Ion soliton observation with laser induced fluorescence

Many theoretical and experimental studies of solitons in plasma have been performed [Phys. Fluids 16 (1973) 1668; Plasma Phys. 25 (1983) 943; IEEE Trans. Plasma Phys. PS 10 (1982) 180; Plasma Phys. 5 (1998) 4144] and most of the properties such as the relation between the amplitude, the velocity and the width, for soliton or soliton-dust interaction, have been obtained. The agreement between experiment and theoretical model is not always good [Phil. Mag. Ser. 39 (1895) 422; Phys. Rev. Lett. 17 (1966) 996; Phys. Rev. E 51 (1995) 4796]. The experimental observations typically involve Langmuir probes. However, the ion acoustic soliton propagation can be observed by laser induced fluorescence (LIF) in double plasma device. This direct observation of ion perturbation with LIF points out the importance of the optical pumping effect [Rev. Sci. Instrum. 72 (2001) 4372] in the measurement of fast velocity propagation of ion phenomena like solitons are. With the LIF we discovered that a train of soliton propagates easier in the device if a weak backward ion flux plasma, having a drift velocity in the range of 200 m/s is present; as faster the ion flux is, as close to the grid the solitons separation occurs; the precursors ions is in fact a collective phenomenon.     

Quasi-cycles and sensitive dependence on seed values in edge of chaos behaviour in a class of self-evolving maps

In a recent paper [Melby P, Kaidel J, Weber N, Hubler A. Adaptation to the edge of chaos in the self-adjusting logistic map. Phys Rev Lett 2000;84:5991–3], Melby et al. attempted to understand edge of chaos behaviour through a very simple model. Based on our exhaustive numerical experiments, here we show that the model, with the definition of the edge of chaos given in the paper, cannot unequivocally support the idea of adaptation to the edge of chaos, let alone allow a conjecture of its generic presence in systems having the same characteristic features.     

How to excite the internal modes of sine-Gordon solitons

We investigate the dynamics of the sine-Gordon solitons perturbed by spatiotemporal external forces. We prove the existence of internal (shape) modes of sine-Gordon solitons when they are in the presence of inhomogeneous space-dependent external forces, provided some conditions (for these forces) hold. Additional periodic time-dependent forces can sustain oscillations of the soliton width. We show that, in some cases, the internal mode even can become unstable, causing the soliton to decay in an antisoliton and two solitons. In general, in the presence of spatiotemporal forces the soliton behaves as a deformable (non-rigid) object. A soliton moving in an array of inhomogeneities can also present sustained oscillations of its width. There are very important phenomena (like the soliton–antisoliton collisions) where the existence of internal modes plays a crucial role. We show that, under some conditions, the dynamics of the soliton shape modes can be chaotic. A short report of some of our results has been published in [Phys. Rev. E 65 (2002) 065601(R)].     

Numerical simulation of dynamic sand dunes

The physics of granular materials is interesting from many points of view because they exhibit a wealth of phenomena that have both fluid and solid aspects [C.S. Campbell, Annu. Rev. Fluid. Mech. 22 (1990) 57, H.M. Jaeger, S.R. Nagel, R.P. Behringer, Phys. Today 494 (1996) 32]. Recently a difficult pattern was observed if sand falls in the space between two plates and passes an obstacle [Y. Amarouchene, J.F. Boudet, H. Kellay, Phys. Rev. Lett. 86 (2001) 4286]. The interesting behaviour occurs on top of the obstacle where a dynamic dune with a parabolic tip is formed. Inside this parabola, a triangular region of non- or very slow flowing sand is observed. Using factor analysis it is possible to extract latent parameters from a dynamic process. Applying a three factor model we can clearly identify the inner triangle (1st factor) and the outer parabolic pattern (3rd factor). The second factor we interpret as shock wave. Most interactions between particles take place in a relatively small region. We show that the pattern formation process depends on the restitution coefficients (particle–particle and particle–obstacle) and also on the particle size. These findings cannot be observed if standard velocity profiles are used to analyse the data. Our findings show, that most interactions take place in a relatively small area correlating with the particle size. If the interactions between different particles and particle–obstacle are elastic the formation of a non-flowing triangular region is more difficult as if inelastic collisions are used. The factor curves also clearly show that a pattern formation process has to be finished, before the next pattern can be formed.     

Solitary wave solutions for high dispersive cubic-quintic nonlinear Schrödinger equation

We consider the higher-order dispersive nonlinear Schrödinger equation including fourth-order dispersion effects and a quintic nonlinearity. This equation describes the propagation of femtosecond light pulses in a medium that exhibits a parabolic nonlinearity law. By adopting the ansatz solution of Li et al. [Zhonghao Li, Lu Li, Huiping Tian, Guosheng Zhou. New types of solitary wave solutions for the higher-order nonlinear Schrödinger equation. Phys Rev Lett 2000;84:4096], we find two different solitary wave solutions under certain parametric conditions. These solutions are in the form of bright and dark soliton solutions.     

