Self-organized Vortex Research Articles

Self-organized vortex phases and hydrodynamic interactions in Bos taurus sperm cells.

Flocking behavior is observed in biological systems from the cellular to superorganismal length scales, and the mechanisms and purposes of this behavior are objects of intense interest. In this paper, we study the collective dynamics of bovine sperm cells in a viscoelastic fluid. These cells appear not to spontaneously flock, but transition into a long-lived flocking phase after being exposed to a transient ordering pulse of fluid flow. Surprisingly, this induced flocking phase has many qualitative similarities with the spontaneous polar flocking phases predicted by Toner-Tu theory, such as anisotropic giant number fluctuations and nontrivial transverse density correlations, despite the induced nature of the phase and the clearly important role of momentum conservation between the swimmers and the surrounding fluid in these experiments. We also find a self-organized global vortex state of the sperm cells, and map out an experimental phase diagram of states of collective motion as a function of cell density and motility statistics. We compare our experiments with a parameter-matched computational model of persistently turning active particles and find that the experimental order-disorder phase boundary as a function of cell density and persistence time can be approximately predicted from measures of single-cell properties. Our results may have implications for the evaluation of sample fertility by studying the collective phase behavior of dense groups of swimming sperm.

Quadruple Beltrami field structures in electron–positron multi-ion plasma

Abstract A quadruple Beltrami (QB) equilibrium state for a four-component plasma that consists of inertial electrons, positrons, lighter positive (H +) ions and heavier negative ions O 2 − $\left({\mathrm{O}}_{2}^{-}\right)$ is derived and investigated. The QB relaxed state is a linear superposition of four distinct single Beltrami fields and provides the possibility of the formation of four self-organized vortices of different length scales. In addition, robust magnetofluid coupling characterizes this non-force-free state. The analysis of the QB state also shows that by adjusting the generalized helicities and densities of plasma species, the formation of multiscale structures as well as the paramagnetic and diamagnetic behavior of the relaxed state can be controlled.

Globally correlated states and control of vortex lattices in active roller fluids

Active fluids demonstrate complex collective behavior and self-organization often resulting in the emergence of localized vortices. We report on a combined experimental and computational study of the spontaneous formation of globally correlated vortex lattices formed in active roller fluids. The vortices are comprised of active ferromagnetic rollers placed on a patterned substrate promoting localization of self-organized vortices in a lattice with square symmetry. Each individual vortex spontaneously selects its chiral state (clockwise or counterclockwise). Nevertheless, confined to a square lattice, an ensemble of interacting active vortices is capable of developing correlations between chiral states of neighboring vortices. We show that such ensembles of active vortices can spontaneously evolve towards a globally correlated state with the antiferromagnetic ordering of their vorticities. We explore the correlations between chiral states of neighboring vortex pairs in response to changes in the geometry of the confining lattice. The results are supported by numerical simulations based on phenomenological coarse grained particle dynamics coupled to shallow water Navier-Stokes hydrodynamics. We show that these ordered vortex lattices formed by magnetic rollers have the ability to self-heal the antiferromagnetic order and stabilize individual vortical states in the activity regimes beyond optimal conditions for the collective vortex states. The results provide insights into the collective behavior of active magnetic roller fluids in the presence of geometrical confinement.

Self-organized multiscale structures in thermally relativistic electron-positron-ion plasmas

The self-organization of a thermally relativistic magnetized plasma comprising of electrons, positrons and static ions is investigated. The self-organized state is found to be the superposition of three distinct Beltrami fields known as triple Beltrami (TB) state. In general, the eigenvalues associated with the multiscale self-organized vortices may be a pair of complex conjugate and real one. It is shown that all the eigenvalues become real when thermal energy increases or the positron density decreases. The impact of relativistic temperature and positron density on the formation of self-organized structures is investigated. The self-organized field and flow vortices may vary simultaneously on vastly different length scales. The disparate variation of self-organized vortices is important in the context of dynamo theory. The present work is useful to study the formation of multiscale vortices and dynamo mechanisms in multi-species thermally relativistic plasmas.

