Correlation Functions of Multisite Interaction Spin-S models on the Bethe-like Lattices

Multisite interaction spin-S models in an external magnetic field are studied recursively on the Bethe-like lattices. The transfer-matrix method is extended to calculate exactly the two-spin correlation functions. The exact expressions for the correlation length and magnetic susceptibility are derived for spin-1/2 models. The singularity of the correlation length with critical index $\nu =1$ and the proportionality of magnetic susceptibility to correlation length in the second order phase transition region of spin-1/2 ferromagnetic models on the Bethe-like lattices are established analytically.Comment: 13 pages, In Press Int. J. Mod. Phys.

Three-dimensional simulation of a new cooling strategy for proton exchange membrane fuel cell stack using a non-isothermal multiphase model

In this study, a new cooling strategy for a proton exchange membrane (PEM) fuel cell stack is investigated using a three-dimensional (3D) multiphase non-isothermal model. The new cooling strategy follows that of the Honda's Clarity design and further extends to a cooling unit every five cells in stacks. The stack consists of 5 fuel cells sharing the inlet and outlet manifolds for reactant gas flows. Each cell has 7-path serpentine flow fields with a counter-flow configuration arranged for hydrogen and air streams. The coolant flow fields are set at the two sides of the stack and are simplified as the convective heat transfer thermal boundary conditions. This study also compares two thermal boundary conditions, namely limited and infinite coolant flow rates, and their impacts on the distributions of oxygen, liquid water, current density and membrane hydration. The difference of local temperature between these two cooling conditions is as much as 6.9 K in the 5-cell stack, while it is only 1.7 K in a single cell. In addition, the increased vapor concentration at high temperature (and hence water saturation pressure) dilutes the oxygen content in the air flow, reducing local oxygen concentration. The higher temperature in the stack also causes low membrane hydration, and consequently poor cell performance and non-uniform current density distribution, as disclosed by the simulation. The work indicates the new cooling strategy can be optimized by increasing the heat transfer coefficient between the stack and coolant to mitigate local overheating and cell performance reduction

Optical transitions and nature of Stokes shift in spherical CdS quantum dots

We study the structure of the energy spectra along with the character of the states participating in optical transitions in colloidal CdS quantum dots (QDs) using the {\sl ab initio} accuracy charge patching method combined with the %pseudopotential based folded spectrum calculations of electronic structure of thousand-atom nanostructures. In particular, attention is paid to the nature of the large resonant Stokes shift observed in CdS quantum dots. We find that the top of the valence band state is bright, in contrast with the results of numerous {\bf k$\cdot$p} calculations, and determine the limits of applicability of the {\bf k$\cdot$p} approach. The calculated electron-hole exchange splitting suggests the spin-forbidden valence state may explain the nature of the ``dark exciton'' in CdS quantum dots.Comment: 5 pages, 4 figure

Propagation of high amplitude higher order sounds in slightly soft rectangular ducts, carrying mean flow

The resonance expansion method, developed to study the propagation of sound in rigid rectangular ducts is applied to the case of slightly soft ducts. Expressions for the generation and decay of various harmonics are obtained. The effect of wall admittance is seen through a dissipation function in the system of nonlinear differential equations, governing the generation of harmonics. As the wall admittance increases, the resonance is reduced. For a given wall admittance this phenomenon is stronger at higher input intensities. Both the first and second order solutions are obtained and the results are extended to the case of ducts having mean flow

Varieties of Mathematics in Economics- A Partial View

Real analysis, founded on the Zermelo-Fraenkel axioms, buttressed by the axiom of choice, is the dominant variety of mathematics utilized in the formalization of economic theory. The accident of history that led to this dominance is not inevitable, especially in an age when the digital computer seems to be ubiquitous in research, teaching and learning. At least three other varieties of mathematics, each underpinned by its own mathematical logic, have come to be used in the formalization of mathematics in more recent years. To set theory, model theory, proof theory and recursion theory correspond, roughly speaking, real analysis, non-standard analysis, constructive analysis and computable analysis. These other varieties, we claim, are more consistent with the intrinsic nature and ontology of economic concepts. In this paper we discuss aspects of the way real analysis dominates the mathematical formalization of economic theory and the prospects for overcoming this dominance.

