An analysis of interacting bistable magnetic microwires: from ordered to chaotic behaviours

Fe-based magnetostrictive amorphous wires are bistable exhibiting square-shaped longitudinal hysteresis loops. This is a consequence of their particular domain structure that allows them to be approached as magnetic dipoles. Arrays of such bistables wires are accordingly shown to be coupled by magnetostatic interactions. Furthermore, an analysis of these interactions allows us to conclude that depending on the relative strength of the magnetostatic and Zeeman interactions, ordered, complex or chaotic behaviours are found in the temporal variation of the array magnetisation.     

A challenge to chaotic itinerancy from brain dynamics

Brain hermeneutics and chaotic itinerancy proposed by Tsuda are attractive characterizations of perceptual dynamics in the mammalian olfactory system. This theory proposes that perception occurs at the interface between itinerant neural representation and interaction with the environment. Quantifiable application of these dynamics has been hampered by the lack of definable history and action processes which characterize the changes induced by behavioral state, attention, and learning. Local field potentials measured from several brain areas were used to characterize dynamic activity patterns for their use as representations of history and action processes. The signals were recorded from olfactory areas (olfactory bulb, OB, and pyriform cortex) and hippocampal areas (entorhinal cortex and dentate gyrus, DG) in the brains of rats. During odor-guided behavior the system shows dynamics at three temporal scales. Short time-scale changes are system-wide and can occur in the space of a single sniff. They are predictable, associated with learned shifts in behavioral state and occur periodically on the scale of the intertrial interval. These changes occupy the theta (2-12 Hz), beta (15-30 Hz), and gamma (40-100 Hz) frequency bands within and between all areas. Medium time-scale changes occur relatively unpredictably, manifesting in these data as alterations in connection strength between the OB and DG. These changes are strongly correlated with performance in associated trial blocks (5-10 min) and may be due to fluctuations in attention, mood, or amount of reward received. Long time-scale changes are likely related to learning or decline due to aging or disease. These may be modeled as slow monotonic processes that occur within or across days or even weeks or years. The folding of different time scales is proposed as a mechanism for chaotic itinerancy, represented by dynamic processes instead of static connection strengths. Thus, the individual maintains continuity of experience within the stability of fast periodic and slow monotonic processes, while medium scale events alter experience and performance dramatically but temporarily. These processes together with as yet to be determined action effects from motor system feedback are proposed as an instantiation of brain hermeneutics and chaotic itinerancy.     

Hybrid model for chaotic front dynamics: from semiconductors to water tanks

We present a general method for studying front propagation in nonlinear systems with a global constraint in the language of hybrid tank models. The method is illustrated in the case of semiconductor superlattices, where the dynamics of the electron accumulation and depletion fronts shows complex spatiotemporal patterns, including chaos. We show that this behavior may be elegantly explained by a tank model, for which analytical results on the emergence of chaos are available. In particular, for the case of three tanks the bifurcation scenario is characterized by a modified version of the one-dimensional iterated tent map.     

Macroscopic quantum phenomena in superfluids and superconductors

In this paper I will discuss the common macroscopic quantum phenomena in the three superfluid systems known in condensed matter, the superconducting state of a metal, the superfluid phase of liquid⁴He, and the superfluid phases of liquid³He. The discussed phenomena will be persistent currents and their decay, critical velocities and critical magnetic fields, quantization of magnetic flux and of circulation, the two-dimensional flux and vortex lattices, and eventually the Josephson effects.Invited paper at the International Conference on Macroscopic Quantum Phenomena, Smolenice Castle, Czechoslovakia, September 18–22, 1989.     

高压下的铁基超导体:现象与物理

始于2008年的铁基超导体研究续写了高温超导发展史的新篇章.回顾过去十年对铁基超导体的研究,在理论、实验及应用方面都取得了辉煌的成绩,丰富了人们对高温超导电性的认识,为突破高温超导机理研究、最终实现超导材料的人工设计与更广泛的应用奠定了坚实的基础.本文主要介绍了通过高压实验研究手段在铁基超导体的研究中取得的一些重要进展及呈现出的新现象和新物理,例如压致超导现象、压力导致的超导再进入现象、压力对超导转变温度的提升效应、压力研究对铁基超导体超导转变温度的预测、相分离结构对超导电性的影响及反铁磁-超导双临界点的发现等.希望这些高压研究结果与本文报道的其他各类实验与理论研究成果一起,为全面、深入地理解铁基超导体勾画出一幅较为完整的物理图像.     