Self-Organized Vortex and Antivortex Patterns in Laser Arrays

Recently it is shown that dissipatively coupled laser arrays simulate the classical XY model. We show that phase-locking of laser arrays can give rise to the spontaneous formation of vortex and antivortex phase patterns that are analogous to topological defects of the XY model. These patterns are stable although their formation is less likely in comparison to the ground state lasing mode. In addition, we show that small ratios of photon-to-gain lifetime destabilizes vortex and antivortex phase patterns. These findings are important for studying topological effects in optics as well as for designing laser array devices.

Emergence and melting of active vortex crystals

Melting of two-dimensional (2D) equilibrium crystals is a complex phenomenon characterized by the sequential loss of positional and orientational order. In contrast to passive systems, active crystals can self-assemble and melt into an active fluid by virtue of their intrinsic motility and inherent non-equilibrium stresses. Currently, the non-equilibrium physics of active crystallization and melting processes is not well understood. Here, we establish the emergence and investigate the melting of self-organized vortex crystals in 2D active fluids using a generalized Toner-Tu theory. Performing extensive hydrodynamic simulations, we find rich transition scenarios. On small domains, we identify a hysteretic transition as well as a transition featuring temporal coexistence of active vortex lattices and active turbulence, both of which can be controlled by self-propulsion and active stresses. On large domains, an active vortex crystal with solid order forms within the parameter range corresponding to active vortex lattices. The melting of this crystal proceeds through an intermediate hexatic phase. Generally, these results highlight the differences and similarities between crystalline phases in active fluids and their equilibrium counterparts.

Численное моделирование когерентных и турбулентных структур излучения методом нелинейных интегральных отображений

The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of geometries relevant to typical problems of nonlinear optics, numerical modeling by reducing to dynamical systems with discrete time and continuous spatial variables to iterates of local nonlinear Feigenbaum and Ikeda mappings and nonlocal diffusion-dispersion linear integral transforms is equivalent to partial differential equations of the Ginzburg-Landau type in a fairly wide range of parameters. Such nonlocal mappings , which are the products of matrix operators in the numerical implementation, turn out to be stable numerical-difference schemes, provide fast convergence and an adequate approximation of solutions. The realism of this approach allows one to take into account the effect of noise on nonlinear dynamics by superimposing a spatial noise specified in the form of a multimode random process at each iteration and selecting the stable wave configurations. The nonlinear wave formations described by this method include optical phase singularities, spatial solitons, and turbulent states with fast decay of correlations. The particular interest is in the periodic configurations of the electromagnetic field obtained by this numerical method that arise as a result of phase synchronization, such as optical lattices and self-organized vortex clusters.

Large-scale intermittency and rare events boosted at dimensional crossover in anisotropic turbulence

Understanding rare events in turbulence provides a basis for the science of extreme weather, for which the atmosphere is modeled by Navier-Stokes equations (NSEs). In solutions of NSEs for isotropic fluids, various quantities, such as fluid velocities, roughly follow Gaussian distributions, where extreme events are prominent only in small-scale quantities associated with the dissipation-dominating length scale or anomalous scaling regime. Using numerical simulations, this study reveals another universal promotion mechanism at much larger scales if three-dimensional fluids accompany strong two-dimensional anisotropies, as is the case in the atmosphere. The dimensional crossover between two and three dimensions generates prominent fat-tailed non-Gaussian distributions with intermittency accompanied by colossal chain-like structures with densely populated self-organized vortices (serpentinely organized vortices (SOV)). The promotion is caused by a sudden increase of the available phase space at the crossover length scale. Since the discovered intermittency can involve much larger energies than those in the conventional intermittency in small spatial scales, it governs extreme events and chaotic unpredictability in the synoptic weather system.

