Velocity fluctuations in forced Burgers turbulence

We propose a simple method to compute the velocity difference statistics in forced Burgers turbulence in any dimension. Within a reasonnable assumption concerning the nucleation and coalescence of shocks, we find in particular that the `left' tail of the distribution decays as an inverse square power, which is compatible with numerical data. Our results are compared to those of various recent approaches: instantons, operator product expansion, replicas.Comment: 10 pages latex, one postcript figur

Nontrivial Velocity Distributions in Inelastic Gases

We study freely evolving and forced inelastic gases using the Boltzmann equation. We consider uniform collision rates and obtain analytical results valid for arbitrary spatial dimension d and arbitrary dissipation coefficient epsilon. In the freely evolving case, we find that the velocity distribution decays algebraically, P(v,t) ~ v^{-sigma} for sufficiently large velocities. We derive the exponent sigma(d,epsilon), which exhibits nontrivial dependence on both d and epsilon, exactly. In the forced case, the velocity distribution approaches a steady-state with a Gaussian large velocity tail.Comment: 4 pages, 1 figur

Soluble Infinite-Range Model of Kinetic Roughening

A modified Kardar-Parisi-Zhang (KPZ) equation is introduced, and solved exactly in the infinite-range limit. In the low-noise limit the system exhibits a weak-to-strong coupling transition, rounded for non-zero noise, as a function of the KPZ non-linearity. The strong-coupling regime is characterised by a double-peaked height distribution in the stationary state. The nonstationary dynamics is quite different from that of the stationary state.Comment: 13 pages, revtex, 1 postscript figur

Theory of periodic swarming of bacteria: application to Proteus mirabilis

The periodic swarming of bacteria is one of the simplest examples for pattern formation produced by the self-organized collective behavior of a large number of organisms. In the spectacular colonies of Proteus mirabilis (the most common species exhibiting this type of growth) a series of concentric rings are developed as the bacteria multiply and swarm following a scenario periodically repeating itself. We have developed a theoretical description for this process in order to get a deeper insight into some of the typical processes governing the phenomena in systems of many interacting living units. All of our theoretical results are in excellent quantitative agreement with the complete set of available observations.Comment: 11 pages, 8 figure

The Granular Phase Diagram

The kinetic energy distribution function satisfying the Boltzmann equation is studied analytically and numerically for a system of inelastic hard spheres in the case of binary collisions. Analytically, this function is shown to have a similarity form in the simple cases of uniform or steady-state flows. This determines the region of validity of hydrodynamic description. The latter is used to construct the phase diagram of granular systems, and discriminate between clustering instability and inelastic collapse. The molecular dynamics results support analytical results, but also exhibit a novel fluctuational breakdown of mean-field descriptions.Comment: 15 pages, 4 figure

On the velocity distributions of the one-dimensional inelastic gas

We consider the single-particle velocity distribution of a one-dimensional fluid of inelastic particles. Both the freely evolving (cooling) system and the non-equilibrium stationary state obtained in the presence of random forcing are investigated, and special emphasis is paid to the small inelasticity limit. The results are obtained from analytical arguments applied to the Boltzmann equation along with three complementary numerical techniques (Molecular Dynamics, Direct Monte Carlo Simulation Methods and iterative solutions of integro-differential kinetic equations). For the freely cooling fluid, we investigate in detail the scaling properties of the bimodal velocity distribution emerging close to elasticity and calculate the scaling function associated with the distribution function. In the heated steady state, we find that, depending on the inelasticity, the distribution function may display two different stretched exponential tails at large velocities. The inelasticity dependence of the crossover velocity is determined and it is found that the extremely high velocity tail may not be observable at ``experimentally relevant'' inelasticities.Comment: Latex, 14 pages, 12 eps figure

Variability of Hot Supergiant IRAS 19336-0400 in the Early Phase of its Planetary Nebula Ionization

We present photoelectric and spectral observations of a hot candidate proto-planetary nebula - early B-type supergiant with emission lines in spectrum - IRAS 19336-0400. The light and color curves display fast irregular brightness variations with maximum amplitudes Delta V=0.30 mag, Delta B=0.35 mag, Delta U=0.40 mag and color-brightness correlations. By the variability characteristics IRAS 19336-0400 appears similar to other hot proto-planetary nebulae. Based on low-resolution spectra in the range lambda 4000-7500 A we have derived absolute intensities of the emission lines H_alpha, H_beta, H_gamma, [SII], [NII], physical conditions in gaseous nebula: n_e=10^4 cm^{-3}, T_e=7000 \pm 1000 K. The emission line H_alpha, H_beta equivalent widths are found to be considerably variable and related to light changes. By UBV-photometry and spectroscopy the color excess has been estimated: E_{B-V}=0.50-0.54. Joint photometric and spectral data analysis allows us to assume that the star variability is caused by stellar wind variations.Comment: 11 pages, 6 figures, 2 tables, accepted for publication in Pis'ma Astron. Zh. (Astronomy Letters