Introduction to real-space renormalization-group methods in critical and chaotic phenomena

The methods of the real-space renormalization group, and their application to critical and chaotic phenomena are reviewed. The article consists of two parts: the first part deals with phase transitions and critical phenomena; the second part, bifurcations and transitions to chaos. We begin with an introduction to the phenomenology of phase transitions and critical phenomena. Seminal concepts such as scaling and universality, and their characterization by critical exponents are discussed. The basic ideas of the renormalization group are then explained. A survey of real-space renormalization-group methods: decimation, Migdal-Kadanoff approximation, cumulant and cluster expansions, is given. The Hamiltonian formulation of classical statistical systems into quantum mechanical systems by the method of the transfer matrix is introduced. Quantum renormalization-group methods of truncation and projection, and their application to the transcribed quantum mechanical Ising model in a transverse field are illustrated. Finally, the quantum cumulant-expansion method as applied to the one-dimensional quantum mechanical XY model is discussed. The second part of the article is devoted to the subject of bifurcations and transitions to chaos. The three most commonly discussed kinds of bifurcations: the pitchfork, tangent and Hopf bifurcations, and the associated routes to chaos: period doubling, intermittency and quasiperiodicity are discussed. Period doubling based on the logistic map is explained in detail. Universality and its expression in terms of functional renormalization-group equations is discussed. The Liapunov characteristic exponent and its analogy to the order parameter are introduced. The effect of external noise and its universal scaling feature are shown. The simplest characterizations of the Hénon strange attractor are intuitively illustrated. The purpose of this article is primarily pedagogical. The similarity between critical and chaotic phenomena is a recurrent theme that underlines the importance and usefulness of such concepts as scaling, renormalization and universality.     

Phase diagram in ferromagnetic superconductors

In ferromagnetic superconductors, the spin-spiral phase and the self-induced vortex phase have been predicted to be caused by the interplay between the persistent current and the magnetic moments. Along with these two phases, the Meissner phase, the ferromagnetic normal phase, and the paramagnetic normal phase are also expected to appear in the system. From the calculation of the free energies, the phase-diagrams for these phases are obtained in the planes of temperature-the Landau parameter, -magnetization, and -the concentration of magnetic ions.     

Resonances in chaotic dynamics

We present a discussion and some numerical results on the actual possibility of making accessible, by numerical techniques, the complex singularities of the power spectrum (resonances) for a chaotic signal. Hénon's transformation is investigated in detail, showing that the position of the leading resonance in the complex frequency plane determines the kind of mixing rate in the time evolution.     

Lattice gas dynamics: application to driven vortices in two dimensional superconductors

A continuous time Monte Carlo lattice gas dynamics is developed to model driven steady states of vortices in two dimensional superconducting networks. Dramatic differences are found when compared to a simpler Metropolis dynamics. Subtle finite size effects are found at low temperature, with a moving smectic that becomes unstable to an anisotropic liquid on sufficiently large length scales.     

Self-heating-induced phenomena in long reentrant ferromagnetic thin film superconductors

We predict several novel self-heating-induced features of the current-voltage characteristics at bath temperatures below the lower critical temperature as well as the temperature dependence of the various critical currents of long reentrant ferromagnetic thin film superconductors on the basis of existing theories and available experimental results. Further we point out how the experimental investigation of the above can lead to a better understanding of reentrant superconductivity and magnetic Kapitza resistance.     

One to four-wing chaotic attractors coined from a novel 3D fractional-order chaotic system with complex dynamics

A novel 3D fractional-order chaotic system is proposed in this paper. And the system equations consist of nine terms including four nonlinearities. It's interesting to see that this new fractional-order chaotic system can generate one-wing, two-wing, three-wing and four-wing attractors by merely varying a single parameter. Moreover, various coexisting attractors with respect to same system parameters and different initial values and the phenomenon of transient chaos are observed in this new system. The complex dynamical properties of the presented fractional-order systems are investigated by means of theoretical analysis and numerical simulations including phase portraits, equilibrium stability, bifurcation diagram and Lyapunov exponents, chaos diagram, and so on. Furthermore, the corresponding implementation circuit is designed. The Multisim simulations and the hardware experimental results are well in accordance with numerical simulations of the same system on the Matlab platform, which verifies the correctness and feasibility of this new fractional-order chaotic system.