On the classification of elliptic fibrations with a small number of singular fibres over a base of genus 1 (original) (raw)
Related papers
Plasma and the universe: large scale dynamics, filamentation, and radiation
Astrophysics and Space Science, 1995
One of the earliest predictions about the morphology of the universe is that it be filamentary (Alfvén, 1950). This prediction followed from the fact that volumewise, the universe is 99.999% matter in the plasma state. When the plasma is energetic, it is generally inhomogeneous with constituent parts in motion. Plasmas in relative motion are coupled by the currents they drive in each other and nonequilibrium plasma often consists of current-conducting filaments. In the laboratory and in the Solar System, filamentary and cellular morphology is a well-known property of plasma. As the properties of the plasma state of matter is believed not to change beyond the range of our space probes, plasma at astrophysical dimensions must also be filamentary. During the 1980s a series of unexpected observations showed filamentary structure on the Galactic, intergalactic, and supergalactic scale. By this time, the analytical intractibility of complex filamentary geometries, intense self-fields, nonlinearities, and explicit time dependence had fostered the development of fully three-dimensional, fully electromagnetic, particle-in-cell simulations of plasmas having the dimensions of galaxies or systems of galaxies. It had been realized that the importance of applying electromagnetism and plasma physics to the problem of radiogalaxy and galaxy formation derived from the fact that the universe is largely aplasma universe. In plasma, electromagnetic forces exceed gravitational forces by a factor of 1036, and electromagnetism is ≈ 107 times stronger than gravity even in neutral hydrogen regions, where the degree of ionization is a miniscule 10−4. The observational evidence for galactic-dimensioned Birkeland currents is given based on the direct comparison of the synchrotron radiation properties of simulated currents to those of extra-galactic sources including quasars and double radio galaxies.
Light Filaments without Self-Channeling
Physical Review Letters, 2004
An examination of the propagation of intense 200 fs pulses in water reveals light filaments not sustained by the balance between Kerr-induced self-focusing and plasma-induced defocusing. Their appearance is interpreted as the consequence of a spontaneous reshaping of the wave packet form a gaussian into a conical wave, driven by the requirement of maximum localization, minimum losses and stationarity in the presence of non-linear absorption.
Phase-space description of plasma waves. Part 1. Linear theory
Journal of Plasma Physics, 1992
We develop an (r, k) phase-space description of waves in plasmas by introducing Gaussian window functions to separate short-scale oscillations from long-scale modulations of the wave fields and variations in the plasma parameters. To obtain a wave equation that unambiguously separates conservative dynamics from dissipation in an inhomogeneous and time-varying background plasma, we first discuss the proper form of the current response function. In analogy with the particle distribution function f(v, r, t), we introduce a wave density N(k, r, t) on phase space. This function is proved to satisfy a simple continuity equation. Dissipation is also included, and this allows us to describe the damping or growth of wave density along rays. Problems involving geometric optics of continuous media often appear simpler when viewed in phase space, since the flow of N in phase space is incompressible.
Modeling ultrashort filaments of light
2009
Laser sources nowadays deliver optical pulses reaching few cycles in duration and peak powers exceeding several terawatt (TW). When such pulses propagate in transparent media, they first self-focus in space, until they generate a tenuous plasma by photo-ionization. These pulses evolve as self-guided objects, resulting from successive equilibria between the Kerr focusing process, the defocusing action of the electron plasma and the chromatic dispersion of the medium. Discovered ten years ago, this self-channeling mechanism reveals a new physics, having direct applications in the long-distance propagation of TW beams in air, supercontinuum emission as well as pulse self-compression. This review presents the major progress in this field. Particular emphasis is laid to the derivation of the propagation equations, for single as well as coupled wave components. Physics is discussed from numerical simulations and explained by analytical arguments. Attention is also paid to the multifilamentation instability, which breaks up broad beams into small-scale cells. Several experimental data validate theoretical descriptions.
Ultrashort filaments of light in weakly ionized, optically transparent media
2007
Modern laser sources nowadays deliver ultrashort light pulses reaching few cycles in duration and peak powers exceeding several terawatt (TW). When such pulses propagate through optically transparent media, they first self-focus in space and grow in intensity, until they generate a tenuous plasma by photo-ionization. For free electron densities and beam intensities below their breakdown limits, these pulses evolve as self-guided objects, resulting from successive equilibria between the Kerr focusing process, the chromatic dispersion of the medium and the defocusing action of the electron plasma. Discovered one decade ago, this self-channeling mechanism reveals a new physics, widely extending the frontiers of nonlinear optics. Implications include long-distance propagation of TW beams in the atmosphere, supercontinuum emission, pulse shortening as well as high-order harmonic generation. This review presents the landmarks of the 10-odd-year progress in this field. Particular emphasis is laid on the theoretical modeling of the propagation equations, whose physical ingredients are discussed from numerical simulations. The dynamics of single filaments created over laboratory scales in various materials such as noble gases, liquids and dielectrics reveal new perspectives in pulse shortening techniques. Far-field spectra provide promising diagnostics. Attention is also paid to the multifilamentation instability of broad beams, breaking up the energy distribution into small-scale cells along the optical path. The robustness of the resulting filaments in adverse weathers, their large conical emission exploited for multipollutant remote sensing, nonlinear spectroscopy and the possibility of guiding electric discharges in air are finally addressed on the basis of experimental results.
Indian Journal of Science and Technology, 2015
Recent observations show the existence of high energy electrons in various astrophysical plasmas which their distribution functions are highly non thermal. The presence of dust ion acoustic localized waves in plasmas which contain non thermal electrons and ions with kinematic viscosity along with stationary charged dust is investigated. Solitary shock waves are derived as solutions of nonlinear wave equation of the medium using the reductive perturbation method by employing suitable stretching coordinates. Both rarefactive and compressive shock profiles are created in the medium according to the initial values of the medium parameters. We report that increasing the electron number density makes a growth in the amplitude of negative shock waves while it decreases the amplitude of positive shock profile. Some behavior of observed transience in the plasma waves can be explained using the presented results.