Adaptive synchronization of weighted complex dynamical networks through pinning

This paper considers the problem of controlling weighted complex dynamical networks by applying adaptive control to a fraction of network nodes. We investigate the local and global synchronization of the controlled dynamical network through the construction of a master stability function and a Lyapunov function. Analytical results show that a certain number of nodes can be controlled by using adaptive pinning to ensure the synchronization of the entire network. We present numerical simulations to verify the effectiveness of the proposed scheme. In comparison with feedback pinning, the proposed pinning control scheme is robust when tested by noise, different weighting and coupling structures, and time delays.     

Research on flux-flow oscillators induced different types of pinning potentials

We have studied dynamics of Josephson vortices in strongly coupled long Josephson junctions stack, such as an intrinsic Josephson junction, by numerical simulations based on coupled sine–Gordon equations considering a periodic pinning potential. In this report, we investigate flux-flow oscillators induced two types of pinning potentials. One is magnetic periodic pinning potential, the other is periodic bias currents. Our results demonstrate that the periodic pinning potential can develop the generated power of flux-flow oscillator in certain condition.     

Phase transitions of colloidal monolayers in periodic pinning arrays

We study the phase behavior of two-dimensional paramagnetic colloidal systems on square pinning arrays, the latter being created by a holographic optical tweezer technique. When the particle interaction strength is decreased, a transition from an incommensurate to a commensurate solid is observed. At even smaller pair potentials, the interstitial particles start to melt, whereas the particles at the substrate pinning sites are still localized. Our results are in good agreement with recent numerical studies on vortex melting in periodic pinning arrays.     

RF impedance of intrinsic Josephson junction in flux-flow state with a periodic pinning potential and its optimum condition for RF radiation

We reported dynamics of Josephson vortices interacting with electromagnetic waves in strongly coupled long Josephson junctions stack, such as an intrinsic Josephson junction (IJJ), by numerical simulations based on coupled sine-Gordon equations considering a periodic pinning potential of sinusoidal form. The numerical simulation results for the influence of the electromagnetic waves on flux-flow properties show that the periodic pinning potential induces an in-phase motion of Josephson vortices over the junction stacks, which achieve high performances of IJJ flux-flow oscillator. In order to prove it from another viewpoint, we calculate RF impedance of long Josephson junction stacks in flux-flow state. A remarkable negative real part region of RF impedance appears at 1st harmonic step, it means that the long Josephson junction stacks in flux-flow state acts as an oscillator at the negative real part region. In this study, we evaluate the optimum condition for RF radiation with the periodic pinning potential.     

Numerical simulation evidence of dynamical transverse meissner effect and moving bose glass phase

We present 3D numerical simulation results of moving vortex lattices in the presence of 1D correlated disorder at zero temperature. Our results with field tilting confirm the theoretical predictions of a moving Bose glass phase, characterized by transverse pinning and dynamical transverse Meissner effect, the moving flux lines being localized along the correlated disorder direction. Beyond a critical transverse field, vortex lines exhibit along all their length a "kink" structure resulting from an effective static "tin roof" pinning potential in the transverse direction.     

Pinning impulsive synchronization of stochastic delayed coupled networks

In this paper,the pinning synchronization problem of stochastic delayed complex network (SDCN) is investigated by using a novel hybrid pinning controller. The proposed hybrid pinning controller is composed of adaptive controller and impulsive controller,where the two controllers are both added to a fraction of nodes in the network. Using the Lyapunov stability theory and the novel hybrid pinning controller,some sufficient conditions are derived for the exponential synchronization of such dynamical networks in mean square. Two numerical simulation examples are provided to verify the effectiveness of the proposed approach. The simulation results show that the proposed control scheme has a fast convergence rate compared with the conventional adaptive pinning method.     

Flux vortex pinning in a simple model system

Results of numerical calculations of flux vortex pinning by random one and two dimensional arrays of identical pinning centres are reported. Three different methods for determining the critical state flux gradient are described and the critical state concept is shown to break down for samples smaller than a certain size.     

Controlling the motion of magnetic flux quanta

We study the transport of vortices in superconductors with triangular arrays of boomerang- or V-shaped asymmetric pinning wells, when applying an alternating electrical current. The asymmetry of the pinning landscape induces a very efficient "diode" effect, that allows the sculpting at will of the magnetic field profile inside the sample. We present the first quantitative study of magnetic "lensing" of fluxons inside superconductors. Our proposed vortex lens provides a near threefold increase of the vortex density at its "focus" regions. The main numerical features have been derived analytically.     

