Spherical Functions Associated With the Three Dimensional Sphere

In this paper, we determine all irreducible spherical functions \Phi of any K -type associated to the pair (G,K)=(\SO(4),\SO(3)). This is accomplished by associating to \Phi a vector valued function H=H(u) of a real variable u, which is analytic at u=0 and whose components are solutions of two coupled systems of ordinary differential equations. By an appropriate conjugation involving Hahn polynomials we uncouple one of the systems. Then this is taken to an uncoupled system of hypergeometric equations, leading to a vector valued solution P=P(u) whose entries are Gegenbauer's polynomials. Afterward, we identify those simultaneous solutions and use the representation theory of \SO(4) to characterize all irreducible spherical functions. The functions P=P(u) corresponding to the irreducible spherical functions of a fixed K-type \pi_\ell are appropriately packaged into a sequence of matrix valued polynomials (P_w)_{w\ge0} of size (\ell+1)\times(\ell+1). Finally we proved that \widetilde P_w={P_0}^{-1}P_w is a sequence of matrix orthogonal polynomials with respect to a weight matrix W. Moreover we showed that W admits a second order symmetric hypergeometric operator \widetilde D and a first order symmetric differential operator \widetilde E.Comment: 49 pages, 2 figure

Felix Alexandrovich Berezin and his work

This is a survey of Berezin's work focused on three topics: representation theory, general concept of quantization, and supermathematics.Comment: LaTeX, 27 page

Warehouse commodity classification from fundamental principles. Part II: Flame heights and flame spread

In warehouse storage applications, it is important to classify the burning behavior of commodities and rank them according to their material flammability for early fire detection and suppression operations. In this study, a preliminary approach towards commodity classification is presented that models the early stage of large-scale warehouse fires by decoupling the problem into separate processes of heat and mass transfer. Two existing nondimensional parameters are used to represent the physical phenomena at the large-scale: a mass transfer number that directly incorporates the material properties of a fuel, and the soot yield of the fuel that controls the radiation observed in the large-scale. To facilitate modeling, a mass transfer number (or B-number) was experimentally obtained using mass-loss (burning rate) measurements from bench-scale tests, following from a procedure that was developed in Part I of this paper. Two fuels are considered: corrugated cardboard and polystyrene. Corrugated cardboard provides a source of flaming combustion in a warehouse and is usually the first item to ignite and sustain flame spread. Polystyrene is typically used as the most hazardous product in large-scale fire testing. The nondimensional mass transfer number was then used to model in-rack flame heights on 6.19.1 m (2030 ft) stacks of 'C' flute corrugated cardboard boxes on rack-storage during the initial period of flame spread (involving flame spread over the corrugated cardboard face only). Good agreement was observed between the model and large-scale experiments during the initial stages of fire growth, and a comparison to previous correlations for in-rack flame heights is included. © 2011 Elsevier Ltd. All rights reserved

Warehouse commodity classification from fundamental principles. Part I: Commodity & burning rates

An experimental study was conducted to investigate the burning behavior of an individual Group A plastic commodity over time. The objective of the study was to evaluate the use of a nondimensional parameter to describe the time-varying burning rate of a fuel in complex geometries. The nondimensional approach chosen to characterize burning behavior over time involved comparison of chemical energy released during the combustion process with the energy required to vaporize the fuel, measured by a B-number. The mixed nature of the commodity and its package, involving polystyrene and corrugated cardboard, produced three distinct stages of combustion that were qualitatively repeatable. The results of four tests provided flame heights, mass-loss rates and heat fluxes that were used to develop a phenomenological description of the burning behavior of a plastic commodity. Three distinct stages of combustion were identified. Time-dependent and time-averaged B-numbers were evaluated from mass-loss rate data using assumptions including a correlation for turbulent convective heat transfer. The resultant modified B-numbers extracted from test data incorporated the burning behavior of constituent materials, and a variation in behavior was observed as materials participating in the combustion process varied. Variations between the four tests make quantitative values for each stage of burning useful only for comparison, as errors were high. Methods to extract the B-number with a higher degree of accuracy and future use of the results to improve commodity classification for better assessment of fire danger are discussed. © 2011 Elsevier Ltd. All rights reserved