Strictly substochastic semigroups with application to conservative and shattering solutions to fragmentation equations with mass loss

In the paper we shall present a survey of recent results on substochastic semigroups and provide new methods for determining their honesty. These methods are applied to the fragmentation equation with mass loss, yielding sufficient conditions for the existence of conservative and shattering solutions. Our results provide a mathematical framework that clarifies the discussion of [Phys. Rev. A 43 (1991) 656, Phys. Rev. A 41 (1990) 5755, J. Phys. A 24 (1991) 3967] on shattering fragmentation in such models showing, among others, that there occurs an unexpected mass loss associated with shattering which is not accounted for by the discrete and continuous mass loss, contrary to the conjecture of [Phys. Rev. A 43 (1991) 656, Phys. Rev A 41 (1990) 5755].     

Estimating parameters of chaotic systems under noise-induced synchronization

Kim et al. introduced in 2002 [Kim CM, Rim S, Kye WH. Sequential synchronization of chaotic systems with an application to communication. Phys Rev Lett 2002;88:014103] a hierarchically structured communication scheme based on sequential synchronization, a modification of noise-induced synchronization (NIS). We propose in this paper an approach that can estimate the parameters of chaotic systems under NIS. In this approach, a dimensionally-expanded parameter estimating system is first constructed according to the original chaotic system. By feeding chaotic transmitted signal and external driving signal, the parameter estimating system can be synchronized with the original chaotic system. Consequently, parameters would be estimated. Numerical simulation shows that this approach can estimate all the parameters of chaotic systems under two feeding modes, which implies the potential weakness of the chaotic communication scheme under NIS or sequential synchronization.     

Dual synchronization based on two different chaotic systems: Lorenz systems and Rössler systems

In this paper, we improve and extend the works of Liu and Davids [Dual synchronization of chaos, Phys. Rev. E 61 (2000) 2176–2179] which only introduce the dual synchronization of 1-D discrete chaotic systems. The dual synchronization of two different 3-D continuous chaotic systems, Lorenz systems and Rössler systems, is discussed. And a sufficient condition of dual synchronization about the two different chaotic systems is obtained. Theories and numerical simulations show the possibility of dual synchronization and the effectiveness of the method.     

A System of ODEs for a Perturbation of a Minimal Mass Soliton

We study soliton solutions to the nonlinear Schrödinger equation (NLS) with a saturated nonlinearity. NLS with such a nonlinearity is known to possess a minimal mass soliton. We consider a small perturbation of a minimal mass soliton and identify a system of ODEs extending the work of Comech and Pelinovsky (Commun. Pure Appl. Math. 56:1565–1607, 2003), which models the behavior of the perturbation for short times. We then provide numerical evidence that under this system of ODEs there are two possible dynamical outcomes, in accord with the conclusions of Pelinovsky et al. (Phys. Rev. E 53(2):1940–1953, 1996). Generically, initial data which supports a soliton structure appears to oscillate, with oscillations centered on a stable soliton. For initial data which is expected to disperse, the finite dimensional dynamics initially follow the unstable portion of the soliton curve.     

Localization and universality of Poisson statistics for the multidimensional Anderson model at weak disorder

We prove Anderson localization with the mean-field Lyapunov exponent and Poisson statistics for eigenvalue spacing for the multi-dimensional Anderson model at weak disorder. These results are obtained by developing the supersymmetric formalism initiated in [W1] (see also [SjW]). rid Oblatum 9-XII-2000 & 6-VI-2001?Published online: 24 August 2001     

Strange nonchaotic attractors in the externally modulated Rayleigh–Bénard system

The amplitude equation associated with an externally modulated Rayleigh–Bénard system of binary mixtures near the codimension-two point is considered. Strange nonchaotic dynamics and chaotic behaviour are investigated numerically. The creation of strange nonchaotic attractors as well as the onset of chaos are studied through an analysis of Poincaré surfaces, a construction of the bifurcation diagram and a new method for computing Lyapunov exponents that exploits the underlying symplectic structure of Hamiltonian dynamics [Phys. Rev. Lett. 74 (1995) 70].     

Inverse scattering transformation and soliton stability for a nonlinear Gross–Pitaevskii equation with external potentials

We consider the Gross–Pitaevskii(GP) equation with the combination of periodic and harmonic external potentials. In particular, the method of inverse scattering transformation is applied to the GP equation with external potentials. Furthermore, some exact soliton solutions are obtained for the GP equation by using inverse scattering transformation, in which some physically relevant bright solutions are described. The stabilities of the obtained matter-wave solutions are addressed numerically such that some stable solutions are found, and some solitons can be stable in a wide region. These results may raise the possibility of relative experiments and potential applications.     

Anderson Localization for a Class of Models with a Sign-Indefinite Single-Site Potential via Fractional Moment Method

A technically convenient signature of Anderson localization is exponential decay of the fractional moments of the Green function within appropriate energy ranges. We consider a random Hamiltonian on a lattice whose randomness is generated by the sign-indefinite single-site potential, which is however sign-definite at the boundary of its support. For this class of Anderson operators, we establish a finite-volume criterion which implies that the fractional moment decay property holds. This constructive criterion is satisfied at typical perturbative regimes, e.g. at spectral boundaries which satisfy “Lifshitz tail estimates” on the density of states and for sufficiently strong disorder. We also show how the fractional moment method facilitates the proof of exponential (spectral) localization for such random potentials.     

