Current-driven dynamics in Josephson junction networks with an asymmetric potential

Current-driven dynamics of Josephson junction networks (JJNs) is studied using numerical simulations. We consider a JJN with an asymmetric and periodic potential of vortices, which is realized by saw-tooth modulation of junction critical currents. When external ac currents are applied to the JJN in a magnetic field, there appears a ratchet effect, and then directed motion of vortices is induced in certain system parameter regimes. A ratchet behavior is observed even for JJNs with weak structural disorder. We clarify the vortex pinning and dynamics in the JJN as a ratchet system.     

Directed transport and complex dynamics of vortices in a Josephson junction network driven by modulated currents

Directed transport of vortices in a Josephson junction network (JJN) with structural disorder is studied using a numerical simulation. Using spatiotemporal modulation of driving currents, the directed transport of vortices occurs even in the presence of disorder under certain conditions. From the analyses of the current–voltage and local voltage characteristics, it is found that the collective motion of vortices has an importance for the occurrence of directed transport.     

Probing the discrete motion of vortices with rf excitations

In this work we present experimental results on the rectification of vortices in a superconductor/ferromagnet system under a high frequency drive. The two-dimensional pinning landscape, induced by the stray fields of the ferromagnetic template, has no intrinsic asymmetry. Nevertheless, an asymmetric potential is artificially induced by an applied dc bias. The experimental results unambiguously show a biased, discrete motion of the vortices in the periodic potential at frequencies above 10 MHz. This synchronized motion is very sensitive to the external applied field. Increasing temperature leads to a reduction of the pinning potential, which in turn results in a lower ac power needed to drive the vortex lattice.     

Self-assembly and vortices formed by microparticles in weak electrolytes

We carried out experimental studies of the self-assembly of metallic micron-size particles in poorly conducting liquid subject to a constant electric field. Depending on the experimental conditions, the particles self-assemble into long chains directed along the electric field lines and form vortices and other structures. The vortices perform Brownian-type random motion due to self-induced chaotic hydrodynamic flows. We measured the diffusivity constant of the vortices and the conductivity and mechanical stiffness of the chains.     

Dynamics of poles with position-dependent strengths and its optical analogues

The dynamics of point vortices is generalized in two ways: first by making the strengths complex, which allows for sources and sinks in superposition with the usual vortices, second by making them functions of position. These generalizations lead to a rich dynamical system, which is nonlinear and yet has conservation laws coming from a Hamiltonian-like formalism. We then discover that in this system the motion of a pair mimics the behavior of rays in geometric optics. We describe several exact solutions with optical analogues, notably Snell’s law and the law of reflection off a mirror, and perform numerical experiments illustrating some striking behavior.     

Simulation of Dynamics in Two-Dimensional Vortex Systems in Random Media

Dynamics in two-dimensional vortex systems with random pinning centres is investigated using molecular dynamical simulations. The driving force and temperature dependences of vortex velocity are investigated. Below the critical depinning force Fc, a creep motion of vortex is found at low temperature. At forces slightly above Fc, a part of vortices flow in winding channels at zero temperature. In the vortex channel flow region, we observe the abnormal behaviour of vortex dynamics： the velocity is roughly independent of temperature or even decreases with temperature at low temperatures. A phase diagram that describes different dynamics of vortices is presented.     

How do singularities move in potential flow?

The equations of motion of point vortices embedded in incompressible flow go back to Kirchhoff. They are a paradigm of reduction of an infinite-dimensional dynamical system, namely the incompressible Euler equation, to a finite-dimensional system, and have been called a “classical applied mathematical playground”. The equation of motion for a point vortex can be viewed as the statement that the translational velocity of the point vortex is obtained by removing the leading-order singularity due to the point vortex when computing its velocity. The approaches used to obtain this result are reviewed, along with their history and limitations. A formulation that can be extended to study the motion of higher singularities (e.g. dipoles) is then presented. Extensions to more complex physical situations are also discussed.     

