A mixture representation of the Linnik distribution

Cataloged from PDF version of article.Linnik distribution with the characteristic function ~o,(tl = 1/(1 + Itl=), 0 < ~ < 2, is shown to possess the following property. Let X,,Xp be random variables possessing the Linnik distribution with parameters ~ and (0 < ~ < fl ~< 2). Denote by Y~ an independent of X~ non-negative random variable with the density ,q(s;~,fl) = sin 1 + s 2~ + 2s cos~ Then X, -'- X e Y~p, fl respectively where - denotes the equality in the sense of distributions. Infinite divisibility of mixtures of Linnik distributions with respect to the parameter ~ and scale is obtained as a corollary. AMS 1980 Subject Classification." Primary 62H05, 60El0; Secondary 33A4

Modulational instability in nonlocal Kerr-type media with random parameters

Modulational instability of continuous waves in nonlocal focusing and defocusing Kerr media with stochastically varying diffraction (dispersion) and nonlinearity coefficients is studied both analytically and numerically. It is shown that nonlocality with the sign-definite Fourier images of the medium response functions suppresses considerably the growth rate peak and bandwidth of instability caused by stochasticity. Contrary, nonlocality can enhance modulational instability growth for a response function with negative-sign bands.Comment: 6 pages, 12 figures, revTeX, to appear in Phys. Rev.

Langmuir wave linear evolution in inhomogeneous nonstationary anisotropic plasma

Equations describing the linear evolution of a non-dissipative Langmuir wave in inhomogeneous nonstationary anisotropic plasma without magnetic field are derived in the geometrical optics approximation. A continuity equation is obtained for the wave action density, and the conditions for the action conservation are formulated. In homogeneous plasma, the wave field E universally scales with the electron density N as E ~ N^{3/4}, whereas the wavevector evolution varies depending on the wave geometry

Modulational instability and nonlocality management in coupled NLS system

The modulational instability of two interacting waves in a nonlocal Kerr-type medium is considered analytically and numerically. For a generic choice of wave amplitudes, we give a complete description of stable/unstable regimes for zero group-velocity mismatch. It is shown that nonlocality suppresses considerably the growth rate and bandwidth of instability. For nonzero group-velocity mismatch we perform a geometrical analysis of a nonlocality management which can provide stability of waves otherwise unstable in a local medium.Comment: 15 pages, 12 figures, to be published in Physica Script

Methanol masers and star formation

Methanol masers which are traditionally divided into two classes provide possibility to study important parts of the star forming regions: Class II masers trace vicinities of the massive YSOs while class I masers are likely to trace more distant parts of the outflows where newer stars can form. There are many methanol transitions which produce observed masers. This allows to use pumping analysis for estimation of the physical parameters in the maser formation regions and its environment, for the study of their evolution. Extensive surveys in different masing transitions allow to conclude on the values of the temperatures, densities, dust properties, etc. in the bulk of masing regions. Variability of the brightest masers is monitored during several years. In some cases it is probably caused by the changes of the dust temperature which follow variations in the brightness of the central YSO reflecting the character of the accretion process. A unified catalogue of the class II methanol masers consisting of more than 500 objects is compiled. Analysis of the data shows that: physical conditions within the usual maser source vary considerably; maser brightness is determined by parameters of some distinguished part of the object - maser formation region; class II methanol masers are formed not within the outflows but in the regions affected by their propagation. It is shown that the "near" solutions for the kinematic distances to the sources can be used for statistical analysis. The luminosity function of the 6.7 GHz methanol masers is constructed. It is shown that improvement of the sensitivity of surveys can increase number of detected maser sources considerably. The distribution of class II methanol masers in the Galaxy is constructed on the basis of estimated kinematic distances. It is shown that most of the sources are located in the Molecular Ring and that the dependence of the number of sources on the distance from the Galactic Center has significant peaks at the positions corresponding to the spiral arms. A survey of CS(2-1) line emission tracing dense gas is performed at Mopra toward the positions of the brightest class II methanol masers. Velocity correlations between the maser and CS lines are analyzed. It is shown that the sources with 1 from 320 to 350 deg in which the masers are relatively blue-shifted, form a group which is located in the region of the Scutum-Centaurus spiral arm. This can reflect existence of a grand design, i.e., grouping of the sources with similar peculiarity of morphology or evolutionary stage of the massive star forming regions. © 2005 International Astronomical Union

Ferroelectric C* phase induced in a nematic liquid crystal matrix by a chiral non-mesogenic dopant

We report on a ferroelectric chiral smectic C (C*) phase obtained in a mixture of a nematic liquid crystal (NLC) and a chiral nonmesogenic dopant. The existence of C* phase was proven by calorimetric, dielectric and optical measurements, and also by X-rays analysis. The smectic C* which is obtained in such a way can flow, allowing to restore the ferroelectric liquid crystal layer structure in the electro-optical cells after action of the mechanical stress, as it happens with the cells filled with NLC. The proposed method of obtaining smectic C* material allows us to create innovative electro-optical cell combining the advantages of NLC (mechanical resilience) and smectic C* (high switching speed

Regular spatial structures in arrays of Bose-Einstein condensates induced by modulational instability

We show that the phenomenon of modulational instability in arrays of Bose-Einstein condensates confined to optical lattices gives rise to coherent spatial structures of localized excitations. These excitations represent thin disks in 1D, narrow tubes in 2D, and small hollows in 3D arrays, filled in with condensed atoms of much greater density compared to surrounding array sites. Aspects of the developed pattern depend on the initial distribution function of the condensate over the optical lattice, corresponding to particular points of the Brillouin zone. The long-time behavior of the spatial structures emerging due to modulational instability is characterized by the periodic recurrence to the initial low-density state in a finite optical lattice. We propose a simple way to retain the localized spatial structures with high atomic concentration, which may be of interest for applications. Theoretical model, based on the multiple scale expansion, describes the basic features of the phenomenon. Results of numerical simulations confirm the analytical predictions.Comment: 17 pages, 13 figure