Modeling of irreversible switching and viscosity phenomena in perpendicular thin films

We have developed a simple numerical model for simulating domains as well as remanence and viscosity curves in the slow dynamics regime, for thin films characterized by perpendicular magnetization and irregular domain configurations due to strong disorder. The physical system is represented as constituted of identical switching units, described by proper switching field distributions and energy barrier laws for pinning and nucleation processes. The model also includes an effective field which accounts for magnetic forces proportional to magnetization, on average. Simulations of DCD curves show that when the reversal of magnetization is governed by pinning, the coercive field depends on the physical size of the film area on which the external field is applied. In the case of viscosity phenomena described by a linear energy barrier law associated with a single predominant reversal process (pinning or nucleation), universal viscosity curves can be generated by properly transforming the DCD curve of the system. We also demonstrate that a reduction of the maximum viscosity coefficient can coexist with a reduction of the energy barrier heights.     

Domain wall pinning in narrow ferromagnetic ring structures probed by magnetoresistance measurements

We present a magnetoresistance study of magnetization reversal and domain wall pinning effects in a mesoscopic narrow ferromagnetic Permalloy ring structure containing notches. The size and strength of the attractive pinning potential created by a notch is measured and the resistance minimum at remanence is found to occur when a single transverse domain wall is pinned at the notch, in agreement with the results of numerical simulations of the anisotropic magnetoresistance. When a field is applied in the direction corresponding to a potential well edge, a novel magnetic state with a very wide domain wall is stabilized, giving rise to a characteristic signature in the magnetoresistance at such angles.     

Static and dynamic behaviours of multivortex states in a superconducting sample with mesoscopic pinning sites

This preliminary work has focused on the static transitions between the multivortex states interacting with square arrays of the mesoscopic pinning sites in superconducting samples. Our results were obtained from an extensive series of numerical simulations as functions of the magnetic field, pinning radius, and sample size. We have presented a wide range of multivortex configurations from commensurate dimer states to more concentric vortex shells at the matching fields. The stability of these states was also studied by means of the current-voltage V(I) curves which illustrate dynamic phase transitions as a function of applied driving force. These transitions manifested themselves as either a sudden jump in velocity or a nonlinear increase with velocity fluctuations in V(I) curves. We have investigated whether that the phase transitions between the pinned regime and the elastic flow regime are indicative of the stability of the initial vortex states. The variety of intermediate flow phases is attributed to large pinning size (reentrant behavior), strong commensurability and caging effects. In particular, three-shell vortex structures were obtained in the presence of larger pinning sites at adequate matching magnetic fields.     

Pinning consensus analysis of multi-agent networks with arbitrary topology

In this paper the pinning consensus of multi-agent networks with arbitrary topology is investigated. Based on the properties of M-matrix, some criteria of pinning consensus are established for the continuous multi-agent network and the results show that the pinning consensus of the dynamical system depends on the smallest real part of the eigenvalue of the matrix which is composed of the Laplacian matrix of the multi-agent network and the pinning control gains. Meanwhile, the relevant work for the discrete-time system is studied and the corresponding criterion is also obtained. Particularly, the fundamental problem of pinning consensus, that is, what kind of node should be pinned, is investigated and the positive answers to this question are presented. Finally, the correctness of our theoretical findings is demonstrated by some numerical simulated examples.     

Coercivity mechanisms in nanostructured permanent magnets

Coercivity mechanism in permanent magnets has been debated for many years.In this paper, various models of the coercivity mechanism are classified and re-examined by the comparison and contrast.Coherent rotation and curling models can reveal the underlying reversal mechanism clearly based on isolated grains with elliptic shapes.By contrast, the numerical methods consider inter-grain interactions while simulating the evolution of the spins and hysteresis loops with complicated shapes.However, an exact simulation of magnetic reversal in permanent nanomagnets requires many meshes to mimic the thin domain wall well.Nucleation and pinning are the two main coercivity mechanisms in permanent magnets.The former signifies the beginning of the magnetic reversal, whilst the latter completes it.Recently, it is proposed that the large difference between the intrinsic magnetic properties of the nucleation centers and those of the main phase can result in a large pinning field(self-pinning), which has the attributes of both traditional nucleation and pinning.Such a pinning explains the experimental data of permanent magnets very well, including the enhancement of the coercivity by the grain boundary pinning.     

