Three-dimensional motion of a vortex filament and its relation to the localized induction hierarchy

Three-dimensional motion of a slender vortex tube, embedded in an inviscid incompressible fluid, is investigated under the localized induction approximation for the Euler equations. Using the method of matched asymptotic expansions in a small parameter ε, the ratio of core radius to curvature radius, the velocity of a vortex filament is derived to O(ε³), whereby the influence of elliptical deformation of the core due to the self-induced strain is taken into account. It is found that there is an integrable line in the core whose evolution obeys a summation of the first and third terms of the localized induction hierarchy. Received 2 October 2001 / Received in final form 10 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: yasuhide@math.kyushu-u.ac.jp     

Magnetic induction by coherent vortex motion

We investigate experimentally the advection of a magnetic field by a flow of conducting fluid, at moderate magnetic Reynolds numbers. More specifically, we study the influence of a large scale intense vortex on an externally applied field. We show that at large scales the magnetic field lines are distorted in a way that is consistent with a scenario of magnetic field expulsion by vorticity. Measurements at small scales show that the magnetic fluctuations are also quite sensitive to the large scale vortex motion. Received 27 October 1999 and Received in final form 16 March 2000     

Master equation for the density matrix and Boltzmann equation of localized electrons in crystals

A Master equation for the density matrix and a Boltzmann equation for the occupation number of electrons in a crystal are derived. The wave function of an electron is localized within a sub crystal by a superposition of the corresponding Wannier functions. The electrons are coupled to an external electrical field, to phonons, and to a particle reservoir, describing phenomena as transport, damping, and electron sources on the surface of contact.     

Sound radiation by a plane localized vortex

A classical problem on small-scale fluctuations of the Rankine vortex in a compressible gas has been numerically simulated. Euler equations for a compressible gas have been solved by the CABARET method. Simulation results well predict the value of the eigenfrequency of the boundary fluctuations for the azimuthal harmonic n = 2 and almost coincide with the analytic solution. The value of the acoustic instability increment has been quantitatively predicted despite the fact that it is small and it has been revealed at a fluctuation number higher than 100.     

Origin of reversed vortex ratchet motion

We experimentally demonstrate that the origin of multiply reversed rectified vortex motion in an asymmetric pinning landscape not only is a consequence of the vortex-vortex interactions but also essentially depends on the ratio between the characteristic interaction distance and the period of the asymmetric pinning potential. We study four samples with different periods d of the asymmetric potential. For large d the dc voltage V(dc) recorded under a ac excitation indicates that the average vortex drift is from bigger to smaller dots for all explored positive fields. As d is reduced, a series of sign reversals in the dc response are observed as a function of field. We show that the number of sign reversals increases as d decreases. These findings are in agreement with recent computer simulations and illustrate the relevance of the different characteristic lengths for the vortex rectification effects.     

Rotating vortex solitons supported by localized gain

We show that ringlike localized gain landscapes imprinted in focusing cubic (Kerr) nonlinear media with strong two-photon absorption support new types of stable higher-order vortex solitons containing multiple phase singularities nested inside a single core. The phase singularities are found to rotate around the center of the gain landscape, with the rotation period being determined by the strength of the gain and the nonlinear absorption.     

相对转动运动学方程的级数解

为解决相对转动体非线性运动微分方程的计算难题，构造了一种级数解耦方法，把微分方程转化为代数方程求解，得到了相对转动体运动方程的级数解.据此可以计算工程应用中稳态相对转动体的真实转速波动.同时该法可实现测控标定仪器的转动体匀速旋转时的不均匀性测量误差分离，也为大型复杂重型旋转轴系在线实时扭振监测提供了高效算法. 关键词： 相对转动 运动学方程 速度波动 级数解     

Statistics of diffusive and localized fields in the vortex core

The statistics of the field structure in the vortex core surrounding phase singularities in random wave fields are measured and calculated for diffusive and localized waves. Excellent agreement is found between experiment and theory. The variation of phase with the geometric angle is deterministic, depending only upon the eccentricity of elliptical intensity contours, epsilon, whose probability distribution is shown to be universal. The distribution of vorticity is shown to reflect both the vorticity distributions within a Gaussian random wave field with a given value of the total transmission and the mesoscopic distribution of total transmission.     

Damping of the vortex motion in the cuprate superconductors

We have investigated the flux-flow resistivity in different cuprate superconductors. The subjects summarized in the following revealed unexpected novel features and were of particular interest.     

Master equation for the quasi-incoherent motion of Frenkel excitons

Starting from the Haken-Strobl-model for the coupled coherent and incoherent motion of Frenkel excitons, a master equation is derived describing the quasi-incoherent motion of these excitations. In contrast to previous derivations no use is made of special symmetries. Therefore this equation may also describe the energy transfer in materials with non-periodic structure, which play a role in biological systems. The master equation is solved for crystals with one and two molecules in the unit cell, and explicit expressions are given for the case of nearest neighbour interaction too. Furtheron, asymptotic forms of the solutions are discussed.     

Three vortex motion in the slightly viscous flow

The dynamics of three vortices moving in an ideal fluid in a plane can be expressed in Hamiltonian form. However, when viscosity can not be ignored, the system of point vortices has not this delicious structure. This investigation focuses on the viscosity effect on the motion of three vortices. Since the viscous diffusion of vortices is simulated by Brownian motion, the equations of intervortical distances are obtained by Ito formula. These equations show that there exist two viscosity effects on intervortical distances: stable expansion and random impulse. Furthermore, via employing the asymptotic solution to these equations, these two viscous effects have been shown to destroy the self-similar process of collapse and make it into a new configuration, which is similar to the near collapse in the ideal case.     

