Vanishing Viscosity Approach to the Compressible Euler Equations for Transonic Nozzle and Spherically Symmetric Flows

We are concerned with globally defined entropy solutions to the Euler equations for compressible fluid flows in transonic nozzles with general cross-sectional areas. Such nozzles include the de Laval nozzles and other more general nozzles whose cross-sectional area functions are allowed at the nozzle ends to be either zero (closed ends) or infinity (unbounded ends). To achieve this, in this paper, we develop a vanishing viscosity method to construct globally defined approximate solutions and then establish essential uniform estimates in weighted $L^p$ norms for the whole range of physical adiabatic exponents $\gamma\in (1, \infty)$, so that the viscosity approximate solutions satisfy the general $L^p$ compensated compactness framework. The viscosity method is designed to incorporate artificial viscosity terms with the natural Dirichlet boundary conditions to ensure the uniform estimates. Then such estimates lead to both the convergence of the approximate solutions and the existence theory of globally defined finite-energy entropy solutions to the Euler equations for transonic flows that may have different end-states in the class of nozzles with general cross-sectional areas for all $\gamma\in (1, \infty)$. The approach and techniques developed here apply to other problems with similar difficulties. In particular, we successfully apply them to construct globally defined spherically symmetric entropy solutions to the Euler equations for all $\gamma\in (1, \infty)$.Comment: 32 page

Nuclear Magnetic Resonance Implementation of a Quantum Clock Synchronization Algorithm

The quantum clock synchronization algorithm proposed by I. L. Chuang (Phys. Rev. Lett, 85, 2006(2000)) has been implemented in a three qubit nuclear magnetic resonance quantum system. The effective-pure state is prepared by the spatial averaging approach. The time difference between two separated clocks can be determined by reading out directly through the NMR spectra.Comment: 13 pages, 5 figure

Nonlinearity and hysteresis of resonant strain gauges

Nonlinearity and hysteresis effects of electrostatically activated, voltage driven resonant microbridges have been studied theoretically and experimentally. It is shown, that, in order to avoid vibration instability and hysteresis to occur, the choices of the ax. and d.c. driving voltages and of the quality factor of a resonator, with a given geometry and choice of materials, are limited by a hysteresis criterion. The limiting conditions are also formulated as hysteresis-free design rules. An expression for the maximum attainable figure of merit is also given. Experimental results, as obtained from electrostatically driven vacuum-encapsulated polysilicon microbridges, are presented and show good agreement with the theory

Scattering by a contact potential in three and lower dimensions

We consider the scattering of nonrelativistic particles in three dimensions by a contact potential $\Omega\hbar^2\delta(r)/ 2\mu r^\alpha$ which is defined as the $a\to 0$ limit of $\Omega\hbar^2\delta(r-a)/2\mu r^\alpha$. It is surprising that it gives a nonvanishing cross section when $\alpha=1$ and $\Omega=-1$. When the contact potential is approached by a spherical square well potential instead of the above spherical shell one, one obtains basically the same result except that the parameter $\Omega$ that gives a nonvanishing cross section is different. Similar problems in two and one dimensions are studied and results of the same nature are obtained.Comment: REVTeX, 9 pages, no figur

Canonical Charmonium Interpretation for Y(4360) and Y(4660)

In this work, we consider the canonical charmonium assignments for Y(4360) and Y(4660). Y(4660) is good candidate of $\rm 5 ^3S_1$ $c\bar{c}$ state, the possibility of Y(4360) as a $\rm 3 ^3D_1$ $c\bar{c}$ state is studied, and the charmonium hybrid interpretation of Y(4360) can not be excluded completely. We evaluate the $e^{+}e^{-}$ leptonic widths, E1 transitions, M1 transitions and the open flavor strong decays of Y(4360) and Y(4660). Experimental tests for the charmonium assignments are suggested.Comment: 32 pages, 4 figure

Klotho controls the brain-immune system interface in the choroid plexus.

Located within the brain's ventricles, the choroid plexus produces cerebrospinal fluid and forms an important barrier between the central nervous system and the blood. For unknown reasons, the choroid plexus produces high levels of the protein klotho. Here, we show that these levels naturally decline with aging. Depleting klotho selectively from the choroid plexus via targeted viral vector-induced knockout in Klotho flox/flox mice increased the expression of multiple proinflammatory factors and triggered macrophage infiltration of this structure in young mice, simulating changes in unmanipulated old mice. Wild-type mice infected with the same Cre recombinase-expressing virus did not show such alterations. Experimental depletion of klotho from the choroid plexus enhanced microglial activation in the hippocampus after peripheral injection of mice with lipopolysaccharide. In primary cultures, klotho suppressed thioredoxin-interacting protein-dependent activation of the NLRP3 inflammasome in macrophages by enhancing fibroblast growth factor 23 signaling. We conclude that klotho functions as a gatekeeper at the interface between the brain and immune system in the choroid plexus. Klotho depletion in aging or disease may weaken this barrier and promote immune-mediated neuropathogenesis