Solving conical diffraction with integral equations

Off-plane scattering of time-harmonic plane waves by a diffraction grating with arbitrary conductivity and general border profile is considered in a rigorous electromagnetic formulation. The integral equations for conical diffraction were obtained using the boundary integrals of the single and double layer potentials including the tangential derivative of single layer potentials interpreted as singular integrals. We derive an important formula for the calculation of the absorption in conical diffraction. Some rules which are expedient for the numerical implementation of the theory are presented. The efficiencies and polarization angles compared with those obtained by Lifeng Li for transmission and reflection gratings are in a good agreement. The code developed and tested is found to be accurate and efficient for solving off-plane diffraction problems including high-conductive surfaces, borders with edges, real border profiles, and gratings working at short wavelengths

Sensitivity analysis of 2D photonic band gaps of any rod shape and conductivity using a very fast conical integral equation method

The conical boundary integral equation method has been proposedto calculate the sensitive optical response of 2D photonic band gaps (PBGs),including dielectric, absorbing, and high-conductive rods of various shapes working in any wavelength range. It is possible to determine the diffracted field by computing the scattering matrices separately for any gratingboundary profile. The computation of the matrices is based on the solution of a 2 x 2system of singular integral equations at each interface between two different materials. The advantage of our integral formulation is that the discretization of the integral equations system and the factorization of the discrete matrices, which takes the major computing time, are carried out only oncefor a boundary. It turned out that a small number of collocation points per boundary combined with a high convergence rate can provide adequate description of the dependence on diffracted energy of very different PBGs illuminated at arbitrary incident and polarization angles. Thenumerical results presented describe the significant impact of rod shape on diffraction in PBGs supporting polariton-plasmon excitation, particularly in the vicinity of resonances and at high fillingratios. The diffracted energy response calculated vs. array cell geometry parameters was found to vary from a few percent up to a few hundred percent. The influence of other types of anomalies (i.e. waveguide anomalies, cavity modes, Fabry-Perot and Bragg resonances, Rayleigh orders, etc), conductivity, and polarization states on the optical response has been demonstrated

The Entrepreneurial Mindset: Strategies for Continuously Creating Opportunity in an Age of Uncertainty

This book summarizes the practical implications of our accumulation of experience, research studies, and active teaching and working with business organizations attempting to deal with uncertainty and with entrepreneurs learning to launch and grow their businesses. The primary thrust of the book—that uncertainty can yield tremendous opportunity when looked at in the right way—has long been topic at the heart of the academic study of entrepreneurship. Using lessons drawn from leading entrepreneurs and entrepreneurial companies, this book presents a set of practices for capitalizing on certainty and rapid change. Throughout this book, we have provided figures and tables that allow readers to generate scores and derive conclusions. These material are based on considerable theoretical and empirical research

The effect of copper doping on martensite shear stress in porous TiNi (Mo, Fe, Cu) alloys

The properties of alloys based on porous nickel-titanium (TiNi) with copper additives have bee

An alternate model for magnetization plateaus in the molecular magnet V_15

Starting from an antiferromagnetic Heisenberg Hamiltonian for the fifteen spin-1/2 ions in V_15, we construct an effective spin Hamiltonian involving eight low-lying states (spin-1/2 and spin-3/2) coupled to a phonon bath. We numerically solve the time-dependent Schrodinger equation of this system, and obtain the magnetization as a function of temperature in a time-dependent magnetic field. The magnetization exhibits unusual patterns of hysteresis and plateaus as the field sweep rate and temperature are varied. The observed plateaus are not due to quantum tunneling but are a result of thermal averaging. Our results are in good agreement with recent experimental observations.Comment: Revtex, 4 pages, 5 eps figure

Conservation equation on braneworlds in six dimensions

We study braneworlds in six-dimensional Einstein-Gauss-Bonnet gravity. The Gauss-Bonnet term is crucial for the equations to be well-posed in six dimensions when non-trivial matter on the brane is included (the also involved induced gravity term is not significant for their structure), and the matching conditions of the braneworld are known. We show that the energy-momentum of the brane is always conserved, independently of any regular bulk energy-momentum tensor, contrary to the situation of the five-dimensional case.Comment: References added, minor changes, 3 pages, RevTeX, to app. in Class. Quant. Gra

The Calder\'{o}n inverse problem for isotropic quasilinear conductivities

We prove a global uniqueness result for the Calder\'{o}n inverse problem for a general quasilinear isotropic conductivity equation on a bounded open set with smooth boundary in dimension $n\ge 3$. Performing higher order linearizations of the nonlinear Dirichlet--to--Neumann map, we reduce the problem of the recovery of the differentials of the quasilinear conductivity, which are symmetric tensors, to a completeness property for certain anisotropic products of solutions to the linearized equation. The completeness property is established using complex geometric optics solutions to the linearized conductivity equation, whose amplitudes concentrate near suitable two dimensional planes

Rational Strain Engineering in Delafossite Oxides for Highly Efficient Hydrogen Evolution Catalysis in Acidic Media

The rational design of hydrogen evolution reaction (HER) electrocatalysts which are competitive with platinum is an outstanding challenge to make power-to-gas technologies economically viable. Here, we introduce the delafossites PdCrO$_2$, PdCoO$_2$ and PtCoO$_2$ as a new family of electrocatalysts for the HER in acidic media. We show that in PdCoO$_2$ the inherently strained Pd metal sublattice acts as a pseudomorphic template for the growth of a strained (by +2.3%) Pd rich capping layer under reductive conditions. The surface modification continuously improves the electrocatalytic activity by simultaneously increasing the exchange current density j$_0$ from 2 to 5 mA/cm$^2_{geo}$ and by reducing the Tafel slope down to 38 mV/decade, leading to overpotentials $\eta_{10}$ < 15 mV for 10 mA/cm$^2_{geo}$, superior to bulk platinum. The greatly improved activity is attributed to the in-situ stabilization of a $\beta$-palladium hydride phase with drastically enhanced surface catalytic properties with respect to pure or nanostructured palladium. These findings illustrate how operando induced electrodissolution can be used as a top-down design concept for rational surface and property engineering through the strain-stabilized formation of catalytically active phases

Classical Stabilization of Homogeneous Extra Dimensions

If spacetime possesses extra dimensions of size and curvature radii much larger than the Planck or string scales, the dynamics of these extra dimensions should be governed by classical general relativity. We argue that in general relativity, it is highly nontrivial to obtain solutions where the extra dimensions are static and are dynamically stable to small perturbations. We also illustrate that intuition on equilibrium and stability built up from non-gravitational physics can be highly misleading. For all static, homogeneous solutions satisfying the null energy condition, we show that the Ricci curvature of space must be nonnegative in all directions. Much of our analysis focuses on a class of spacetime models where space consists of a product of homogeneous and isotropic geometries. A dimensional reduction of these models is performed, and their stability to perturbations that preserve the spatial symmetries is analyzed. We conclude that the only physically realistic examples of classically stabilized large extra dimensions are those in which the extra-dimensional manifold is positively curved.Comment: 25 pages; minor changes, improved reference