相关论文: Fresnel coefficients as hyperbolic rotations

We prove Fourier restriction estimates by means of the polynomial partitioning method for compact subsets of any sufficiently smooth hyperbolic hypersurface in threedimensional euclidean space. Our approach exploits in a crucial way the…

We consider a diffusion process with coefficients that are periodic outside of an 'interface region' of finite thickness. The question investigated in the articles [1,2] is the limiting long time / large scale behaviour of such a process…

By using some tools of analysis, we establish some analytical properties such as monotonicity and inequalities involving the hyperbolic sine integral function. As applications of some of the established properties, we obtain some rational…

Matrix factorizations of a hypersurface yield a description of the asymptotic structure of minimal free resolutions over the hypersurface. We introduce a new concept of matrix factorizations for complete intersections that allows us to…

This work considers the propagation of high-frequency waves in highly-scattering media where physical absorption of a nonlinear nature occurs. Using the classical tools of the Wigner transform and multiscale analysis, we derive semilinear…

Hyperbolic propagation offers exciting opportunities in nanophotonics, from sub-diffraction imaging to enhanced local density of states. This transport regime is typically induced by strong modulation of conductivity, i.e., with alternating…

We consider the nonlinear degenerate parabolic equation of porous medium type, whose diffusion is driven by the (spectral) fractional Laplacian on the hyperbolic space. We provide existence results for solutions, in an appropriate weak…

By expressing the time-independent Schrodinger equation in one dimension as a system of two first-order differential equations, the transfer matrix for a rectangular potential barrier is obtained making use of the matrix exponential. It is…

Polaritons travelling along a hyperbolic medium's surface have recently sparked significant interest in nanophotonics for the unprecedented manipulation ability on light at the nanoscale in a planar way, promising potential nano-optical…

Magnetically induced topological transitions of isofrequency surfaces of bulk waves propagating through an unbounded biaxial gyrotropic medium are studied. The medium is constructed from a two-component superlattice composed of magnetized…

The purpose of the paper is to suggest a new method which allows one to study multiple coherent reflection/transmissions by partially transparent interfaces (e.g. in multi-layer mesoscopic structures or grain boundaries in high-Tc's) in the…

We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…

We present a number of arguments to demonstrate that a quantum analog of Cherenkov effect occurs when two dispersive objects are in relative motion. Specifically we show that two semi-infinite plates experience friction beyond a threshold…

The interaction of radio-frequency waves with a plasma is described by a Fokker-Planck equation with an added quasilinear term. Methods for solving this equation on a computer are discussed.

We introduce a coarse flow space for relatively hyperbolic groups and use it to verify a regularity condition for the action of relatively hyperbolic groups on their boundaries. As an application the Farrell-Jones Conjecture for relatively…

The geometry of hypersurfaces is generalized to pseudo-hypersurfaces, which are defined by Pfaff equations. The general methods are then applied to modeling the kinematics of motion constrained by a single linear, non-holonomic constraint.…

Diffusion within porous media, such as biological tissues, exhibits departures from conventional Fick's laws, which could result in space-fractional diffusion. The paper considers a reaction-diffusion system with two spatial compartments --…

By means of a particle model that includes interactions only via the local particle concentration, we show that hyperballistic diffusion may result. This is done by findng the exact solution of the corresponding non-linear diffusion…

The paper investigates solutions of the fractional hyperbolic diffusion equation in its most general form with two fractional derivatives of distinct orders. The solutions are given as spatial-temporal homogeneous and isotropic random…

The two-dimensional transient problem that is studied concerns a semi-infinite crack in an isotropic solid comprising an infinite strip and a half-plane joined together and having the same elastic constants. The crack propagates along the…