Equivalence Principle, Higher Dimensional Moebius Group and the Hidden Antisymmetric Tensor of Quantum Mechanics

We show that the recently formulated Equivalence Principle (EP) implies a basic cocycle condition both in Euclidean and Minkowski spaces, which holds in any dimension. This condition, that in one-dimension is sufficient to fix the Schwarzian equation [6], implies a fundamental higher dimensional Moebius invariance which in turn univocally fixes the quantum version of the Hamilton-Jacobi equation. This holds also in the relativistic case, so that we obtain both the time-dependent Schroedinger equation and the Klein-Gordon equation in any dimension. We then show that the EP implies that masses are related by maps induced by the coordinate transformations connecting different physical systems. Furthermore, we show that the minimal coupling prescription, and therefore gauge invariance, arises quite naturally in implementing the EP. Finally, we show that there is an antisymmetric two-tensor which underlies Quantum Mechanics and sheds new light on the nature of the Quantum Hamilton-Jacobi equation.Comment: 1+48 pages, LaTeX. Expanded version, two appendices, several comments, including comparison with Einstein Equivalence Principle, added. Typos corrected, one reference added. To appear in CQ

Cryogenic seal concept for static and dynamic conditions

Seal rings reduce cryogenic pump seal leakage under static and dynamic conditions. The rings are fitted into annular diaphragms, which are affected by cryogenic pressure and temperature, to move against a mating ring, to increase seal-bearing loads under static conditions

Solid particle erosion and viscoelastic properties of thermoplastic polyurethanes

The wear resistance of several thermoplastic polyurethanes (TPUs) having different chemical nature and micronscale arrangement of the hard and soft segments has been investigated by means of erosion and abrasion tests. The goal was correlating the erosion performances of the materials to their macroscopic mechanical properties. Unlike conventional tests, such as hardness and tensile measurements, viscoelastic analysis proved to be a valuable tool to study the erosion resistance of TPUs. In particular, a strict correlation was found between the erosion rate and the high-frequency (~10^7 Hz) loss modulus. The latter reflects the actual ability of TPU to dissipate the impact energy of the erodent particles

Flux control of cytochrome c oxidase in human skeletal muscle

In the present work, by titrating cytochrome c oxidase (COX) with the specific inhibitor KCN, the flux control coefficient and the metabolic reserve capacity of COX have been determined in human saponin-permeabilized muscle fibers. In the presence of the substrates glutamate and malate, a 2.3 ± 0.2-fold excess capacity of COX was observed in ADP-stimulated human skeletal muscle fibers. This value was found to be dependent on the mitochondrial substrate supply. In the combined presence of glutamate, malate, and succinate, which supported an approximately 1.4-fold higher rate of respiration, only a 1.4 ± 0.2-fold excess capacity of COX was determined. In agreement with these findings, the flux control of COX increased, in the presence of the three substrates, from 0.27 ± 0.03 to 0.36 ± 0.08. These results indicate a tight in vivo control of respiration by COX in human skeletal muscle. This tight control may have significant implications for mitochondrial myopathies. In support of this conclusion, the analysis of skeletal muscle fibers from two patients with chronic progressive external ophthalmoplegia, which carried deletions in 11 and 49% of their mitochondrial DNA, revealed a substantially lowered reserve capacity and increased flux control coefficient of COX, indicating severe rate limitations of oxidative phosphorylation by this enzyme

On fractional Choquard equations

We investigate a class of nonlinear Schrodinger equations with a generalized Choquard nonlinearity and fractional diffusion. We obtain regularity, existence, nonexistence, symmetry as well as decays properties.Comment: revised version, 22 page

Spin Susceptibility of Interacting Two-dimensional Electrons with Anisotropic Effective Mass

We report measurements of the spin susceptibility in dilute (rs up to 10) AlAs two-dimensional (2D) electrons occupying a single conduction-band valley with an anisotropic in-plane Fermi contour, characterized by longitudinal and transverse effective masses, ml and mt. As the density is decreased, the spin susceptibility is significantly enhanced over its band value, reflecting the role of interaction. Yet the enhancement is suppressed compared to the results of quantum Monte Carlo based calculations that take the finite thickness of the electron layer into account but assume an isotropic effective mass equal to sqrt(ml.mt). Proper treatment of an interacting 2D system with an anisotropic effective mass therefore remains a theoretical challenge.Comment: 4 pages, 3 figures, accepted for publication in Phys. Rev.

Black holes in asymptotically Lifshitz spacetimes with arbitrary critical exponent

Recently, a class of gravitational backgrounds in 3+1 dimensions have been proposed as holographic duals to a Lifshitz theory describing critical phenomena in 2+1 dimensions with critical exponent $z\geq 1$. We numerically explore black holes in these backgrounds for a range of values of $z$. We find drastically different behavior for $z>2$ and $z2$ ($z<2$) the Lifshitz fixed point is repulsive (attractive) when going to larger radial parameter $r$. For the repulsive $z>2$ backgrounds, we find a continuous family of black holes satisfying a finite energy condition. However, for $z<2$ we find that the finite energy condition is more restrictive, and we expect only a discrete set of black hole solutions, unless some unexpected cancellations occur. For all black holes, we plot temperature $T$ as a function of horizon radius $r_0$. For $z\lessapprox 1.761$ we find that this curve develops a negative slope for certain values of $r_0$ possibly indicating a thermodynamic instability.Comment: 23 pages, 6 figures, references corrected, graphs made readable in greyscal

Thermodynamics of black branes in asymptotically Lifshitz spacetimes

Recently, a class of gravitational backgrounds in 3+1 dimensions have been proposed as holographic duals to a Lifshitz theory describing critical phenomena in 2+1 dimensions with critical exponent $z\geq 1$. We continue our earlier work \cite{Bertoldi:2009vn}, exploring the thermodynamic properties of the "black brane" solutions with horizon topology $\mathbb{R}^2$. We find that the black branes satisfy the relation $\mathcal{E}=\frac{2}{2+z}Ts$ where $\mathcal{E}$ is the energy density, $T$ is the temperature, and $s$ is the entropy density. This matches the expected behavior for a 2+1 dimensional theory with a scaling symmetry $(x_1,x_2)\to \lambda (x_1,x_2)$, $t\to \lambda^z t$.Comment: 8 pages, references added and regroupe

Electromagnetic shape resonances of a dielectric sphere and radiation of portable telephones

The frequency band used by cellular telephones includes the eigenfrequencies of a dielectric sphere with physical characteristics close to those of a human head. Proceeding from the spatial features of the natural modes of such a sphere we propose an independent and clear evident accuracy test for the complicated numerical calculations which are conducted when estimating the potential hazard due to the use of cellular telephones, in particular, for the check of a proper handling of the electromagnetic shape resonances of a human head.Comment: 10 pages, 1 figure with 2 eps file