the mathematical aspect of cartographic mapping is a process which establishes a unique connection between points of the earth’s sphere and their images on a plane. it was proven in differential geometry that an isometric mapping of a sphere onto a plane with all corresponding distances on both surfaces remaining identical can never be achieved since the two surfaces do not possess the same gau...

An analytical solution is presented that reconstructs residual stress field from limited and incomplete data.  The inverse problem of reconstructing residual stresses is solved using an appropriate form of the airy stress function.  This function is chosen to satisfy the stress equilibrium equations together with the boundary conditions for a domain within a convex polygon.  The analytical solu...

We establish that the static height fluctuations of a particular growth model, the PNG droplet, converges upon proper rescaling to a limit process, which we call the Airy process, A(y). The Airy process is stationary, it has continuous sample paths, its single “time” (fixed y) distribution is the Tracy–Widom distribution of the largest eigenvalue of a GUE random matrix, and the Airy process has...

An analytic expression of transmittance based on the Airy wavefunctions approach has been derived for an electron through an anisotropic heterostructure with an applied voltage to the barrier of the heterostructure. The Si(110)|Si0.5Ge0.5|Si(110) heterostructure was used to examine the analytic expression. In order to evaluate the Airy wavefunctions approach, the transfer matrix method, which i...

We establish that the static height fluctuations of a particular growth model, the PNG droplet, converges upon proper rescaling to a limit process, which we call the Airy process, A(y). The Airy process is stationary, it has continuous sample paths, its single “time” (fixed y) distribution is the Tracy–Widom distribution of the largest eigenvalue of a GUE random matrix, and the Airy process has...

We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0 F 3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the ano...

A compact all-fiber plasmonic Airy-like beam generator is demonstrated. A single slit and a 1D groove array were fabricated by focused ion beam milling on the gold deposited end facet of a single-mode optical fiber. The single slit excites the surface plasmonic polaritons (SPPs), which are decoupled into free space by the groove array. The phase of decoupling SPPs is adjusted by the grooves pos...

We compare observed Pioneer Venus orbiter (PVO) gravity profiles over Aphrodite Terra to profiles predicted from models of thermal isostasy, mantle convection, and Airy compensation. Similar approaches are used in order to investigate how well the models can be distinguished with the PVO data. Topography profiles across Aphrodite are compared to model spreading ridge profiles in order to furthe...

We examine selective reflection (SR) spectrum of an Airy beam at an interface between a dielectric and a homogeneous atomic medium. It is shown that both the general reflection (GR) and the SR of Airy beams exhibit accelerating dynamics with a parabolic trajectory, however, the accelerating rate for the SR is slightly greater than that for the GR. Due to interaction of atoms and the Airy beams ...