Riddling and chaotic synchronization of coupled piecewise-linear Lorenz maps

We investigate the parametric evolution of riddled basins related to synchronization of chaos in two coupled piecewise-linear Lorenz maps. Riddling means that the basin of the synchronized attractor is shown to be riddled with holes belonging to another basin in an arbitrarily fine scale, which has serious consequences on the predictability of the final state for such a coupled system. We found that there are wide parameter intervals for which two piecewise-linear Lorenz maps exhibit riddled basins (globally or locally), which indicates that there are riddled basins in coupled Lorenz equations, as previously suggested by numerical experiments. The use of piecewise-linear maps makes it possible to prove rigorously the mathematical requirements for the existence of riddled basins.     

耦合映射混沌同步系统在加性噪声中的筛形域性态

由于实际系统中噪声不可避免，噪声使得同步混沌吸引子A变成具有一定生存时间<τ>的准稳态吸引子A′.以加性噪声作用下的二维耦合映射混沌同步系统为例，给定系统实验时间长 度T，解析发现：仅当<τ>>2T时准稳态同步混沌吸引子的筛形吸引域才可被定性观察到；而 当<τ><2T时则不复存在，此时，根据原无噪声时的筛形吸引域特征的不同，筛形域不仅可 以转变成时变筛形结构，还可以转变成分形结构.同时利用数值模拟作了进一步验证.该结果 对于二维耦合映射混沌同步系统具有普遍意义. 关键词： 混沌同步 筛形吸引域 瞬态混沌 耦合映射 加性噪声     

耦合帐篷映射混沌同步系统的筛形吸引域

讨论了两个线性耦合的标准帐篷映射混沌同步系统的同步混沌吸引子的吸引域,证明其是筛形吸引域.提出了筛形品质因子的概念,并据之给出了系统的同步混沌吸引子的吸引域发生 从局部筛形到全局筛形的转变的耦合参数临界值.修正了当系统出现筛形吸引域时的横截Lyapunov指数的解析表达式.指出考查筛形吸引域在混沌同步系统中有着重要意义. 关键词： 混沌同步 筛形吸引域 耦合帐篷映射     

The isolated critical value phenomenon in local－global riddling bifurcation

A chaotic synchronized system of two coupled skew tent maps is discussed in this paper. The locally and globally riddled basins of the chaotic synchronized attractor are studied. It is found that there is a novel phenomenon in the local－global riddling bifurcation of the attractive basin of the chaotic synchronized attractor in some specific coupling intervals. The coupling parameter corresponding to the locally riddled basin has a single value which is embedded in the coupling parameter interval corresponding to the globally riddled basin, just like a breakpoint. Also, there is no relation between this phenomenon and the form of the chaotic synchronized attractor. This phenomenon is found analytically. We also try to explain it in a physical sense. It may be that the chaotic synchronized attractor is in the critical state, as it is infinitely close to the boundary of its attractive basin. We conjecture that this isolated critical value phenomenon will be common in a system with a chaotic attractor in the critical state, in spite of the system being discrete or differential.     

Riddled basins of attraction for synchronized type-I intermittency

Chaotic motion restricted to an invariant subspace of total phase space may be associated with basins of attraction that are riddled with holes belonging to the basin of another limiting state. We study the emergence of such basins for a system of two coupled one-dimensional maps, each exhibiting type-I intermittency.     

Predicting the liquid-vapor critical point from the crystal anharmonicity

A "universal" dependence is predicted of the reduced critical parameters, k(B)T(c) / E0(gamma), V(c) / V0(gamma), and P(c)V(c)/k(B)T(c) = Z(c)(gamma), on the crystal anharmonicity gamma (closely related to the Gruneisen parameter gamma(G)). It is based on a simplified embedded-atom type approach which enables one to utilize the universal zero-temperature equation of state in a version of fluid perturbation theory. This model's critical temperature and density agree with the experimental results for both the heavy rare gases ( gamma approximately 2.85) and heavy alkali metals ( gamma approximately 1.35). Predicted critical parameters for many other liquid metals are consistent with previous estimates, but the model is not applicable when directional bonding is important.     

