Rotating bound states of dissipative solitons in systems of reaction-diffusion type

We report on the formation of stable rotating bound states consisting of self-organized well localized solitary structures with particle-like behaviour in systems of reaction-diffusion type. These dissipative solitons are detected in an experimental planar d.c. gas-discharge system with a high ohmic barrier, as well as in numerical solutions of related three-component reaction-diffusion equations where the formation of rotating bound states is investigated in the context of a particle ansatz.Received: 15 July 2003, Published online: 15 March 2004PACS: 89.75.Fb Structures and organization in complex systems - 82.40.Ck Pattern formation in reactions with diffusion, flow and heat transfer - 52.80.Tn Other gas discharges     

基于统计方法的动态光谱差值提取

为实现血液成分无创检测,针对动态光谱(dynamic spectrum, DS)时域单拍提取法存在的不足,提出时域差值提取法,即顺序提取各波长对数光电脉搏波上相距理想差值间隔的两对应采样点的绝对差值构成差值DS,利用统计方法优选若干有效差值DS进行叠加平均获取最终DS输出。对48例志愿者的实验数据分别利用差值提取法和单拍提取法进行DS提取,结果表明：差值提取法提取DS的去噪效果略优于单拍提取法;对单一个体可获取有效DS的平均个数由48个改善为130个,有效DS间均方误差的平均值由0.39改善为0.006,运算速度提升了近20倍。新方法显著提高了DS提取的质量。     

Convection-induced stabilization of optical dissipative solitons

In spatially extended convective systems, the reflection symmetry breaking induced by drift effects leads to a striking nonlinear effect that drastically affects the formation and stability of dissipative solitons in optical parametric oscillators. The phenomenon of nonlinear-induced convection dynamics is revealed using a model of the complex quintic Ginzburg-Landau equation with nonlinear gradient terms in it. Mechanisms leading to stabilization of dissipative solitons by convection are singled out. The predictions are in very good agreement with numerical solutions found from the governing equations of the optical parametric oscillators.     

Exploding dissipative solitons in the cubic-quintic complex Ginzburg-Landau equation in one and two spatial dimensions

We review the work on exploding dissipative solitons in one and two spatial dimensions. Features covered include: the transition from modulated to exploding dissipative solitons, the analogue of the Ruelle-Takens scenario for dissipative solitons, inducing exploding dissipative solitons by noise, two classes of exploding dissipative solitons in two spatial dimensions, diffusing asymmetric exploding dissipative solitons as a model for a two-dimensional extended chaotic system. As a perspective we outline the interaction of exploding dissipative solitons with quasi one-dimensional dissipative solitons, breathing quasi one-dimensional solutions and their possible connection with experimental results on convection, and the occurence of exploding dissipative solitons in reaction-diffusion systems. It is a great pleasure to dedicate this work to our long-time friend Hans (Prof. Dr. Hans Jürgen Herrmann) on the occasion of his 60th birthday.     

Conservative and dissipative fiber Bragg solitons (a review)

We present a comparative review of two classes of optical solitons—conservative and dissipative solitons—propagating in single-mode optical fibers in which refractive-index gratings are induced such that their period is comparable with the radiation wavelength. Fibers that have the Kerr nonlinearity and negligibly small losses and that do not gain radiation (conservative system) are described by traditional equations of the approximation of slowly varying amplitudes, and effects caused by the nonlinearity of the medium, such as nonlinear switching, optical bistability, and formation of conservative Bragg solitons are considered. It is shown that the passage beyond the scope of the approximation of slowly varying amplitudes makes it possible to describe new important effects, including localization of soliton centers near maxima of the refractive-index grating. Bright and dark conservative solitons are demonstrated, which are formed when the Kerr nonlinearity is replaced by the nonlinearity of two-level atomic systems. The properties of conservative solitons in resonance semiconductor Bragg structures with quantum wells are considered. Results of experimental studies of nonlinear effects in fibers with Bragg gratings are presented. For an active single-mode fiber with a Bragg refractive-index grating and nonlinear gain and absorption, dissipative solitons are described using the approximation of slowly varying amplitudes and inertialess nonlinearity. It is shown that the dissipative factors qualitatively change the properties of solitons compared to the conservative case. Using the Maxwell-Bloch equations, it is demonstrated that the ratio between the gain and absorption relaxation times significantly affects the stability of localized structures. The interaction of dissipative optical Bragg solitons is described. It is shown that, beyond the scope of the approximation of slowly varying amplitudes, the average velocity of propagating dissipative Bragg solitons acquires only discrete values, and formation of pairs of solitons with two values of the phase difference becomes possible. For a birefringent fiber, dissipative vector optical Bragg solitons are demonstrated.     