强钉扎高温超导体与永磁体系统的悬浮力数值模型

本文从数值模拟和实验两方面研究了熔融织构Y-Ba-Cu-O(YBCO)高温超导块材与永磁体组成的磁悬浮系统的悬浮特性.通过理论与实验结果的比较,在Hikihara-Moon超导磁悬浮动力学唯像模型的基础上,提出了强钉扎磁悬浮力模型,并进一步研究了熔融织构YBCO块材在不同条件下的悬浮特性,包括:场冷高度(FCH)和零场冷却(ZFC)的对磁浮力的影响,以及由不同运动速度导致的磁悬浮力的变化等.结果表明,强钉扎磁悬浮力模型适合于精确描述由熔融织构YBCO高温超导块材与永磁体所组成的磁悬浮系统的悬浮特性.     

混沌神经网络的控制

提出了一种针对混沌神经网络的钉扎控制方法.利用此方法对混沌神经网络进行控制,使网络的输出稳定在网络的一个存储的模式上.实现了混沌神经网络的信息搜索,并对影响混沌神经网络控制效果的几个因素进行了讨论. 关键词： 混沌控制 混沌神经网络 钉扎控制方法     

Quantum tunneling of a vortex between two pinning potentials

A vortex can tunnel between two pinning potentials in an atomic Bose-Einstein condensate on a time scale of the order of 1s under typical experimental conditions. This makes it possible to detect the tunneling experimentally. We calculate the tunneling rate by phenomenologically treating vortices as charged particles moving in an inhomogeneous magnetic field. The obtained results are in close agreement with numerical simulations based on the stochastic c-field theory.     

Properties of solitons in the Frenkel-Kontorova model

An exact numerical calculation is presented for the properties of solitons in the discrete model of Frenkel and Kontorova. We have calculated the single soliton energy, the Peierls pinning energy and the soliton-soliton interaction energy. The exponential behaviour predicted for the soliton-soliton interaction by the continuum approximation is found to hold even for large soliton densities and very strong substrate potentials though in the latter case, the coefficients differ substantially from those of the continuum approximation.     

Local impurity phase pinning and pinning force in charge density waves

Starting from the static Fukuyama-Lee-Rice equation for a three-dimensional incommensurate charge density wave (CDW) in quasi one-dimensional conductors a solvable model for local phase pinning by impurities is defined and studied. We find that average CDW energy and average pinning force show critical behaviour with respect to the pinning parameter h. Specifically the pinning force exhibits a threshold at h=1 with exponent . Our model exemplifies a general concept of local impurity pinning in which the force exerted by the impurity on the periodic CDW structure becomes multivalued and metastable states appear beyond a threshold. It is found that local impurity pinning becomes less effective at low temperatures and may eventually cease completely. These results are independent of spatial dimensionality as expected for local impurity pinning. Comparison with Larkin's model is also made. Received 8 July 1998     

Modelling thin-film dewetting on structured substrates and templates: Bifurcation analysis and numerical simulations

We study the dewetting process of a thin liquid film on a chemically patterned solid substrate (template) by means of a thin-film evolution equation incorporating a space-dependent disjoining pressure. Dewetting of a thin film on a homogeneous substrate leads to fluid patterns with a typical length scale, that increases monotonously in time (coarsening). Conditions are identified for the amplitude and periodicity of the heterogeneity that allow to transfer the template pattern onto the liquid structure ("pinning") emerging from the dewetting process. A bifurcation and stability analysis of the possible liquid ridge solutions on a periodically striped substrate reveal parameter ranges where pinning or coarsening ultimately prevail. We obtain an extended parameter range of multistability of the pinning and coarsening morphologies. In this regime, the selected pattern depends sensitively on the initial conditions and potential finite perturbations (noise) in the system as we illustrate with numerical integrations in time. Finally, we discuss the instability to transversal modes leading to a decay of the ridges into rows of drops and show that it may diminish the size of the parameter range where the pinning of the thin film to the template is successful.Received: 29 January 2003, Published online: 15 July 2003PACS: 68.15.+e Liquid thin films - 81.16.Rf Nanoscale pattern formation - 47.20.Ky Nonlinearity (including bifurcation theory)     

Numerical calculation of elastic pinning parameters by point pins

One-dimensional numerical simulations of the pinned vortex lattice have been carried out using an inverted model in which widely spaced and weak point pinning centres are distorted by a rigid lattice. This allows us to simulate a much larger array than if we had to find the position of each vortex separately. Using steepest descent and molecular dynamics methods, the Labusch parameter is found to have similar power law dependencies on the density of pins and elementary pinning force to the bulk pinning force. This implies that the maximum reversible displacement is a constant and it is found to be roughly 0.2 of a vortex spacing. The results are in agreement with the Larkin-Ovchinnikov theory of collective pinning. Quasi-static shifting of the pins over the rigid vortex lattice allowed the size of avalanches in the flow state to be measured. The distribution of avalanche sizes displays power law behaviour over several decades.