Related papers: Electromagnetic analysis of arbitrarily shaped pin…
We establish spectral expansions of homogeneous and isotropic random fields taking values in the $3$-dimensional Euclidean space $E^3$ and in the space $\mathsf{S}^2(E^3)$ of symmetric rank $2$ tensors over $E^3$. The former is a model of…
This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors.…
We examine some of the optical properties of a metamaterial consisting of thin layers of alternating metal and dielectric. We can model this material as a homogeneous effective medium with anisotropic dielectric permittivity. When the…
This paper presents a technique, combining the integral equations (IE) and the Generalized Sheet Transition Conditions (GSTCs) with bianisotropic susceptibility tensors, to compute electromagnetic wave scattering by cylindrical metasurfaces…
Designing anisotropic structured materials by reducing symmetry results in unique behaviors, such as shearing under uniaxial compression or tension. This direction-dependent coupled mechanical phenomenon is crucial for applications such as…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
We study the reflectional symmetry of a surface in the Euclidean 3-dimensional space with a cross-cap singularity with respect to planes. This symmetry is picked up by the singularities of folding maps on the cross-cap. We give a list of…
This paper presents a mathematical framework for a flexible pressure-sensor model using electrical impedance tomography (EIT). When pressure is applied to a conductive membrane patch with clamped boundary, the pressure-induced surface…
We develop, from first principles, a general and compact formalism for predicting the electromagnetic response of a metamaterial with non-magnetic inclusions in the long wavelength limit, including spatial dispersion up to the second order.…
The application of transformation optics to the development of intriguing electromagnetic devices can produce weakly anisotropic or isotropic media with the assistance of quasi-conformal and/or conformal mapping, as opposed to the strongly…
Conductive organic polymers can be formulated with polymers that incorporate fine dispersed metallic particles. In this work, we present a general model for ferrogels which are chemically cross-linked polymer networks swollen with a…
Permittivity tensors of arbitrary shaped invisibility devices are obtained using effective medium approach in general relativity. As special cases, analytical expressions for the permittivity tensors of invisibility cloaks for the elliptic…
We present a hydrodynamic theory of anisotropic and inversion-asymmetric moving active permeable fluid membranes. These are described by an anisotropic Kardar-Parisi-Zhang equation. Depending upon the anisotropy parameters, the membrane is…
We present a high-accuracy procedure for electronic structure calculations of strongly correlated materials. To address limitations in current electronic structure methods, we employ density functional theory in combination with the…
We derive an expression for the Maxwell stress tensor in a magnetic dielectric medium specified by its permittivity "epsilon" and permeability "mu." The derivation proceeds from the generalized form of the Lorentz law, which specifies the…
We propose a general method to arbitrarily manipulate an electromagnetic wave propagating in a two-dimensional medium, without introducing any scattering. This leads to a whole class of isotropic spatially varying permittivity and…
This paper introduces a method to synthesize a 3D tensor field within a constrained geometric domain represented as a tetrahedral mesh. Whereas previous techniques optimize for isotropic fields, we focus on anisotropic tensor fields that…
Coordinate-transformation approaches to invisibility cloaking rely on the design of an anisotropic, spatially inhomogeneous "transformation medium" capable of suitably re-routing the energy flux around the region to conceal without causing…
In this article we characterize the range of the attenuated and non-attenuated $X$-ray transform of compactly supported symmetric tensor fields in the Euclidean plane. The characterization is in terms of a Hilbert-transform associated with…
In many applications it is advantageous to construct effective slip boundary conditions, which could fully characterize flow over patterned surfaces. Here we focus on laminar shear flows over smooth anisotropic surfaces with arbitrary…