The magnetic phase transition in amorphous ferromagnets and in spin glasses

The magnetic phase transition in materials with exchange disorder (amorphous ferromagnets, spin glasses) is discussed. In the critical temperature range the behavior of amorphous ferromagnetic transition metal-metalloid glasses is found to be similar to the one derived for a three-dimensional homogeneous Heisenberg ferromagnet. The most prominent difference between disordered and homogeneous materials is manifested in a large temperature range of deviations from the mean field behavior beyond the critical region, as observed experimentally for the temperature dependence of the linear susceptibility of amorphous ferromagnets and of the nonlinear susceptibility of spin glasses. A molecular field theory with correlations in space and time is developed, which relates the deviations from the mean field behavior to the interplay between the temperature dependent thermal correlations in the spin system and the spatial fluctuations of the material. Application to dynamical processes (kinetic critical slowing down) is discussed.     

Dynamics of Optical Bistability with Kerr-nonlinear Blackbody Radiation Reservoir

In this paper we investigate the nonlinear dynamics for optical bistabile(OB) model of homogeneously broadened two-level atomic medium interacting with a single mode of the ring cavity in the presence of a Kerr-nonlinear blackbody(KNB) radiation reservoir. We show the impact of the relative temperature of the reservoir on the transition between the dynamical states via bifurcation diagrams that represents the relation between maximum values of the output field and the relative temperature for fixed input field. Specifically, decreasing the relative temperature(T_b)causes the system to bifurcate from periodic to chaotic behavior and in turn reverts back to periodic behavior with further decrease of T_b. Varying atomic detuning leads to a change in the nature of the dynamic transition between the system's states from self pulsing to chaotic behavior.     

Qualitative dynamical properties of a phantom field with an arbitrary potential

We study the qualitative dynamical behaviour of a phantom field minimally coupled to gravity, with an arbitrary self-interacting potential. We show that the dynamics of this system is surprisingly simple, independently of the form of the potential. Periodic or oscillatory behaviour of the scale factor or periodic behaviour of the scalar field is not possible. We characterize all the possible asymptotic behaviours of the dynamical variables.     

Composite band-gap solitons in nonlinear optically induced lattices

We introduce novel optical solitons that consist of a periodic and a spatially localized component coupled nonlinearly via cross-phase modulation. The spatially localized optical field can be treated as a gap soliton supported by the optically induced nonlinear grating. We find different types of these band-gap composite solitons and demonstrate their dynamical stability.     

Slow relaxation in microcanonical warming of a Ising lattice

We study the warming process of a semi-infinite cylindrical Ising lattice initially ordered and coupled at the boundary to a heat reservoir. The adoption of a proper microcanonical dynamics allows a detailed study of the time evolution of the system. As expected, thermal propagation displays a diffusive character and the spatial correlations decay exponentially in the direction orthogonal to the heat flow. However, we show that the approach to equilibrium presents an unexpected slow behavior. In particular, when the thermostat is at infinite temperature, correlations decay to their asymptotic values by a power law. This can be rephrased in terms of a correlation length vanishing logarithmically with time. At finite temperature, the approach to equilibrium is also a power law, but the exponents depend on the temperature in a non-trivial way. This complex behavior could be explained in terms of two dynamical regimes characterizing finite and infinite temperatures, respectively. When finite sizes are considered, we evidence the emergence of a much more rapid equilibration, and this confirms that the microcanonical dynamics can be successfully applied on finite structures. Indeed, the slowness exhibited by correlations in approaching the asymptotic values are expected to be related to the presence of an unsteady heat flow in an infinite system.     

一类相对转动非线性动力学系统周期解的唯一性与精确周期解

研究了一类具有线性刚度、非线性阻尼力和强迫周期力项的相对转动非线性动力学系统周期解的唯一性和精确周期解.讨论了一类自治系统极限环的唯一性与稳定性.应用定性分析方法,给出了一类相对转动非线性动力学系统具有唯一周期解的必要条件,并在一定条件下得到了系统的一类精确周期解.     

