Comparison of methodologies for describing relaxation in nonequilibrium gaseous systems

The heat transfer process in hypervelocity vehicles is dominated by nonequilibrium gas dynamics. One model used in computational fluid dynamics (CFD) codes to predict hypervelocity heat transfer is the 'two-temperature' model. An analysis has been made to test the validity of the two-temperature model for predicting another nonequilibrium phenomenon, sound absorption and deviation of signal speed in a high temperature gas. It is found that the two temperature model's prediction capabilities degenerate with increasing temperature. These results are felt to have significance concerning the two-temperature's ability to predict heat transfer in hypervelocity flows

K−K^- and pˉ\bar p Spectra for Au+Au Collisions at s\sqrt{s} = 200 GeV from STAR, PHENIX and BRAHMS in Comparison to Core-Corona Model Predictions

Based on results obtained with event generators we have launched the core-corona model. It describes in a simplified way but quite successfully the centrality dependence of multiplicity and $$ of identified particles observed in heavy-ion reaction at beam energies between $\sqrt{s}$ = 17 GeV and 200 GeV. Also the centrality dependence of the elliptic flow, $v_2$, for all charged and identified particles could be explained in this model. Here we extend this analysis and study the centrality dependence of single particle spectra of $K^-$ and ${\bar p}$ measured by the PHENIX, STAR and BRAHMS collaborations. We find that also for these particles the analysis of the spectra in the core-corona model suffers from differences in the data published by the different experimental groups, notably for the pp collisions. As for protons and $K^+$ for each experience the data agree well with the prediction of the core-corona model but the value of the two necessary parameters depends on the experiments. We show as well that the average momentum as a function of the centrality depends in a very sensitive way on the particle species and may be quite different for particles which have about the same mass. Therefore the idea to interpret this centrality dependence as a consequence of a collective expansion of the system, as done in blast way fits may be premature.Comment: Invited talk to the CPOD conference Dubna August 201

Cut Size Statistics of Graph Bisection Heuristics

We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut sizes found by ``local'' algorithms becomes peaked as the number of vertices in the graphs becomes large. Evidence is given that this distribution tends towards a Gaussian whose mean and variance scales linearly with the number of vertices of the graphs. Given the distribution of cut sizes associated with each heuristic, we provide a ranking procedure which takes into account both the quality of the solutions and the speed of the algorithms. This procedure is demonstrated for a selection of local graph bisection heuristics.Comment: 17 pages, 5 figures, submitted to SIAM Journal on Optimization also available at http://ipnweb.in2p3.fr/~martin

Transport properties near the Anderson transition

The electronic transport properties in the presence of a temperature gradient in disordered systems near the metal-insulator transition [MIT] are considered. The d.c. conductivity $\sigma$, the thermoelectric power $S$, the thermal conductivity $K$ and the Lorenz number $L_0$ are calculated for the three-dimensional Anderson model of localization using the Chester-Thellung-Kubo-Greenwood formulation of linear response. We show that $\sigma$, S, K and $L_0$ can be scaled to one-parameter scaling curves with a single scaling paramter $k_BT/|{\mu-E_c}/E_c|$.Comment: 4 pages, 4 EPS figures, uses annalen.cls style [included]; presented at Localization 1999, to appear in Annalen der Physik [supplement

Thermoelectric Transport Properties in Disordered Systems Near the Anderson Transition

We study the thermoelectric transport properties in the three-dimensional Anderson model of localization near the metal-insulator transition [MIT]. In particular, we investigate the dependence of the thermoelectric power S, the thermal conductivity K, and the Lorenz number L_0 on temperature T. We first calculate the T dependence of the chemical potential from the number density of electrons at the MIT using averaged density of state obtained by diagonalization. Without any additional approximation, we determine from the chemical potential the behavior of S, K and L_0 at low T as the MIT is approached. We find that the d.c. conductivity and K decrease to zero at the MIT as T -> 0 and show that S does not diverge. Both S and L_0 become temperature independent at the MIT and depend only on the critical behavior of the conductivity.Comment: 11 pages, 10 eps figures, coded with the EPJ macro package, submitted to EPJ

From Loop Groups to 2-Groups

We describe an interesting relation between Lie 2-algebras, the Kac-Moody central extensions of loop groups, and the group String(n). A Lie 2-algebra is a categorified version of a Lie algebra where the Jacobi identity holds up to a natural isomorphism called the "Jacobiator". Similarly, a Lie 2-group is a categorified version of a Lie group. If G is a simply-connected compact simple Lie group, there is a 1-parameter family of Lie 2-algebras g_k each having Lie(G) as its Lie algebra of objects, but with a Jacobiator built from the canonical 3-form on G. There appears to be no Lie 2-group having g_k as its Lie 2-algebra, except when k = 0. Here, however, we construct for integral k an infinite-dimensional Lie 2-group whose Lie 2-algebra is equivalent to g_k. The objects of this 2-group are based paths in G, while the automorphisms of any object form the level-k Kac-Moody central extension of the loop group of G. This 2-group is closely related to the kth power of the canonical gerbe over G. Its nerve gives a topological group that is an extension of G by K(Z,2). When k = +-1, this topological group can also be obtained by killing the third homotopy group of G. Thus, when G = Spin(n), it is none other than String(n).Comment: 40 page