In this paper we demonstrate uniqueness of a transparent obstacle, of coefficients of rather general boundary transmission condition, and of potential coefficient inside obstacle from partial Dirichlet-to Neumann map or from complete scattering data at fixed frequency. The proposed transmission problem includes in particular isotropic elliptic equation with discontinuous conductivity coefficien...

We study the equilibrium properties of a quantum dot connected to a bulk lead by a single-mode quantum point contact. The ground state energy and other thermodynamic characteristics of the grain show periodic dependence on the gate voltage (Coulomb blockade). We consider the case of almost perfect transmission, and show that the oscillations exist as long as the transmission coefficient of the ...

A local-orbital based ab initio approach to obtain the Green’s function for large heterogeneous systems is developed. First a Green’s function formalism is introduced based on exact diagonalization. Then the self energy is constructed from an incremental scheme, rendering the procedure feasible, while at the same time physical insight into different local correlation contributions is obtained. ...

Animal social network is the key to understand many ecological and epidemiological processes. We used real-time location system (RTLS) to accurately track cattle position, analyze their proximity networks, and tested the hypothesis of temporal stationarity and spatial homogeneity in these networks during different daily time periods and in different areas of the pen. The network structure was a...

We introduce an inside-outside duality approach for the determination of interior transmission eigenvalues of a possibly anisotropic dielectric electromagnetic scattering object using timeharmonic electromagnetic far field data. To this end, we exploit a self-adjoint factorization of the far field operator to link the electromagnetic interior transmission eigenvalues to the maximal or minimal p...

Transmission eigenvalues are points in the spectrum of the interior transmission operator, a coupled 2x2 system of elliptic partial differential equations, where one unknown function must satisfy two boundary conditions and the other must satisfy none. We show that the interior transmission eigenvalues are discrete and depend continuously on the contrast by proving that the interior transmissio...

We consider the transmission eigenvalue problem corresponding to the scattering problem for anisotropic media for both the scalar Helmholtz equation and Maxwell’s equations in the case when the contrast in the scattering media occurs in two independent functions. We prove the existence of an infinite discrete set of transmission eigenvalues provided that the two contrasts are of opposite signs....

We consider the interior transmission eigenvalue problem corresponding to the inverse scattering problem for an isotropic inhomogeneous medium. We first prove that transmission eigenvalues exist for media with index of refraction greater or less than one without assuming that the contrast is sufficiently large. Then we show that for an arbitrary Lipshitz domain with constant index of refraction...

A model for diffusion in liquids that couples the dynamics of tracer particles to a fluctuating Stokes equation for the fluid is investigated in the limit of large Schmidt number. In this limit, the concentration of tracers is shown to satisfy a closed-form stochastic advection-diffusion equation that is used to investigate the collective diffusion of hydrodynamically-correlated tracers through...