Nonparaxial elliptic waves and solitary waves in coupled nonlinear Helmholtz equations

We obtain a class of elliptic wave solutions of coupled nonlinear Helmholtz (CNLH) equations describing nonparaxial ultra-broad beam propagation in nonlinear Kerr-like media, in terms of the Jacobi elliptic functions and also discuss their limiting forms (hyperbolic solutions). Especially, we show the existence of non-trivial solitary wave profiles in the CNLH system. The effect of nonparaxiality on the speed, pulse width and amplitude of the nonlinear waves is analysed in detail. Particularly a mechanism for tuning the speed by altering the nonparaxial parameter is proposed. We also identify a novel phase-unlocking behaviour due to the presence of nonparaxial parameter.Comment: 19 pages, 7 figure

The Astrochemical Evolution of Turbulent Giant Molecular Clouds : I - Physical Processes and Method of Solution for Hydrodynamic, Embedded Starless Clouds

Contemporary galactic star formation occurs predominantly within gravitationally unstable, cold, dense molecular gas within supersonic, turbulent, magnetized giant molecular clouds (GMCs). Significantly, because the chemical evolution timescale and the turbulent eddy-turnover timescale are comparable at typical GMC conditions, molecules evolve via inherently non-equilibrium chemistry which is strongly coupled to the dynamical evolution of the cloud. Current numerical simulation techniques, which include at most three decades in length scale, can just begin to bridge the divide between the global dynamical time of supersonic turbulent GMCs, and the thermal and chemical evolution within the thin post-shock cooling layers of their background turbulence. We address this GMC astrochemical scales problem using a solution methodology, which permits both complex three-dimensional turbulent dynamics as well as accurate treatment of non-equilibrium post-shock thermodynamics and chemistry. We present the current methodology in the context of the larger scope of physical processes important in understanding the chemical evolution of GMCs, including gas-phase chemistry, dust grains and surface chemistry, and turbulent heating. We present results of a new Lagrangian verification test for supersonic turbulence. We characterize the evolution of these species according to the dimensionless local post-shock Damk\"{o}hler number, which quantifies the ratio of the dynamical time in the post-shock cooling flow to the chemical reaction time of a given species. Lastly, we discuss implications of this work to the selection of GMC molecular tracers, and the zeroing of chemical clocks of GMC cores.Comment: 35 pages, 7 figures, 16 tables. Accepted to MNRAS. Revised to correct some typographic error

Leading Large N Modification of QCD_2 on a Cylinder by Dynamical Fermions

We consider 2-dimensional QCD on a cylinder, where space is a circle. We find the ground state of the system in case of massless quarks in a $1/N$ expansion. We find that coupling to fermions nontrivially modifies the large $N$ saddle point of the gauge theory due to the phenomenon of `decompactification' of eigenvalues of the gauge field. We calculate the vacuum energy and the vacuum expectation value of the Wilson loop operator both of which show a nontrivial dependence on the number of quarks flavours at the leading order in $1/N$.Comment: 24 pages, TIFR-TH-94/3

Self-energy corrections in an antiferromagnet -- interplay of classical and quantum effects on quasiparticle dispersion

Self-energy corrections due to fermion-magnon interaction are studied in the antiferromagnetic state of the $t-t'-t''$ Hubbard model within the rainbow (noncrossing) approximation in the full $U$ range from weak to strong coupling. The role of classical (mean-field) features of fermion and magnon dispersion, associated with finite $U,t',t''$, are examined on quantum corrections to quasiparticle energy, weight, one-particle density of states etc. A finite-$U$ induced classical dispersion term, absent in the $t-J$ model, is found to play an important role in suppressing the quasiparticle weight for states near ${\bf k}=(0,0)$, as seen in cuprates. For intermediate $U$, the renormalized AF band gap is found to be nearly half of the classical value, and the weak coupling limit is quite non-trivial due to strongly suppressed magnon amplitude. For finite $t'$, the renormalized AF band gap is shown to vanish at a critical interaction strength $U_c$, yielding a spin fluctuation driven first-order AF insulator - PM metal transition. Quasiparticle dispersion evaluated with the same set of Hubbard model cuprate parameters, as obtained from a recent magnon spectrum fit, provides excellent agreement with ARPES data for $\rm Sr_2 Cu O_2 Cl_2$.Comment: 11 pages, 17 figure

Exclusion of Tiny Interstellar Dust Grains from the Heliosphere

The distribution of interstellar dust grains (ISDG) observed in the Solar System depends on the nature of the interstellar medium-solar wind interaction. The charge of the grains couples them to the interstellar magnetic field (ISMF) resulting in some fraction of grains being excluded from the heliosphere while grains on the larger end of the size distribution, with gyroradii comparable to the size of the heliosphere, penetrate the termination shock. This results in a skewing the size distribution detected in the Solar System. We present new calculations of grain trajectories and the resultant grain density distribution for small ISDGs propagating through the heliosphere. We make use of detailed heliosphere model results, using three-dimensional (3-D) magnetohydrodynamic/kinetic models designed to match data on the shape of the termination shock and the relative deflection of interstellar neutral H and He flowing into the heliosphere. We find that the necessary inclination of the ISMF relative to the inflow direction results in an asymmetry in the distribution of the larger grains (0.1 micron) that penetrate the heliopause. Smaller grains (0.01 micron) are completely excluded from the Solar System at the heliopause.Comment: 5 pages, 5 figures, accepted for publication in the Solar Wind 12 conference proceeding

Exact Moving and Stationary Solutions of a Generalized Discrete Nonlinear Schrodinger Equation

We obtain exact moving and stationary, spatially periodic and localized solutions of a generalized discrete nonlinear Schr\"odinger equation. More specifically, we find two different moving periodic wave solutions and a localized moving pulse solution. We also address the problem of finding exact stationary solutions and, for a particular case of the model when stationary solutions can be expressed through the Jacobi elliptic functions, we present a two-point map from which all possible stationary solutions can be found. Numerically we demonstrate the generic stability of the stationary pulse solutions and also the robustness of moving pulses in long-term dynamics.Comment: 22 pages, 7 figures, to appear in J. Phys.