Pinning dynamic systems of networks with Markovian switching couplings and controller-node set

In this paper, we study pinning control problem of coupled dynamical systems with stochastically switching couplings and stochastically selected controller-node set. Here, the coupling matrices and the controller-node sets change with time, induced by a continuous-time Markovian chain. By constructing Lyapunov functions, we establish tractable sufficient conditions for exponentially stability of the coupled system. Two scenarios are considered here. First, we prove that if each subsystem in the switching system, i.e. with the fixed coupling, can be stabilized by the fixed pinning controller-node set, and in addition, the Markovian switching is sufficiently slow, then the time-varying dynamical system is stabilized. Second, in particular, for the problem of spatial pinning control of network with mobile agents, we conclude that if the system with the average coupling and pinning gains can be stabilized and the switching is sufficiently fast, the time-varying system is stabilized. Two numerical examples are provided to demonstrate the validity of these theoretical results, including a switching dynamical system between several stable sub-systems, and a dynamical system with mobile nodes and spatial pinning control towards the nodes when these nodes are being in a pre-designed region.Comment: 9 pages; 3 figure

Importance of low-angle grain boundaries in YBa2Cu3O7-delta coated conductors

Over the past ten years the perception of grain boundaries in YBa2Cu3O7-δ conductors has changed greatly. They are no longer a problem to be eliminated but an inevitable and potentially favourable part of the material. This change has arisen as a consequence of new manufacturing techniques which result in excellent grain alignment, reducing the spread of grain boundary misorientation angles. At the same time there is considerable recent evidence which indicates that the variation of properties of grain boundaries with mismatch angle is more complex than a simple exponential decrease in critical current. This is due to the fact that low-angle grain boundaries represent a qualitatively different system to high angle boundaries. The time is therefore right for a targetted review of research into low-angle YBa2Cu3O7-δ grain boundaries. This article does not purport to be a comprehensive review of the physics of grain boundaries as found in YBa2Cu3O7-δ in general; for a broader overview we would recommend that the reader consult the comprehensive review of Hilgenkamp and Mannhart (Rev. Mod. Phys., 74, 485, 2002). The purpose of this article is to review the origin and properties of the low-angle grain boundaries found in YBa2Cu3O7-δ coated conductors both individually and as a collective system.EPSR

Dislocation networks in helium-4 crystals

The mechanical behavior of crystals is dominated by dislocation networks, their structure and their interactions with impurities or thermal phonons. However, in classical crystals, networks are usually random with impurities often forming non-equilibrium clusters when their motion freezes at low temperature. Helium provides unique advantages for the study of dislocations: crystals are free of all but isotopic impurities, the concentration of these can be reduced to the ppb level, and the impurities are mobile at all temperatures and therefore remain in equilibrium with the dislocations. We have achieved a comprehensive study of the mechanical response of 4He crystals to a driving strain as a function of temperature, frequency and strain amplitude. The quality of our fits to the complete set of data strongly supports our assumption of string-like vibrating dislocations. It leads to a precise determination of the distribution of dislocation network lengths and to detailed information about the interaction between dislocations and both thermal phonons and 3He impurities. The width of the dissipation peak associated with impurity binding is larger than predicted by a simple Debye model, and much of this broadening is due to the distribution of network lengths.Comment: accepted by Phys. Rev.

Deblocking of interacting particle assemblies: from pinning to jamming

A wide variety of interacting particle assemblies driven by an external force are characterized by a transition between a blocked and a moving phase. The origin of this deblocking transition can be traced back to the presence of either external quenched disorder, or of internal constraints. The first case belongs to the realm of the depinning transition, which, for example, is relevant for flux-lines in type II superconductors and other elastic systems moving in a random medium. The second case is usually included within the so-called jamming scenario observed, for instance, in many glassy materials as well as in plastically deforming crystals. Here we review some aspects of the rich phenomenology observed in interacting particle models. In particular, we discuss front depinning, observed when particles are injected inside a random medium from the boundary, elastic and plastic depinning in particle assemblies driven by external forces, and the rheology of systems close to the jamming transition. We emphasize similarities and differences in these phenomena.Comment: 20 pages, 8 figures, submitted for a special issue of the Brazilian Journal of Physics entitled: Statistical Mechanics of Irreversible Stochastic Models - I

Quantum Phase Transitions and Vortex Dynamics in Superconducting Networks

Josephson junction arrays are ideal model systems where a variety of phenomena, phase transitions, frustration effects, vortex dynamics, chaos, to mention a few of them, can be studied in a controlled way. In this review we focus on the quantum dynamical properties of low capacitance Josephson junction arrays. The two characteristic energy scales in these systems are the Josephson energy, associated to the tunneling of Cooper pairs between neighboring islands, and the charging energy, which is the energy cost to add an extra electron charge to a neutral island. The phenomena described in this review stem from the competition between single electron effects with the Josephson effect. One example is the (quantum) Superconductor-Insulator phase transition which occurs by varying the ratio between the coupling constants and/or by means of external magnetic/electric fields. We will describe how the phase diagram depends on the various control paramters and the transport properties close to the quantum critical point. The relevant topological excitations on the superconducting side of the phase diagram are vortices. In low capacitance junction arrays vortices behave as massive underdamped particles that can exhibit quantum behaviour. We will report on the various experiments and theoretical treatments on quantum vortex dynamics.Comment: To be published in Physics Reports. Better quality figures can be obtained upon reques

Magnetization reversal in spin patterns with complex geometry

We study field-driven dynamics of spins with antiferromagnetic interaction along the links of a complex substrate geometry, which is modeled by graphs of a controlled connectivity distribution. The magnetization reversal occurs in avalanches of spin flips, which are pinned by the topological constraints of the underlying graph. The hysteresis loop and avalanche sizes are analyzed and classified in terms of graph's connectivity and clustering. The results are relevant for magnets with a hierarchical spatial inhomogeneity and for design of nanoscale magnetic devices.Comment: 4 pages, 3 color figures, revtex