Electrodynamics under a Possible Alternative to the Lorentz Transformation

A generalization of the classical electrodynamics for systems in absolute motion is presented using a possible alternative to the Lorentz transformation. The main hypothesis assumed in this work are: a) The inertial transformations relate two inertial frames: the privileged frame S and the moving frame S' with velocity v with respect to S. b) The transformation of the fields from S to the moving frame S' is given by H'=a(H - v D) and E'=a(E + v B) where a is a matrix whose elements depend of the absolute velocity of the system. c) The constitutive relations in the moving frame S' are given by D'= \epsilon E', B'= \mu H' and J'=\eta E'. It is found that Maxwell's equations, which are transformed to the moving frame, take a new form depending on the absolute velocity of the system. Moreover, differing from classical electrodynamics, it is proved that the electrodynamics proposed explains satisfactorily the Wilson effect.Comment: LaTeX, 15page

Airborne Fraunhofer Line Discriminator

Airborne Fraunhofer Line Discriminator enables prospecting for fluorescent materials, hydrography with fluorescent dyes, and plant studies based on fluorescence of chlorophyll. Optical unit design is the coincidence of Fraunhofer lines in the solar spectrum occurring at the characteristic wavelengths of some fluorescent materials

The Cube Recurrence

We construct a combinatorial model that is described by the cube recurrence, a nonlinear recurrence relation introduced by Propp, which generates families of Laurent polynomials indexed by points in $\mathbb{Z}^3$. In the process, we prove several conjectures of Propp and of Fomin and Zelevinsky, and we obtain a combinatorial interpretation for the terms of Gale-Robinson sequences. We also indicate how the model might be used to obtain some interesting results about perfect matchings of certain bipartite planar graphs

Traffic Analysis in Random Delaunay Tessellations and Other Graphs

In this work we study the degree distribution, the maximum vertex and edge flow in non-uniform random Delaunay triangulations when geodesic routing is used. We also investigate the vertex and edge flow in Erd\"os-Renyi random graphs, geometric random graphs, expanders and random $k$-regular graphs. Moreover we show that adding a random matching to the original graph can considerably reduced the maximum vertex flow.Comment: Submitted to the Journal of Discrete Computational Geometr

Topological changes of two-dimensional magnetic textures

We investigate the interaction of magnetic vortices and skyrmions with a spin-polarized current. In a square lattice, fixed classical spins and quantum itinerant electrons, evolve according to the coupled Landau-Lifshitz and Schr\"odinger equations. Changes in the topology occur at microscopic time and length scales, and are shown to be triggered by the nucleation of a nontrivial electron-spin structure at the vortex core.Comment: See supplementary material (high resolution figures and movies) https://drive.google.com/folderview?id=0By4j_RJ9SKLpQ2R5UklXLURvbEE&usp=sharing --- v2: Extended versio