Complex dynamics in the Oregonator model with linear delayed feedback

The Belousov-Zhabotinsky (BZ) reaction can display a rich dynamics when a delayed feedback is applied. We used the Oregonator model of the oscillating BZ reaction to explore the dynamics brought about by a linear delayed feedback. The time-delayed feedback can generate a succession of complex dynamics: period-doubling bifurcation route to chaos; amplitude death; fat, wrinkled, fractal, and broken tori; and mixed-mode oscillations. We observed that this dynamics arises due to a delay-driven transition, or toggling of the system between large and small amplitude oscillations, through a canard bifurcation. We used a combination of numerical bifurcation continuation techniques and other numerical methods to explore the dynamics in the strength of feedback-delay space. We observed that the period-doubling and quasiperiodic route to chaos span a low-dimensional subspace, perhaps due to the trapping of the trajectories in the small amplitude regime near the canard; and the trapped chaotic trajectories get ejected from the small amplitude regime due to a crowding effect to generate chaotic-excitable spikes. We also qualitatively explained the observed dynamics by projecting a three-dimensional phase portrait of the delayed dynamics on the two-dimensional nullclines. This is the first instance in which it is shown that the interaction of delay and canard can bring about complex dynamics.     

Symbolic synchronization and the detection of global properties of coupled dynamics from local information

We study coupled dynamics on networks using symbolic dynamics. The symbolic dynamics is defined by dividing the state space into a small number of regions (typically 2), and considering the relative frequencies of the transitions between those regions. It turns out that the global qualitative properties of the coupled dynamics can be classified into three different phases based on the synchronization of the variables and the homogeneity of the symbolic dynamics. Of particular interest is the homogeneous unsynchronized phase, where the coupled dynamics is in a chaotic unsynchronized state, but exhibits qualitative similar symbolic dynamics at all the nodes in the network. We refer to this dynamical behavior as symbolic synchronization. In this phase, the local symbolic dynamics of any arbitrarily selected node reflects global properties of the coupled dynamics, such as qualitative behavior of the largest Lyapunov exponent and phase synchronization. This phase depends mainly on the network architecture, and only to a smaller extent on the local chaotic dynamical function. We present results for two model dynamics, iterations of the one-dimensional logistic map and the two-dimensional Henon map, as local dynamical function.     

Collective dynamics of multicellular systems

We have studied the collective behaviour of a one-dimensional ring of cells for conditions when the individual uncoupled cells show stable, bistable and oscillatory dynamics. We show that the global dynamics of this model multicellular system depends on the system size, coupling strength and the intrinsic dynamics of the cells. The intrinsic variability in dynamics of the constituent cells are suppressed to stable dynamics, or modified to intermittency under different conditions. This simple model study reveals that cell–cell communication, system size and intrinsic cellular dynamics can lead to evolution of collective dynamics in structured multicellular biological systems that is significantly different from its constituent single-cell behaviour.     

Financial heat machine

We consider dynamics of financial markets as dynamics of expectations and discuss such a dynamics from the point of view of phenomenological thermodynamics. We describe a financial Carnot cycle and the financial analog of a heat machine. We see, that while in physics a perpetuum mobile is absolutely impossible, in economics such mobile may exist under some conditions.     

Nonlinear dynamics of charged particles in an oblique electromagnetic wave

We study dynamics of a charged particle under action of an electromagnetic wave that propagates obliquely to a background uniform magnetic field. The dynamics is described by a slow-fast Hamiltonian system. We show that long-term dynamics is dominated by phenomena of capture of particle into resonance with the wave and escape from this resonance, as well as of scattering on resonance. We find that the variation of the particle?s kinetic energy on the time interval between capture and escape is bounded and accumulated in the motion along the background field. We discuss possible applications of the obtained results.     