Transport of magnetic vortices by surface acoustic waves

In a thin film of superconducting Y Ba₂Cu₃O₇ the impact of surface acoustic waves (SAWs) traveling on the piezoelectric substrate is investigated. A pronounced interaction between the ultrasonic waves and the vortex system in the type II superconductor is observed. The occurrence of a SAW-induced dc voltage perpendicular to the sound path is interpreted as dragging of vortices by the piezoacoustic SAW, which acts as a conveyor for the flux quanta. The antisymmetry of this voltage with respect to the magnetic field directly evidences the induced, directed flux motion. This dynamic manipulation of vortices can be seen as an important step towards flux-based electronic devices.     

Synchronization of oscillating reactions in an extended fluid system

We present experiments on the synchronization of a dynamical, chemical process in an extended, flowing, fluid system. The oscillatory Belousov-Zhabotinsky chemical reaction is the process studied, and the flow is an annular chain of counterrotating vortices. Azimuthal motion of the vortices is controlled externally, enabling us to vary the type of transport. We find that oscillations of the Belousov-Zhabotinsky reaction synchronize throughout the extended fluid system only if transport in the flow is superdiffusive, with tracers in the flow undergoing rapid, distant jumps called Lévy flights.     

Rectified vortex motion in an Nb film with a spacing-graded array of holes

Superconducting Nb thin films with a spacing-graded array of holes were prepared by electron beam lithography. Two films with different hole gradients were fabricated. The ac-driven vortices were investigated in Nb superconductors with a spacing-graded array of holes. The measurements revealed pronounced rectified voltage when the vortex lattice is driven by an ac injected current. The rectified voltage is mainly caused by the strength of the vortex–vortex interaction. The rectified motion of a vortex is affected by the pinning potential of the spacing-graded array and the applied magnetic field. The vortex–vortex interaction strength changes the effective pinning landscape of the vortices and an asymmetric potential is formed. Vortices depin easily from high concentration to low concentration of pinning sites. In both samples, the ac-driven vortices exhibit a variety of dynamical responses and the rectified voltage is tunable with the applied magnetic field.     

矩形磁性纳米点动力学反磁化过程的微磁学研究

采用微磁学模拟方法研究了初始态为C形磁结构的矩形CoFe纳米点在方波脉冲场作用下的动力学反磁化过程.研究发现,随着脉冲场强的增强,磁体的反磁化模式发生了改变.当场强较弱时反磁化过程通过畴壁移动-单涡旋的形成和移动来完成;当场强较大时反磁化过程模式转变为畴壁移动-双涡旋的形成与移动;在更强的场强下反磁化过程通过畴壁的移动-多涡旋的形成与湮没来实现.由于反磁化模式随场强的变化而改变,反磁化时间随场强的增大出现振荡变化现象. 关键词： 动力学反磁化过程 反磁化时间 微磁学模拟     

Direct observation of rectified motion of vortices in a niobium superconductor

Using Lorentz microscopy to directly image vortices, we investigate vortex motion control and rectification in a niobium superconductor. We directly observe a net motion of vortices along microfabricated channels with a spatially asymmetric potential, even though the vortices were driven by an oscillatory field. By observing the individual motion of vortices, we clarify elementary processes involved in this rectification. To further demonstrate the ability to control the motion of vortices, we created a tiny vortex "racetrack" to monitor the motion of vortices in a closed circuit channel.     

