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

Chaos in Shear Flows

Almost 25 years ago Lorenz published his seminal study on the existence of a strange attractor in the phase space of a severely truncated model system arising from the hydrodynamical equations describing two-dimensional convection. Nearly a century ago Poincare published his famous treatise Les Methodes Noovelles de la Mecaniaue Celeste (1892) in which the possible complexity of behavior in nonintegrable, conservative systems was first envisioned. Both these works address an age old puzzle: How do apparently stochastic outputs arise from an entirely deterministic system subject to non-stochastic inputs

Perbandingan Tingkat Kesegaran Jasmani Siwa Kelas V Sdn 012 Harapan Jaya dengan Siswa Sdn 010 Karya Mukti Kabupaten Rokan Hilir

, Background problem in this study originated from differences in the location of the school, students\u27 physical activity, facilities and infrastructure in schools so that the resulting differences in physical fitness level of the students of SDN 012 Harapan Jaya and SDN Karya Mukti 0101. However, in the absence of accurate data on the level of physical fitness student researcher interested in conducting research on these issues. Therefore, the purpose of this study was to determine whether there are differences in the level of physical fitness at students class V SDN 012 and SDN 010 Harapan jaya Karya Mukti Rokan Hilir District. This type of research is classified in Comparative research, Sugiono in Ridwan (2002: 50) argues that "Comparative research is research that aims to compare the results of the two groups of data". The research data was obtained from the measurement results TKJI test. The sample in this study is the female students class V from each school totaling 28 people (purposive sampling). Based on the research results can be concluded as follows: Once t test then obtained thitung (2.49)> t table (2.179), where Ho is rejected and Ha is received, it can be concluded that there are differences in the physical fitness of students SDN 012 Harapan Jaya SDN 010 KaryaMukti Rokan Hilir District, where the level of physical fitness of students SDN 012 Harapan Jaya better when compared with students of SDN 010 Karya Mukti Rokan Hilir

Excitable media in open and closed chaotic flows

We investigate the response of an excitable medium to a localized perturbation in the presence of a two-dimensional smooth chaotic flow. Two distinct types of flows are numerically considered: open and closed. For both of them three distinct regimes are found, depending on the relative strengths of the stirring and the rate of the excitable reaction. In order to clarify and understand the role of the many competing mechanisms present, simplified models of the process are introduced. They are one-dimensional baker-map models for the flow and a one-dimensional approximation for the transverse profile of the filaments.Comment: 14 pages, 16 figure

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

Echoes in classical dynamical systems

Echoes arise when external manipulations to a system induce a reversal of its time evolution that leads to a more or less perfect recovery of the initial state. We discuss the accuracy with which a cloud of trajectories returns to the initial state in classical dynamical systems that are exposed to additive noise and small differences in the equations of motion for forward and backward evolution. The cases of integrable and chaotic motion and small or large noise are studied in some detail and many different dynamical laws are identified. Experimental tests in 2-d flows that show chaotic advection are proposed.Comment: to be published in J. Phys.