Modal Dynamics for Positive Operator Measures

The modal interpretation of quantum mechanics allows one to keep the standard classical definition of realism intact. That is, variables have a definite status for all time and a measurement only tells us which value it had. However, at present modal dynamics are only applicable to situations that are described in the orthodox theory by projective measures. In this paper we extend modal dynamics to include positive operator measures (POMs). That is, for example, rather than using a complete set of orthogonal projectors, we can use an overcomplete set of nonorthogonal projectors. We derive the conditions under which Bell's stochastic modal dynamics for projective measures reduce to deterministic dynamics, showing (incidentally) that Brown and Hiley's generalization of Bohmian mechanics [quant-ph/0005026, (2000)] cannot be thus derived. We then show how deterministic dynamics for positive operators can also be derived. As a simple case, we consider a Harmonic oscillator, and the overcomplete set of coherent state projectors (i.e., the Husimi POM). We show that the modal dynamics for this POM in the classical limit correspond to the classical dynamics, even for the nonclassical number state |n>. This is in contrast to the Bohmian dynamics, which for energy eigenstates, the dynamics are always non-classical.     

Anti-deterministic behaviour of discrete systems that are less predictable than noise

We present a new type of deterministic dynamical behaviour that is less predictable than white noise. We call it anti-deterministic (AD) because time series corresponding to the dynamics of such systems do not generate deterministic lines in recurrence plots for small thresholds. We show that although the dynamics is chaotic in the sense of exponential divergence of nearby initial conditions and although some properties of AD data are similar to white noise, the AD dynamics is in fact, less predictable than noise and hence is different from pseudo-random number generators.     

Dynamical motifs: building blocks of complex dynamics in sparsely connected random networks

Spatiotemporal network dynamics is an emergent property of many complex systems that remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs-small subnetworks with periodic and chaotic dynamics. We simulate randomly connected neural networks and, with increasing density of connections, observe the transition from quiescence to periodic and chaotic dynamics. This transition is explained by the appearance of dynamical motifs in the structure of these networks. We also observe domination of periodic dynamics in simulations of spatially distributed networks with local connectivity and explain it by the absence of chaotic and the presence of periodic motifs in their structure.     

Dynamics and hysteresis of the contact line between liquid hydrogen and cesium substrates

We have measured both the hysteresis and the dynamics of the edge of a liquid hydrogen meniscus on several solid cesium substrates. We find that the dynamics of the contact line is thermally activated. For all substrates, we find that the activation energy is of the order of the hysteresis. We show that the pinning of the contact line on mesoscopic defects of the Cs substrate is likely to control both the hysteresis and the dynamics of the contact line at low velocity, close to the depinning threshold. Such a mechanism could be relevant also for simple room-temperature systems.     

Suppression of superconductivity in high-T c cuprates due to nonmagnetic impurities: Implications for the order parameter symmetry

We show explicitly that the broad histogram single-spin-flip random walk dynamics does not give correct microcanonical average even in one dimension. The dynamics violates the detailed balance condition by an amount proportional to the inverse system size. As a result, in distribution different configurations with the same energy can have different probabilities. We propose a modified dynamics which ensures detailed balance and the histogram obtained from this dynamics is exactly flat. The broad histogram equation relating the average number of potential moves to density of states is generally valid. Received 2 October 1998 and Received in final form 13 October 1998     

Measuring the ‘complexity’ of sound

Sounds in the natural environment form an important class of biologically relevant non-stationary signals. We propose a dynamic spectral measure to characterize the spectral dynamics of such non-stationary sound signals and classify them based on rate of change of spectral dynamics. We categorize sounds with slowly varying spectral dynamics as simple and those with rapidly changing spectral dynamics as complex. We propose rate of spectral dynamics as a possible scheme to categorize sounds in the environment.     

利用SERS效应研究表面吸附动力学过程

本文提出了利用表面增强喇曼散射(SERS)效应研究表面吸附动力学过程的设想.基于此设想,我们对固-液界面吸附动力学进行了理论探讨,讨论了SERS信号强度随时间的依赖性,从而得到有关表面吸附动力学参量,并利用银胶体系对对氨基苯甲酸的吸附动态过程进行初步实验研究.结果表明,利用SERS效应对表面吸附动力学、尤其是微量吸附动力学的研究是非常有效的. 关键词：     

The non-Gaussian dynamics of glycerol

We have combined incoherent quasielastic neutron scattering experiments and atomistic molecular simulations to investigate the microscopic dynamics of glycerol moving away from the hydrodynamic limit. We relate changes in the momentum transfer (Q) dependence of the relaxation time to distinct changes of the single-particle dynamics. Going from small to large values of Q, a first crossover at about 0.5 ?(-1) is related to the coupling of the translational diffusion dynamics to the non-Debye structural relaxation, while the second crossover at a Q-value near the main diffraction peak is associated with the Gaussian to non-Gaussian crossover of the short-time molecular dynamics, related to the decaging processes. We offer an unprecedented extension of previous studies on polymeric systems towards the case of the typical low-molecular-weight glass-forming system glycerol.     