Supernarrow spectral peaks near a kinetic phase transition in a driven nonlinear micromechanical oscillator

We measure the spectral densities of fluctuations of an underdamped nonlinear micromechanical oscillator. By applying a sufficiently large periodic excitation, two stable dynamical states are obtained within a particular range of driving frequency. White noise is injected into the excitation, allowing the system to overcome the activation barrier and switch between the two states. While the oscillator predominately resides in one of the two states for most frequencies, a narrow range of frequencies exist where the occupations of the two states are approximately equal. At these frequencies, the oscillator undergoes a kinetic phase transition that resembles the phase transition of thermal equilibrium systems. We observe a supernarrow peak in the spectral densities of fluctuations of the oscillator. This peak is centered at the excitation frequency and arises as a result of noise-induced transitions between the two dynamical states.     

Temperature field in inhomogeneous strongly anisotropic medium with sources

Using an “on-average exact” asymptotic method in a first approximation we constructed an analytical solution to the problem on the temperature field of heat sources in an anisotropic layer and ambient medium with dominant vertical thermal conduction. Results on temperature calculations in application to oil-gas formations are presented. It is shown that in the Laplace-Carson space, the zero and first expansion coefficients of the exact solution in terms of the asymptotic parameter coincide with those constructed on the base of the proposed method.     

Diffusive energy growth in classical and quantum driven oscillators

We study the long-time stability of oscillators driven by time-dependent forces originating from dynamical systems with varying degrees of randomness. The asymptotic energy growth is related to ergodic properties of the dynamical system: when the autocorrelation of the force decays sufficiently fast one typically obtains linear diffusive growth of the energy. For a system with good mixing properties we obtain a stronger result in the form of a central limit theorem. If the autocorrelation decays slowly or does not decay, the behavior can depend on subtle properties of the particular model. We study this dependence in detail for a family of quasiperiodic forces. The solution involves the analysis of a small-denominator problem that can be treated by fairly elementary methods. In the special case of a periodic force the quantum stability problem can be expressed in terms of spectral properties of the Floquet operator. In the presence of resonances the spectrum is absolutely continuous. We find explicitly the eigenvalues and eigenfunctions for the nonresonant case.     

Towards nonlinear stability of sources via a modified Burgers equation

Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at x=±∞ to spatially periodic travelling waves. This paper is concerned with sources which are coherent structures for which the group velocities in the far field point away from the core. Sources actively select wave numbers and therefore often organize the overall dynamics in a spatially extended system. Determining their nonlinear stability properties is challenging as localized perturbations may lead to a non-localized response even on the linear level due to the outward transport. Using a Burgers-type equation as a model problem that captures some of the essential features of sources, we show how this phenomenon can be analysed and asymptotic nonlinear stability be established in this simpler context.     

Strange attractors and their periodic repetition

In this paper, we present some important findings regarding a comprehensive characterization of dynamical behavior in the vicinity of two periodically perturbed homoclinic solutions. Using the Duffing system, we illustrate that the overall dynamical behavior of the system, including strange attractors, is organized in the form of an asymptotic invariant pattern as the magnitude of the applied periodic forcing approaches zero. Moreover, this invariant pattern repeats itself with a multiplicative period with respect to the magnitude of the forcing. This multiplicative period is an explicitly known function of the system parameters. The findings from the numerical experiments are shown to be in great agreement with the theoretical expectations.     

Sound modes in composite incommensurate crystals

We propose a simple phenomenological model describing composite crystals, constructed from two parallel sets of periodic inter-penetrating chains. In the harmonic approximation and neglecting thermal fluctuations we find the eigenmodes of the system. It is shown that at high frequencies there are two longitudinal sound modes with standard attenuation, while in the low frequency region there is one propagating sound mode and an over-damped phase mode. The crossover between these two regions is analyzed numerically and the dynamical structure factor is calculated. It is shown that the qualitative features of the experimentally observed spectra can be consistently described by our model. Received 28 November 2001 and Received in final form 23 January 2002     

立方五次方非线性Schrodinger方程的动力学性质研究

采用辛算法数值求解了一维立方五次方非线性Schrödinger方程,研究了不同非线性参数下非线性Schrödinger方程的动力学性质.数值结果表明,随着立方非线性参数的增加,系统经历了拟周期状态、混沌状态和周期状态,且在五次方项的调制下,呼吸子解可以退化为单孤子解. 关键词： 非线性Schrödinger方程 动力学性质 孤子 辛算法     