Mean wind in convective turbulence of mercury

The large-scale circulation, often called "wind," in the confined thermal turbulence of mercury is studied experimentally. The instantaneous velocity profile at 128 points is directly measured using ultrasonic velocimetry. The periodic velocity oscillation is observed in the case of the aspect-ratio Gamma = 1,2 but not in Gamma = 0.5. Its peak frequency is scaled by f(c) proportional Ra(gamma(c)), where Ra is the Rayleigh number and gamma(c) = 0.43,0.45 for Gamma = 1,2. f(c) is close to the wind circulation frequency f(p), and has the same order of transit time from the bottom to the top of the convection cell. A single roll circulation is expected in Gamma = 1; however, axisymmetric toroidal rings may exist near the upper and lower plate for Gamma = 0.5, which are stable up to Ra = 7 x 10 (10).     

The Finite-Size Scaling Study of the Ising Model for the Fractals

The fractals are obtained by using the model of diffusion-limited aggregation (DLA) for 40 ≤ L ≤ 240. The two-dimensional Ising model is simulated on the Creutz cellular automaton for 40 ≤ L ≤ 240. The critical exponents and the fractal dimensions are computed to be β = 0.124(8), γ = 1.747(10), α = 0.081(21), δ = 14.994(11), η = 0.178(10), ν = 0.960(23) and \(d_{f}^{\beta } =1.876(8), \,d_{f}^{\gamma } =3.747(10), \,d_{f}^{\alpha } =2.081(68), \,d_{f}^{\delta } =1.940(22)\), \(d_{f}^{\eta } =2.178(10)\), \(d_{f}^{\nu } =2.960(22)\), which are consistent with the theoretical values of β = 0.125, γ = 1.75, α = 0, δ = 15, η = 0.25, ν = 1 and \(d_{f}^{\beta } =1.875, \,d_{f}^{\gamma } =3.75, \,d_{f}^{\alpha } =2, \,d_{f}^{\delta } =1.933, \,d_{f}^{\eta } =2.25, \,d_{f}^{\nu } =3\).     

A dynamical phase transition in a caricature of a spin glass

This paper studies the rate of convergence to equilibrium of Glauber dynamics (Gibbs Sampler) for a system ofN Ising spins with random energy (at inverse temperature >0). For each of the 2 ^N spin configurations the energy is drawn independently from the values 0 and-logN with probabilities 1-N ^–7, resp.N ^– (>0), and is kept fixed during the evolution. The main result is an estimate of the coupling time of two Glauber dynamics starting from different configurations and coupled via the same updating noise. AsN the system exhibits two dynamical phase transitions: (1) at =1 the coupling time changes from polynomial (>1) to stretched exponential (<1) inN; (2) if <1, then at = the almost coupling time [i.e., the first time that the two dynamics are within distanceo(N)] changes from polynomial (<) to stretched exponential (>) inN. The techniques used to control the randomness in the coupling are static and dynamic large-deviation estimates and stochastic domination arguments.     

Strange properties of early time evolution of the projection of a state vector

Using the equation for a projection of a state vector, the exponent of a damping factor for a given state, corresponding to the effective decay width appearing in the case of multiple measured unstable states, is obtained numerically in some models for early time period t 0. is found to be nonzero (even for stable states) at this time period; thus, for early times, this damping factor is always smaller than unity. It is shown that at finitet's may be smaller or greater than the standard decay width in Weisskopf-Wigner theory depending on the parameters of a model considered.     

Bifurcation structures and transient chaos in a four-dimensional Chua model

A four-dimensional four-parameter Chua model with cubic nonlinearity is studied applying numerical continuation and numerical solutions methods. Regarding numerical solution methods, its dynamics is characterized on Lyapunov and isoperiodic diagrams and regarding numerical continuation method, the bifurcation curves are obtained. Combining both methods the bifurcation structures of the model were obtained with the possibility to describe the shrimp-shaped domains and their endoskeletons. We study the effect of a parameter that controls the dimension of the system leading the model to present transient chaos with its corresponding basin of attraction being riddled.     

