Model of the evolution of acoustic emission as the randomization of transient processes in coupled nonlinear oscillators

The behavior of a crack as a resonator radiating acoustic emission (AE) pulses at instants of sudden growth is investigated theoretically and experimentally. This resonance behavior of a growing crack is determined to a large extent by surface waves propagating along its edges. The crack can therefore be regarded as an acoustic resonator excited at the instant of growth of its tip. Transformations in the form of high-frequency harmonic and combination-frequency subharmonic generation are observed in the spectra of the AE signals. The final stage in the evolution of AE is characterized by the transition to a wideband noise spectrum. These facts lead to the hypothesis that bifurcations analogous to those encountered in the onset of dynamic chaos take place in the AE process. This hypothesis forms the basis of a mathematical model of the AE process as a system of coupled nonlinear oscillators, each corresponding to an individual crack. The initial displacement in one of the interacting cracks is adopted as the bifurcation parameter. Spectra calculated by computer simulation exhibit qualitative agreement with the evolution of the spectra obtained in the processing of data from physical experiments

Symmetry broken motion of a periodically driven Brownian particle: nonadiabatic regime

We report a theoretical study of an overdamped Brownian particle dynamics in the presence of both a spatially modulated one-dimensional periodic potential and a periodic alternating force (AF). As the periodic potential has a low symmetry (a ratchet potential) the Brownian particle displays a broken symmetry motion with a nonzero time average velocity. By making use of the Green function method and a mapping to the theory of Brillouin bands the probability distribution of the particle coordinate is derived and the nonlinear dependence of the macroscopic velocity on the frequency and the amplitude of AF is found. In particular, our theory allows to go beyond the adiabatic limit and to explain the peculiar reversal of the velocity sign found previously in the numerical analysis.Comment: 4 pages, 2 figure

On the influence of noise on chaos in nearly Hamiltonian systems

The simultaneous influence of small damping and white noise on Hamiltonian systems with chaotic motion is studied on the model of periodically kicked rotor. In the region of parameters where damping alone turns the motion into regular, the level of noise that can restore the chaos is studied. This restoration is created by two mechanisms: by fluctuation induced transfer of the phase trajectory to domains of local instability, that can be described by the averaging of the local instability index, and by destabilization of motion within the islands of stability by fluctuation induced parametric modulation of the stability matrix, that can be described by the methods developed in the theory of Anderson localization in one-dimensional systems.Comment: 10 pages REVTEX, 9 figures EP

Diffusion and Current of Brownian Particles in Tilted Piecewise Linear Potentials: Amplification and Coherence

Overdamped motion of Brownian particles in tilted piecewise linear periodic potentials is considered. Explicit algebraic expressions for the diffusion coefficient, current, and coherence level of Brownian transport are derived. Their dependencies on temperature, tilting force, and the shape of the potential are analyzed. The necessary and sufficient conditions for the non-monotonic behavior of the diffusion coefficient as a function of temperature are determined. The diffusion coefficient and coherence level are found to be extremely sensitive to the asymmetry of the potential. It is established that at the values of the external force, for which the enhancement of diffusion is most rapid, the level of coherence has a wide plateau at low temperatures with the value of the Peclet factor 2. An interpretation of the amplification of diffusion in comparison with free thermal diffusion in terms of probability distribution is proposed.Comment: To appear in PR

Noise-Induced Phase Separation: Mean-Field Results

We present a study of a phase-separation process induced by the presence of spatially-correlated multiplicative noise. We develop a mean-field approach suitable for conserved-order-parameter systems and use it to obtain the phase diagram of the model. Mean-field results are compared with numerical simulations of the complete model in two dimensions. Additionally, a comparison between the noise-driven dynamics of conserved and nonconserved systems is made at the level of the mean-field approximation.Comment: 12 pages (including 6 figures) LaTeX file. Submitted to Phys. Rev.

INFLUENCE OF THE METASTABLE ATOMS LIFETIME ON THE RUNNING STRIATION EXCITATION

It is known that in the noble gas discharges inside a region of the running striation excitation there can be a relatively small region of currents and pressures in which there are no striation /1/. The boundaries of this region depend on the gas composition and discharge tube dimensions /2,3/. The investigation of a non-striation region is of great practical interest because the operating ranges of pressures and currents in helium-neon lasers usually overlap it /3/. In this work the presence of a non-striation region is explained by the finite lifetime of the metastable atoms

OSCILLATION ANALYSIS OF NUMERICAL SOLUTIONS FOR NONLINEAR DELAY DIFFERENTIAL EQUATIONS OF POPULATION DYNAMICS

This paper is concerned with oscillations of numerical solutions for the nonlinear delay differential equation of population dynamics. The equation proposed by Mackey and Glass for a ”dynamic disease” involves respiratory disorders and its solution resembles the envelope of lung ventilation for pathological breathing, called Cheyne-Stokes respiration. Some conditions under which the numerical solution is oscillatory are obtained. The properties of non-oscillatory numerical solutions are investigated. To verify our results, we give numerical experiments