The Angular Momentum Distribution within Halos in Different Dark Matter Models

We study the angular momentum profile of dark matter halos for a statistical sample drawn from a set of high-resolution cosmological simulations of $256^3$ particles. Two typical Cold Dark Matter (CDM) models have been analyzed, and the halos are selected to have at least $3\times 10^4$ particles in order to reliably measure the angular momentum profile. In contrast with the recent claims of Bullock et al., we find that the degree of misalignment of angular momentum within a halo is very high. About 50 percent of halos have more than 10 percent of halo mass in the mass of negative angular momentum $j$. After the mass of negative $j$ is excluded, the cumulative mass function $M(<j)$ follows approximately the universal function proposed by Bullock et al., though we still find a significant fraction of halos ($\sim 50$) which exhibit systematic deviations from the universal function. Our results, however, are broadly in good agreement with a recent work of van den Bosch et al.. We also study the angular momentum profile of halos in a Warm Dark Matter (WDM) model and a Self-Interacting Dark Matter (SIDM) model. We find that the angular momentum profile of halos in the WDM is statistically indistinguishable from that in the CDM model, but the angular momentum of halos in the SIDM is reduced by the self-interaction of dark matter.Comment: 23 pages, 10 figures, 2 tables. Revised version, added a new table, accepted for publication in MNRA

Effect of charged impurities on graphene thermoelectric power near the Dirac point

In graphene devices with a varying degree of disorders as characterized by their carrier mobility and minimum conductivity, we have studied the thermoelectric power along with the electrical conductivity over a wide range of temperatures. We have found that the Mott relation fails in the vicinity of the Dirac point in high-mobility graphene. By properly taking account of the high temperature effects, we have obtained good agreement between the Boltzmann transport theory and our experimental data. In low-mobility graphene where the charged impurities induce relatively high residual carrier density, the Mott relation holds at all gate voltages

Fermionic realization of two-parameter quantum affine algebra Ur,s(sln)U_{r,s}({sl_n})

We construct all fundamental modules for the two parameter quantum affine algebra of type $A$ using a combinatorial model of Young diagrams. In particular we also give a fermionic realization of the two-parameter quantum affine algebra

Growth Tight Actions

We introduce and systematically study the concept of a growth tight action. This generalizes growth tightness for word metrics as initiated by Grigorchuk and de la Harpe. Given a finitely generated, non-elementary group $G$ acting on a $G$--space $\mathcal{X}$, we prove that if $G$ contains a strongly contracting element and if $G$ is not too badly distorted in $\mathcal{X}$, then the action of $G$ on $\mathcal{X}$ is a growth tight action. It follows that if $\mathcal{X}$ is a cocompact, relatively hyperbolic $G$--space, then the action of $G$ on $\mathcal{X}$ is a growth tight action. This generalizes all previously known results for growth tightness of cocompact actions: every already known example of a group that admits a growth tight action and has some infinite, infinite index normal subgroups is relatively hyperbolic, and, conversely, relatively hyperbolic groups admit growth tight actions. This also allows us to prove that many CAT(0) groups, including flip-graph-manifold groups and many Right Angled Artin Groups, and snowflake groups admit cocompact, growth tight actions. These provide first examples of non-relatively hyperbolic groups admitting interesting growth tight actions. Our main result applies as well to cusp uniform actions on hyperbolic spaces and to the action of the mapping class group on Teichmueller space with the Teichmueller metric. Towards the proof of our main result, we give equivalent characterizations of strongly contracting elements and produce new examples of group actions with strongly contracting elements.Comment: 29 pages, 4 figures v2 added references v3 40 pages, 6 figures, expanded preliminary sections to make paper more self-contained, other minor improvements v4 updated bibliography, to appear in Pacific Journal of Mathematic

Na/beta-alumina/NaAlCl4, Cl2/C circulating cell

A study was made of a high specific energy battery based on a sodium negative electrode and a chlorine positive electrode with molten AlCl3-NaCl electrolyte and a solid beta alumina separator. The basic performance of a Na beta-alumina NaAlCl4, Cl2/C circulating cell at 200 C was demonstrated. This cell can be started at 150 C. The use of melting sodium chloroaluminate electrolyte overcomes some of the material problems associated with the high working temperatures of present molten salt systems, such as Na/S and LiAl/FeS, and retains the advantages of high energy density and relatively efficient electrode processes. Preliminary investigations were conducted on a sodium-chlorine static cell, material compability, electrode design, wetting, and theoretical calculations to assure a better chance of success before assembling a Na/Cl2 circulating cell. Mathematical models provide a theoretical explanation for the performance of the NaCl2 battery. The results of mathematical models match the experimental results very well. According to the result of the mathematical modeling, an output at 180 mA/sq cm and 3.2 V can be obtained with optimized cell design

A Conjecture about Raising Operators for Macdonald Polynomials

A multivariable hypergeometric-type formula for raising operators of the Macdonald polynomials is conjectured. It is proved that this agrees with Jing and Jozefiak's expression for the two-row Macdonald polynomials, and also with Lassalle and Schlosser's formula for partitions with length three.Comment: 13 page

Quantum entropy of the Kerr black hole arising from gravitational perturbation

The quantum entropy of the Kerr black hole arising from gravitational perturbation is investigated by using Null tetrad and \'t Hooft\'s brick-wall model. It is shown that effect of the graviton\'s spins on the subleading correction is dependent of the square of the spins and the angular momentum per unit mass of the black hole, and contribution of the logarithmic term to the entropy will be positive, zero, and negative for different value of $a/r_+$.Comment: 8 pages, 1 figure, Latex. to appear in Phys. Rev.

Accurate determination of the Lagrangian bias for the dark matter halos

We use a new method, the cross power spectrum between the linear density field and the halo number density field, to measure the Lagrangian bias for dark matter halos. The method has several important advantages over the conventional correlation function analysis. By applying this method to a set of high-resolution simulations of 256^3 particles, we have accurately determined the Lagrangian bias, over 4 magnitudes in halo mass, for four scale-free models with the index n=-0.5, -1.0, -1.5 and -2.0 and three typical CDM models. Our result for massive halos with $M \ge M_*$ ($M_*$ is a characteristic non-linear mass) is in very good agreement with the analytical formula of Mo & White for the Lagrangian bias, but the analytical formula significantly underestimates the Lagrangian clustering for the less massive halos $M < M_*. Our simulation result however can be satisfactorily described, with an accuracy better than 15%, by the fitting formula of Jing for Eulerian bias under the assumption that the Lagrangian clustering and the Eulerian clustering are related with a linear mapping. It implies that it is the failure of the Press-Schechter theories for describing the formation of small halos that leads to the inaccuracy of the Mo & White formula for the Eulerian bias. The non-linear mapping between the Lagrangian clustering and the Eulerian clustering, which was speculated as another possible cause for the inaccuracy of the Mo & White formula, must at most have a second-order effect. Our result indicates that the halo formation model adopted by the Press-Schechter theories must be improved.Comment: Minor changes; accepted for publication in ApJ (Letters) ; 11 pages with 2 figures include