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Metamaterials are composite structures whose properties arise from a mesoscale organization of their constituents. Provided this organization occurs on scales smaller than the characteristic lengths associated with their response, it is…
A 3D layered system of charges with logarithmic interaction parallel to the layers and random dipoles is studied via a novel variational method and an energy rationale which reproduce the known phase diagram for a single layer. Increasing…
Let $M$ be a smooth projective variety and $\mathbf{D}$ an ample normal crossings divisor. From topological data associated to the pair $(M, \mathbf{D})$, we construct, under assumptions on Gromov-Witten invariants, a series of…
Strained coherent heteroepitaxy of III-V semiconductor films such as In$_x$Ga$_{1-x}$As/GaAs has potential for electronic and optoelectronic applications such as high density logic, quantum computing architectures, laser diodes, and other…
Using a collective coordinate numerical optimization procedure, we construct ground-state configurations of interacting particle systems in various space dimensions so that the scattering of radiation exactly matches a prescribed pattern…
The marriage between a two-dimensional layered material (2DLM) and a complex transition metal oxide (TMO) results in a variety of physical and chemical phenomena that would not have been achieved in either material alone. Interesting recent…
Characterization of medium-range order in amorphous materials and its relation to short-range order is discussed. A new topological approach is presented here to extract a hierarchical structure of amorphous materials, which is robust…
Second-order nonlinear optics is the base for a large variety of devices aimed at the active manipulation of light. However, physical principles restrict its occurrence to non-centrosymmetric, anisotropic matter. This significantly limits…
Using transfer operator and fundamental measure theories, we examine the structural and thermodynamic properties of hard rectangles confined between two parallel hard walls. The side lengths of the rectangle ($L$ and $D$, $L>D$) and the…
In this paper, we give a geometric interpretation of optimal functionals in the context of intersection of symmetry planes and cyclic polytopes. For 1D CFTs, we demonstrate that at given derivative order, the functional is given by a…
The two-dimensional XY-model with random phase-shifts on bonds is studied. The analysis is based on a renormalization group for the replicated system. The model is shown to have an ordered phase with quasi long-range order. This ordered…
Polymorphism, the ability of a compound to crystallize in multiple distinct structures, plays a vital role in determining the physical, chemical, and functional properties of materials. Accurate identification and prediction of polymorphic…
A wide range of synthesized crystalline inorganic materials exhibit compositional disorder, where multiple atomic species partially occupy the same crystallographic site. As a result, the physical and chemical properties of such materials…
Low-symmetry 2D materials---such as ReS$_2$ and ReSe$_2$ monolayers, black phosphorus monolayers, group-IV monochalcogenide monolayers, borophene, among others---have more complex atomistic structures than the honeycomb lattices of…
Potentially new, single-atom thick semiconducting 2D-graphene-like material, called Anisotropic-cyclicgraphene, have been generated by the two stage searching strategy linking molecular and ab initio approach. The candidate derived from the…
Optical metamaterials (OMs) at visible wavelengths have been extensively developed. OMs reported recently are all composed of periodic structure, and fabricated by top-down approaches. Here demonstrated are the colored visible light…
Kerr-type nonlinearities form the basis for our physical understanding of nonlinear optical phenomena in condensed matter, such as self-focusing, solitary waves, and wave mixing. In strong fields, they are complemented by higher-order…
We analyze the universal size characteristics of flexible ring polymers in solutions in presence of structural obstacles (impurities) in d dimensions. One encounters such situations when considering polymers in gels, colloidal solutions,…
W-transforms are introduced as uniformity-preserving univariate transformations on the unit interval induced by distribution functions and piecewise strictly monotone functions, and their properties are investigated. When applied…
We analyze the performance of a reduced-order simulation of geometric meta-materials based on zigzag patterns using a simplified representation. As geometric meta-materials we denote planar cellular structures which can be fabricated in 2d…