Search

In this paper, we examine a population model with carrying capacity, time delay, and sources of additive and multiplicative environmental noise. We find that time delay, noise sources and their correlation induce regime shifts and transitions between the population survival state and the extinction state. To explore the transition mechanism between these two states, we analyzed the shift time to extinction, or the delayed extinction time, of populations. The main finding is that the extinction transition time as a function of the noise intensity shows a maximum, indicating the existence of an appropriate noise intensity leading to a maximal delayed extinction. This nonmonotonic behavior, with a maximum, is a signature of the noise-enhanced stability phenomenon, observed in many physical and complex metastable systems. In particular, this maximum increases (or decreases) as the cross-correlation intensity or the delay time in the death process increases. Furthermore, the signal-to-noise ratio as a function of noise intensity shows a maximum, which is a signature of the stochastic resonance phenomenon in the population dynamics model investigated in the presence of time delay and environmental noise. Graphic abstract

By studying the time series of logistic maps, dark lines in bifurcation diagrams and cobweb diagrams, characteristics of sequential iterations of the map are found. Before the merging together two chaotic bands, sequential iterations of the map present an ordered state. After that, with the instability of the hyperstable periodic orbit, sequential iterations of the map appear disordered. Therefore, the statistical results of time correlation of direction phase are introduced to describe the transition of the collective behaviour. Based on the two-dimensional coupled map lattice, the relationship between bifurcation parameters and order parameters with the change of coupling strength is studied. We show that when the coupling strength is weak, the critical bifurcation parameters are positively correlated with the coupling strength. When the coupling strength is large, the phase order of the system is not affected by the coupling strength. The transition of collective behaviour in a modular network is also studied. By fixing modularity and bifurcation parameters, with the change of coupling strength, the collective behaviour presents a transition process from spatiotemporal chaos to phase-ordered state. There are periodic orbits in the spatiotemporal chaotic region. A phase synchronisation region can be present in the antiphase synchronisation region. Furthermore, there exist multistable solutions in the region.

We uncover a route from low-dimensional to high-dimensional chaos in nonsmooth dynamical systems as a bifurcation parameter is continuously varied. The striking feature is the existence of a finite parameter interval of periodic attractors in between the regimes of low- and high-dimensional chaos. That is, the emergence of high-dimensional chaos is preceded by the system's settling into a totally nonchaotic regime. This is characteristically distinct from the situation in smooth dynamical systems where high-dimensional chaos emerges directly and smoothly from low-dimensional chaos. We carry out an analysis to elucidate the underlying mechanism for the abrupt emergence and disappearance of the periodic attractors and provide strong numerical support for the typicality of the transition route in the pertinent two-dimensional parameter space. The finding has implications to applications where high-dimensional and robust chaos is desired., 9 pages, 8 figures

Li2MgTiO4 ceramics were prepared with Li2CO3, TiO2 and MgO by high energy ball mill method. After mixtures ball-milling 30 h and calcining at 700°C, the homogenate Li2MgTiO4 powders with average particle size of 160 nm were obtained. The pure phase obtained temperature was about 300°C lower than that by a conventional solid-state reaction process. Due to Li+ evaporation, the Li2MgTiO4 ceramics sintered at high temperature existed with some Mg2TiO4. The Li2MgTiO4 ceramics at 1250°C had an excellent microwave dielectric properties ϵr = 12.17, Q × f = 42000 GHz and an τf = −23 ppm/°C

The AWO4 (A = Ca, Sr, Ba) compounds with scheelite structure were synthesized by high energy ball milling for 30 min and the average particle size was reduced to about 120 nm after milling 30 h. AWO4 ceramics were well sintered at relatively low temperatures of 900–1000 °C, 200–400 °C lower than those required by a conventional solid state reaction technique. The samples of CaWO4, SrWO4, and BaWO4 ceramics have dense microstructures and excellent microwave dielectric properties, ɛr = 10.7, 8.6, 8.4; Q × f = 62,100 GHz, 57,500 GHz, 58,800 GHz; and τf = −48 ppm/°C, −52 ppm/°C, −64 ppm/°C, respectively.