Desynchronization of chaos in coupled logistic maps

When identical chaotic oscillators interact, a state of complete or partial synchronization may be attained in which the motion is restricted to an invariant manifold of lower dimension than the full phase space. Riddling of the basin of attraction arises when particular orbits embedded in the synchronized chaotic state become transversely unstable while the state remains attracting on the average. Considering a system of two coupled logistic maps, we show that the transition to riddling will be soft or hard, depending on whether the first orbit to lose its transverse stability undergoes a supercritical or subcritical bifurcation. A subcritical bifurcation can lead directly to global riddling of the basin of attraction for the synchronized chaotic state. A supercritical bifurcation, on the other hand, is associated with the formation of a so-called mixed absorbing area that stretches along the synchronized chaotic state, and from which trajectories cannot escape. This gives rise to locally riddled basins of attraction. We present three different scenarios for the onset of riddling and for the subsequent transformations of the basins of attraction. Each scenario is described by following the type and location of the relevant asynchronous cycles, and determining their stable and unstable invariant manifolds. One scenario involves a contact bifurcation between the boundary of the basin of attraction and the absorbing area. Another scenario involves a long and interesting series of bifurcations starting with the stabilization of the asynchronous cycle produced in the riddling bifurcation and ending in a boundary crisis where the stability of an asynchronous chaotic state is destroyed. Finally, a phase diagram is presented to illustrate the parameter values at which the various transitions occur.     

Neutralino pair production in a $\gamma \gamma $ collider

We present a complete one-loop study of the process and the predicted cross section in a Linear Collider. A suitable numerical code, PLATONlc, valid for any set of real MSSM parameters, is released. This study and code are complementary to those suitable for dark matter detection through the inverse process describing neutralino-neutralino annihilation at rest, which were presented previously. If SUSY is realized in nature, both codes should be very helpful in future astrophysical and collider studies of the neutralino sector.Received: 6 November 2003, Published online: 9 January 2004Programme dActions Intégrées Franco-Hellenique, Platon 04100 UM.     

Pulsed-laser sputtering of atoms and molecules. Part I: Basic solutions for gas-dynamic effects

When gases are released from a pulsed nozzle or when solids are sputtered with intense laser pulses, effusion-like expansions take place which terminate abruptly. The resulting gas-dynamic processes depend on , the heat capacity ratio, as well as on whether particles backscattered to the effusing surface are subject to recondensation or reflection. Certain aspects of these terminating expansions have already been treated but we consider it appropriate to examine the problem further. In particular the following topics are emphasized. (a) Following previous work, the expansions are shown to consist of a series of regions separated by lines of contact, i.e. abrupt changes of slope. (b) For conditions of recondensation, there are two regions separated by one line of contact, the first region lying in part behind the effusing surface. For conditions of reflection, there are three regions, the first of which begins at the surface. Both types of expansion terminate with a region which is a remanent of the release process. (c) The nearsurface region under conditions of reflection permits an analytical approximation valid for all in which the sound speed is invariant with distance and the flow velocity is linear with distance. (d) The surface itself under conditions of recondensation permits an analytical approximation valid for all for the sound speed. More generally the near-surface region can be resolved by the method of Stanyukovich. (e) The various analytical solutions and approximations are shown to compare favorably with numerical results. (f) Plots of density and flow velocity versus distance are found to be roughly independent of , thence of the nature of the sputtered particles. (g) Tabulated results are presented to enable a more general use of gas-dynamic ideas.For Part II, which deals with recondensation, see [1]     

Four-fermion production at $\gamma\gamma$ colliders: 1. Lowest-order predictions and anomalous couplings

We have constructed a Monte Carlo generator (the corresponding FORTRAN code can be obtained from the authors upon request) for lowest-order predictions for the processes and in the standard model and extensions thereof by an effective coupling as well as anomalous triple and quartic gauge-boson couplings. Polarization is fully supported, and a realistic photon beam spectrum can be taken into account. For the processes all helicity amplitudes are explicitly given in a compact form. The presented numerical results contain, in particular, a survey of cross sections for representative final states and their comparison to results obtained with the program package Whizard/Madgraph. The impact of a realistic beam spectrum on cross sections and distributions is illustrated. Moreover, the size of various contributions to cross sections, such as from weak charged- or neutral-current, or from strong interactions, is analyzed. Particular attention is paid to W-pair production channels where we investigate the impact of background diagrams, possible definitions of the W-pair signal, and the issue of gauge-invariance violation caused by finite gauge-boson widths. Finally, the effects of triple and quartic anomalous gauge-boson couplings on cross sections as well as the possibility to constrain these anomalous couplings at future colliders are discussed.Received: 19 May 2004, Published online: 16 July 2004     

A model field theory in which two Nambu-Goldstone symmetries are realised by one massless pseudoscalar boson

