1/f noise spectrum of the chaotic motion in a whisker mapping

The power spectrum of the chaotic motion in a whisker mapping is investigated. The 1/f noise spectrum is observed in wide parameter regions. It is shown that the 1/f spectrum is well explained by the framework of the renewal process.     

Barkhausen jumps in the motion of a single ferroelectric domain wall

It is shown that the motion of a domain wall in the improper ferroelectric-ferroelastic gadolinium molybdate Gd₂(MoO₄)₃ demonstrates a self-organized critical behavior under polarization reversal. Barkhausen pulses are measured experimentally during the jumpwise motion of a single plane domain wall in monocrystalline plates with artificial pinning centers of the “field inhomogeneity” type.     

Stress response of Barkhausen noise in a tempered C-Mn steel

The dependence of Barkhausen noise on tensile stress is measured in a high strength vanadium microalloyed C-Mn steel after tempering at 200, 400, 500, 600 and 650°C. Simultaneously, the coercive force and two field parameters related to the magnetic reversal curve are recorded for some of the specimens tempered at 500, 600 and 650°C. Tempering causes a maximum in Barkhausen noise vs. stress curve and minima in the field strength vs. stress curves. An increase in the impedimental force due to stress gradients experienced by domain walls is suggested as the cause of the maximum. Stress gradients with short “wavelenghts” are thought to be produced in lath-or plate-like martensitic/bainitic structures. The effect appears in the course of tempering, as recovery processes reduce the dislocation density, and vanishes as recrystallization leads to an almost complete elimination of these dislocations.     

Asymptotic solution of a chaotic motion

A three-dimensional differential system is proposed, in which the motion becomes chaotic at some parameter value. The asymptotic solution is calculated by using Kuzmak's method.     

谐和激励与有界噪声作用下具有同宿和异宿轨道的Duffing振子的混沌运动

研究了具有同宿轨道、异宿轨道的双势阱Duffing振子在谐和激励与有界噪声摄动下的混沌运动.基于同宿分叉和异宿分叉，由Melnikov理论推导了系统出现混沌运动的必要条件及出现分形边界的充分条件.结果表明：当Wiener过程的强度参数大于某一临界值时，噪声增大了诱发混沌运动的有界噪声的临界幅值，相应地缩小了参数空间的混沌域，且产生混沌运动的临界幅值随着噪声强度的增大而增大.同时数值计算了最大Lyapunov指数，由最大Lyapunov指数为零从另一角度得到了系统出现混沌运动的有界噪声的临界幅值，发现在Wi 关键词： 混沌 同宿和异宿分叉 随机Melnikov方法 最大Lyapunov指数     

The analysis of rovibrational motion equations of a diatomic molecule in the linear regime

The motion equations of diatomic molecules are here extended from the absolute vibrational case to a more general and real rotational and vibrational (rovibrational) case. The rovibrational Hamiltonian is heuristically formed by substituting the respective number and angular momentum operators for the vibrational and rotational quantum numbers in the energy eigenvalues of a diatomic molecule which was first introduced by Dunham. The motion equations of observable quantities such as the position and linear momentum are then determined by implementing the well-known Heisenberg relation in quantum mechanics. We face with the second-order imaginary differential equations for describing the temporal variations of the relative position and the linear momentum of two oscillating atoms, which are coupled in the x–y horizontal plane. The possible rovibrational oscillations are distinguished by the three quantum numbers n, l and m associated with the energy and angular momentum quantities. It is finally demonstrated that the simultaneous solutions of rovibrational equations satisfy the energy conservation during all quantised oscillations of a diatomic molecule in space.     

The semiclassical regime of the chaotic quantum-classical transition

An analysis of the semiclassical regime of the quantum-classical transition is given for open, bounded, one-dimensional chaotic dynamical systems. Environmental fluctuations-characteristic of all realistic dynamical systems-suppress the development of a fine structure in classical phase space and damp nonlocal contributions to the semiclassical Wigner function, which would otherwise invalidate the approximation. This dual regularization of the singular nature of the semiclassical limit is demonstrated by a numerical investigation of the chaotic Duffing oscillator.     

The invariant density of a chaotic dynamical system with small noise

We consider a chaotic dynamical system perturbed by noise and calculate an approximate invariant density when the noise level is small. Because of the special structure of the dynamical system, the effective support of the invariant density is much smaller than the noiseless attractor. This behavior is captured by the asymptotic form of the invariant density, which is given explicitly.     

Application of the group pulse processes in the theory of Barkhausen noise

In the paper the 2nd-order periodic group pulse process is considered a statistical model of the Barkhausen voltage. Using this model an analytical formula for the power spectrum is derived and further specified to fit the measured spectrograms of Barkhausen noise. The results are interpreted with respect to the generating physical mechanism and examples of several numerical values are given.     

Effects of noise on a nonuniform chaotic map

Nonuniform separation of orbits initially close to each other is measured by several quantities which are derived from the statistics of growth rates of small perturbations. Using these measures of nonuniformity, a Belousov-Zhabotinsky map (BZ map), the logistics map, and the tent map are compared. The extremely nonuniform BZ map shows a remarkable response to external noise: the state predictability can be improved by an increase in noise power.     

