This study provides a least-squares-based numerical approach to estimate the boundary value geodesic trajectory and associated parametric velocity on curved surfaces. The is based Theory of Functional Connections, an analytical framework perform functional interpolation. Numerical examples are provided for set two-dimensional quadrics, including ellipsoid, elliptic hyperboloid, paraboloid, hype...

In this paper we describe the formation of fingers from ionization fronts for a hydrodynamic plasma model. The fingers result from a balance between the destabilizing effect of impact ionization and the stabilizing effect of electron diffusion on ionization fronts. We show that electron diffusion acts as an effective surface tension on moving fronts and estimate analytically the size of the fin...

As an analog model of general relativity, optics on some two-dimensional (2D) curved surfaces has received increasing attention in the past decade. Here, light Huygens–Fresnel principle, we propose a theoretical frame to study propagation along arbitrary geodesics any 2D surfaces. This theory not only enables us solve enigma “infinite intensity” that existed previously at artificial singulariti...

First, an acceleration to compute the impedance matrix obtained from electric field integral equation (EFIE) discretized by Galerkin method of moments (MoM) with Rao–Wilton–Glisson basis functions is addressed. It based on a far-field approximation and makes it possible avoid looping source observation triangles. Next, split into strong weak interactions; latter compressed expressing Toeplitz s...

In this article, we check and develop further some postulates of the theory and mathematical modeling of combined toxic effect that we proposed earlier [1]. To this end, we have analyzed the results of an experiment on rats exposed during 6 weeks to repeated intraperitoneal injections of lead acetate, sodium fluoride or both. The development of intoxication was estimated quantitatively with 54 ...

Parabolic compound refractive lenses (CRLs) for hard X rays have been used to image the electron beam at undulator and bending-magnet beamlines at the ESRF. The measurements yield the shape and size of the synchrotron radiation source, and show that CRLs with paraboloid surface shape can be used as a beam diagnostics tool at highenergy electron storage rings. The optical resolution of the imagi...

Modern space modules are susceptible to EM radiation from both external and internal sources within the space module. Since the EM waves for various operations are frequently in the high-frequency domain, asymptotic raytheoretic methods are often the most optimal choice for deterministic EM field analysis. In this work, surface modeling of a typical manned space module is done by hybridizing a ...