We consider a model field theory consisting of two Nambu-Jona-Lasinio spin 1/2 fields interacting via a coupling \(f(\bar \psi _1 \gamma ^\mu \gamma ^5 \psi _1 )(\bar \psi _2 \gamma _\mu \gamma ^5 \psi _2 )\) and which is therefore invariant under the two symmetries \(\psi _1 (x) \to e^{i\alpha _1 } \gamma ^5 \psi _1 (x)\) and \(\psi _2 (x) \to e^{i\alpha _2 } \gamma ^5 \psi _2 (x)\) . We look for solutions in which these symmetries are spontaneously broken by giving the fermions non-zero masses. Each of the two pairs of axial-vector vertex functions in the theory satisfy two coupled integral equations, which are solved in the ‘chain approximation’. We find that all four vertex functions have the same singularity structure, in particular a pole atq ²=0 corresponding to a massless pseudoscalar Nambu-Goldstone boson, and another pole corresponding to an axial-vector boson whose mass is cut-off dependent, but which for a certain range of values off ² is a stable particle. By considering the coupling of the strings of nucleon-antinucleon psuedoscalar ‘bubbles’ which generate the massless Nambu-Goldstone bosons associated with fermions 1 and 2, we show explicitly that there is only one massless Nambu-Goldstone boson in the theory.     

Defect trapping by100Pd in fcc metals

Lattice defects in Al, Cu, Ag and Au were studied by the perturbed angular correlation technique (PAC) using the probe atom¹⁰⁰Pd/¹⁰⁰Rh. The comparison of data obtained on interstitial trapping in Cu and Au at different probe atoms (¹⁰⁰pd,¹¹¹In) allows defect characterisation less affected by the respective probe. The trapping efficiency of¹⁰⁰Pd for vacancy like defects is quite different to that of¹¹¹In atoms.     

Effect of f-c hybridization on the $\gamma\to \alpha$ phase transition of cerium studied by lanthanum doping

The hybridization between the localized 4f level (f) with conduction (c) electrons in $\gamma $-Ce upon cooling has been previously revealed in single crystalline thin films experimentally and theoretically, whereas its influence on the $\gamma \to \alpha $ phase transition was not explicitly verified, due to the fact that the phase transition happened in the bulk-layer, leaving the surface in the $\gamma $ phase. Here in our work, we circumvent this issue by investigating the effect of alloying addition of La on Ce, by means of crystal structure, electronic transport and angle resolved photoemission spectroscopy measurements, together with a phenomenological periodic Anderson model and a modified Anderson impurity model. Our current researches indicate that the weakening of f-c hybridization is the major factor in the suppression of $\gamma \to \alpha $ phase transition by La doping. The consistency of our results with the effects of other rare earth and actinide alloying additions on the $\gamma \to \alpha $ phase transition of Ce is also discussed. Our work demonstrates the importance of the interaction between f and c electrons in understanding the unconventional phase transition in Ce, which is intuitive for further researches on other rare earth and actinide metals and alloys with similar phase transition behaviors.     

Four-fermion production at $\gamma\gamma$ colliders: 2. Radiative corrections in double-pole approximation

The electroweak radiative corrections to within the electroweak standard model are calculated in double-pole approximation (DPA). Virtual corrections are treated in DPA, leading to a classification into factorizable and non-factorizable contributions, and real-photonic corrections are based on complete lowest-order matrix elements for . Soft and collinear singularities appearing in the virtual and real corrections are combined alternatively in two different ways, namely by using the dipole subtraction method or by applying phase-space slicing. The radiative corrections are implemented in a Monte Carlo generator called Coffer - the computer code can be obtained from the authors upon request - which optionally includes anomalous triple and quartic gauge-boson couplings in addition and performs a convolution over realistic spectra of the photon beams. A detailed survey of numerical results comprises corrections to integrated cross sections as well as to angular, energy, and invariant-mass distributions. Particular attention is paid to the issue of collinear safety in the observables.Received: 3 June 2005, Published online: 5 August 2005     

Scaling of directed dynamical small-world networks with random responses

A dynamical model of small-world networks, with directed links which describe various correlations in social and natural phenomena, is presented. Random responses of sites to the input message are introduced to simulate real systems. The interplay of these ingredients results in the collective dynamical evolution of a spinlike variable S(t) of the whole network. The global average spreading length (s) and average spreading time (s) are found to scale as p(-alpha)ln(N with different exponents. Meanwhile, S(t) behaves in a duple scaling form for N>N(*): S approximately f(p(-beta)q(gamma)t), where p and q are rewiring and external parameters, alpha, beta, and gamma are scaling exponents, and f(t) is a universal function. Possible applications of the model are discussed.