反应扩散系统中时空斑图研究

时空斑图广泛地存在于反应扩散系统中,在延展的布鲁塞尔振子模型中,一维的时空斑图已经被研究过.本文中,我们对布鲁塞尔振子模型进行线性稳定性分析,模拟出两维的时空斑图,进一步阐明斑图形成的机制,形成斑图的机制是由于霍普夫失稳、短波失稳和图灵失稳以及它们之间的相互作用.当系统处于非平衡状态下,布鲁塞尔振子模型可以得到有序的时空斑图.?     

Dynamics of the Langevin model subjected to colored noise: Functional-integral method

We have discussed the dynamics of Langevin model subjected to colored noise, by using the functional-integral method (FIM) combined with equations of motion for mean and variance of the state variable. Two sets of colored noise have been investigated: (a) one additive and one multiplicative colored noise, and (b) one additive and two multiplicative colored noise. The case (b) is examined with relevance to a recent controversy on the stationary subthreshold voltage distribution of an integrate-and-fire model including stochastic excitatory and inhibitory synapses and a noisy input. We have studied the stationary probability distribution and dynamical responses to time-dependent (pulse and sinusoidal) inputs of the linear Langevin model. Model calculations have shown that results of the FIM are in good agreement with those of direct simulations (DSs). A comparison is made among various approximate analytic solutions such as the universal colored noise approximation (UCNA). It has been pointed out that dynamical responses to pulse and sinusoidal inputs calculated by the UCNA are rather different from those of DS and the FIM, although they yield the same stationary distribution.     

QUANTUM FLUCTUATION OF THE ORDER PARAMETER AND THE OPTICAL ABSORPTION IN POLYACETYLENEO

We study in this paper the effects of lattice quantum fluctuations upon the order parametert in the Peierls systems by using the Green's function technique.We start from the discrete Su-Schrief fer-Heeger model with quantized phonon field and derive a coupled system of equations for the order parameter and Green's functions.It turns out that the order parameter is reduced compared with the adiabatic value but the Peierls instability survives the quantum fluctuations in agreement with,Monte Carlo results.The band-to-band optical absorption coefficient of polyacetylene with lattice fluctuation being accounted for is also calculated and compared with the experimental data.     

Molecular,metabolic, and genetic control: An introduction

The living cell is a miniature, self-reproducing, biochemical machine. Like all machines, it has a power supply, a set of working components that carry out its necessary tasks, and control systems that ensure the proper coordination of these tasks. In this Special Issue, we focus on the molecular regulatory systems that control cell metabolism, gene expression, environmental responses, development, and reproduction. As for the control systems in human-engineered machines, these regulatory networks can be described by nonlinear dynamical equations, for example, ordinary differential equations, reaction-diffusion equations, stochastic differential equations, or cellular automata. The articles collected here illustrate (i) a range of theoretical problems presented by modern concepts of cellular regulation, (ii) some strategies for converting molecular mechanisms into dynamical systems, (iii) some useful mathematical tools for analyzing and simulating these systems, and (iv) the sort of results that derive from serious interplay between theory and experiment. (c) 2001 American Institute of Physics.     

Supercontinuum generation employing the high-energy wave-breaking-free pulse in a compact all-fiber laser system

Supercontinuum (SC) generation is experimentally achieved in a compact all-fiber laser system by using high-energy wave-breaking-free dissipative soliton (DS) pulses. The pulses exhibit Gaussian (rectangular) shape profiles in spectral (temporal) domain, which is even reversed of the typical rectangular-spectrum DSs. With the increase of pump power the pulse duration enlarges dramatically whereas the bandwidth and peak power of the pulse keep almost constant, which enables the pulse to accumulate much higher energy during the pulse-shaping process. When inputting the amplified pulse into the single-mode fiber, SC with excellent flatness is generated with the spectral range from about 1550 to 1700 nm. Broader SC with the bandwidth of even larger than 1000 nm can also be generated by this kind of pulse in the near-zero-dispersion-flattened photonic-crystal fiber through strong nonlinear effects.     

Nonlinear waves in nonequilibrium systems of the oscillatory type,part I

Nonlinear waves in mathematical models of nonequilibrium spatially uniform media with the oscillatory instability of the trivial state are considered. The models are based on the generalized Ginsburg-Landau equations. For the long-wave system, i.e. that described by two-component reaction-diffusion equations, we obtain the full stability conditions for monochromatic plane travelling waves. The basic part of the paper is devoted to the short-wave system which can be described by reaction-diffusion equations with not less than three components or by a two-component system with residual nonlocality. We construct the Ginsburg-Landau equation for this system, and we find its general quasistationary one-dimensional solution which is a travelling wave modulated by a travelling envelope wave. The stability of this solution is investigated with the especial emphasis on different important particular cases. The obtained results are compared with experimental observations of different waves on fronts of detonation and non-gaseous combustion (which also are characterized by the oscillatory short-wave instability of the trivial state), and the qualitative agreement between theoretical and experimental results is demonstrated.     

