Self-similar deflagration in laser half-plasmas

The self-similar motion of a half-space plasma, generated by a linear pulse of laser radiation absorbed anomalously at the critical density, has been studied. The resulting plasma structure has been completely determined for [pulse duration (critical density)maximum irradiation] large enough

Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation

The equation ∂tu = u∂xx2u − (c − 1)(∂xu)2 is known in literature as a qualitative mathematical model of some biological phenomena. Here this equation is derived as a model of the groundwater flow in a water-absorbing fissurized porous rock; therefore, we refer to this equation as a filtration-absorption equation. A family of self-similar solutions to this equation is constructed. Numerical investigation of the evolution of non-self-similar solutions to the Cauchy problems having compactly supported initial conditions is performed. Numerical experiments indicate that the self-similar solutions obtained represent intermediate asymptotics of a wider class of solutions when the influence of details of the initial conditions disappears but the solution is still far from the ultimate state: identical zero. An open problem caused by the nonuniqueness of the solution of the Cauchy problem is discussed.

Modeling of Self-similar Traffic

Modeling of self-similar traffic is performed for the queuing system of G/M/1/K type using Weibull distribution. To study the self-similar traffic the simulation model is developed by using SIMULINK software package in MATLAB environment. Approximation of self-similar traffic on the basis of spline functions. Modeling self-similar traffic is carried outfor QS of W/M/1/K type using the Weibull distribution. Initial data are: the value of Hurst parameter H=0,65, the shape parameter of the distribution curve α≈0,7 and distribution parameter β≈0,0099. Considering that the self-similar traffic is characterized by the presence of "splashes" and long-termdependence between the moments of requests arrival in this study under given initial data it is reasonable to use linear interpolation splines.

Shock-bounded, self-similar flows with volumetric mass, momentum, and energy addition.

"DCAS-TDR-62-135. Report no. TDR-69 (2230-01)TR-2. Contract no. AF 04(695)-69."

A self-similar array model of single-walled carbon nanotubes

To describe single-walled carbon nanotube (SWNT) arrays, we propose a self-similar array model. For isolated SWNT bundles, the self-similar array model is consistent with the classical triangular array model; for SWNT bundle arrays, it can present hierarchy structures and specify different array configurations. Based on this self-similar array model, we calculated the energetics of SWNT arrays, investigated the driving force for the formation of macroscopic SWNT arrays, and briefly discussed the hierarchy structures in real macroscopic SWNT arrays. (c) 2005 American Institute of Physics.

Self-similar parabolic optical solitary waves

We study solutions of the nonlinear Schrödinger equation (NLSE) with gain, describing optical pulse propagation in an amplifying medium. We construct a semiclassical self-similar solution with a parabolic temporal variation that corresponds to the energy-containing core of the asymptotically propagating pulse in the amplifying medium. We match the self-similar core through Painlevé functions to the solution of the linearized equation that corresponds to the low-amplitude tails of the pulse. The analytic solution accurately reproduces the numerically calculated solution of the NLSE.

Self-similar parabolic optical solitary waves

We study solutions of the nonlinear Schrödinger equation (NLSE) with gain, describing optical pulse propagation in an amplifying medium. We construct a semiclassical self-similar solution with a parabolic temporal variation that corresponds to the energy-containing core of the asymptotically propagating pulse in the amplifying medium. We match the self-similar core through Painlevé functions to the solution of the linearized equation that corresponds to the low-amplitude tails of the pulse. The analytic solution accurately reproduces the numerically calculated solution of the NLSE.

Self-similar parabolic plasmonic beams

We demonstrate that an interplay between diffraction and defocusing nonlinearity can support stable self-similar plasmonic waves with a parabolic profile. Simplicity of a parabolic shape combined with the corresponding parabolic spatial phase distribution creates opportunities for controllable manipulation of plasmons through a combined action of diffraction and nonlinearity. © 2013 Optical Society of America.

Pulse generation without gain-bandwidth limitation in a laser with self-similar evolution

With existing techniques for mode-locking, the bandwidth of ultrashort pulses from a laser is determined primarily by the spectrum of the gain medium. Lasers with self-similar evolution of the pulse in the gain medium can tolerate strong spectral breathing, which is stabilized by nonlinear attraction to the parabolic self-similar pulse. Here we show that this property can be exploited in a fiber laser to eliminate the gain-bandwidth limitation to the pulse duration. Broad (∼200 nm) spectra are generated through passive nonlinear propagation in a normal-dispersion laser, and these can be dechirped to ∼20-fs duration. © 2012 Optical Society of America.