Dynamics of two-sign point vortices in positive and negative temperature states

Dynamics of two-sign point vortices in two-dimensional circular boundary is examined by numerical simulations with MDGRAPE-2. The vortex system is characterized by the inverse temperature beta as determined from the density of states of the microcanonical ensemble of numerically generated 10(7) states. The massive simulation shows that different configurations appear in the time-asymptotic state depending on the sign of beta. Condensation of the same-sign vortices is observed when beta<0, while the both-sign vortices tend to be uniformly neutralized when beta>0. During the condensation, a part of the vortices gains energy to form clumps (patches), and the other part of the vortices loses energy to keep the total energy constant and mixes with vortices of the other sign. This observation demonstrates a characteristic feature of negative beta states that the system energy concentrates into the clumps of the same-sign vortices.     

TRANSIENT OPTICAL VORTICES IN THE PROCESS OF PATTERN FORMATION IN A KERR SLICE SYSTEM WITH SINGLE FEEDBACK

The transient process of the optical pattern formation in a Kerr medium is numerically studied. We find that the process is accompanied by transient optical vortices in the far field. The temporal evolutions of the appearance and disappearance of the vortices are presented. All vortices will vanish when the system approaches its steady state. The number of vortices versus time is given.     

On the relationship between the temperature and the geometry of the two-dimensional superconducting system

A set of vortices in the superconducting system being a two-dimensional region with a boundary has been considered. Here the system under study is described by the model of the Ginzburg-Landau potential in the dual point. This model predicts that in the bounded superconducting system non-interacting vortices appear. These vortices make the absolute minima of this potential. It turned out that in the thermodynamic equilibrium for the fixed number of vortices, the temperature of the system and the geometry of the boundary are related to each other. The simultaneous change of the temperature of the system and of the geometry of the boundary has been investigated under the assumption that the number of vortices is fixed. In the case of the flat disc the explicit form of the temperature vs. area relation has been obtained for two different boundary conditions.Received: 29 April 2004, Published online: 31 August 2004PACS: 74.25.Bt Thermodynamic properties - 74.25.Dw Superconductivity phase diagrams     

Phase singularities and coherence vortices in linear optical systems

It is demonstrated for a time-invariant linear optical system that there exists a definite connection between the optical vortices (phase singularities of the field amplitude) which appear when it is illuminated by spatially coherent light and the coherence vortices (phase singularities of the field correlation function) which appear when it is illuminated by partially coherent light. Optical vortices are shown to evolve into coherence vortices when the state of coherence of the field is decreased. Examples of the connection are given. Furthermore, the generic behavior of coherence vortices in linear optical systems is described.     

Phase transitions in double-layered josephson junction arrays

A system of two parallel Josephson junction arrays coupled by interlayer capacitances is considered in the situation where one layer is in the vortex-dominated and the other in the charge-dominated regime. This system shows a symmetry (duality) of the relevant degrees of freedom, i.e. the vortices in one layer and the charges in the other. The charges feel the magnetic field created by vortices, and, vice versa, the vortices feel a gauge field created by charges. For long-range interaction of the charges the system exhibits two Berezinskii-Kosterlitz-Thouless transitions, one for vortices and another one for charges. The interlayer capacitance suppresses the temperature of vortex-unbinding transition. It further replaces the charge-unbinding transition by a crossover, which is smeared already for weak interlayer coupling.     

Fine structure of optical vortices in a crystal: A monochromatic singular beam

The fine structure of optical vortices in a perturbed singular beam past the uniaxial crystal-polarization filter system is considered. The method of determination of the relative weight of the partial vortices contained in the perturbed vortex is discussed. The dependence of the relative weight of the partial vortices on the displacement of the perturbed vortex from the beam axis is presented.     

Two-dimensional mesoscopic vortex clusters in a superconducting ring: Shell structure and melting

The structure and phase transitions in the mesoscopic system of vortices in a quasi-two-dimensional superconducting ring are investigated. The shell structure of the mesoscopic system of vortices is studied, and its variation with the number of vortices and the parameters of the superconducting ring is analyzed. Two mechanisms of formation of new shells in vortex clusters with an increasing number of vortices in an increasing magnetic field are discovered: the generation of a new shell in a cluster and the splitting of the internal shell into two shells. The melting of vortex clusters and their thermodynamic parameters are analyzed using the Monte Carlo method. It is found that the melting of shell-type clusters occurs in two stages, orientation melting taking place at the lower temperature (during which nearly crystalline adjacent shells start rotating relative to each other) and blurring of the vortex structure occurring at the higher temperature. The shells obtained by splitting upon an increase in the number of vortices do not participate in orientational melting. The two-stage form of melting is associated with the smaller height of potential barriers being surmounted during the rotation of shells relative to one another as compared to the barrier for vortices jumping from one shell to another.     

