Interaction of point sources and vortices for incompressible planar fluids

We consider a new system of differential equations which is at the same time gradient and locally Hamiltonian. It is obtained by just replacing a factor in the equations of interaction for N point vortices, and it is interpreted as an interaction of N point sources. Because of the local Hamiltonian structure and the symmetries it obeys, it does possess some of the first integrals that appear in the N vortex problem. We will show that binary collisions are easily blown up in this case since the equations of motion are of first order. This method may be easily generalized to the blow up of higher order collisions. We then generalize the model further to interactions of sources and vortices.Comment: 9 page

Vortex crystals

Vortex crystals is one name in use for the subject of vortex patterns that move without change of shape or size. Most of what is known pertains to the case of arrays of parallel line vortices moving so as to produce an essentially two-dimensional flow. The possible patterns of points indicating the intersections of these vortices with a plane perpendicular to them have been studied for almost 150 years. Analog experiments have been devised, and experiments with vortices in a variety of fluids have been performed. Some of the states observed are understood analytically. Others have been found computationally to high precision. Our degree of understanding of these patterns varies considerably. Surprising connections to the zeros of 'special functions' arising in classical mathematical physics have been revealed. Vortex motion on two-dimensional manifolds, such as the sphere, the cylinder (periodic strip) and torus (periodic parallelogram) has also been studied, because of the potential applications, and some results are available regarding the problem of vortex crystals in such geometries. Although a large amount of material is available for review, some results are reported here for the first time. The subject seems pregnant with possibilities for further development.published or submitted for publicationis peer reviewe

Viscous evolution of point vortex equilibria: The collinear state

When point vortex equilibria of the 2D Euler equations are used as initial conditions for the corre- sponding Navier-Stokes equations (viscous), typically an interesting dynamical process unfolds at short and intermediate time scales, before the long time single peaked, self-similar Oseen vortex state dom- inates. In this paper, we describe the viscous evolution of a collinear three vortex structure that cor- responds to an inviscid point vortex fixed equilibrium. Using a multi-Gaussian 'core-growth' type of model, we show that the system immediately begins to rotate unsteadily, a mechanism we attribute to a 'viscously induced' instability. We then examine in detail the qualitative and quantitative evolution of the system as it evolves toward the long-time asymptotic Lamb-Oseen state, showing the sequence of topological bifurcations that occur both in a fixed reference frame, and in an appropriately chosen rotating reference frame. The evolution of passive particles in this viscously evolving flow is shown and interpreted in relation to these evolving streamline patterns.Comment: 17 pages, 15 figure

Self-adaptive hybrid genetic algorithm using an ant-based algorithm

The pheromone trail metaphor is a simple and effective way to accumulate the experience of the past solutions in solving discrete optimization problems. Ant-based optimization algorithms have been successfully employed to solve hard optimization problems. The problem of achieving an optimal utilization of a hybrid genetic algorithm search time is actually a problem of finding its optimal set of control parameters. In this paper, a novel form of hybridization between an ant-based algorithm and a genetic-local hybrid algorithm is proposed. An ant colony optimization algorithm is used to monitor the behavior of a genetic-local hybrid algorithm and dynamically adjust its control parameters to optimize the exploitation-exploration balance according to the fitness landscape

Accelerating genetic schema processing through local search

peer reviewedAchieving a balance between the exploration and exploitation capabilities of genetic algorithms is a key factor for their success in solving complicated search problems. Incorporating a local search method within a genetic algorithm can enhance the exploitation of local knowledge but it risks decelerating the schema building process. This paper defines some features of a local search method that might improve the balance between exploration and exploitation of genetic algorithms. Based on these features a probabilistic local search method is proposed. The proposed search method has been tested as a secondary method within a staged hybrid genetic algorithm and as a standalone method. The experiments conducted showed that the proposed method can speed up the search without affecting the schema processing of genetic algorithms. The experiments also showed that the proposed algorithm as a standalone algorithm can, in some cases, outperform a pure genetic algorithm

Kontribusi Daya Ledak Otot Tungkai dan Koordinasi Mata dan Kaki dengan Akurasi Shooting Ssb Patriot Muda Kuok

Based on observations on a player School Football Patriot Muda Kuok that shooting players who follow exercise football still not good, it is revealed that limited capability players especially in doing shooting who directed and effectively who is in what. The purpose of this research is to know how big contribution explosive power limb muscles and coordination eyes and feet with accuracy shooting in School Football Patriot Muda Kuok. Population in this study a whole object research, namely soccer players players school football patriot young kuok, consisting of 18 people, by using total of sampling, so sample in this research was 18 people. An instrument too was vertical synchronization jump, coordination eyes and feet and test shooting. Data obtained in analysis with employing correlation product moment, To determine contribution used the coefficients determinan. Of the results obtained explosive power limb muscles have become with accuracy shooting in Schools Football Patriot Muda Kuok is as much as 25,81 %. Of the results obtained coordination the ankles have become with accuracy shooting in School Football Patriot Muda Kuok 32,26 % as much as. There were the contribution of jointly between explosive power limb muscles and coordination the eye the foot against the accuracy of the shooting scene in schools football young patriot kuok 34,69 % as much as

Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities

We examine in detail the relative equilibria in the four-vortex problem where two pairs of vortices have equal strength, that is, \Gamma_1 = \Gamma_2 = 1 and \Gamma_3 = \Gamma_4 = m where m is a nonzero real parameter. One main result is that for m > 0, the convex configurations all contain a line of symmetry, forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for all m but the isosceles trapezoid case exists only when m is positive. In fact, there exist asymmetric convex configurations when m < 0. In contrast to the Newtonian four-body problem with two equal pairs of masses, where the symmetry of all convex central configurations is unproven, the equations in the vortex case are easier to handle, allowing for a complete classification of all solutions. Precise counts on the number and type of solutions (equivalence classes) for different values of m, as well as a description of some of the bifurcations that occur, are provided. Our techniques involve a combination of analysis and modern and computational algebraic geometry