Selective spreading and jetting of electrically driven dielectric films

We study the electrically driven spreading of dielectric liquid films in wedge-shaped gaps across which a potential difference is applied. Our experiments are in a little-studied regime where, throughout the dynamics, the electrical relaxation time is long compared to the time for charge to be convected by the fluid motion. We observe that at a critical normal electric field the hump-shaped leading edge undergoes an instability in the form of a single Taylor cone and periodic jetting ensues, after which traveling waves occur along the trailing thin film. We propose a convection-dominated mechanism for charge transport to describe the observed dynamics and rationalize the viscosity dependence of the self-excited dynamics.     

Local simulation algorithms for Coulomb interactions

Long ranged electrostatic interactions are time consuming to calculate in molecular dynamics and Monte Carlo simulations. We introduce an algorithmic framework for simulating charged particles which modifies the dynamics so as to allow equilibration using a local Hamiltonian. The method introduces an auxiliary field with constrained dynamics so that the equilibrium distribution is determined by the Coulomb interaction. We demonstrate the efficiency of the method by simulating a simple, charged lattice gas.     

Spin-orbital phase synchronization in the magnetic field-driven electron dynamics in a double-well potential

We study the dynamics of an electron confined in a one-dimensional double-well potential in the presence of driving external magnetic fields. The orbital motion of the electron is coupled to the spin dynamics by spin-orbit interaction of the Dresselhaus type. We derive an effective time-dependent model Hamiltonian for the orbital motion of the electron and obtain a condition for synchronization of the orbital and the spin dynamics. We find an analytical expression for the Arnold 'tongue' and propose an experimental scheme for realizing the proposed synchronization.     

Short-time dynamics of a packing of polyhedral grains under horizontal vibrations

We analyze the dynamics of a 3D granular packing composed of particles of irregular polyhedral shape confined inside a rectangular box with a retaining wall subjected to horizontal harmonic forcing. The simulations are performed by means of the contact dynamics method for a broad set of loading parameters. We explore the vibrational dynamics of the packing, the evolution of solid fraction and the scaling of dynamics with the loading parameters. We show that the motion of the retaining wall is strongly anharmonic as a result of jamming and grain rearrangements. It is found that the mean particle displacement scales with inverse square of frequency, the inverse of the force amplitude and the square of gravity. The short-time compaction rate grows in proportion to frequency up to a characteristic frequency, corresponding to collective particle rearrangements between equilibrium states, and then it declines in inverse proportion to frequency.     

Chaotic itinerancy, temporal segmentation and spatio-temporal combinatorial codes

We study a deterministic dynamics with two time scales in a continuous state attractor network. To the usual (fast) relaxation dynamics towards point attractors (“patterns”) we add a slow coupling dynamics that makes the visited patterns lose stability, leading to an itinerant behavior in the form of punctuated equilibria. One finds that the transition frequency matrix for transitions between patterns shows non-trivial statistical properties in the chaotic itinerant regime. We show that mixture input patterns can be temporally segmented by the itinerant dynamics. The viability of a combinatorial spatio-temporal neural code is also demonstrated.     

Entanglement Dynamics of Two Coupled Spins in a Spin Star Environment

We theoretically study the entanglement dynamics of two coupled spins in a spin star environment, whose elements are coupled to local bosonic baths. It is shown that the dynamics of the entanglement depends on the initial state of the system and the coupling strength between the two coupled central spins, the interactions between the central system and the environment, as well as interactions between the bath spin and the reservoir. We also investigate the effect of non-Markovian dynamics in contrast with the Markovian case. It is found that the non-Markovian dynamics has a significant effect on the disentanglement between the two central spins.