Barkhausen effect in stepped motion of a plane domain boundary in gadolinium molybdate

Barkhausen pulses generated in stepped motion of a single plane domain boundary (PDB) are investigated experimentally in single-crystalline wafers of the extrinsic ferroelastic ferroelectric gadolinium molybdate containing artificial pinning centers of the “field inhomogeneity” type near the edges of the sample. Two scenarios of the evolution of a PDB in interaction with “defects” are proposed on the basis of analyzing the shape of the pulses in a linearly increasing field: small changes of the pulse shape in a weak field and the generation of wedge domains in a strong field. The proposed mechanism of PDB motion due to the generation of steps near the edge of the sample and their longitudinal motion provides a means for explaining the experimentally observed linear field dependence of the PDB velocity and for determining the velocity of the steps. Fiz. Tverd. Tela (St. Petersburg) 41, 301–305 (February 1999)     

Shot noise through a quantum dot in the Kondo regime

The shot noise in the current through a quantum dot is calculated as a function of voltage from the high-voltage Coulomb-blockaded regime to the low-voltage Kondo regime. Using several complementary approaches, it is shown that the zero-frequency shot noise (scaled by the voltage) exhibits a nonmonotonic dependence on voltage, with a peak around the Kondo temperature. Beyond giving a good estimate of the Kondo temperature, it is shown that the shot noise yields additional information on the effects of electronic correlations on the local density of states in the Kondo regime, unaccessible in traditional transport measurements.     

Stress response of Barkhausen noise and coercive force in 9Ni steel

The stress response curves of barkhausen noise, coercive force and lattice parameter of ratained austenite are measured for 9Ni steel in as-received condition (quenched and tempered plate), in tempered states following annealing for 1 to 243 h at 590°C, and in a coarse-grained state after annealing at 1200°C. The stress response is strong in all cases, but depends on the content of retained austenite, exhibiting the strongest response at 3 to 5 vol% austenite. The total range of retained austenite content was from 1.5 to 11.1%. The coercive force rises from about 500 to 850 A/m at temperings from 1 to 243 h, and contains a major contribution from dislocation of the fresh martensite formed furing cooling. The figures for austenite content and the lattice parameter measurements reveal that the austenite begins to lose stability after a few of tempering.     

Statistical properties in the chaotic regime of the Maxwell-Bloch equations

The statistical properties of the electric field solution of the Maxwell-Bloch equations describing a single mode, homogeneously broadened laser in the mean field limit are investigated in the strange attractor regime. The electric field distribution sis calculated and it is found that the low order intensity moments are somewhat higher than those for thermal-chaotic light whilst the higher order moments are substantially lower. The field and intensity correlation functions are also calculated and found to exhibit radically different behaviour. The results are interpreted in terms of iterative map which is dederived using multiple time-scale perturbation theory. It is shown that a simple random phasor model is compatible with the numerical data.     

Distortions of the statistical distribution of Barkhausen noise measured by magneto-optical Kerr effect

In magneto-optical Kerr measurements of the Barkhausen noise, a magnetization jump ΔM due to a domain reversal produces a variation ΔI of the intensity of a laser beam reflected by the sample, which is the physical quantity actually measured. Due to the non-uniform beam intensity profile, the magnitude of ΔI depends both on ΔM and on its position on the laser spot. This could distort the statistical distribution p(ΔI) of the measured ΔI with respect to the true distribution p(ΔM) of the magnetization jumps ΔM. In this work the exact relationship between the two distributions is derived in a general form, which will be applied to some possible beam profiles. It will be shown that in most cases the usual Gaussian beam produces a negligible statistical distortion. Moreover, for small ΔI the noise of the experimental setup can also distort the statistical distribution p(ΔI), by erroneously rejecting small ΔI as noise. This effect has been calculated for white noise, and it will be shown that it is relatively small but not totally negligible as the measured ΔI approaches the detection limit.     

Regular and chaotic motion of coupled rotators

We consider a classical Hamiltonian H = L_z+M_z+L_xM_x, where the components of L and M satisfy Poisson brackets similar to those of angular momenta. There are three constants of motion: H, L² and M². By studying Poincaré surfaces of section, we find that the motion is regular when L² or M² is very small or very large. It is chaotic when both L² and M² have intermediate values. The interest of this model lies in its quantization, which involves finite matrices only.     

Control of noisy chaotic motion in a system with nonlinear excitation and restoring forces

In this study we examine the complex and chaotic oscillations of a dynamical system with nonlinear excitation and restoring forces for the purpose of controlling these oscillatory states. The physical system, modeled as a system of first-order nonlinear ordinary differential equations, takes into account a geometric nonlinearity in the restoring force, a quadratic viscous drag, and a harmonic excitation force. It is controlled using small perturbations about a selected unstable cycle and control is instigated for periodic cycles of varying periodicities. The controller, when applied on the dynamical system with additive random noise in the excitation, successfully controls the system with noise levels in excess of 5% of the total energy, giving the first evidence that (stochastic) control of these systems is possible. (c) 1997 American Institute of Physics.     

Period-doubling bifurcations and chaotic motion for a parametrically forced pendulum

A parametrically forced pendulum is studied numerically both with and without friction. In both cases, period-doubling sequences of bifurcation are found. In the dissipative case, the period-doubling sequence leads to strange attractors, while in the conservative case, the sequence is responsible for the destruction of stable zones.