293 research outputs found
Discrete instability in nonlinear lattices
The discrete multiscale analysis for boundary value problems in nonlinear
discrete systems leads to a first order discrete modulational instability above
a threshold amplitude for wave numbers beyond the zero of group velocity
dispersion. Applied to the electrical lattice [Phys. Rev. E, 51 (1995) 6127 ],
this acurately explains the experimental instability at wave numbers beyond
1.25 . The theory is also briefly discussed for sine-Gordon and Toda lattices.Comment: 1 figure, revtex, published: Phys. Rev. Lett. 83 (1999) 232
Fusion in the entwined category of Yetter--Drinfeld modules of a rank-1 Nichols algebra
We rederive a popular nonsemisimple fusion algebra in the braided context,
from a Nichols algebra. Together with the decomposition that we find for the
product of simple Yetter-Drinfeld modules, this strongly suggests that the
relevant Nichols algebra furnishes an equivalence with the triplet W-algebra in
the (p,1) logarithmic models of conformal field theory. For this, the category
of Yetter-Drinfeld modules is to be regarded as an \textit{entwined} category
(the one with monodromy, but not with braiding).Comment: 36 pages, amsart++, times, xy. V3: references added, an unnecessary
assumption removed, plus some minor change
Pattern generation by dissipative parametric instability
Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems, ranging from biology to galaxy buildup. We propose a new instability mechanism leading to pattern formation in spatially extended nonlinear systems, which is based on a periodic antiphase modulation of spectrally dependent losses arranged in a zigzag way: an effective filtering is imposed at symmetrically located wave numbers k and -k in alternating order. The properties of the dissipative parametric instability differ from the features of both key classical concepts of modulation instabilities, i.e., the Benjamin-Feir instability and the Faraday instabiltyity. We demonstrate how the dissipative parametric instability can lead to the formation of stable patterns in one- and two-dimensional systems. The proposed instability mechanism is generic and can naturally occur or can be implemented in various physical systems
Investigation of interaction femtosecond laser pulses with skin and eyes mathematical model
We present a mathematical model of linear and nonlinear processes that takes place under the action of femtosecond laser radiation on the cutaneous covering. The study is carried out and the analytical solution of the set of equations describing the dynamics of the electron and atomic subsystems and investigated the processes of linear and nonlinear interaction of femtosecond laser pulses in the vitreous of the human eye, revealed the dependence of the pulse duration on the retina of the duration of the input pulse and found the value of the radiation power density, in which there is a self-focusing is obtained. The results of the work can be used to determine the maximum acceptable energy, generated by femtosecond laser systems, and to develop Russian laser safety standards for femtosecond laser systems
Modulation instability in high power laser amplifiers
The modulation instability (MI) is one of the main factors responsible for the degradation of beam quality in high-power laser systems. The so-called B-integral restriction is commonly used as the criteria for MI control in passive optics devices. For amplifiers the adiabatic model, assuming locally the Bespalov-Talanov expression for MI growth, is commonly used to estimate the destructive impact of the instability. We present here the exact solution of MI development in amplifiers. We determine the parameters which control the effect of MI in amplifiers and calculate the MI growth rate as a function of those parameters. The safety range of operational parameters is presented. The results of the exact calculations are compared with the adiabatic model, and the range of validity of the latest is determined. We demonstrate that for practical situations the adiabatic approximation noticeably overestimates MI. The additional margin of laser system design is quantified
RESEARCH OF LINEAR AND NONLINEAR PROCESSES AT FEMTOSECOND LASER RADIATION PROPAGATION IN THE MEDIUM SIMULATING THE HUMAN EYE VITREOUS
The paper deals with mathematical model of linear and nonlinear processes occurring at the propagation of femtosecond laser
pulses in the vitreous of the human eye. Methods of computing modeling are applied for the nonlinear spectral equation
solution describing the dynamics of a two-dimensional TE-polarized radiation in a homogeneous isotropic medium with
cubic fast-response nonlinearity without the usage of slowly varying envelope approximation. Environments close to the
optical media parameters of the eye were used for the simulation. The model of femtosecond radiation propagation takes into
account the process dynamics for dispersion broadening of pulses in time and the occurence of the self-focusing near the retina when passing through the vitreous body of the eye. Dependence between the pulse duration on the retina has been
revealed and the duration of the input pulse and the values of power density at which there is self-focusing have been found.
It is shown that the main mechanism of radiation damage with the use of titanium-sapphire laser is photoionization. The
results coincide with those obtained by the other scientists, and are usable for creation Russian laser safety standards for
femtosecond laser systems
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
Strong Collapse Turbulence in Quintic Nonlinear Schr\"odinger Equation
We consider the quintic one dimensional nonlinear Schr\"odinger equation with
forcing and both linear and nonlinear dissipation. Quintic nonlinearity results
in multiple collapse events randomly distributed in space and time forming
forced turbulence. Without dissipation each of these collapses produces finite
time singularity but dissipative terms prevents actual formation of
singularity. In statistical steady state of the developed turbulence the
spatial correlation function has a universal form with the correlation length
determined by the modulational instability scale. The amplitude fluctuations at
that scale are nearly-Gaussian while the large amplitude tail of probability
density function (PDF) is strongly non-Gaussian with power-like behavior. The
small amplitude nearly-Gaussian fluctuations seed formation of large collapse
events. The universal spatio-temporal form of these events together with the
PDF for their maximum amplitudes define the power-like tail of PDF for large
amplitude fluctuations, i.e., the intermittency of strong turbulence.Comment: 14 pages, 17 figure
A Chandra Search for Coronal X Rays from the Cool White Dwarf GD 356
We report observations with the Chandra X-ray Observatory of the single,
cool, magnetic white dwarf GD 356. For consistent comparison with other X-ray
observations of single white dwarfs, we also re-analyzed archival ROSAT data
for GD 356 (GJ 1205), G 99-47 (GR 290 = V1201 Ori), GD 90, G 195-19 (EG250 = GJ
339.1), and WD 2316+123 and archival Chandra data for LHS 1038 (GJ 1004) and GD
358 (V777 Her). Our Chandra observation detected no X rays from GD 356, setting
the most restrictive upper limit to the X-ray luminosity from any cool white
dwarf -- L_{X} < 6.0 x 10^{25} ergs/s, at 99.7% confidence, for a 1-keV
thermal-bremsstrahlung spectrum. The corresponding limit to the electron
density is n_{0} < 4.4 x 10^{11} cm^{-3}. Our re-analysis of the archival data
confirmed the non-detections reported by the original investigators. We discuss
the implications of our and prior observations on models for coronal emission
from white dwarfs. For magnetic white dwarfs, we emphasize the more stringent
constraints imposed by cyclotron radiation. In addition, we describe (in an
appendix) a statistical methodology for detecting a source and for constraining
the strength of a source, which applies even when the number of source or
background events is small.Comment: 27 pages, 4 figures, submitted to the Astrophysical Journa
Temporal self-restoration of compressed optical filaments
We numerically investigate the propagation of a self-compressed optical
filament through a gas-glass-gas interface. Few-cycle light pulses survive a
sudden and short order-of-magnitude increase of nonlinearity and dispersion,
even when all conservative estimates predict temporal spreading or spatial
breakup. Spatio-temporal distortions are shown to self-heal upon further
propagation when the pulse refocuses in the second gas. This self-healing
mechanism has important implications for pulse compression techniques handled
by filamentation and explains the robustness of such sources.Comment: 4 Pages, 4 figure
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