Dynamics of topological multipoles: II. Creation, annihilation, and evolution of nonparaxial optical vortices

The behavior of nonparaxial combined beams transferring two or four optical vortices with opposite topological charges (topological dipole or quadrupole) is studied. The paraxial and nonparaxial approaches are compared. It is shown that the behavior of a topologically neutral wave system is well characterized by the position of a representative point on the parametric plane. It is found that there exists a large region on this plane for which spatial trajectories of the optical vortices, both for dipoles and quadrupoles, do not intersect the focal plane, i.e., the vortices cannot exist within the forbidden zone. At the edges of the forbidden zone, the vortices are either created or annihilated. In contrast, there exists a region on the parametric plane for which the optical vortices can exist only near the waist plane.     

Decay of MHD-scale Kelvin-Helmholtz vortices mediated by parasitic electron dynamics

We have simulated nonlinear development of MHD-scale Kelvin-Helmholtz (KH) vortices by a two-dimensional two-fluid system including finite electron inertial effects. In the presence of moderate density jump across a shear layer, in striking contrast to MHD results, MHD KH vortices are found to decay by the time one eddy turnover is completed. The decay is mediated by smaller vortices that appear within the parent vortex and stays effective even when the shear layer width is made larger. It is shown that the smaller vortices are basically of MHD nature while the seeding for these is achieved by the electron inertial effect. Application of the results to the magnetotail boundary layer is discussed.     

偶极-偶极相互作用下玻色-爱因斯坦凝聚体中涡旋的非线性动力学研究

基于平均场理论和分裂算符谱算法, 研究了偶极-偶极相互作用下玻色爱因斯坦凝聚体中涡旋的非线性动力学. 研究发现外势运动速度小于临界值时,偶极-偶极相互作用对系统涡旋的非线性动力学影响较小,而外势运动速度超过临界速度时,偶极-偶极相互作用对涡旋的非线性动力学影响很大,可使系统产生涡旋对、涡旋偶极子和简单涡旋,并使它们形成涡街.     

偶极-偶极相互作用下玻色-爱因斯坦凝聚体中涡旋的非线性动力学研究

基于平均场理论和分裂算符谱算法,研究了偶极-偶极相互作用下玻色爱因斯坦凝聚体中涡旋的非线性动力学.研究发现外势运动速度小于临界值时,偶极-偶极相互作用对系统涡旋的非线性动力学影响较小,而外势运动速度超过临界速度时,偶极-偶极相互作用对涡旋的非线性动力学影响很大,可使系统产生涡旋对、涡旋偶极子和简单涡旋,并使它们形成涡街.     

Coherence-vortex lattice formed via Mie scattering of partially coherent light by several dielectric nanospheres

We previously demonstrated that Mie scattering of stationary partially coherent light by dielectric spheres generates coherence vortices. In this Letter, we demonstrate that a lattice of coherence vortices can be generated by Mie scattering of partially coherent electromagnetic waves by a system of three coplanar dielectric spheres. Spontaneous coherence-vortex creation and destruction is observed in our computer modeling of this system.     

On the vortex formation at the moving front of lightweight granular particles

The formation of vortices at a moving front of lightweight granular particles is investigated experimentally. The particles used in this study are made of polystyrene foam with three different diameters of nearly uniform size. Pairs of vortices are found to emerge at the moving front at regular intervals, thereby forming a wavy pattern. Once the vortices are produced, the flow velocity tends to increase. A simple analysis suggests the existence of a velocity boundary layer at the moving front, whose thickness increases with increasing particle diameter. The frontal radius of each vortex pair is about the size of this boundary layer; when the radius exceeds this size, the front tends to bifurcate into a train of vortices with the size of the boundary layer. The formation of twin vortices leads to a reduction in the air drag force exerted on the system, and thereby the system attains a higher flow velocity, i.e., a higher conversion rate of gravitational potential energy to the kinetic energy of the particle motion. The higher conversion rate of potential energy thus feeds back to the development of the vortex motion, resulting in the twin vortex formation.     

The laminar horseshoe vortex upstream of a short-cylinder confined in a channel formed by a pair of parallel plates

A flow visualization experiment was performed in order to characterize the laminar horseshoe vortex system that appears upstream of the junction of a short cylinder and a pair of flat parallel plates. The experiments were performed in a water tunnel and the technique used for flow visualization was laser illumination of seeded particles whose traces were captured using long exposure photography. Geometrical and flow parameters, such as Reynolds number and height-to-diameter ratio of the cylinders, are varied during the experiments and the flow regimes are analyzed as a function of these parameters. The behavior of vortex systems is reported. For low Reynolds number cases, the vortices stay in a fixed position, as the Reynolds number is increased the number of vortices grows and for larger Reynolds numbers the vortex system becomes oscillatory and for further increases it becomes periodic. As for the dimensionless height of the cylinders, the vortex system is weak for short cylinders and increases its strength and number of vortices as the cylinder height-to-diameter ratio is increased. For further increases in height the vortex system do not change, which shows that the flow becomes independent of the height-to-diameter ratio for sufficiently tall cylinders. Information of the frequency of appearance of periodic vortices is also included.     

