Dimension dependent hypercontractivity for Gaussian kernels

We derive sharp, local and dimension dependent hypercontractive bounds on the Markov kernel of a large class of diffusion semigroups. Unlike the dimension free ones, they capture refined properties of Markov kernels, such as trace estimates. They imply classical bounds on the Ornstein-Uhlenbeck semigroup and a dimensional and refined (transportation) Talagrand inequality when applied to the Hamilton-Jacobi equation. Hypercontractive bounds on the Ornstein-Uhlenbeck semigroup driven by a non-diffusive L\'evy semigroup are also investigated. Curvature-dimension criteria are the main tool in the analysis.Comment: 24 page

Light propagation in non-trivial QED vacua

Within the framework of effective action QED, we derive the light cone condition for homogeneous non-trivial QED vacua in the geometric optics approximation. Our result generalizes the ``unified formula'' suggested by Latorre, Pascual and Tarrach and allows for the calculation of velocity shifts and refractive indices for soft photons travelling through these vacua. Furthermore, we clarify the connection between the light velocity shift and the scale anomaly. This study motivates the introduction of a so-called effective action charge that characterizes the velocity modifying properties of the vacuum. Several applications are given concerning vacuum modifications caused by, e.g., strong fields, Casimir systems and high temperature.Comment: 13 pages, REVTeX, 3 figures, to appear in Phys. Rev.

Topological Charged Black Holes in High Dimensional Spacetimes and Their Formation from Gravitational Collapse of a Type II Fluid

Topological charged black holes coupled with a cosmological constant in $R^{2}\times X^{D-2}$ spacetimes are studied, where $X^{D-2}$ is an Einstein space of the form ${}^{(D-2)}R_{AB} = k(D-3) h_{AB}$. The global structure for the four-dimensional spacetimes with $k = 0$ is investigated systematically. The most general solutions that represent a Type $II$ fluid in such a high dimensional spacetime are found, and showed that topological charged black holes can be formed from the gravitational collapse of such a fluid. When the spacetime is (asymptotically) self-similar, the collapse always forms black holes for $k = 0, -1$, in contrast to the case $k = 1$, where it can form either balck holes or naked singularities.Comment: 14 figures, to appear in Phys. Rev.

Universal control of quantum subspaces and subsystems

We describe a broad dynamical-algebraic framework for analyzing the quantum control properties of a set of naturally available interactions. General conditions under which universal control is achieved over a set of subspaces/subsystems are found. All known physical examples of universal control on subspaces/systems are related to the framework developed here.Comment: 4 Pages RevTeX, Some typos fixed, references adde

One-group interfacial area transport in vertical air-water bubbly flow

In the two-fluid model for two-phase flows, interfacial area concentration is one of the most important closure relations that should be obtained from careful mechanistic modeling. The objective of this study is to develop a one-group interfacial area transport equation together with the modeling of the source and sink terms due to bubble breakage and coalescence. For bubble coalescence, two mechanisms are considered to be dominant in vertical two-phase bubbly flow. These are the random collisions between bubbles due to turbulence in the flow field, and the wake entrainment process due to the relative motion of the bubbles in the wake region of a seeding bubble. For bubble breakup, the impact of turbulent eddies is considered. These phenomena are modeled individually, resulting in a one-group interfacial area concentration transport equation with certain parameters to be determined from experimental data. Compared to the measured axial distribution of the interfacial area concentration under various flow conditions, these parameters are obtained for the reduced one-group, one-dimensional transport equation. The results indicate that the proposed models for bubble breakup and coalescence are appropriate

Apparent giant dielectric constants, dielectric relaxation, and ac-conductivity of hexagonal perovskites La1.2Sr2.7BO7.33 (B = Ru, Ir)

We present a thorough dielectric investigation of the hexagonal perovskites La1.2Sr2.7IrO7.33 and La1.2Sr2.7RuO7.33 in a broad frequency and temperature range, supplemented by additional infrared measurements. The occurrence of giant dielectric constants up to 10^5 is revealed to be due to electrode polarization. Aside of dc and ac conductivity contributions, we detect two intrinsic relaxation processes that can be ascribed to ionic hopping between different off-center positions. In both materials we find evidence for charge transport via hopping of localized charge carriers. In the infrared region, three phonon bands are detected, followed by several electronic excitations. In addition, these materials provide further examples for the occurrence of a superlinear power law in the broadband ac conductivity, which recently was proposed to be a universal feature of all disordered matter.Comment: 8 pages, 7 figure

