Diffusion dominated dynamics of avalanching systems

A surprisingly large number of systems in nature are thought to be governed by internal dynamics which causes avalanches of various sizes. In such systems energy, which is delivered from outside, is redistributed as a result of the occurrence of localized avalanches. Starting an avalanche requires that some threshold condition be satisfied. Random driving (energy input) brings the system into a strongly inhomogeneous state, so that the probability of triggering an avalanche in a large part of the system is small. In most physical systems energy redistribution may occur due to diffusive processes without avalanches. Diffusion also makes the system more uniform, making large avalanche triggering more probable. The observed behavior of a such system may crucially depend on the competition between diffusion and driving. In this paper, the effects of diffusive processes are investigated using a dissipative, isotropic one-dimensional model, in which avalanches can propagate in both directions. It is shown that the system behavior changes progressively as the diffusion rate increases. In the absence of diffusion, many small avalanches are triggered. Increasing the diffusion rate gradually suppresses these small avalanches and leads to the development of large, quasi-periodic bursts.     

共振Kuiper带天体轨道稳定性的数值模拟

对当前观测到的具有可靠轨道根数的共振Kuiper带天体的轨道未来演化进行数值模拟发现,它们的轨道在一亿年的时间演化中具有相对稳定性,即仍处于各自的共振区中,但稳定程度不同,且共振天体的轨道稳定性和其初始轨道半长径、偏心率和倾角有关.根据其轨道半长径、偏心率和倾角随时间的演化行为,这些共振天体可以分为具有"规则轨道"和"混沌轨道"两种类型.     

Dislocation-source shutdown and the plastic behavior of single-crystal micropillars

Dislocation dynamics simulations have been used to study the stress-strain response of single-crystal micropillars containing initial dislocation networks generated via a relaxation procedure intended to approximate real thermal annealing processes. We find that, when such networks are loaded, they exhibit periods of plastic deformation, caused by the operation of single junction-stabilized spiral sources, followed by intervals of purely elastic straining when the sources shut down. The results provide insight into the mechanisms responsible for the experimentally observed staircase stress-strain behavior.     

Particle motion in a photon gas: friction matters

The motion of a particle in the Tolman metric generated by a photon gas source is discussed. Both the case of geodesic motion and motion with nonzero friction, due to photon scattering effects, are analyzed. In the Minkowski limit, the particle moves along a straight line segment with a decelerated motion, reaching the endpoint at zero speed. The curved case shows a qualitatively different behavior; the geodesic motion consists of periodic orbits, confined within a specific radial interval. Under the effect of frictional drag, this radial interval closes up in time and in all our numerical simulations the particle ends up in the singularity at the center.     

Diffusion and scaling in escapes from two-degrees-of-freedom Hamiltonian systems

This paper summarizes an investigation of the statistical properties of orbits escaping from three different two-degrees-of-freedom Hamiltonian systems which exhibit global stochasticity. Each time-independent H=H(0)+ varepsilon H('), with H(0) an integrable Hamiltonian and varepsilon H(') a nonintegrable correction, not necessarily small. Despite possessing very different symmetries, ensembles of orbits in all three potentials exhibit similar behavior. For varepsilon below a critical varepsilon (0), escapes are impossible energetically. For somewhat higher values, escape is allowed energetically but still many orbits never escape. The escape probability P computed for an arbitrary orbit ensemble decays toward zero exponentially. At or near a critical value varepsilon (1)> varepsilon (0) there is a rather abrupt qualitative change in behavior. Above varepsilon (1), P typically exhibits (1) an initial rapid evolution toward a nonzero P(0)( varepsilon ), the value of which is independent of the detailed choice of initial conditions, followed by (2) a much slower subsequent decay toward zero which, in at least one case, is well fit by a power law P(t) proportional, variant t(-&mgr;), with &mgr; approximately 0.35-0.40. In all three cases, P(0) and the time T required to converge toward P(0) scale as powers of varepsilon - varepsilon (1), i.e., P(0) proportional, variant ( varepsilon - varepsilon (1))(alpha) and T proportional, variant ( varepsilon - varepsilon (1))(beta), and T also scales in the linear size r of the region sampled for initial conditions, i.e., T proportional, variant r(-delta). To within statistical uncertainties, the best fit values of the critical exponents alpha, beta, and delta appear to be the same for all three potentials, namely alpha approximately 0.5, beta approximately 0.4, and delta approximately 0.1, and satisfy alpha-beta-delta approximately 0. The transitional behavior observed near varepsilon (1) is attributed to the breakdown of some especially significant KAM tori or cantori. The power law behavior at late times is interpreted as reflecting intrinsic diffusion of chaotic orbits through cantori surrounding islands of regular orbits. (c) 1999 American Institute of Physics.     

