Collective dynamics of interacting molecular motors

The collective dynamics of N interacting processive molecular motors are considered theoretically when an external force is applied to the leading motor. We show, using a discrete lattice model, that the force-velocity curves strongly depend on the effective dynamic interactions between motors and differ significantly from those of a simple approach where the motors equally share the force. Moreover, they become essentially independent of the number of motors if N is large enough (N> or approximately 5 for conventional kinesin). We show that a two-state ratchet model has a very similar behavior to that of the coarse-grained lattice model with effective interactions. The general picture is unaffected by motor attachment and detachment events.     

Embedded random matrix ensembles for complexity and chaos in finite interacting particle systems

Universal properties of simple quantum systems whose classical counter parts are chaotic, are modeled by the classical random matrix ensembles and their interpolations/deformations. However for finite interacting many-particle systems such as atoms, molecules, nuclei and mesoscopic systems (atomic clusters, helium droplets, quantum dots, etc.) for wider range of phenomena, it is essential to include information such as particle number, number of single-particle orbits, lower particle rank of the interaction, etc. These considerations led to resurgence of interest in investigating in detail the so-called embedded random matrix ensembles and their various deformed versions. Besides giving a overview of the basic results of embedded ensembles for the smoothed state densities and transition matrix elements, recent progress in investigating these ensembles with various deformations, for deriving a statistical mechanics (with relationships between quantum chaos, thermalization, phase transitions and Fock space localization, etc.) for isolated finite systems with few particles is briefly discussed. These results constitute new progress in deriving a basis for statistical spectroscopy (introduced and applied in nuclear structure physics and more recently in atomic physics) and its domains of applicability.     

Reconstructing phase dynamics of oscillator networks

We generalize our recent approach to the reconstruction of phase dynamics of coupled oscillators from data [B. Kralemann et al., Phys. Rev. E 77, 066205 (2008)] to cover the case of small networks of coupled periodic units. Starting from a multivariate time series, we first reconstruct genuine phases and then obtain the coupling functions in terms of these phases. Partial norms of these coupling functions quantify directed coupling between oscillators. We illustrate the method by different network motifs for three coupled oscillators and for random networks of five and nine units. We also discuss nonlinear effects in coupling.     

Collective firm bankruptcies and phase transition in rating dynamics

We present a simple model of firm rating evolution. We consider two sources of defaults: individual dynamics of economic development and Potts-like interactions between firms. We show that such a defined model leads to phase transition, which results in collective defaults. The existence of the collective phase depends on the mean interaction strength. For small interaction strength parameters, there are many independent bankruptcies of individual companies. For large parameters, there are giant collective defaults of firm clusters. In the case when the individual firm dynamics favors dumping of rating changes, there is an optimal strength of the firm’s interactions from the systemic risk point of view.     

Collective dynamics near a phase transition in confined fluids

We performed molecular dynamics simulations in the microcanonical ensemble (MEMD) for a "simple" fluid confined between two solid substrates. From the calculation of the intermediate scattering function F(k( parallel ),t) and through the memory function formalism, we extract material ( i.e. transport and thermodynamics) coefficients in the vicinity of the liquid-gas phase transition. Our results show that approaching the limit of stability ( i.e. the spinodal), the dynamics of the system changes markedly.     

Collective modes of quantum dot ensembles in microcavities

Emission spectra of quantum dot arrays in zero-dimensional microcavities are studied theoretically. It is shown that their form is determined by the competition between collective superradiant mode formation and inhomogeneous broadening. A random sources method is used to calculate the photoluminescence spectra from an nonresonant pumped microcavity, and a standard diagram technique is used to provide a microscopic justification for the random sources method. The emission spectra of a microcavity are analyzed taking into account the spread of exciton energy due to inhomogeneous distribution of quantum dots and tunneling between them. It is demonstrated that the luminescence spectra of strongly tunnel-coupled quantum dots are sensitive to the dot positions, and the collective mode can (under certain conditions) be stabilized by random tunneling links.     

Transient chaos in smooth memristor oscillator

This paper presents a new smooth memristor oscillator, which is derived from Chua's oscillator by replacing Chua's diode with a flux-controlled memristor and a negative conductance. Novel parameters and initial conditions are dependent upon dynamical behaviours such as transient chaos and stable chaos with an intermittence period and are found in the smooth memristor oscillator. By using dynamical analysis approaches including time series, phase portraits and bifurcation diagrams, the dynamical behaviours of the proposed memristor oscillator are effectively investigated in this paper.     

Distinguishing fingerprints of hyperchaotic and stochastic dynamics in optical chaos from a delayed opto-electronic oscillator

In the dynamics of optical systems, one commonly needs to cope with the problem of coexisting deterministic and stochastic components. The separation of these components is an important, although difficult, task. Often the time scales at which determinism and noise dominate the system's dynamics differ. In this Letter we propose to use information-theory-derived quantifiers, more precisely, permutation entropy and statistical complexity, to distinguish between the two behaviors. Based on experiments of a paradigmatic opto-electronic oscillator, we demonstrate that the time scales at which deterministic or noisy behavior dominate can be identified. Supporting numerical simulations prove the accuracy of this identification.     

Order and chaos in the interacting boson model

We investigate both quantum and classical signatures of order/chaos interplay within the symmetry triangle of the interacting boson model. Special attention is devoted to the increased regularity in the Alhassid-Whelan semiregular arc inside the symmetry triangle. Significant changes in properties of classical trajectories therein are found to accompany the strong bunching of levels in the 0⁺ spectrum. The text was submitted by the authors in English.     