Measurements of interfacial area concentration in two-phase bubbly flow

Interfacial area concentration is an important parameter in the two-fluid model for two-phase flow analysis, which is defined as the total interface area per unit mixture volume and has the following local time-averaged expression: {bar a}{sup t} = 1/{Delta}T {Sigma}{sub j}(1/{vert_bar}V{sub i} {center_dot} n{sub i}{vert_bar}){sub j}, where j denotes the j-th interface that passes the point of interest in a time interval {Delta}T. V{sub i} and n{sub i} refer to the bubble interface velocity and surface normal vector, respectively. To measure this parameter, the double-sensor probe technique is commonly used. Due to the influences of the bubble lateral motions, however, the measurement results should be interpreted via a certain statistic approach. Recently, to take into account the effects of the probe spacing, Wu and Ishii provided the following new formula to correlate the measurable values to the interfacial area concentration: {bar a}{sub i}{sup t} = 2N{sub b}/{Delta}T ({Delta}{bar t}/{Delta}s) [2 + (1.2{sigma}{sub {Delta}t}/{Delta}{bar t}){sup 2.25}], for D = 1.2 {approximately} 2.8 {Delta}s, where N{sub b} refers to the number of the bubbles that hit the probe front tip during time interval {Delta}T, {Delta}s denotes the distance between the two probe tips, D is the bubble diameter, {Delta}{bar t} represents the measured average time interval for an interface to travel through the two probe tips, and {sigma}{sub {Delta}t} is the standard deviation of {Delta}t. The theoretical accuracy of this formula is within {+-} 5% if the sample size is sufficiently large. The purpose of this study is to evaluate this method experimentally using an image processing method

Polymer-Layered Silicate Nanocomposites for Cryotank Applications

Previous composite cryotank designs have relied on the use of conventional composite materials to reduce microcracking and permeability. However, revolutionary advances in nanotechnology derived materials may enable the production of ultra-lightweight cryotanks with significantly enhanced durability and damage tolerance, as well as reduced propellant permeability. Layered silicate nanocomposites are especially attractive in cryogenic storage tanks based on results that have been reported for epoxy nanocomposite systems. These materials often exhibit an order of magnitude reduction in gas permeability when compared to the base resin. In addition, polymer-silicate nanocomposites have been shown to yield improved dimensional stability, strength, and toughness. The enhancement in material performance of these systems occurs without property trade-offs which are often observed in conventionally filled polymer composites. Research efforts at NASA Glenn Research Center have led to the development of epoxy-clay nanocomposites with 70% lower hydrogen permeability than the base epoxy resin. Filament wound carbon fiber reinforced tanks made with this nanocomposite had a five-fold lower helium leak rate than the corresponding tanks made without clay. The pronounced reduction observed with the tank may be due to flow induced alignment of the clay layers during processing. Additionally, the nanocomposites showed CTE reductions of up to 30%, as well as a 100% increase in toughness

Generalized Contour Dynamics: A Review

Contour dynamics is a computational technique to solve for the motion of vortices in incompressible inviscid flow. It is a Lagrangian technique in which the motion of contours is followed, and the velocity field moving the contours can be computed as integrals along the contours. Its best-known examples are in two dimensions, for which the vorticity between contours is taken to be constant and the vortices are vortex patches, and in axisymmetric flow for which the vorticity varies linearly with distance from the axis of symmetry. This review discusses generalizations that incorporate additional physics, in particular, buoyancy effects and magnetic fields, that take specific forms inside the vortices and preserve the contour dynamics structure. The extra physics can lead to time-dependent vortex sheets on the boundaries, whose evolution must be computed as part of the problem. The non-Boussinesq case, in which density differences can be important, leads to a coupled system for the evolution of both mean interfacial velocity and vortex sheet strength. Helical geometry is also discussed, in which two quantities are materially conserved and whose evolution governs the flow