Effect of the link lifetime in a dynamical lattice on the properties of the avalanche processes on it

The properties of the avalanche processes that develop on a dynamical lattice, the structure of links in which changes due to a specific characteristic of each lattice node, namely, its “activity,” which determines the probability of connection of a certain node with neighboring nodes in one step of lattice evolution. The statistics of the sizes of the avalanches appearing in the lattice system is studied as a function of the node activity and the link lifetime (the lifetime of the links formed in the system). It is analytically and numerically shows that the type of avalanche dynamics in the system changes as a function of these parameters. The following three regimes can take place in the system: (1) avalanches of any sizes, from small to catastrophic, can appear, which is reflected in the power-law behavior of the probability density function of the appearance of avalanches of certain sizes; (2) avalanches of a certain average size mainly appear in the system, and the probability density is close to that of a normal distribution; and (3) transient regime, where the probability density function of the appearance of avalanches of certain sizes is close to an exponential function. These results open up the possibilities of controlling the behavior of a complex system; in particular, they can be used to prevent catastrophic avalanches by changing the link lifetime and the average node activity.     

Mixing effects for the structural relaxation in binary hard-sphere liquids

We report extensive molecular-dynamics-simulation results for binary mixtures of hard spheres for different size disparities and different mixing percentages, for packing fractions up to 0.605, and over a characteristic time interval spanning up to 5 orders in magnitude. We explore the changes in the evolution of glassy dynamics due to mixing and discover two opposite scenarios: For large size disparity, increasing the mixing percentage of small particles leads to a speed up of long-time dynamics, while small disparity leads to a slowing down. These results agree with predictions based on the mode-coupling theory for ideal-glass transitions.     

Periodic orbits, damped transitions and targeted energy transfers in oscillators with vibro-impact attachments

We study complex damped and undamped dynamics and targeted energy transfers (TETs) in systems of coupled oscillators, consisting of single-degree-of-freedom primary linear oscillators (LOs) with vibro-impact attachments, acting, in essence, as vibro-impact nonlinear energy sinks (VI NESs). First, the complicated dynamics of such VI systems is demonstrated by computing the VI periodic orbits of underlying Hamiltonian systems and depicting them in appropriate frequency–energy plots (FEPs). Then, VI damped transitions and distinct ways of passive TETs from the linear oscillators to the VI attachments for various parameter ranges and initial conditions are investigated. As in the case of smooth stiffness nonlinearity [Y. Lee, G. Kerschen, A. Vakakis, P. Panagopoulos, L. Bergman, D.M. McFarland, Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment, Physica D 204 (1–2) (2005) 41–69], both fundamental and subharmonic TET can be realized in the VI systems under consideration. It is found that the most efficient mechanism for VI TET is through the excitation of highly energetic VI impulsive orbits (IOs), i.e., of periodic or quasiperiodic orbits corresponding to zero initial conditions except for the initial velocities of the linear oscillators. In contrast to NESs with smooth essential nonlinearities considered in previous works, VI NESs are capable of passively absorbing and locally dissipating significant portions of the energies of the primary systems to which they are attached, at fast time scale. This renders such devices suitable for applications, like seismic mitigation, where dissipation of vibration energy in the early, highly energetic regime of the motion is a critical requirement.     

Normally attracting manifolds and periodic behavior in one-dimensional and two-dimensional coupled map lattices

We consider diffusively coupled logistic maps in one- and two-dimensional lattices. We investigate periodic behaviors as the coupling parameter varies, i.e., existence and bifurcations of some periodic orbits with the largest domain of attraction. Similarity and differences between the two lattices are shown. For small coupling the periodic behavior appears to be characterized by a number of periodic orbits structured in such a way to give rise to distinct, reverse period-doubling sequences. For intermediate values of the coupling a prominent role in the dynamics is played by the presence of normally attracting manifolds that contain periodic orbits. The dynamics on these manifolds is very weakly hyperbolic, which implies long transients. A detailed investigation allows the understanding of the mechanism of their formation. A complex bifurcation is found which causes an attracting manifold to become unstable. (c) 1994 American Institute of Physics.     