The speed and paths of synchronization play a key role in the function of a system, which has not received enough attention up to now. In this work, we study the synchronization process of coupled logistic maps that reveals the common features of low-dimensional dissipative systems. A slowing down of synchronization process is observed, which is a novel phenomenon. The result shows that there are two typical kinds of transient process before the system reaches complete synchronization, which is demonstrated by both the coupled multiple-period maps and the coupled multiple-band chaotic maps. When the coupling is weak, the evolution of the system is governed mainly by the local dynamic, i.e., the node states are attracted by the stable orbits or chaotic attractors of the single map and evolve toward the synchronized orbit in a less coherent way. When the coupling is strong, the node states evolve in a high coherent way toward the stable orbit on the synchronized manifold, where the collective dynamics dominates the evolution. In a mediate coupling strength, the interplay between the two paths is responsible for the slowing down. The existence of different synchronization paths is also proven by the finite-time Lyapunov exponent and its distribution.

The most basic local conversion is local operations and classical communications (LOCC), which is also the most natural restriction in quantum information processing. We investigate the conversions between the ground states in quantum critical systems via LOCC and propose an novel method to reveal the different convertibility via majorization relation when a quantum phase transition occurs. The ground-state local convertibility in the one-dimensional transverse field Ising model is studied. It is shown that the LOCC convertibility changes nearly at the phase transition point. The relation between the order of quantum phase transitions and the LOCC convertibility is discussed. Our results are compared with the corresponding results using the Renyi entropy and the LOCC convertibility with assisted entanglement., Comment: 4 pages, 4 figures

The multiple Devil's staircase reported by Qu, Wu and He in 1997 was composed of many tower-like structures. Each of which include two branches of the conventional complete Devil's staircases that connect the "single-exit" top and bottom steps. Their analytic conclusion show that all the conventional Devil's staircases are confined by two smooth curves with similar function forms W ∝ 1/ln ∊. These may be addressed as a kind of consonance. Our recent study found that it happens only in a few cases. Actually, in their system, 16 different kinds of tower branches exist in most parts of the parameter space. A lot of the steps lose the consonant property which are the so-called dissonant structures. The number of types of the corresponding dissonant branches is employed to describe the dissonance of the staircase. When the number of the discontinuous regions n, in the system develops, the dissonance of the staircase increases with 2n3- n rule. The numerical result shows that the conclusion is valid for a general discontinuous circle map.

The influence of the surface structure and vibration mode on the resistivity of Cu films and the corresponding size effect are investigated. The temperature dependent conductivities of the films with different surface morphologies are calculated by the algorithm based upon the tight-binding linear muffin-tin orbital method and the Green's function technique. The thermal effect is introduced by setting the atomic displacements according to the Gaussian distribution with the mean-square amplitude estimated by the Debye model. The result shows that the surface atomic vibration contributes significantly to the resistivity of the systems. Comparing the conductivities for three different vibration modes, it is suggested that freezing the surface vibration is necessary for practical applications to reduce the resistivity induced by the surface electron-phonon scattering.

A simple bulk model of electron-phonon coupling in metals has been partially successful in explaining experiments on metal films that actually involve surface- or other low-dimensional phonons. However, by an exact application of this standard model to a semi-infinite substrate with a free surface, making use of the actual vibrational modes of the substrate, we show that such agreement is fortuitous, and that the model actually predicts a low-temperature crossover from the familiar ${T}^{5}$ temperature dependence to a stronger ${T}^{6}\phantom{\rule{0.2em}{0ex}}\mathrm{log}\phantom{\rule{0.2em}{0ex}}T$ scaling. Comparison with existing experiments suggests a widespread breakdown of the standard model of electron-phonon coupling in metals.

There is great interest in the development of novel nanomachines that use charge, spin, or energy transport, to enable new sensors with unprecedented measurement capabilities. Electrical and thermal transport in these mesoscopic systems typically involves wave propagation through a nanoscale geometry such as a quantum wire. In this paper we present a general theoretical technique to describe wave propagation through a curved wire of uniform cross-section and lying in a plane, but of otherwise arbitrary shape. The method consists of (i) introducing a local orthogonal coordinate system, the arclength and two locally perpendicular coordinate axes, dictated by the shape of the wire; (ii) rewriting the wave equation of interest in this system; (iii) identifying an effective scattering potential caused by the local curvature; and (iv), solving the associated Lippmann-Schwinger equation for the scattering matrix. We carry out this procedure in detail for the scalar Helmholtz equation with both hard-wall and stress-free boundary conditions, appropriate for the mesoscopic transport of electrons and (scalar) phonons. A novel aspect of the phonon case is that the reflection probability always vanishes in the long-wavelength limit, allowing a simple perturbative (Born approximation) treatment at low energies. Our results show that, in contrast to charge transport, curvature only barely suppresses thermal transport, even for sharply bent wires, at least within the two-dimensional scalar phonon model considered. Applications to experiments are also discussed., 9 pages, 11 figures, RevTex