Shape-changing Collisions of Coupled Bright Solitons in Birefringent Optical Fibers

Wecritically review the recent progress in understanding soliton propagation in birefringent optical fibers.By constructing the most general bright two-soliton solution of the integrable coupled nonlinear Schroedinger equation (Manakov model) we point out that solitons in birefringent fibers can in general change their shape after interaction due to a change in the intensity distribution among the modes even though the total energy is conserved. However, the standard shape-preserving collision (elastic collision) property of the (1+1)-dimensional solitons is recovered when restrictions are imposed on some of the soliton parameters. As a consequence the following further properties can be deduced using this shape-changing collision. (i) The exciting possibility of switching of solitons between orthogonally polarized modes of the birefringent fiber exists. (ii) When additional effects due to periodic rotation of birefringence axes are considered, the shape changing collision can be used as a switch to suppress or to enhance the periodic intensity exchange between the orthogonally polarized modes. (iii) For ultra short optical soliton pulse propagation in non-Kerr media, from the governing equation an integrable system of coupled nonlinear Schroedinger equation with cubic-quintic terms is identified. It admits a nonlocal Poisson bracket structure. (iv) If we take the higher-order terms in the coupled nonlinear Schroedinger equation into account then their effect on the shape-changing collision of solitons, during optical pulse propagation, can be studied by using a direct perturbational approach.Comment: 14 pages, ROMP31, 4 EPS figure

Comment of Global dynamics of biological systems

In a recent study, (Grigorov, 2006) analyzed temporal gene expression profiles (Arbeitman et al., 2002) generated in a Drosophila experiment using SSA in conjunction with Monte-Carlo SSA. The author (Grigorov, 2006) makes three important claims in his article, namely: Claim1: A new method based on the theory of nonlinear time series analysis is used to capture the global dynamics of the fruit-fly cycle temporal gene expression profiles. Claim 2: Flattening of a significant part of the eigen-spectrum confirms the hypothesis about an underly-ing high-dimensional chaotic generating process. Claim 3: Monte-Carlo SSA can be used to establish whether a given time series is distinguishable from any well-defined process including deterministic chaos. In this report we present fundamental concerns with respect to the above claims (Grigorov, 2006) in a systematic manner with simple examples. The discussion provided especially discourages the choice of SSA for inferring nonlinear dynamical structure form time series obtained in any biological paradigm.Comment: 6 pages, 2 figure

The eggs of marine crabs - an unexploited resource

Marine crabs belonging to the family Portunidae form bycatch of shrimp trawlers in India. They are sold at low prices and consumers discard eggs and consume the meat. The paper details the nutritional value of eggs of Portunus pelagicus

Fast algorithms for combustion kinetics calculations: A comparison

To identify the fastest algorithm currently available for the numerical integration of chemical kinetic rate equations, several algorithms were examined. Findings to date are summarized. The algorithms examined include two general-purpose codes EPISODE and LSODE and three special-purpose (for chemical kinetic calculations) codes CHEMEQ, CRK1D, and GCKP84. In addition, an explicit Runge-Kutta-Merson differential equation solver (IMSL Routine DASCRU) is used to illustrate the problems associated with integrating chemical kinetic rate equations by a classical method. Algorithms were applied to two test problems drawn from combustion kinetics. These problems included all three combustion regimes: induction, heat release and equilibration. Variations of the temperature and species mole fraction are given with time for test problems 1 and 2, respectively. Both test problems were integrated over a time interval of 1 ms in order to obtain near-equilibration of all species and temperature. Of the codes examined in this study, only CREK1D and GCDP84 were written explicitly for integrating exothermic, non-isothermal combustion rate equations. These therefore have built-in procedures for calculating the temperature

Measurement of two particle pseudorapidity correlations in Pb+Pb collisions at sNN\sqrt{s_{NN}} = 2.76 TeV with the ATLAS detector

Two-particle pseudorapidity correlations, measured using charged particles with $p_{\mathrm{T}} >$ 0.5 GeV and $|\eta| <$ 2.4, from $\sqrt{s_{NN}}$ = 2.76 TeV Pb+Pb collisions collected in 2010 by the ATLAS experiment at the LHC are presented. The correlation function $C_N(\eta_1,\eta_2)$ is measured for different centrality intervals as a function of the pseudorapidity of the two particles, $\eta_1$ and $\eta_2$. The correlation function shows an enhancement along $\eta_- \equiv \eta_1 - \eta_2 \approx$ 0 and a suppression at large $\eta_-$ values. The correlation function also shows a quadratic dependence along the $\eta_+ \equiv \eta_1$ + $\eta_2$ direction. These structures are consistent with a strong forward-backward asymmetry of the particle multiplicity that fluctuates event to event. The correlation function is expanded in an orthonormal basis of Legendre polynomials, $T_n(\eta_1)T_m(\eta_2)$, and corresponding coefficients $a_{n,m}$ are measured. These coefficients are related to mean-square values of the Legendre coefficients, $a_n$, of the single particle longitudinal multiplicity fluctuations: $a_{n,m} = \langle a_na_m \rangle$. Significant values are observed for the diagonal terms $\langle a_n^2 \rangle$ and mixed terms $\langle a_na_{n+2}\rangle$. Magnitude of $\langle a_{\mathrm{1}}^{\mathrm{2}} \rangle$ is the largest and the higher order terms decrease quickly with increase in $n$. The centrality dependence of the leading coefficient $\langle a_{\mathrm{1}}^{\mathrm{2}} \rangle$ is compared to that of the mean-square value of the asymmetry of the number of participating nucleons between the two colliding nuclei, and also to the $\langle a_{\mathrm{1}}^{\mathrm{2}} \rangle$ calculated from HIJING.Comment: 4 pages, 3 figures, proceedings of the 7th International Conference on Hard and Electromagnetic Probes of High Energy Nuclear Collisions (Hard Probes 2015), Montrea