On the Incompressible Fluid Limit and the Vortex Motion Law of the Nonlinear Schrödinger Equation

The nonlinear Schr?dinger equation (NLS) has been a fundamental model for understanding vortex motion in superfluids. The vortex motion law has been formally derived on various physical grounds and has been around for almost half a century. We study the nonlinear Schr?dinger equation in the incompressible fluid limit on a bounded domain with Dirichlet or Neumann boundary condition. The initial condition contains any finite number of degree ± 1 vortices. We prove that the NLS linear momentum weakly converges to a solution of the incompressible Euler equation away from the vortices. If the initial NLS energy is almost minimizing, we show that the vortex motion obeys the classical Kirchhoff law for fluid point vortices. Similar results hold for the entire plane and periodic cases, and a related complex Ginzburg–Landau equation. We treat as well the semi-classical (WKB) limit of NLS in the presence of vortices. In this limit, sound waves propagate through steady vortices. Received: 1 December 1997 / Accepted: 27 June 1998     

Ratchet motion and current reversal of coupled Brownian motors in pulsating symmetric potentials

In this study, we investigate the collective directed transport of coupled Brownian particles in spatially symmetric periodic potentials under time-periodic pulsating modulations. We find that the coupling between two particles can induce symmetry breaking and consequently collective directed motion. Moreover, the direction of motion can be reversed under certain conditions. The dependence of directed current on various parameters is systematically studied. reverse motion can be achieved by modulating the coupling free length and the phase shift of the pulsating potential. The dynamical mechanism of these transport properties is understood in terms of the effective-potential theory and the space-time transformation invariance. The directed transport of coupled Brownian motors can be manipulated and optimized by adjusting the coupling strength, pulsating frequency, or noise intensity.     

On the vortex flow in bounded domains

We consider the motion ofN vortices in bounded domains in IR². We prove that the set of initial positions which lead to a collapse of two or more vortices has Lebesgue measure zero. We extend this result to the stochastic motion of the vortices, where the stochasticity comes from a Wiener-noise term, which is added to the deterministic equation of motion.On leave of the Fachbereich Mathematik, RUB, 4630 Bochum, Federal Republic of Germany. Supported by a DFG-fellowshipPartially supported by Italian CNR     

On Vortex Dynamics in the Self-Dual Chern–Simons–Higgs System

The dynamics of n vortices in the self-dual Chern–Simons–Higgs system defined on the infinite plane is investigated. In adiabatic approximation, the vortex dynamics is determined by considering a rigid motion of a vortex configuration and a motion around a fixed center of mass. A motion of two vortices is studied in detail.     

两类非对称涡流动所诱导的摇滚运动

文章详细讨论了两类非对称涡流动诱发的模型摇滚运动.第1类是针对旋成体机身组合体模型, 其摇滚运动是由前体非对称涡流动诱发的, 运功形态呈现不确定性, 由模型头尖部的扰动触发形成.文章提出了快速旋转头尖部扰动的控制技术, 以抑制该类模型的大攻角摇滚运动.第2类是针对非常规机身的组合体模型, 其摇滚运动的主控流动是非常规机身和机翼的前缘分离涡流动, 这些流动是由组合体模型的边界条件确定的, 从而运动形态具有很好的确定性.所以, 这类模型的自由摇滚运动必须通过改变边界条件来改变诱发摇滚运动的流动, 以达到抑制模型自由摇滚运动的目的.最后, 文章还讨论了这类运动是由非对称的机翼涡涡强主控的.      

Dynamical instability of a doubly quantized vortex in a Bose-Einstein condensate

Doubly quantized vortices were topologically imprinted in /F=1> 23Na condensates, and their time evolution was observed using a tomographic imaging technique. The decay into two singly quantized vortices was characterized and attributed to dynamical instability. The time scale of the splitting process was found to be longer at higher atom density.     

Dynamical interactions of cosmic strings and flux vortices in superconductors

We perform a numerical simulation of the dynamical interactions of vortex excitations in the abelian Higgs model. These structures can be interpreted as cross sections of cosmic strings or of magnetic flux tubes trapped in a superconductor. Although at a critical value of the coupling constant the interaction energy between static vortices vanishes, colliding vortices interact nontrivially by scattering at 90° in a head-on collision, and are therefore not solitons. We also observe 90° scattering at non-critical values of the coupling constant.