Bulk-fragment and tube-like structures of AuN (N=2-26)

Using the relativistic all-electron density-functional calculations on the AuN (N=2-26) in the generalized gradient approximation, combined with the guided simulated annealing, we have found that the two- to three-dimensional structural transition for AuN occurs between N=13 and 15, and the AuN (16<= N <=25) prefer also the pyramid-based bulk fragment structures in addition to the Au20. More importantly, the tubelike structures are found to be the most stable for Au24 and Au26, offering another powerful structure competitor with other isomers, e.g., amorphous, bulk fragment, and gold fullerene. The mechanism to cause these unusual AuN may be attributed to the stronger s-d hybridization and the d-d interaction enhanced by the relativistic effects.Comment: 12 pages and 3 figure

Superspace Formulation in a Three-Algebra Approach to D=3, N=4,5 Superconformal Chern-Simons Matter Theories

We present a superspace formulation of the D=3, N=4,5 superconformal Chern-Simons Matter theories, with matter supermultiplets valued in a symplectic 3-algebra. We first construct an N=1 superconformal action, and then generalize a method used by Gaitto and Witten to enhance the supersymmetry from N=1 to N=5. By decomposing the N=5 supermultiplets and the symplectic 3-algebra properly and proposing a new super-potential term, we construct the N=4 superconformal Chern-Simons matter theories in terms of two sets of generators of a (quaternion) symplectic 3-algebra. The N=4 theories can also be derived by requiring that the supersymmetry transformations are closed on-shell. The relationship between the 3-algebras, Lie superalgebras, Lie algebras and embedding tensors (proposed in [E. A. Bergshoeff, O. Hohm, D. Roest, H. Samtleben, and E. Sezgin, J. High Energy Phys. 09 (2008) 101.]) is also clarified. The general N=4,5 superconformal Chern-Simons matter theories in terms of ordinary Lie algebras can be rederived in our 3-algebra approach. All known N=4,5 superconformal Chern-Simons matter theories can be recovered in the present superspace formulation for super-Lie-algebra realization of symplectic 3-algebras.Comment: 37 pages, minor changes, published in PR

Dynamic Structure Function in 3he-4he Mixtures

Relevant features of the dynamic structure function $S(q,\omega)$ in $^3$He-$^4$He mixtures at zero temperature are investigated starting from known properties of the ground state. Sum rules are used to fix rigorous constraints to the different contributions to $S(q,\omega)$, coming from $^3$He and $^4$He elementary excitations, as well as to explore the role of the cross term $S^{(3,4)}(q,\omega)$. Both the low-$q$ (phonon-roton $^4$He excitations and 1p-1h $^3$He excitations) and high-$q$ (deep inelastic scattering) ranges are discussed.Comment: 29 pages, Plain TeX, 11 figures available by request from [email protected]

Thermalized Displaced Squeezed Thermal States

In the coordinate representation of thermofield dynamics, we investigate the thermalized displaced squeezed thermal state which involves two temperatures successively. We give the wavefunction and the matrix element of the density operator at any time, and accordingly calculate some quantities related to the position, momentum and particle number operator, special cases of which are consistent with the results in the literature. The two temperatures have diffenent correlations with the squeeze and coherence components. Moreover, different from the properties of the position and momentum, the average value and variance of the particle number operator as well as the second-order correlation function are time-independent.Comment: 7 pages, no figures, Revtex fil

Antiferromagnetically Driven Electronic Correlation in Iron Pnictides and Cuprates

The iron pnictides and the cuprates represent two families of materials, where strong antiferromagnetic correlation drives three other distinct ordering tendencies: (1) superconducting pairing, (2) Fermi surface distortion, and (3) orbital current order. We propose that (1)-(3) and the antiferromagnetic correlation are the hallmarks of a class of strongly correlated materials to which the cuprates and pnictides belong. In this paper we present the results of the functional renormalization group studies to support the above claim. In addition, we show that as a function of the interlayer hopping parameter, the double layer Hubbard model nicely interpolates between the cuprate and the iron pnictide physics. Finally, as a check, we will present the renormalization group study of a ladder version of the iron pnictide, and compare the results to those of the two-dimensional model.Comment: 18 pages, 20 figures, revised version, one more figure added and references update