Atom counting statistics in ensembles of interacting Rydberg atoms

We show that the probability distributions for the number of Rydberg excitations in small ensembles of cold atoms, excited using short (100 ns) laser pulses, can be highly sub-Poissonian. The phenomenon occurs if the atom density and the principal quantum number of the excited Rydberg level are sufficiently high. Our observations are attributed to a blockade of the Rydberg atom excitation.     

Self-organized quasiperiodicity in oscillator ensembles with global nonlinear coupling

We describe a transition from fully synchronous periodic oscillations to partially synchronous quasiperiodic dynamics in ensembles of identical oscillators with all-to-all coupling that nonlinearly depends on the generalized order parameters. We present an analytically solvable model that predicts a regime where the mean field does not entrain individual oscillators, but has a frequency incommensurate to theirs. The self-organized onset of quasiperiodicity is illustrated with Landau-Stuart oscillators and a Josephson junction array with a nonlinear coupling.     

Hyperbolic chaos in the klystron-type microwave vacuum tube oscillator

The ring-loop oscillator consisting of two coupled klystrons which is capable of generating hyperbolic chaotic signal in the microwave band is considered. The system of delayed-differential equations describing the dynamics of the oscillator is derived. This system is further reduced to the two-dimensional return map under the assumption of the instantaneous build-up of oscillations in the cavities. The results of detailed numerical simulation for both models are presented showing that there exists large enough range of control parameters where the sustained regime corresponds to the structurally stable hyperbolic chaos.     

Collective states of interacting ferromagnetic nanoparticles

Discontinuous magnetic multilayers [CoFe/Al₂O₃] are studied by use of magnetometry, susceptometry and numeric simulations. Soft ferromagnetic Co₈₀Fe₂₀ nanoparticles are embedded in a diamagnetic insulating a-Al₂O₃ matrix and can be considered as homogeneously magnetized superspins exhibiting randomness of size (viz. moment), position and anisotropy. Lacking intra-particle core-surface ordering, generic freezing processes into collective states rather than individual particle blocking are encountered. With increasing particle density one observes first superspin glass and then superferromagnetic domain state behavior. The phase diagram resembles that of a dilute disordered ferromagnet. Criteria for the identification of the individual phases are given.     

Space-time chaos in the system of weakly interacting hyperbolic systems

We consider infinite-dimensional dynamical systems which are lattices of some weakly-interacting hyperbolic systems. We describe the construction of their BRS-measures which are mixing with respect to the group of space-time shifts. The proofs use methods of statistical mechanics.     

Collective dynamics and self-diffusion in a diblock copolymer melt in the body-centered cubic phase

The structure and dynamics of a strongly asymmetric poly(ethylene propylene)-poly(dimethylsiloxane) (PEP-PDMS) diblock copolymer in the melt have been studied over a wide temperature range. Small-angle neutron scattering reveals that the sample exhibits two stable phases in this temperature range: Above the order-to-disorder transition temperature, it is disordered, whereas the domain structure is body-centered cubic (bcc) below, being stable down to the lowest temperatures measured. In the disordered state, dynamic light scattering (DLS) in the polarized geometry reveals the heterogeneity mode and the cluster mode. In the bcc phase, the PEP and the PDMS blocks form the micellar cores and the matrix, respectively. Here, two modes are observed in DLS, and the diffusion coefficients measured using pulsed field gradient (PFG) NMR are broadly distributed with the most probable diffusion coefficient coinciding with the slow DLS mode. We attribute the fast process in the bcc state to concentration fluctuations of the micellar cores (PEP), relaxing by mutual diffusion of the micelles with copolymers dissolved in the PDMS matrix. The slower process in the bcc state is ascribed to activated long-range self-diffusion of single copolymers from micelle to micelle through the PDMS matrix. This assignment is corroborated by the good coincidence of the reduced diffusivities with the ones from the literature. However, this mode may also be assigned to the rearrangement of entire micelles.This paper is dedicated to the memory of G. Fleischer     

简并光学参量振荡器混沌反控制

提出一种实现简并光学参量振荡器混沌反控制的方法，用正弦信号调制简并光学参量振荡器的基模衰减率，使简并光学参量振荡器从定态输出转化为混沌态.数值模拟结果表明，选择不同的调制幅度和调制角频率，只要满足系统的最大李雅谱诺夫指数大于零，即可实现不同的混沌轨道重构.通过比较最大李雅谱诺夫指数λ_max随调制幅度和调制角频率变化曲线， 指出系统从周期态调制到混沌态比从无亚谐波输出的定态调制到混沌态更容易，有更宽的调制幅度和调制角频率选择范围. 关键词： 简并光学参量振荡器 混沌反控制 调制     

Collective patterns arising out of spatio-temporal chaos

We present a simple mathematical model in which a time averaged pattern emerges out of spatio-temporal chaos as a result of the collective action of chaotic fluctuations. Our evolution equation possesses spatial translational symmetry under periodic boundary conditions. Thus the spatial inhomogeneity of the statistical state arises through spontaneous symmetry breaking. The transition from a state of homogeneous spatio-temporal chaos to one exhibiting spatial order is explained by introducing a collective viscosity which relates the averaged pattern with a correlation of the fluctuations. (c) 1996 American Institute of Physics.