Manipulation of emergent vortices in swarms of magnetic rollers

Active colloids are an emergent class of out-of-equilibrium materials demonstrating complex collective phases and tunable functionalities. Microscopic particles energized by external fields exhibit a plethora of fascinating collective phenomena, yet mechanisms of control and manipulation of active phases often remains lacking. Here we report the emergence of unconfined macroscopic vortices in a system of ferromagnetic rollers energized by a vertical alternating magnetic field and elucidate the complex nature of a magnetic roller-vortex interactions with inert scatterers. We demonstrate that active self-organized vortices have an ability to spontaneously switch the direction of rotation and move across the surface. We reveal the capability of certain non-active particles to pin the vortex and manipulate its dynamics. Building on our findings, we demonstrate the potential of magnetic roller vortices to effectively capture and transport inert particles at the microscale.

Self-organized vortices of circling self-propelled particles and curved active flagella

Self-propelled pointlike particles move along circular trajectories when their translocation velocity is constant and the angular velocity related to their orientation vector is also constant. We investigate the collective behavior of ensembles of such circle swimmers by Brownian dynamics simulations. If the particles interact via a "velocity-trajectory coordination" rule within neighboring particles, a self-organized vortex pattern emerges. This vortex pattern is characterized by its particle-density correlation function Gρ, the density correlation function Gc of trajectory centers, and an order parameter S representing the degree of the aggregation of the particles. Here we systematically vary the system parameters, such as the particle density and the interaction range, in order to reveal the transition of the system from a light-vortex-dominated to heavy-vortex-dominated state, where vortices contain mainly a single and many self-propelled particles, respectively. We also study a semidilute solution of curved, sinusoidal-beating flagella, as an example of circling self-propelled particles with explicit propulsion mechanism and excluded-volume interactions. Our simulation results are compared with previous experimental results for the vortices in sea-urchin sperm solutions near a wall. The properties of the vortices in simulations and experiments are found to agree quantitatively.

Numerical simulation and flow visualization using soap film of the self-organized vortex structure in the wake of an array of cylinders

With the aid of computational fluid dynamics (CFD) and simple flow visualization technique using flowing soap-film, we present here the wake structures behind an array of cylinders for Reynolds numbers corresponding to both laminar and turbulent flow regimes. The image results illustrate interesting vortex interactions past these equally spaced cylinders; for low Reynolds number flow, well-organized wake pattern persists and manifests unsteadily to different symmetry states. An increase of free stream flow velocity causes the wake transition, resulting in the formation of asymmetric flow wake with chaotic mixing at the far wake. Observations from both the numerical simulations and soap-film are in good agreement at least qualitatively.

Self-organized vortex multiplets in swirling flow

The possibility of double vortex multiplet formation at the center of an intensively swirling cocurrent flow generated in a cylindrical container by its rotating lid is reported for the first time. The boundary of the transition to unsteady flow regimes, which arise as a result of the equilibrium rotation of self-organized vortex multiplets (triplet, double triplet, double doublet, and quadruplet), has been experimentally determined for cylinders with the aspect (height to radius) ratios in a wider interval than that studied previously.

Poetry in Motion

The cooperative organization of dynamic biological processes often requires coordination via chemical signaling. Riedel et al. found that, when attached to a surface, a critical number of sperm cells self-organized into a hexagonally packed array of rotating vortices where each vortex consisted of about 10 hydrodynamically synchronized cells forming a quantized rotating wave. This spatial-temporal pattern of entrained sperm cells formed in the absence of chemical cell-cell signaling, leading to a new coordination concept of cooperative cilia and flagella. Thus, single cells and microorganisms can be hydrodynamically coordinated without the need for chemical signaling. I. H. Riedel, K. Kruse, J. Howard, A self-organized vortex array of hydrodynamically entrained sperm cells. Science 309 , 300-303 (2005). [Abstract] [Full Text]

A Self-Organized Vortex Array of Hydrodynamically Entrained Sperm Cells

Many patterns in biological systems depend on the exchange of chemical signals between cells. We report a spatiotemporal pattern mediated by hydrodynamic interactions. At planar surfaces, spermatozoa self-organized into dynamic vortices resembling quantized rotating waves. These vortices formed an array with local hexagonal order. Introducing an order parameter that quantifies cooperativity, we found that the array appeared only above a critical sperm density. Using a model, we estimated the hydrodynamic interaction force between spermatozoa to be approximately 0.03 piconewtons. Thus, large-scale coordination of cells can be regulated hydrodynamically, and chemical signals are not required.