Rescattering processes for elliptical polarization: A quantum trajectory analysis

High-harmonic generation and high-order above-threshold ionization spectra calculated in the strong-field approximation are analyzed in terms of the complex space-time orbits that result from a saddle point analysis of the underlying integrals. For elliptical polarization, the plateaus of the spectra of high-harmonic generation and high-order above-threshold ionization each turn into a staircase of very similar appearance. Each step of the stair can be traced to a particular pair of orbits which are almost identical in both cases.     

Dynamics of some piecewise smooth Fermi-Ulam models

We find a normal form which describes the high energy dynamics of a class of piecewise smooth Fermi-Ulam ping pong models. Depending on the value of a single real parameter, the dynamics can be either hyperbolic or elliptic. In the first case, we prove that the set of orbits undergoing Fermi acceleration has zero measure but full Hausdorff dimension. We also show that for almost every orbit, the energy eventually falls below a fixed threshold. In the second case, we prove that, generically, we have stable periodic orbits for arbitrarily high energies and that the set of Fermi accelerating orbits may have infinite measure.     

Heteroclinic contours and self-replicated solitary waves in a reaction–diffusion lattice with complex threshold excitation

The space–time dynamics of the network system modeling collective behavior of electrically coupled nonlinear cells is investigated. The dynamics of a local cell is described by the FitzHugh–Nagumo system with complex threshold excitation. Heteroclinic orbits defining traveling wave front solutions are investigated in a moving frame system. A heteroclinic contour formed by separatrix manifolds of two saddle-foci is found in the phase space. The existence of such structure indicates the appearance of complex wave patterns in the network. Such solutions have been confirmed and analyzed numerically. Complex homoclinic orbits found in the neighborhood of the heteroclinic contour define the propagation of composite pulse excitations that can be self-replicated in collisions leading to the appearance of complex wave patterns.     

Dynamics of impact cratering in shallow sand layers

When a solid sphere impacts a shallow layer of sand deposited on a solid surface, a crater can be obtained. The dynamics of the opening of the crater can be followed accurately. During this opening, the radius of the crater can be conveniently modeled by an exponential saturation with a well-defined time constant. The crater then closes up partially once the opening phase is over as the sand avalanches down the slope of the crater. We here present a detailed study of the full dynamics of the crater formation as well as the dynamics of the corrola formed during this process. A simple model accounts for most of our observations.     

Survival Probability of the Néel State in Clean and Disordered Systems: An Overview

In this work we provide an overview of our recent results about the quench dynamics of one-dimensional many-body quantum systems described by spin-1/2 models. To illustrate those general results, here we employ a particular and experimentally accessible initial state, namely the Néel state. Both cases are considered: clean chains without any disorder and disordered systems with static random on-site magnetic fields. The quantity used for the analysis is the probability for finding the initial state later in time, the so-called survival probability. At short times, the survival probability may decay faster than exponentially, Gaussian behaviors and even the limit established by the energy-time uncertainty relation are displayed. The dynamics at long times slows down significantly and shows a powerlaw behavior. For both scenarios, we provide analytical expressions that agree very well with our numerical results.     

On a New Observable for Measuring the Lense–Thirring Effect with Satellite Laser Ranging

For a pair of twin Earth orbiting artificial satellites placed in identical orbits with supplementary inclinations, in addition to the sum of the residuals of the nodal rates, already proposed for the LAGEOS–LARES mission, also the difference of the residuals of the perigee rates could be employed, in principle, for measuring the general relativistic Lense–Thirring effect. Indeed, on one hand, the gravitomagnetic secular precessions of the perigees of two supplementary satellites in identical orbits are equal and opposite, and, on the other, the classical secular precessions induced by the multipolar expansion of the terrestrial gravitational field are equal, so that their aliasing effect cancels out in the difference of the perigees' rates. If the eccentricities of the two satellites would be chosen to be equal, contrary to the LAGEOS–LARES project, such cancellation would occur at a very accurate level. Among the time–dependent perturbations, the proposed observable would allow to cancel out the even and odd zonal gravitational tidal perturbations and some non–gravitational perturbations. With a proper choice of the inclination of the two satellites, the periods of all the uncancelled time–dependent perturbations could be made short enough to allow to fit and remove them from the signal over observational time spans of a few years. The linear perturbation induced by the terrestrial Yarkovski–Rubincam effect would affect the proposed measurement at a level well below 10^–3.     

