Properties of soliton surfaces associated with integrable CPN−1\mathbb{C}P^{N-1} sigma models

We investigate certain properties of $\mathfrak{su}(N)$-valued two-dimensional soliton surfaces associated with the integrable $\mathbb{C}P^{N-1}$ sigma models constructed by the orthogonal rank-one Hermitian projectors, which are defined on the two-dimensional Riemann sphere with finite action functional. Several new properties of the projectors mapping onto one-dimensional subspaces as well as their relations with three mutually different immersion formulas, namely, the generalized Weierstrass, Sym-Tafel and Fokas-Gel'fand have been discussed in detail. Explicit connections among these three surfaces are also established by purely analytical descriptions and, it is demonstrated that the three immersion formulas actually correspond to the single surface parametrized by some specific conditions.Comment: 17 page

Effect of Temperature on the Complexity of Solid Argon System

We study the measure of complexity in solid Argon system from the time series data of kinetic energy of single Argon atoms at different equilibrated temperatures. To account the inherent multi-scale dependence of the complexity, the multi-scale entropy of the time series of kinetic energy of individual Argon atoms are computed at different equilibrated temperatures. The multi-scale entropy study reveals that the dynamics of an atom becomes more complex at higher temperatures and the result corroborates well with the variation of the pair correlation function of the atoms in the solid Argon crystal. Also, we repeat the multi-scale entropy analysis for program generated Levy noise time series and for time series data obtained from the outcomes of exponential decay with noise dx(t) = -x(t) dt + sigma dB(t) (Langevin equation). Our study establishes that the scale dependence of sample entropy for time series of kinetic energy of individual atoms in solid Argon system has similar tendency as that of Levy noise time series and the outcomes of exponential decay with noise (Langevin equation).Comment: 8 pages, 14 figures, Accepted in Indian Journal of Physics for publicatio

The connection between the nuclear matter mean-field equation of state and the quark and gluon condensates at high density

It is known now that chiral symmetry restoration requires the meson-nucleon coupling to be density dependent in nuclear-matter mean-field models. We further show that quite generally, the quark and gluon condensates in medium are related to the trace of energy-momentum tensor of nuclear matter and in these models the incompressibility, K, must be less than thrice the chemical potential, $\mu$. In the critical density $\rho _c$, the gluon condensate is only reduced by $20\%$ indicating a larger effective nucleon mass.Comment: 10 pages latex file, 3 Postscript figures after being uncompressed. Submitted to Phys. Rev. Let

Constrained infinite group relaxations of MIPs

Recently minimal and extreme inequalities for continuous group relaxations of general mixed integer sets have been characterized. In this paper, we consider a stronger relaxation of general mixed integer sets by allowing constraints, such as bounds, on the free integer variables in the continuous group relaxation. We generalize a number of results for the continuous infinite group relaxation to this stronger relaxation and characterize the extreme inequalities when there are two integer variables.

Behaviour of the EAS Age Parameter in the Knee Energy Region

Analyzing simulated EAS events generated with the CORSIKA code, the characteristics of lateral distribution of electrons in EAS around the knee energy region of the primary energy spectrum have been studied and compared with experimental observations. The differences between the EGS4 and the NKG output of CORSIKA in respect to electron radial density distribution have been investigated. The relation between lateral and longitudinal age parameters has been studied after introducing the notion of the local age parameter that reflects the profile of the lateral distribution of electrons in EAS. The present analysis motivates the inclusion of the lateral shower age in a multiparameter study of EAS to extract information on hadronic interactions and primary composition.Comment: Talk presented at XVI International Symposium on Very High Energy Cosmic Ray Interactions (ISVHECRI 2010), Batavia, IL, USA (28 June - 2 July 2010). 4 pages, 5 figure

A Rosetta Stone Relating Conventions In Photo-Meson Partial Wave Analyses

A new generation of complete experiments in pseudoscalar meson photo-production is being pursued at several laboratories. While new data are emerging, there is some confusion regarding definitions of asymmetries and the conventions used in partial wave analyses (PWA). We present expressions for constructing asymmetries as coordinate-system independent ratios of cross sections, along with the names used for these ratios by different PWA groups. (This update reflects a recent change in the definition of an asymmetry as used by one group.)Comment: v2: This update reflects a recent change in the definition of an asymmetry as used by one PWA group -see Table 1. v1: 4 pages. Contribution to the proceedings of the 8th International Workshop on the Physics of Excited Nucleons (NSTAR2011), Newport News, VA, USA, May 17-20, 201