The Maximal Kinematical Invariance Group of Fluid Dynamics and Explosion-Implosion Duality

It has recently been found that supernova explosions can be simulated in the laboratory by implosions induced in a plasma by intense lasers. A theoretical explanation is that the inversion transformation, ($\Sigma: t \to -1/t,~ {\bf x}\to {\bf x}/t$), leaves the Euler equations of fluid dynamics, with standard polytropic exponent, invariant. This implies that the kinematical invariance group of the Euler equations is larger than the Galilei group. In this paper we determine, in a systematic manner, the maximal invariance group ${\cal G}$ of general fluid dynamics and show that it is a semi-direct product ${\cal G} = SL(2,R) \wedge G$, where the $SL(2,R)$ group contains the time-translations, dilations and the inversion $\Sigma$, and $G$ is the static (nine-parameter) Galilei group. A subtle aspect of the inclusion of viscosity fields is discussed and it is shown that the Navier-Stokes assumption of constant viscosity breaks the $SL(2, R)$ group to a two-parameter group of time translations and dilations in a tensorial way. The 12-parameter group ${\cal G}$ is also known to be the maximal invariance group of the free Schr\"odinger equation. It originates in the free Hamilton-Jacobi equation which is central to both fluid dynamics and the Schr\"odinger equation.Comment: Plain TeX File: 19 Page

Are stealth scalar fields stable?

Non-gravitating (stealth) scalar fields associated with Minkowski space in scalar-tensor gravity are examined. Analytical solutions for both non-minimally coupled scalar field theory and for Brans-Dicke gravity are studied and their stability with respect to tensor perturbations is assessed using a covariant and gauge-invariant formalism developed for alternative gravity. For Brans-Dicke solutions, the stability with respect to homogeneous perturbations is also studied. There are regions of parameter space corresponding to stability and other regions corresponding to instability.Comment: 10 pages, 1 table, no figures, to appear in Phys. Rev,

SKI-1 and Furin Generate Multiple RGMa Fragments that Regulate Axonal Growth

SummaryThe nervous system is enormously complex, yet the number of cues that control axonal growth is surprisingly meager. Posttranslational modifications amplify diversity, but the degree to which they are employed is unclear. Here, we show that Furin and SKI-1 combine with autocatalytic cleavage and a disulfide bridge to generate four membrane-bound and three soluble forms of the repulsive guidance molecule (RGMa). We provide in vivo evidence that these proprotein convertases are involved in axonal growth and that RGMa cleavage is essential for Neogenin-mediated outgrowth inhibition. Surprisingly, despite no sequence homology, N- and C-RGMa fragments bound the same Fibronectin-like domains in Neogenin and blocked outgrowth. This represents an example in which unrelated fragments from one molecule inhibit outgrowth through a single receptor domain. RGMa is a tethered membrane-bound molecule, and proteolytic processing amplifies RGMa diversity by creating soluble versions with long-range effects as well

Holographic Superconductors with Power-Maxwell field

With the Sturm-Liouville analytical and numerical methods, we investigate the behaviors of the holographic superconductors by introducing a complex charged scalar field coupled with a Power-Maxwell field in the background of $d$-dimensional Schwarzschild AdS black hole. We note that the Power-Maxwell field takes the special asymptotical solution near boundary which is different from all known cases. We find that the larger power parameter $q$ for the Power-Maxwell field makes it harder for the scalar hair to be condensated. We also find that, for different $q$, the critical exponent of the system is still 1/2, which seems to be an universal property for various nonlinear electrodynamics if the scalar field takes the form of this paper.Comment: 14 pages, 1 figure, and 2 table

Modeling the bremsstrahlung emission from converters

The bremsstrahlung angular and energy theoretical distributions delivered from W and UCx thick converters are reported. This study is focussed on initial kinetic energies of the electron beam included in the range 30-60 MeV, suitable for the production of large radiative yields able to induce the $^{238}$U fission. These results offer the possibility to evaluate the required shielding for a neutron rich nuclei source