Scaling of waves in the bak-tang-wiesenfeld sandpile model

We study probability distributions of waves of topplings in the Bak-Tang-Wiesenfeld model on hypercubic lattices for dimensions D>/=2. Waves represent relaxation processes which do not contain multiple toppling events. We investigate bulk and boundary waves by means of their correspondence to spanning trees, and by extensive numerical simulations. While the scaling behavior of avalanches is complex and usually not governed by simple scaling laws, we show that the probability distributions for waves display clear power-law asymptotic behavior in perfect agreement with the analytical predictions. Critical exponents are obtained for the distributions of radius, area, and duration of bulk and boundary waves. Relations between them and fractal dimensions of waves are derived. We confirm that the upper critical dimension D(u) of the model is 4, and calculate logarithmic corrections to the scaling behavior of waves in D=4. In addition, we present analytical estimates for bulk avalanches in dimensions D>/=4 and simulation data for avalanches in D相似文献   

The existence of arbitrarily many distinct periodic orbits in a two degree of freedom Hamiltonian system

Melnikov's method is used to prove the existence of arbitrarily many elliptic and hyperbolic periodic orbits in the neighborhood of an elliptic orbit of a two degree of freedom Hamiltonian system which is ‘almost integrable’. The existence of such orbits precludes the existence of analytic second integrals of a certain type. The methods used permit a detailed analysis of the way in which resonant tori break up between the KAM irrational tori which are preserved for weak coupling of two independent nonlinear oscillators.     

Crackles and instabilities during lung inflation

In a variety of physico-chemical reactions, the actual process takes place in a reactive zone, called the “active surface”. We define the active surface of the lung as the set of airway segments that are closed but connected to the trachea through an open pathway, which is the interface between closed and open regions in a collapsed lung. To study the active surface and the time interval between consecutive openings, we measured the sound pressure of crackles, associated with the opening of collapsed airway segments in isolated dog lungs, inflating from the collapsed state in 120 s. We analyzed the sequence of crackle amplitudes, inter-crackle intervals, and low frequency energy from acoustic data. The series of spike amplitudes spans two orders of magnitude and the inter-crackle intervals spans over five orders of magnitude. The distribution of spike amplitudes follows a power law for nearly two decades, while the distribution of time intervals between consecutive crackles shows two regimes of power law behavior, where the first region represents crackles coming from avalanches of openings whereas the second region is due to the time intervals between separate avalanches. Using the time interval between measured crackles, we estimated the time evolution of the active surface during lung inflation. In addition, we show that recruitment and instabilities along the pressure–volume curve are associated with airway opening and recruitment. We find a good agreement between the theory of the dynamics of lung inflation and the experimental data which combined with numerical results may prove useful in the clinical diagnosis of lung diseases.     

Local waiting time fluctuations along a randomly pinned crack front

The propagation of an interfacial crack along a heterogeneous weak plane of a transparent Plexiglas block is followed using a high resolution fast camera. We show that the fracture front dynamics is governed by local and irregular avalanches with very large size and velocity fluctuations. We characterize the intermittent dynamics observed, i.e., the local pinnings and depinnings of the crack front by measuring the local waiting time fluctuations along the crack front during its propagation. The deduced local front line velocity distribution exhibits a power law behavior, P(v) alpha v-eta with eta=2.55+/-0.15, for velocities v larger than the average front speed . The burst size distribution is also a power law, P(S) alpha S-gamma with gamma=1.7+/-0.1. Above a characteristic length scale of disorder Ld approximately 15 microm, the avalanche clusters become anisotropic providing an estimate of the roughness exponent of the crack front line, H=0.66.