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We investigate localization properties in the highly anisotropic and intrinsically disordered layered material, which is analogous to high-Tc cuprates. By varying the anisotropy of the system which is parameterized by the interlayer hopping…
Ca3Ru2O7 is a correlated and spin-orbit-coupled system with an extraordinary anisotropy. It is both interesting and unique largely because this material exhibits conflicting phenomena that are often utterly inconsistent with traditional…
We study the possibility of realizing exotic smooth structures on punctured simply connected $4$-manifolds as leaves of a codimension one foliation on a compact manifold. In particular, we show the existence of uncountably many smooth open…
For a given class of materials, universal displacements are those displacements that can be maintained for any member of the class by applying only boundary tractions. In this paper we study universal displacements in compressible…
Multiscale periodic metamaterials have been designed for numerous applications, such as impact absorption, acoustic cloaking, photonic band gaps, and mechanical logic gates. This prior work has focused on optimizing mesoscale structure for…
In this paper we review some recent results concerning inverse problems for thin elastic plates. The plate is assumed to be made by non-homogeneous linearly elastic material belonging to a general class of anisotropy. A first group of…
The Exotic Model arises from adding a special exotic invariant to the Supersymmetric Standard Model. The Exotic Model has a supersymmetry violating mass spectrum without using spontaneous or explicit breaking of supersymmetry. The splitting…
There is an increasing interest in the study of metamaterials and periodic materials across disciplines. These are anisotropic and their properties present directionality. For example, the wave speed depends on the propagation direction.…
This paper studies properly embedded surfaces in the 4-ball that are exotically knotted (i.e., topologically but not smoothly isotopic), and leverages this local phenomenon to study surfaces in larger 4-manifolds. The main results provide a…
The special interest is devoted to such situations when the material space of our object with affine degrees of freedom has generally lower dimension than the one of the physical space. In other words when we have the $m$-dimensional…
The strain-energy formulation of nonlinear elasticity can be extended to the case of significant compression by modulating suitable strain energy terms by a function of relative volume. For isotropic materials this can be accomplished by…
We identify the restricted class of attainable effective deformations in a model of reinforced composites with parallel, long, and fully rigid fibers embedded in an elastic body. In mathematical terms, we characterize the weak limits of…
With the achievement on the additive manufacturing, the mechanical properties of architectured materials can be precisely designed by tailoring microstructures. As one of the primary design objectives, the elastic isotropy is of great…
Periodic structures can be engineered to exhibit unique properties observed at symmetry points, such as zero group velocity, Dirac cones and saddle points; identifying these, and the nature of the associated modes, from a direct reading of…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
The use of discrete material representation in numerical models is advantageous due to the straightforward way it takes into account material heterogeneity and randomness, and the discrete and orientated nature of cracks. Unfortunately, it…
Living materials such as membranes, cytoskeletal assemblies, cell collectives and tissues can often be described as active solids -- materials that are energized from within, with elastic response about a well defined reference…
Nonlinear elastic theory studies the elastic constants of a material (such as Young's modulus or bulk modulus) as a power series in the applied load. The inverse bulk modulus K, for example depends on the compression P: $ {1/ K(P)} = c_0 +…
It is known that the long line supports $2^{\aleph_1}$ many non-diffeomorphic differential structures. We show that the long plane supports a similar number of exotic differential structures, ie structures which are not merely diffeomorphic…
Despite their outstanding mechanical properties, with many industrial applications, a rational and systematic design of new and controlled auxetic materials remains poorly developed. Here a unified framework is established to describe…