非线性传送带系统的复杂分岔

讨论了一类单自由度非线性传送带系统. 首先通过分段光滑动力系统理论得出系统滑动区域的解析分析和平衡点存在性条件; 其次利用数值方法, 对系统几种类型的周期轨道进行单参数和双参数延拓, 得到系统的余维一滑动分岔曲线和若干余维二滑动分岔点, 以及系统在参数空间中的全局分岔图. 通过对系统分岔行为的研究, 反映出传送带速度和摩擦力振幅对系统动力学行为有较大影响, 揭示了非线性传送带系统的复杂动力学现象. 关键词： 传送带系统 滑动分岔 周期运动     

The role of birefringence in modulation instability fiber ring resonators

We considered a high birefringence fiber ring cavity, which can be represented by a system of two incoherently coupled nonlinear Schrödinger equations with periodic boundary conditions. The stability of the system against time domain periodic perturbations could be strongly conditioned by fiber birefringence. We apply both a perturbative approach and a mean field approximation, in order to highlight the dependence of modulation instability on birefringence and ring detuning. We extend the study of the dynamical properties of the system by means of a phase matching interpretation and a selection of numerical solutions of the governing equations.     

Revisiting a magneto-elastic strange attractor

We revisit an early example of a nonlinear oscillator that exhibits chaotic motions when subjected to periodic excitation: the magneto-elastically buckled beam. In the paper of Moons and Holmes (1980) [1] magnetic field calculations were outlined but not carried through; instead the nonlinear forces responsible for creation of a two-well potential and buckling were fitted to a polynomial function after reduction to a single mode model. In the present paper we compute the full magnetic field and use it to approximate the forces acting on the beam, also using a single mode reduction. This provides a complete model that accurately predicts equilibria, bifurcations, and free oscillation frequencies of an experimental device. We also compare some periodic, transient and chaotic motions with those obtained by numerical simulations of the single mode model, further illustrating the rich dynamical behavior of this simple electromechanical system.     

Thermal conductivity in 3D NJL model under external magnetic field

The thermal conductivity of the (2+1)-dimensional NJL model in the presence of a constant magnetic field is calculated in the mean-field approximation and its different asymptotic regimes are analyzed. Taking into account the dynamical generation of a fermion mass due to the magnetic catalysis phenomenon, it is shown that for certain relations among the theory's parameters (particle width, temperature and magnetic field), the profile of the thermal conductivity versus the applied field exhibits kink- and plateau-like behaviors. We point out possible applications to planar condensed matter.     

A holographic description of theta-dependent Yang-Mills theory at finite temperature

Theta-dependent gauge theories can be studied using holographic duality through string theory in certain spacetimes.By this correspondence we consider a stack of N_0 dynamical DO-branes as D-instantons in the background sourced by N_c coincident non-extreme black D4-branes.According to the gauge-gravity duality,this D0-D4 brane system corresponds to Yang-Mills theory with a theta angle at finite temperature.We solve the IIA supergravity action by taking account into a sufficiently small backreaction of the Dinstantons and obtain an analytical solution for our D0-D4-brane configuration.Subsequently,the dual theory in the large N_c limit can be holographically investigated with the gravity solution.In the dual field theory,we find that the coupling constant exhibits asymptotic freedom,as is expected in QCD.The contribution of the theta-dependence to the free energy gets suppressed at high temperatures,which is basically consistent with the calculation using the Yang-Mills instanton.The topological susceptibility in the large N_c limit vanishes,and this behavior remarkably agrees with the implications from the simulation results at finite temperature.Moreover,we finally find a geometrical interpretation of the theta-dependence in this holographic system.     

Nonlinear and nonequilibrium dynamics in geomaterials

The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a simple macroscopic dynamical model. At even higher strains, effects due to a driven nonequilibrium state, and relaxation from it, complicate the characterization of the nonlinear behavior.     

Route to chaos for combustion instability in ducted laminar premixed flames

Complex thermoacoustic oscillations are observed experimentally in a simple laboratory combustor that burns lean premixed fuel-air mixture, as a result of nonlinear interaction between the acoustic field and the combustion processes. The application of nonlinear time series analysis, particularly techniques based on phase space reconstruction from acquired pressure data, reveals rich dynamical behavior and the existence of several complex states. A route to chaos for thermoacoustic instability is established experimentally for the first time. We show that, as the location of the heat source is gradually varied, self-excited periodic thermoacoustic oscillations undergo transition to chaos via the Ruelle-Takens scenario.