磁気顕微鏡による磁束観測

Recently, vortices confined into micro-scale superconductors with shapes like a disk, triangle, square, etc., have attracted much attention because of the quantum phase transition of the self-organized vortex arrangement occurring within such geometrical constraints. Such a transition can be observed using a scanning SQUID microscope with high spatial resolution. We have successfully improved spatial resolution by incorporating a microfabrication technique that reduces both the size of the pick-up coil of the micro DC-SQUID and the standoff distance between the pick-up coil and the sample surface. Using this microscope, we have studied vortex arrangements in micro-scale superconductors made of Nb and YBa2Cu3O7−δ films with various sizes and geometrical shapes. A peculiar oscillating behavior of diamagnetic magnetization corresponding to the particular vortex state was observed.

Defects and self-organized vortices in melt-textured YBa2Cu3O7-x

This paper presents the structural as well as the magnetic properties of high-quality YBa2Cu3O7-x melt-textured material, before and after 2 GeV Au ion irradiation. The irradiation affects a surface layer of about 10% of the whole sample thickness. The core of the paper consists in the investigation of the behaviour of the critical current densities Jc and the pinning forces Fp as a function of the magnetic field. The pinning forces are analysed using a modified Dew-Hughes model. Particular emphasis is given to the influence of different kinds of defects, evaluated at 65 and 75 K, before and after irradiation. The low-current regime is also investigated by means of the irreversibility line evaluation. It is shown that at higher temperature the main properties of the irradiated samples are determined by the competition and/or correlation between surface columnar defects and intrinsic defects, distributed inside the full volume. The vortices trapped in the surface layer by the columnar defects seem to contribute to organize the matching phenomena between the defect lattice and the vortex lattice, at fields near and above the dose-equivalent field.

Self-organized Vortex State in Two-DimensionalDictyosteliumDynamics

We present results of experiments on the dynamics of Dictyostelium discoideum in a novel set-up which constraints cell motion to a plane. After aggregation, the amoebae collect into round ''pancake" structures in which the cells rotate around the center of the pancake. This vortex state persists for many hours and we have explicitly verified that the motion is not due to rotating waves of cAMP. To provide an alternative mechanism for the self-organization of the Dictyostelium cells, we have developed a new model of the dynamics of self-propelled deformable objects. In this model, we show that cohesive energy between the cells, together with a coupling between the self-generated propulsive force and the cell's configuration produces a self-organized vortex state. The angular velocity profiles of the experiment and of the model are qualitatively similar. The mechanism for self-organization reported here can possibly explain similar vortex states in other biological systems.

Classification of self-organized vortices in two-dimensional turbulence: the case of a bounded domain

We calculate steady solutions of the Euler equations for any given value of energy and circulation (and angular momentum in the case of a circular domain). A linear relationship between vorticity and stream function is assumed. These solutions correspond to the predicted self-organization into a maximum-entropy state, in the limit of strong mixing. Vorticity mixing is then only weakly restricted by the constraint of energy conservation. While maximum-entropy solutions depend in general on the whole probability distribution of vorticity levels, these linearized results depend only on a single control parameter, yet keeping much of the general structure of the problem. A convenient classification of the maximum-entropy states is thus provided. We show furthermore how to extend these linearized results as an expansion in energy, involving successive moments of the vorticity probability distribution. They are applied to a rectangular domain and compared with existing numerical and laboratory results. We predict that the flow organizes into a single vortex in the square domain, but into a two-vortex dipolar state in a rectangle with aspect ratio greater than 1.12. The case of a circular domain is also explicitly solved, taking into account the conservation of the angular momentum.