Measuring dark energy with the Eiso−EpE_{\rm iso}-E_{\rm p} correlation of gamma-ray bursts using model-independent methods

In this paper, we use two model-independent methods to standardize long gamma-ray bursts (GRBs) using the $E_{\rm iso}-E_{\rm p}$ correlation, where $E_{\rm iso}$ is the isotropic-equivalent gamma-ray energy and $E_{\rm p}$ is the spectral peak energy. We update 42 long GRBs and try to make constraint on cosmological parameters. The full sample contains 151 long GRBs with redshifts from 0.0331 to 8.2. The first method is the simultaneous fitting method. The extrinsic scatter $\sigma_{\rm ext}$ is taken into account and assigned to the parameter $E_{\rm iso}$. The best-fitting values are $a=49.15\pm0.26$, $b=1.42\pm0.11$, $\sigma_{\rm ext}=0.34\pm0.03$ and $\Omega_m=0.79$ in the flat $\Lambda$CDM model. The constraint on $\Omega_m$ is $0.55<\Omega_m<1$ at the 1$\sigma$ confidence level. If reduced $\chi^2$ method is used, the best-fit results are $a=48.96\pm0.18$, $b=1.52\pm0.08$ and $\Omega_m=0.50\pm0.12$. The second method is using type Ia supernovae (SNe Ia) to calibrate the $E_{\rm iso}-E_{\rm p}$ correlation. We calibrate 90 high-redshift GRBs in the redshift range from 1.44 to 8.1. The cosmological constraints from these 90 GRBs are $\Omega_m=0.23^{+0.06}_{-0.04}$ for flat $\Lambda$CDM, and $\Omega_m=0.18\pm0.11$ and $\Omega_{\Lambda}=0.46\pm0.51$ for non-flat $\Lambda$CDM. For the combination of GRB and SNe Ia sample, we obtain $\Omega_m=0.271\pm0.019$ and $h=0.701\pm0.002$ for the flat $\Lambda$CDM, and for the non-flat $\Lambda$CDM, the results are $\Omega_m=0.225\pm0.044$, $\Omega_{\Lambda}=0.640\pm0.082$ and $h=0.698\pm0.004$. These results from calibrated GRBs are consistent with that of SNe Ia. Meanwhile, the combined data can improve cosmological constraints significantly, comparing to SNe Ia alone. Our results show that the $E_{\rm iso}-E_{\rm p}$ correlation is promising to probe the high-redshift universe.Comment: 10 pages, 6 figures, 4 table, accepted by A&A. Table 4 contains calibrated distance moduli of GRB

Mutual selection in time-varying networks

Copyright @ 2013 American Physical SocietyTime-varying networks play an important role in the investigation of the stochastic processes that occur on complex networks. The ability to formulate the development of the network topology on the same time scale as the evolution of the random process is important for a variety of applications, including the spreading of diseases. Past contributions have investigated random processes on time-varying networks with a purely random attachment mechanism. The possibility of extending these findings towards a time-varying network that is driven by mutual attractiveness is explored in this paper. Mutual attractiveness models are characterized by a linking function that describes the probability of the existence of an edge, which depends mutually on the attractiveness of the nodes on both ends of that edge. This class of attachment mechanisms has been considered before in the fitness-based complex networks literature but not on time-varying networks. Also, the impact of mutual selection is investigated alongside opinion formation and epidemic outbreaks. We find closed-form solutions for the quantities of interest using a factorizable linking function. The voter model exhibits an unanticipated behavior as the network never reaches consensus in the case of mutual selection but stays forever in its initial macroscopic configuration, which is a further piece of evidence that time-varying networks differ markedly from their static counterpart with respect to random processes that take place on them. We also find that epidemic outbreaks are accelerated by uncorrelated mutual selection compared to previously considered random attachment

First principles calculation of lithium-phosphorus co-doped diamond

We calculate the density of states (DOS) and the Mulliken population of the diamond and the co-doped diamonds with different concentrations of lithium (Li) and phosphorus (P) by the method of the density functional theory, and analyze the bonding situations of the Li-P co-doped diamond thin films and the impacts of the Li-P co-doping on the diamond conductivities. The results show that the Li-P atoms can promote the split of the diamond energy band near the Fermi level, and improve the electron conductivities of the Li-P co-doped diamond thin films, or even make the Li-P co-doped diamond from semiconductor to conductor. The effect of Li-P co-doping concentration on the orbital charge distributions, bond lengths and bond populations is analyzed. The Li atom may promote the split of the energy band near the Fermi level as well as may favorably regulate the diamond lattice distortion and expansion caused by the P atom.Comment: 14 pages, 11 figure