. We present a general argument which shows that the homogenization of such…
We analyze geometrical structures necessary to represent bulk and surface interactions of standard and substructural nature in complex bodies. Our attention is mainly focused on the influence of diffuse interfaces on sharp discontinuity…
A new method for direct evaluation of both crystalline structure, bulk modulus B_0, and bulk-modulus pressure derivative B'_0 of solid materials with complex crystal structures is presented. The explicit and exact results presented here…
When two chemically passivated solids are brought into contact, interfacial interactions between the solids compete with intrabulk elastic forces. The relative importance of these interactions, which are length-scale dependent, will be…
The theory of inhomogeneous analytic materials is developed. These are materials where the coefficients entering the equations involve analytic functions. Three types of analytic materials are identified. The first two types involve an…
What characterises a solid is its way to respond to external stresses. Ordered solids, such crystals, display an elastic regime followed by a plastic one, both well understood microscopically in terms of lattice distortion and dislocations.…
Existing methods for calculating substructure characteristic modes require treating interconnected metal structures as a single entity to ensure current continuity between different metal bodies. However, when these structures are treated…
This paper challenges some of the common assumptions underlying the mathematics used to describe the physical world. We start by reviewing many of the assumptions underlying the concepts of real, physical, rigid bodies and the translational…