Haruspicy 2: The anisotropic generating function of self-avoiding polygons is not D-finite

We prove that the anisotropic generating function of self-avoiding polygons is not a D-finite function—proving a conjecture of Guttmann [Discrete Math. 217 (2000) 167-189] and Guttman and Enting [Phys. Rev. Lett. 76 (1996) 344-347]. This result is also generalised to self-avoiding polygons on hypercubic lattices. Using the haruspicy techniques developed in an earlier paper [Rechnitzer, Adv. Appl. Math. 30 (2003) 228-257], we are also able to prove the form of the coefficients of the anisotropic generating function, which was first conjectured in Guttman and Enting [Phys. Rev. Lett. 76 (1996) 344-347].     

Spectral dependence of the localization degree in the one-dimensional disordered Lloyd model

We calculate the Anderson criterion and the spectral dependence of the degree of localization in the first nonvanishing approximation with respect to disorder for one-dimensional diagonally disordered models with a site energy distribution function that has no finite even moments higher than the zeroth. For this class of models (for which the usual perturbation theory is inapplicable), we show that the perturbation theory can be consistently constructed for the joint statistics of advanced and retarded Green’s functions. Calculations for the Lloyd model show that the Anderson criterion in this case is a linear (not quadratic as usual) function of the disorder degree. We illustrate the calculations with computer experiments.     

Non-extensive thermodynamics and stationary processes of localization

We focus our attention on dynamical processes characterized by an entropic index Q<1. According to the probabilistic arguments of Tsallis, C and Bukman, DJ [Phys Rev E 1996;54:R2197] these processes are subdiffusional in nature. The non-extensive generalization of the Kolmogorov–Sinai (KS) entropy yielding the same entropic index implies the stationary condition. We note, on the other hand, that enforcing the stationary property on subdiffusion has the effect of producing a localization process occurring within a finite time scale. We thus conclude that the stationary dynamic processes with Q<1 must undergo a localization process occurring at a finite time. We check the validity of this conclusion by means of a numerical treatment of the dynamics of the logistic map at the critical point.     

Universality of Chaos and Ultrametricity in Mixed p‐Spin Models

We prove disorder universality of chaos phenomena and ultrametricity in the mixed p‐spin model under mild moment assumptions on the environment. This establishes the longstanding belief among physicists that the solution of mean‐field models with Gaussian disorder also holds for different environments. Our results extend to the mixed p‐spin model as well as to different spin glass models. These include universality of quenched disorder chaos in the Edwards‐Anderson (EA) model and quenched concentration for the magnetization in both EA and mixed p‐spin models under non‐Gaussian environments. In addition, we show quenched self‐averaging for the overlap in the random field Ising model under small perturbation of the external field.© 2015 Wiley Periodicals, Inc.     

On two-particle Anderson localization at low energies

We prove exponential spectral localization in a two-particle lattice Anderson model, with a short-range interaction and an external i.i.d. random potential, at sufficiently low energies. The proof is based on the multi-particle multi-scale analysis developed earlier in Chulaevsky and Suhov (2009) [4] in the case of high disorder. Our method applies to a larger class of random potentials than in Aizenman and Warzel (2009) [2] where dynamical localization was proved with the help of the fractional moment method.     

Solitary wave solutions of higher-order NLSE with Raman and self-steepening effect in a cubic–quintic–septic medium

We find bright and dark solitary wave solutions for the higher-order nonlinear Schrodinger equation with cubic–quintic–septic terms adopting the ansatz solution of Li et al. [Li Z, Li L, Tian H, Zhou G. Phys. New types of solitary wave solutions for the higher-order nonlinear Schrödinger equation. Phys Rev Lett 2000;84(18):4096–99.] which may describe propagation of pulses upto the order of 10 fs in a non-Kerr media. In this context, we have taken into account both the Raman and the self-steepening effect. All the solitary wave parameters and the parametric conditions for the solitary wave solutions are worked out.     

Nonlinear dynamics and solitons in the presence of rapidly varying periodic perturbations

Problems of nonlinear dynamics and soliton propagation in the presence of rapidly varying periodic perturbations are considered applying a rigorous analytical approach based on asymptotic expansions. The method we develop allows derivation of an effective nonlinear equation for the slowly varying field component in any order of the asymptotic procedure as expansions in the parameter ω⁻¹, ω being the frequency of the rapidly varying (direct or parametric) driving force. The general approach is demonstrated on several examples of different physical nature, including chaos suppression in the parametrically driven Duffing oscillator, dynamics of the sine-Gordon kinks in the presence of rapidly varying direct or parametric driving force, propagation of envelope (nonlinear Schrödinger) solitons in optical fibres with periodic amplification, stability of solitons on rapidly varying spatial periodic potential, and so on.