Batchelor scaling in fast-flowing soap films

The dynamics of a passive scalar such as a dye in the far dissipative range of fluid turbulence is a central problem in nonlinear physics. An important prediction for this problem was made by Batchelor over 40 years ago and is known as Batchelor's scaling law. We here present strong evidence in favor of this law for the thickness fluctuations in the flow of a soap film past a flat plate. The results also capture the dissipative range of the scalar which turns out to have universal features. The probability density function of the scalar increments and their structure functions come out in nice agreement with theoretical predictions.     

Rayleigh scattering and atomic dynamics in dissipative optical lattices

We investigate Rayleigh scattering in dissipative optical lattices. In particular, following recent proposals [S. Guibal, Phys. Rev. Lett. 78, 4709 (1997)]; C. Jurczak, Phys. Rev. Lett. 77, 1727 (1996)]], we study whether the Rayleigh resonance originates from the diffraction on a density grating and is therefore a probe of transport of atoms in optical lattices. It turns out that this is not the case: the Rayleigh line is instead a measure of the cooling rate, while spatial diffusion contributes to the scattering spectrum with a much broader resonance.     

Experimental investigations of nonlinear acoustic phenomena in polycrystalline zinc

The results of experimental and theoretical investigations of nonlinear acoustic phenomena (nonlinear losses, shift of resonance frequency, generation of the third harmonic, and nonlinear sound-by-sound damping) in polycrystalline zinc nonannealed and annealed resonating rods are presented. The measurements were carried out in the 10(-7)-10(-5) strain range at a frequency of about 3 kHz; the frequency of the weak ultrasonic pulse was about 270 kHz. The experimentally observed phenomena are described in frames of phenomenological equations of state containing elastic hysteresis and dissipative nonlinearity. The nonlinear acoustic parameters of these equations are determined by comparison between theoretical dependencies and experimental results. The influence of structural changes in zinc due to annealing on the nonlinear acoustic phenomena is shown.     

Decoherence in atom–field interactions: A treatment using superoperator techniques

Decoherence is a subject of great importance in quantum mechanics, particularly in the fields of quantum optics, quantum information processing and quantum computing. Quantum computation relies heavily in the unitary character of each step carried out by a quantum computational device and this unitarity is affected by decoherence. An extensive study of master equations is therefore needed for a better understanding on how quantum information is processed when a system interacts with its environment. Master equations are usually studied by using Fokker–Planck and Langevin equations and not much attention has been given to the use of superoperator techniques. In this report we study in detail several approaches that lead to decoherence, for instance a variation of the Schrödinger equation that models decoherence as the system evolves through intrinsic mechanisms beyond conventional quantum mechanics rather than dissipative interaction with an environment. For the study of the dissipative interaction we use a correspondence principle approach. We solve the master equations for different physical systems, namely, Kerr and parametric down conversion. In the case of light-matter interaction we show that although dissipation destroys the quantumness of the field, information of the initial field may be obtained via the reconstruction of quasiprobability distribution functions.     

Stability properties of multiwavelength, incoherent, dissipative spatial solitons

We have investigated the interaction between two dissipative spatial solitons of different frequencies in periodically patterned semiconductor optical amplifiers. The experimental results are in good agreement with the theory. Simulations suggest that multiwavelength interactions do not produce stable bound solitons unless the system's modeling equations are completely symmetric.     

Prognosis of Qualitative Behavior of a Dynamic System by the Observed Chaotic Time Series

An approach to the long-term prognosis of qualitative behavior of a dynamic system (DS) is proposed, which is based on the nonlinear-dynamical analysis of a weakly nonstationary chaotic time series (TS). A method for constructing prognostic models using the observed evolution of a single dynamic variable is described, which employs the proposed approach for prediction of bifurcations of low-dimensional DSs. The method is applied to analyze the TS generated by the Roessler system and the system of equations modeling photochemical processes in the mesosphere. The analysis is performed for a TS calculated in the case of a slow variation in the control parameter of the system. The duration of the observed TS is limited such that the system demonstrates only one, chaotic, type of behavior without any bifurcations during the observed TS. The proposed algorithm allows us to predict correctly the bifurcation sequences for both systems at times much longer than the duration of the observed TS, to point out the expected instants of specific bifurcation transitions and accuracy of determining these instants, as well as to calculate the probabilities to observe the predicted regimes of the system's behavior at the time of interest.     

Simplified Formula of Bending Loss for Optical Fiber Sensors

A simple fiber-optic bending loss formula is achieved for optical fiber sensors. This simple formula considers various bending radii, number of turns, extra bending angle, and wavelength and has good agreement with theoretical and experimental data. We also propose a simplified formula for sensitivity of the fiber-optic bending loss in this article. The defined sensitivity formula has the benefit of showing parameters for fiber-optic bending sensor systems.