On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation

The dynamics of nonlinear reaction-diffusion systems is dominated by the onset of patterns and Fisher equation is considered to be a prototype of such diffusive equations. Here we investigate the integrability properties of a generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlev\'e singularity structure analysis singles out a special case ($m=2$) as integrable. More interestingly, a B\"acklund transformation is shown to give rise to a linearizing transformation for the integrable case. A Lie symmetry analysis again separates out the same $m=2$ case as the integrable one and hence we report several physically interesting solutions via similarity reductions. Thus we give a group theoretical interpretation for the system under study. Explicit and numerical solutions for specific cases of nonintegrable systems are also given. In particular, the system is found to exhibit different types of travelling wave solutions and patterns, static structures and localized structures. Besides the Lie symmetry analysis, nonclassical and generalized conditional symmetry analysis are also carried out.Comment: 30 pages, 10 figures, to appear in Int. J. Bifur. Chaos (2004

Production rates for hadrons, pentaquarks Θ+\Theta ^+ and Θ∗++\Theta ^{*++}, and di-baryon (ΩΩ)0+(\Omega\Omega)_{0^{+}} in relativistic heavy ion collisions by a quark combination model

The hadron production in relativistic heavy ion collisions is well described by the quark combination model. The mixed ratios for various hadrons and the transverse momentum spectra for long-life hadrons are predicted and agree with recent RHIC data. The production rates for the pentaquarks $\Theta ^+$, $\Theta ^{*++}$ and the di-baryon $(\Omega\Omega)_{0^{+}}$ are estimated, neglecting the effect from the transition amplitude for constituent quarks to form an exotic state.Comment: The difference between our model and other combination models is clarified. The scaled transverse momentum spectra for pions, kaons and protoms at both 130 AGeV and 200 AGeV are given, replacing the previous results in transverse momentum spectr

Supra-oscillatory critical temperature dependence of Nb-Ho bilayers

We investigate the critical temperature Tc of a thin s-wave superconductor (Nb) proximity coupled to a helical rare earth ferromagnet (Ho). As a function of the Ho layer thickness, we observe multiple oscillations of Tc superimposed on a slow decay, that we attribute to the influence of the Ho on the Nb proximity effect. Because of Ho inhomogeneous magnetization, singlet and triplet pair correlations are present in the bilayers. We take both into consideration when solving the self consistent Bogoliubov-de Gennes equations, and we observe a reasonable agreement. We also observe non-trivial transitions into the superconducting state, the zero resistance state being attained after two successive transitions which appear to be associated with the magnetic structure of Ho.Comment: Main article: 5 pages, 4 figures; Supplementary materials: 4 pages, 5 figure

Bosonic Super Liouville System: Lax Pair and Solution

We study the bosonic super Liouville system which is a statistical transmutation of super Liouville system. Lax pair for the bosonic super Liouville system is constructed using prolongation method, ensuring the Lax integrability, and the solution to the equations of motion is also considered via Leznov-Saveliev analysis.Comment: LaTeX, no figures, 11 page

Color separate singlets in e+e−e^+e^- annihilation

We use the method of color effective Hamiltonian to study the properties of states in which a gluonic subsystem forms a color singlet, and we will study the possibility that such a subsystem hadronizes as a separate unit. A parton system can normally be subdivided into singlet subsystems in many different ways, and one problem arises from the fact that the corresponding states are not orthogonal. We show that if only contributions of order $1/N_c^2$ are included, the problem is greatly simplified. Only a very limited number of states are possible, and we present an orthogonalization procedure for these states. The result is simple and intuitive and could give an estimate of the possibility to produce color separated gluonic subsystems, if no dynamical effects are important. We also study with a simple MC the possibility that configurations which correspond to "short strings" are dynamically favored. The advantage of our approach over more elaborate models is its simplicity, which makes it easier to estimate color reconnection effects in reactions which are more complicated than the relatively simple $e^+e^-$ annihilation.Comment: Revtex, 24 pages, 7 figures; Compared to the previous version, 1 new figure is added and Monte-Carlo results are re-analyzed, as suggested by the referee; To appear in Phys. Rev.

X-ray Spectral and timing properties of the black hole x-ray transient Swift J1753.5-0127

We have carried out detailed analysis on the black hole candidate (BHC) X- ray transient Swift J1753.5-0127 observed by the Rossi X-Ray Timing Explorer (RXTE) during its outburst in 2005 {2006. The spectral analysis shows that the emissions are dominated by the hard X-rays, thus revealing the low/hard state of the source during the outburst. The peak luminosity is found lower than the typical value of balancing the mass flow and evaporation of the inner edge of disk (Meyer-Hofmeister 2004). As a result, the disk is prevented from extending inward to produce strong soft X-rays, corresponding to the so-called high/soft state. These are the typical characteristics for a small subset of BHCs, i.e. those soft X-ray transients stay at the low/hard state during the outburst. In most observational time, the QPO frequencies are found to vary roughly linearly with the fluxes and the spectral indices, while the deviation from this relationship at the peak luminosity might provide the first observational evidence of a partially evaporated inner edge of the accretion disk. The anti-correlation between the QPO frequency and spectral color suggests that the global disk oscillation model proposed by Titarchuk & Osherovich (2000) is not likely at work.Comment: Accepted by ApJ, 24 pages, 13 figures, 3 table

Optimal Principal Component Analysis in Distributed and Streaming Models

We study the Principal Component Analysis (PCA) problem in the distributed and streaming models of computation. Given a matrix $A \in R^{m \times n},$ a rank parameter $k < rank(A)$, and an accuracy parameter $0 < \epsilon < 1$, we want to output an $m \times k$ orthonormal matrix $U$ for which $$|| A - U U^T A ||_F^2 \le \left(1 + \epsilon \right) \cdot || A - A_k||_F^2,$$ where $A_k \in R^{m \times n}$ is the best rank-$k$ approximation to $A$. This paper provides improved algorithms for distributed PCA and streaming PCA.Comment: STOC2016 full versio

Study of color connections in e+e−e^+ e^- annihilation

We replace in the event generator JETSET the color singlet chain connection with the color separate state one as the interface between the hard and soft sectors of hadronic processes. The modified generator is applied to produce the hadronic events in $e^+ e^-$ annihilation. It describes the experimental data at the same level as the original JETSET with default parameters. This should be understood as a demonstration that color singlet chain is not the unique color connection. We also search for the difference in special sets of three-jet events arising from different color connections, which could subject to further experimental test.Comment: 23 pages, 8 figures, 4 tables, Revtex