Bishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry

We prove a Bishop volume comparison theorem and a Laplacian comparison theorem for three dimensional contact subriemannian manifolds with symmetry

Suppression of Superconducting Critical Current Density by Small Flux Jumps in MgB2MgB_2 Thin Films

By doing magnetization measurements during magnetic field sweeps on thin films of the new superconductor $MgB_2$, it is found that in a low temperature and low field region small flux jumps are taking place. This effect strongly suppresses the central magnetization peak leading to reduced nominal superconducting critical current density at low temperatures. A borderline for this effect to occur is determined on the field-temperature (H-T) phase diagram. It is suggested that the small size of the flux jumps in films is due to the higher density of small defects and the relatively easy thermal diffusion in thin films in comparison with bulk samples.Comment: 7 figures Phys. Rev. B accepted scheduled issue: 01 Feb 200

Non-Fermi liquid behavior and scaling of low frequency suppression in optical conductivity spectra of CaRuO3_3

Optical conductivity spectra $\sigma_1(\omega)$ of paramagnetic CaRuO$_3$ are investigated at various temperatures. At T=10 K, it shows a non-Fermi liquid behavior of $\sigma_1(\omega)\sim 1/{\omega}^{\frac 12}$, similar to the case of a ferromagnet SrRuO$_3$. As the temperature ($T$) is increased, on the other hand, $\sigma_1(\omega)$ in the low frequency region is progressively suppressed, deviating from the 1/{\omega}^{\frac 12%}-dependence. Interestingly, the suppression of $\sigma_1(\omega)$ is found to scale with $\omega /T$ at all temperatures. The origin of the $$ scaling behavior coupled with the non-Fermi liquid behavior is discussed.Comment: 4 pages, 3 figure

Tracing the String: BMN correspondence at Finite J^2/N

Employing the string bit formalism of hep-th/0209215, we identify the basis transformation that relates BMN operators in N=4 gauge theory to string states in the dual string field theory at finite g_2=J^2/N. In this basis, the supercharge truncates at linear order in g_2, and the mixing amplitude between 1 and 2-string states precisely matches with the (corrected) answer of hep-th/0206073 for the 3-string amplitude in light-cone string field theory. Supersymmetry then predicts the order g_2^2 contact term in the string bit Hamiltonian. The resulting leading order mass renormalization of string states agrees with the recently computed shift in conformal dimension of BMN operators in the gauge theory.Comment: 11 pages, 1 figur

Baryonium, tetra-quark state and glue-ball in large N_c QCD

From the large-N_c QCD point of view, baryonia, tetra-quark states, hybrids, and glueballs are studied. The existence of these states is argued for. They are constructed from baryons. In N_f=1 large N_c QCD, a baryonium is always identical to a glueball with N_c valence gluons. The ground state 0^{-+} glueball has a mass about 2450 MeV. f_0(1710) is identified as the lowest 0^{++} glueball. The lowest four-quark nonet should be f_0(1370), a_0(1450), K^*_0(1430) and f_0(1500). Combining with the heavy quark effective theory, spectra of heavy baryonia and heavy tetra-quark states are predicted. 1/N_c corrections are discussed.Comment: 16 pages, 3 figure

Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI0_0

Using the methods developed for the Bianchi I case we have shown that a boostrap argument is also suitable to treat the future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI$_0$. These solutions are asymptotic to the Collins-Stewart solution with dust and the Ellis-MacCallum solution respectively. We have thus generalized the results obtained by Rendall and Uggla in the case of locally rotationally symmetric Bianchi II spacetimes to the reflection symmetric case. However we needed to assume small data. For Bianchi VI$_0$ there is no analogous previous result.Comment: 30 page

The Cauchy problems for Einstein metrics and parallel spinors

We show that in the analytic category, given a Riemannian metric $g$ on a hypersurface $M\subset \Z$ and a symmetric tensor $W$ on $M$, the metric $g$ can be locally extended to a Riemannian Einstein metric on $Z$ with second fundamental form $W$, provided that $g$ and $W$ satisfy the constraints on $M$ imposed by the contracted Codazzi equations. We use this fact to study the Cauchy problem for metrics with parallel spinors in the real analytic category and give an affirmative answer to a question raised in B\"ar, Gauduchon, Moroianu (2005). We also answer negatively the corresponding questions in the smooth category.Comment: 28 pages; final versio

Processing of ultrafine-size particulate metal matrix composites by advanced shear technology

Copyright @ 2009 ASM International. This paper was published in Metallurgical & Materials Transactions A 40A(3) and is made available as an electronic reprint with the permission of ASM International. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplications of any material in this paper for a fee or for commercial purposes, or modification of the content of this paper are prohibited.Lack of efficient mixing technology to achieve a uniform distribution of fine-size reinforcement within the matrix and the high cost of producing components have hindered the widespread adaptation of particulate metal matrix composites (PMMCs) for engineering applications. A new rheo-processing method, the melt-conditioning high-pressure die-cast (MC-HPDC) process, has been developed for manufacturing near-net-shape components of high integrity. The MC-HPDC process adapts the well-established high shear dispersive mixing action of a twin-screw mechanism to the task of overcoming the cohesive force of the agglomerates under a high shear rate and high intensity of turbulence. This is followed by direct shaping of the slurry into near-net-shape components using an existing cold-chamber die-casting process. The results indicate that the MC-HPDC samples have a uniform distribution of ultrafine-sized SiC particles throughout the entire sample in the as-cast condition. Compared to those produced by conventional high-pressure die casting (HPDC), MC-HPDC samples have a much improved tensile strength and ductility.EP-SR

The influence of gene expression time delays on Gierer-Meinhardt pattern formation systems

There are numerous examples of morphogen gradients controlling long range signalling in developmental and cellular systems. The prospect of two such interacting morphogens instigating long range self-organisation in biological systems via a Turing bifurcation has been explored, postulated, or implicated in the context of numerous developmental processes. However, modelling investigations of cellular systems typically neglect the influence of gene expression on such dynamics, even though transcription and translation are observed to be important in morphogenetic systems. In particular, the influence of gene expression on a large class of Turing bifurcation models, namely those with pure kinetics such as the Gierer–Meinhardt system, is unexplored. Our investigations demonstrate that the behaviour of the Gierer–Meinhardt model profoundly changes on the inclusion of gene expression dynamics and is sensitive to the sub-cellular details of gene expression. Features such as concentration blow up, morphogen oscillations and radical sensitivities to the duration of gene expression are observed and, at best, severely restrict the possible parameter spaces for feasible biological behaviour. These results also indicate that the behaviour of Turing pattern formation systems on the inclusion of gene expression time delays may provide a means of distinguishing between possible forms of interaction kinetics. Finally, this study also emphasises that sub-cellular and gene expression dynamics should not be simply neglected in models of long range biological pattern formation via morphogens