Transgression forms and extensions of Chern-Simons gauge theories

A gauge invariant action principle, based on the idea of transgression forms, is proposed. The action extends the Chern-Simons form by the addition of a boundary term that makes the action gauge invariant (and not just quasi-invariant). Interpreting the spacetime manifold as cobordant to another one, the duplication of gauge fields in spacetime is avoided. The advantages of this approach are particularly noticeable for the gravitation theory described by a Chern-Simons lagrangian for the AdS group, in which case the action is regularized and finite for black hole geometries in diverse situations. Black hole thermodynamics is correctly reproduced using either a background field approach or a background-independent setting, even in cases with asymptotically nontrivial topologies. It is shown that the energy found from the thermodynamic analysis agrees with the surface integral obtained by direct application of Noether's theorem.Comment: 28 pages, no figures. Minor changes in the introduction, final comments and reference

Thermal properties of halogen-ethane glassy crystals: Effects of orientational disorder and the role of internal molecular degrees of freedom

The thermal conductivity, specific heat, and specific volume of the orientational glass former 1,1,2-trichloro-1,2,2-trifluoroethane (CCl2F-CClF2, F-113) have been measured under equilibrium pressure within the low-temperature range, showing thermodynamic anomalies at ca. 120, 72, and 20 K. The results are discussed together with those pertaining to the structurally related 1,1,2,2-tetrachloro-1,2-difluoroethane (CCl2F-CCl2F, F-112), which also shows anomalies at 130, 90, and 60 K. The rich phase behavior of these compounds can be accounted for by the interplay between several of their degrees of freedom. The arrest of the degrees of freedom corresponding to the internal molecular rotation, responsible for the existence of two energetically distinct isomers, and the overall molecular orientation, source of the characteristic orientational disorder of plastic phases, can explain the anomalies at higher and intermediate temperatures, respectively. The soft-potential model has been used as the framework to describe the thermal properties at low temperatures. We show that the low-temperature anomaly of the compounds corresponds to a secondary relaxation, which can be associated with the appearance of Umklapp processes, i.e., anharmonic phonon-phonon scattering, that dominate thermal transport in that temperature rangeThis work was financially supported in part by the Spanish Ministry of Science and Innovation (Grant Nos. FIS2014-54734-P, FIS2011-23488, and MAT2014-57866- REDT), by the Catalan Government (Grant No. 2014SGR- 0581) and by the Comunidad de Madrid through program NANOFRONTMAG-CM (No. S2013/MIT-2850), as well as by the joint NAS Ukraine and Russian Foundation for Basic Research project “Metastable states of simple condensed systems” (Agreement No. N 7/-2013

Quantum vortices in systems obeying a generalized exclusion principle

The paper deals with a planar particle system obeying a generalized exclusion principle (EP) and governed, in the mean field approximation, by a nonlinear Schroedinger equation. We show that the EP involves a mathematically simple and physically transparent mechanism, which allows the genesis of quantum vortices in the system. We obtain in a closed form the shape of the vortices and investigate its main physical properties. PACS numbers: 03.65.-w, 03.65.Ge, 05.45.YvComment: 7 pages, 4 figure

The non-linear Schr\"odinger equation and the conformal properties of non-relativistic space-time

The cubic non-linear Schr\"odinger equation where the coefficient of the nonlinear term is a function $F(t,x)$ only passes the Painlev\'e test of Weiss, Tabor, and Carnevale only for $F=(a+bt)^{-1}$, where $a$ and $b$ are constants. This is explained by transforming the time-dependent system into the constant-coefficient NLS by means of a time-dependent non-linear transformation, related to the conformal properties of non-relativistic space-time. A similar argument explains the integrability of the NLS in a uniform force field or in an oscillator background.Comment: Thoroughly revised version, in the light of new interest in non-relativistic conformal tranformation, with a new reference list. 8 pages, LaTex, no figures. To be published in Int. J. Theor. Phy