Global Well-posedness of the 3D Primitive Equations With Partial Vertical Turbulence Mixing Heat Diffusion

The three--dimensional incompressible viscous Boussinesq equations, under the assumption of hydrostatic balance, govern the large scale dynamics of atmospheric and oceanic motion, and are commonly called the primitive equations. To overcome the turbulence mixing a partial vertical diffusion is usually added to the temperature advection (or density stratification) equation. In this paper we prove the global regularity of strong solutions to this model in a three-dimensional infinite horizontal channel, subject to periodic boundary conditions in the horizontal directions, and with no-penetration and stress-free boundary conditions on the solid, top and bottom, boundaries. Specifically, we show that short time strong solutions to the above problem exist globally in time, and that they depend continuously on the initial data

Thermal Entanglement between Alternate Qubits of a Four-qubit Heisenberg XX Chain in a Magnetic Field

The concurrence of two alternate qubits in a four-qubit Heisenberg XX chain is investigated when a uniform magnetic field B is included. It is found that there is no thermal entanglement between alternate qubits if B is close to zero. Magnetic field can induce entanglement in a certain range both for the antiferromagnetic and ferromagnetic cases. Near zero temperature, the entanglement undergoes two sudden changes with increasing value of the magnetic field B. This is due to the changes in the ground state. This novel property may be used as quantum entanglement switch. The anisotropy in the system can also induce the entanglement between two alternate qubits.Comment: 10 pages, 3 figure

Pressure Regularity Criterion for the Three-dimensional Navier-Stokes Equations in Infinite Channel

In this paper we consider the three-dimensional Navier-Stokes equations in an infinite channel. We provide a sufficient condition, in terms of $\partial_z p$, where $p$ is the pressure, for the global existence of the strong solutions to the three-dimensional Navier-Stokes equations

Trivial Stationary Solutions to the Kuramoto-Sivashinsky and Certain Nonlinear Elliptic Equations

We show that the only locally integrable stationary solutions to the integrated Kuramoto-Sivashinsky equation in $R$ and $R^2$ are the trivial constant solutions. We extend our technique and prove similar results to other nonlinear elliptic problems in $\R^N$.Comment: 10 pages, Journal Articl

A new conducting polymer with exceptional visible-light photocatalytic activity derived from varbituric acid polycondensation

Abstract A novel covalent, metal-free, photocatalytic material is prepared by thermal polymerization of barbituric acid (BA). The structure of the photocatalyst is analyzed by using scanning electron microscopy, X-ray diffraction, and infrared, UV?visible, and 1H solution and 13C solid-state NMR spectroscopy. The photodegradation efficiency of BA thermally polymerized at different temperatures is tested by photocatalytic degradation of aquatic rhodamine B (RhB) dye under visible-light irradiation. It is shown that heating BA at an optimized temperature of 300 °C, that is, still in the range that polymer-like polycondensation takes place, results in a photocatalyst that can remove RhB with 96% photodegradation efficiency after 70 min exposure to visible light. The polycondensation reaction of BA is identified to process through precipitation of trimer units as primary building blocks. Reference experiments such as addition of scavengers and saturation with oxygen are studied to understand the photodegradation process. It is shown that the presence of triethanolamine, and excess of oxygen and p-benzoquinone in the solution of RhB and photocatalyst (BA300) is not beneficial, but decreases the photodegradation efficiency