Induced motion of a fast Josephson vortex

A relation is established between the transport current flowing through the entire S ₁ IS ₂ WS ₃ layered structure and the velocity of a fast vortex. The fast vortex exists when the Swihart velocity in the waveguide is significantly higher than that in the Josephson junction. It is demonstrated that the main contribution to the Lorentz force that induces the vortex motion is due to the current flowing through the waveguide and skin layers of the adjacent superconductors.

     

A mean-field equation of motion for the dynamic Ising model

A mean-field type of approximation is used to derive two differential equations, one approximately representing the average behavior of the Ising model with Glauber (spin-flip) stochastic dynamics, and the other doing the same for Kawasaki (spin-exchange) dynamics. The proposed new equations are compared with the Cahn-Allen and Cahn-Hilliard equations representing the same systems and with information about the exact behavior of the microscopic models.     

Field equation for the transverse motion of a two-layered plate

An approximate theory is developed for the transverse motion of a two-layered plate. The two layers are assumed to be elastic, isotropic, homogeneous and welded to each other. The theory is similar to the Timoshenko-Mindlin model for a single-layered plate in which corrections are included for rotary inertia and shear deformation. A single equation of transverse motion is derived that predicts the first four antisymmetric modes and is applicable to practical problems. Phase velocities of these modes are numerically analyzed for a plate consisting of a copper layer and a steel layer.     

Estimating localized oscillatory tissue motion for assessment of the underlying mechanical modulus

The technique of harmonic motion imaging (HMI) uses the localized stimulus of the oscillatory ultrasonic radiation force as produced by two overlapping beams of distinct frequencies, and estimates the resulting harmonic displacement in the tissue in order to assess its underlying mechanical properties. In this paper, we studied the relationship between measured displacement and stiffness in gels and tissues in vitro. Two focused ultrasound transducers with a 100 mm focal length were used at frequencies of 3.7500 MHz and either 3.7502 (or 3.7508 MHz), respectively, in order to produce an oscillatory motion at 200 Hz in the gel or tissue. A 1.1 MHz diagnostic transducer (Imasonics, Inc.) was also focused at 100 mm and acquired 5 ms RF signals (pulse repetition frequency (PRF)=3.5 kHz) at 100 MHz sampling frequency during radiation force application. First, three 50x50 mm(2) acrylamide gels were prepared at concentrations of 4%, 8% and 16%. The resulting displacement was estimated using crosscorrelation techniques between successively acquired RF signals with a 2 mm window and 80% window overlap at 1260 W/cm(2). A normal 1-D indentation instrument (TeMPeST) applied oscillatory loads at 0.1-200 Hz with a 5 mm-diameter flat indenter. Then, 12 displacement measurements in 6 porcine muscle specimens (two measurements/case, as above) were made in vitro, before and after ablation which was performed for 10 s at 1260 W/cm(2). In all gel cases, the harmonic displacement was found to linearly increase with intensity and exponentially decrease with gel concentration. The TeMPeST measurements showed that the elastic moduli for the 4%, 8% and 16% gels equaled 3.93+/-0.06, 17.1+/-0.2 and 75+/-2 kPa, respectively, demonstrating that the HMI displacement estimate depends directly on the gel stiffness. Finally, in the tissues samples, the mean displacement amplitude showed a twofold decrease between non-ablated and ablated tissue, demonstrating a correspondence between the HMI response and an increase in stiffness measured with the TeMPeST instrument.     

Effective one-dimensional equation of motion for nuclear fission

An approach for describing the dynamics of nuclear fission in the framework of generalized quantum mechanics is discussed. The collective kinetic energy is assumed to be two dimensional, and the reduced mass is allowed to vary with the coordinates. The generalized calculus of variation is employed for minimizing the action after being properly quantized as required by Hamilton's principle, employing a curvilinear coordinate system. The corresponding Euler Lagrange equation is identified as the required generalized equation of motion. The proposed generalized two-dimensional equation of motion is separated into a vibrational eigenvalue equation and a set of coupled-channel one-dimensional equations which describe the translational motion, by exploiting the completeness of the vibrational eigenfunctions. Such a system of coupled equations can be decoupled by replacing the coupling matrix elements by a nonlocal interaction, which can be rendered local after employing the effective mass approximation. As a consequence this differential equation is provided with an effective mass, an effective potential barrier, and a differential boundary term which is responsible for restoring the self-adjointness of the kinetic energy differential operator.     

Non-Newtonian dynamics of the fast motion of a magnetic vortex

The dynamics of a magnetic vortex in a thin magnetically soft ferromagnetic disc with a submicron diameter has been analyzed. Under the action of field pulses with a duration of the order of 10–100 ps, the vortex undergoes a complex motion. The analysis of the results of a micromagnetic simulation indicates that this motion is non-Newtonian. It can be described by an equation containing the third time derivative of the displacement of the vortex core.     

Derivation of a wave equation for collective motion

The generator coordinate method based on states derived from the random phase approximation, together with a strong assumption, leads to a differential equation for collective motion similar to the Bohr Hamiltonian with inertial parameters given by a formula related to the cranking model and with a potential almost equal to the ground state energy in the random phase approximation for each deformation.     

Absence of exponentially localized solitons for the Novikov-Veselov equation at positive energy

In this Letter we show that the Novikov-Veselov equation (NV-equation) at positive energy (an analog of KdV in 2+1 dimensions) has no exponentially localized solitons in the two-dimensional sense.