Stabilized Kuramoto-Sivashinsky system

A model consisting of a mixed Kuramoto - Sivashinsky - KdV equation, linearly coupled to an extra linear dissipative equation, is proposed. The model applies to the description of surface waves on multilayered liquid films. The extra equation makes its possible to stabilize the zero solution in the model, opening way to the existence of stable solitary pulses (SPs). Treating the dissipation and instability-generating gain in the model as small perturbations, we demonstrate that balance between them selects two steady-state solitons from their continuous family existing in the absence of the dissipation and gain. The may be stable, provided that the zero solution is stable. The prediction is completely confirmed by direct simulations. If the integration domain is not very large, some pulses are stable even when the zero background is unstable. Stable bound states of two and three pulses are found too. The work was supported, in a part, by a joint grant from the Israeli Minsitry of Science and Technology and Japan Society for Promotion of Science.Comment: A text file in the latex format and 20 eps files with figures. Physical Review E, in pres

Turbulent flow structure in meandering vegetated open channel

River hydrodynamicsTurbulent open channel flow and transport phenomen

Extracting Multidimensional Phase Space Topology from Periodic Orbits

We establish a hierarchical ordering of periodic orbits in a strongly coupled multidimensional Hamiltonian system. Phase space structures can be reconstructed quantitatively from the knowledge of periodic orbits alone. We illustrate our findings for the hydrogen atom in crossed electric and magnetic fields.Comment: 4 pages, 5 figures, accepted for publication in Phys. Rev. Let

Exact Periodic Solutions of Shells Models of Turbulence

We derive exact analytical solutions of the GOY shell model of turbulence. In the absence of forcing and viscosity we obtain closed form solutions in terms of Jacobi elliptic functions. With three shells the model is integrable. In the case of many shells, we derive exact recursion relations for the amplitudes of the Jacobi functions relating the different shells and we obtain a Kolmogorov solution in the limit of infinitely many shells. For the special case of six and nine shells, these recursions relations are solved giving specific analytic solutions. Some of these solutions are stable whereas others are unstable. All our predictions are substantiated by numerical simulations of the GOY shell model. From these simulations we also identify cases where the models exhibits transitions to chaotic states lying on strange attractors or ergodic energy surfaces.Comment: 25 pages, 7 figure

Laser-induced fluorescence imaging of plants using a liquid crystal tunable filter and charge coupled device imaging camera

ArticleReview of Scientific Instruments. 76, 106103 (2005)journal articl

Radial velocity eclipse mapping of exoplanets

Planetary rotation rates and obliquities provide information regarding the history of planet formation, but have not yet been measured for evolved extrasolar planets. Here we investigate the theoretical and observational perspective of the Rossiter-McLauglin effect during secondary eclipse (RMse) ingress and egress for transiting exoplanets. Near secondary eclipse, when the planet passes behind the parent star, the star sequentially obscures light from the approaching and receding parts of the rotating planetary surface. The temporal block of light emerging from the approaching (blue-shifted) or receding (red-shifted) parts of the planet causes a temporal distortion in the planet's spectral line profiles resulting in an anomaly in the planet's radial velocity curve. We demonstrate that the shape and the ratio of the ingress-to-egress radial velocity amplitudes depends on the planetary rotational rate, axial tilt and impact factor (i.e. sky-projected planet spin-orbital alignment). In addition, line asymmetries originating from different layers in the atmosphere of the planet could provide information regarding zonal atmospheric winds and constraints on the hot spot shape for giant irradiated exoplanets. The effect is expected to be most-pronounced at near-infrared wavelengths, where the planet-to-star contrasts are large. We create synthetic near-infrared, high-dispersion spectroscopic data and demonstrate how the sky-projected spin axis orientation and equatorial velocity of the planet can be estimated. We conclude that the RMse effect could be a powerful method to measure exoplanet spins.Comment: 7 pages, 3 figures, 1 table, accepted for publication in ApJ on 2015 June 1

Studies of Phase Turbulence in the One Dimensional Complex Ginzburg-Landau Equation

The phase-turbulent (PT) regime for the one dimensional complex Ginzburg-Landau equation (CGLE) is carefully studied, in the limit of large systems and long integration times, using an efficient new integration scheme. Particular attention is paid to solutions with a non-zero phase gradient. For fixed control parameters, solutions with conserved average phase gradient $\nu$ exist only for $|\nu|$ less than some upper limit. The transition from phase to defect-turbulence happens when this limit becomes zero. A Lyapunov analysis shows that the system becomes less and less chaotic for increasing values of the phase gradient. For high values of the phase gradient a family of non-chaotic solutions of the CGLE is found. These solutions consist of spatially periodic or aperiodic waves travelling with constant velocity. They typically have incommensurate velocities for phase and amplitude propagation, showing thereby a novel type of quasiperiodic behavior. The main features of these travelling wave solutions can be explained through a modified Kuramoto-Sivashinsky equation that rules the phase dynamics of the CGLE in the PT phase. The latter explains also the behavior of the maximal Lyapunov exponents of chaotic solutions.Comment: 16 pages, LaTeX (Version 2.09), 10 Postscript-figures included, submitted to Phys. Rev.

On the shape of a D-brane bound state and its topology change

As is well known, coordinates of D-branes are described by NxN matrices. From generic non-commuting matrices, it is difficult to extract physics, for example, the shape of the distribution of positions of D-branes. To overcome this problem, we generalize and elaborate on a simple prescription, first introduced by Hotta, Nishimura and Tsuchiya, which determines the most appropriate gauge to make the separation between diagonal components (D-brane positions) and off-diagonal components. This prescription makes it possible to extract the distribution of D-branes directly from matrices. We verify the power of it by applying it to Monte-Carlo simulations for various lower dimensional Yang-Mills matrix models. In particular, we detect the topology change of the D-brane bound state for a phase transition of a matrix model; the existence of this phase transition is expected from the gauge/gravity duality, and the pattern of the topology change is strikingly similar to the counterpart in the gravity side, the black hole/black string transition. We also propose a criterion, based on the behavior of the off-diagonal components, which determines when our prescription gives a sensible definition of D-brane positions. We provide numerical evidence that our criterion is satisfied for the typical distance between D-branes. For a supersymmetric model, positions of D-branes can be defined even at a shorter distance scale. The behavior of off-diagonal elements found in this analysis gives some support for previous studies of D-brane bound states.Comment: 29 pages, 16 figure