Mixing solutions for the Muskat problem

We prove the existence of mixing solutions of the incompressible porous media equation for all Muskat type $H^5$ initial data in the fully unstable regime.Comment: 88 pages, 2 figure

Entanglement of two-qubit photon beam by magnetic field

We have studied the possibility of affecting the entanglement measure of 2-qubit system consisting of two photons with different fixed frequencies but with two arbitrary linear polarizations, moving in the same direction, by the help of an applied external magnetic field. The interaction between the magnetic field and the photons in our model is achieved through intermediate electrons that interact with both the photons and the magnetic field. The possibility of exact theoretical analysis of this scheme is based on known exact solutions that describe the interaction of an electron subjected to an external magnetic field (or a medium of electrons not interacting with each other) with a quantized field of two photons. We adapt these exact solutions to the case under consideration. Using explicit wave functions for the resulting electromagnetic field, we calculate the entanglement measure of the photon beam as a function of the applied magnetic field and parameters of the electron medium

An Overview of Mexico’s Citrus Industry

This report looks at Mexico’s citrus industry and its relationship to the United States. Information on Mexico’s citrus production, utilization and trade are discussed.Mexico, citrus industry, International Relations/Trade,

Superconducting states of pure and doped graphene

We study the superconducting phases of the two-dimensional honeycomb lattice of graphene. We find two spin singlet pairing states, s-wave and an exotic $p+ip$ that is possible because of the special structure of the honeycomb lattice. At half filling, the $p+ip$ phase is gapless and superconductivity is a hidden order. We discuss the possibility of a superconducting state in metal coated graphene.Comment: 4 pages, 6 figure