Self-dual Vortices in Schrödinger-Chern-Simons Model

By making use of the U(1) gauge potential decomposition theory and the φ-mapping topological current theory, we investigate the Schrödinger-Chern-Simons model in the thin-film superconductor system and obtain an exact Bogomolny self-dual equation with a topological term. It is revealed that there exist self-dual vortices in the system. We study the inner topological structure of the self-dual vortices and show that their topological charges are topologically quantized and labeled by Hopf indices and Brouwer degrees. Furthermore, the vortices are found generating or annihilating at the limit points and encountering, splitting or merging at the bifurcation points of the vector field φ.     

Possible spacing between linear vortices in a 3D ordered Josephson medium

A method is proposed for solving the nonlinear system of equations of fluxoid quantization for two interacting linear vortices. It is shown that the centers of the vortices may lie in adjacent cells only if the pinning parameter I > 0.91, in alternate cells if I > 0.44, and in each third cell if I > 0.25. These critical values are substantially lower than analogous values for planar vortices. It is shown that, as the value of I tends to zero, the minimal spacing between linear vortices does not increase indefinitely, but attains a certain finite value and then remains unchanged. This means that pinning of linear vortices cannot be ignored even for values of I quite close to zero. It is shown that two linear vortices with centers in the neighboring cells along a diagonal may coexist for indefinitely small values of I.     

Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering

We report a method for generation of arbitrary shape and array of optical vortices by use of a superposition of coherent elementary vortices based on helical phase spatial filtering in spatial frequency domain. In this method, a helical phase spatial filter (HPSF) is placed in the spatial frequency plane of a 4-f imaging processing system. We demonstrated that the output field distribution represents the convolution between the input field and an elementary vortex field introduced by the HPSF, which results in a special shape or array of optical vortices determined by the “degenerate” properties of coherent elementary vortices and the distribution formats of the input field.     

Kinetic theory of point vortices in two dimensions: analytical results and numerical simulations

We develop the kinetic theory of point vortices in two-dimensional hydrodynamics and illustrate the main results of the theory with numerical simulations. We first consider the evolution of the system “as a whole” and show that the evolution of the vorticity profile is due to resonances between different orbits of the point vortices. The evolution stops when the profile of angular velocity becomes monotonic even if the system has not reached the statistical equilibrium state (Boltzmann distribution). In that case, the system remains blocked in a quasi stationary state with a non standard distribution. We also study the relaxation of a test vortex in a steady bath of field vortices. The relaxation of the test vortex is described by a Fokker-Planck equation involving a diffusion term and a drift term. The diffusion coefficient, which is proportional to the density of field vortices and inversely proportional to the shear, usually decreases rapidly with the distance. The drift is proportional to the gradient of the density profile of the field vortices and is connected to the diffusion coefficient by a generalized Einstein relation. We study the evolution of the tail of the distribution function of the test vortex and show that it has a front structure. We also study how the temporal auto-correlation function of the position of the test vortex decreases with time and find that it usually exhibits an algebraic behavior with an exponent that we compute analytically. We mention analogies with other systems with long-range interactions.     

Line vortex pinning and spacing in a three-dimensional ordered Josephson medium

A method of calculating the configuration of two line vortices interacting in a three-dimensional ordered Josephson medium and a minimal distance between them at a given pinning parameter is proposed. The axes of the vortices lie in the middle row of an infinite slab 9 or 13 cells thick with different conditions at the boundaries of the slab. Away from the centers of the vortices, the system of finite-difference equations becomes linear. Fluxoid quantization conditions in cells near the centers of the vortices serve as boundary conditions. An exact solution is approached by iterations in those phase discontinuities which cannot be considered small. This technique provides a much higher calculation accuracy and offers a wider domain of applicability than the earlier methods. Critical values I _d of the pinning parameter at which two initial vortices keep given spacing d between them are calculated. For various vortex configurations, maximal pinning forces are calculated as functions of the pinning parameter and the distance to the nearest vortices. It is shown that the pinning force decreases near parallel vortices and increases near antiparallel ones.     

Nonautonomous Vortices in (2+1)-Dimensional Graded-Index Waveguide

With the help of self-similarity transformation, we construct and study the nonautonomous vortices with different topological charges inside a planar graded-index nonlinear waveguide, analytically, and numerically. Although these vortices are approximate, they can reflect the real properties of self-similar optical beam during a short-term propagation. Existence of these autonomous vortices require delicate balances between the system parameters such as diffraction, nonlinearity, gain, and external potential. We are concerned with some special but interesting situations, and discussing the changes of the height, width, energy, and central position of the vortices as the increase of propagation distance. Moreover, we are also interested in the azimuthal modulational instability of the system, and comparing our prediction for the modulational instability growth rates to numerical results.