Enhancement of the Benjamin-Feir instability with dissipation

It is shown that there is an overlooked mechanism whereby some kinds of dissipation can enhance the Benjamin-Feir instability of water waves. This observation is new, and although it is counterintuitive, it is due to the fact that the Benjamin-Feir instability involves the collision of modes with opposite energy sign (relative to the carrier wave), and it is the negative energy perturbations which are enhanced.Comment: 15 pages, 2 figures To download more papers, go to http://www.cmla.ens-cachan.fr/~dias. Physics of Fluids (2007) to appea

Magnetoelliptic Instabilities

We consider the stability of a configuration consisting of a vertical magnetic field in a planar flow on elliptical streamlines in ideal hydromagnetics. In the absence of a magnetic field the elliptical flow is universally unstable (the ``elliptical instability''). We find this universal instability persists in the presence of magnetic fields of arbitrary strength, although the growthrate decreases somewhat. We also find further instabilities due to the presence of the magnetic field. One of these, a destabilization of Alfven waves, requires the magnetic parameter to exceed a certain critical value. A second, involving a mixing of hydrodynamic and magnetic modes, occurs for all magnetic-field strengths. These instabilities may be important in tidally distorted or otherwise elliptical disks. A disk of finite thickness is stable if the magnetic fieldstrength exceeds a critical value, similar to the fieldstrength which suppresses the magnetorotational instability.Comment: Accepted for publication in Astrophysical Journa

Quadratic invariants for discrete clusters of weakly interacting waves

We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix with entries 1, −1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J ≡ N − M* ≥ N − M, where M* is the number of linearly independent rows in Thus, the problem of finding all independent quadratic invariants is reduced to a linear algebra problem in the Hamiltonian case. We establish that the properties of the quadratic invariants (e.g., locality) are related to the topological properties of the clusters (e.g., types of linkage). To do so, we formulate an algorithm for decomposing large clusters into smaller ones and show how various invariants are related to certain parts of a cluster, including the basic structures leading to M* < M. We illustrate our findings by presenting examples from the Charney–Hasegawa–Mima wave model, and by showing a classification of small (up to three-triad) clusters

On over-reflection and generation of Gravito-Alfven waves in solar-type stars

The dynamics of linear perturbations is studied in magnetized plasma shear flows with a constant shearing rate and with gravity-induced stratification. The general set of linearized equations is derived and the two-dimensional case is considered in detail. The Boussinesq approximation is used in order to examine relatively small-scale perturbations of low-frequency modes: Gravito-Alfven waves (GAW) and Entropy Mode (EM) perturbations. It is shown that for flows with arbitrary shearing rate there exists a finite time interval of non-adiabatic evolution of the perturbations. The non-adiabatic behavior manifests itself in a twofold way, viz. by the over-reflection of the GAWs and by the generation of GAWs from EM perturbations. It is shown that these phenomena act as efficient transformers of the equilibrium flow energy into the energy of the perturbations for moderate and high shearing rate solar plasma flows. Efficient generation of GAW by EM takes place for shearing rates about an order of magnitude smaller than necessary for development of a shear instability. The latter fact could have important consequences for the problem of angular momentum redistribution within the Sun and solar-type stars.Comment: 20 pages (preprint format), 4 figures; to appear in The Astrophysical Journal (August 1, 2007, v664, N2 issue

The evolution of representation in simple cognitive networks

Representations are internal models of the environment that can provide guidance to a behaving agent, even in the absence of sensory information. It is not clear how representations are developed and whether or not they are necessary or even essential for intelligent behavior. We argue here that the ability to represent relevant features of the environment is the expected consequence of an adaptive process, give a formal definition of representation based on information theory, and quantify it with a measure R. To measure how R changes over time, we evolve two types of networks---an artificial neural network and a network of hidden Markov gates---to solve a categorization task using a genetic algorithm. We find that the capacity to represent increases during evolutionary adaptation, and that agents form representations of their environment during their lifetime. This ability allows the agents to act on sensorial inputs in the context of their acquired representations and enables complex and context-dependent behavior. We examine which concepts (features of the environment) our networks are representing, how the representations are logically encoded in the networks, and how they form as an agent behaves to solve a task. We conclude that R should be able to quantify the representations within any cognitive system, and should be predictive of an agent's long-term adaptive success.Comment: 36 pages, 10 figures, one Tabl

Deep GMRT radio observations and a multi-wavelength study of the region around HESS J1858+020

Context. There are a number of very high energy sources in the Galaxy that remain unidentified. Multi-wavelength and variability studies, and catalogue searches, are powerful tools to identify the physical counterpart, given the uncertainty in the source location and extension. Aims. This work carries out a thorough multi-wavelength study of the unidentified, very high energy source HESS J1858+020 and its environs. Methods. We have performed Giant Metrewave Radio Telescope observations at 610 MHz and 1.4 GHz to obtain a deep, low-frequency radio image of the region surrounding HESS J1858+020. We analysed archival radio, infrared, and X-ray data as well. This observational information, combined with molecular data, catalogue sources, and a nearby Fermi gamma-ray detection of unidentified origin, are combined to explore possible counterparts to the very high energy source. Results. We provide with a deep radio image of a supernova remnant that might be related to the GeV and TeV emission in the region. We confirm the presence of an H ii region next to the supernova remnant and coincident with molecular emission. A potential region of star formation is also identified. We identify several radio and X-ray sources in the surroundings. Some of these sources are known planetary nebulae, whereas others may be non-thermal extended emitters and embedded young stellar objects. Three old, background Galactic pulsars also neighbour HESS J1858+020 along the line of sight. Conclusions. The region surrounding HESS J1858+020 is rich in molecular structures and non-thermal objects that may potentially be linked to this unidentified very high energy source. In particular, a supernova remnant interacting with nearby molecular clouds may be a good candidate, but a star forming region, or a non-thermal radio source of yet unclear nature, may also be behind the gamma-ray source. The neighbouring pulsars, despite being old and distant, cannot be discarded as candidates. Further observational studies are needed, however, to narrow the search for a counterpart to the HESS source

The Magnetohydrodynamic Kelvin-Helmholtz Instability: A Three-Dimensional Study of Nonlinear Evolution

We investigate through high resolution 3D simulations the nonlinear evolution of compressible magnetohydrodynamic flows subject to the Kelvin-Helmholtz instability. We confirm in 3D flows the conclusion from our 2D work that even apparently weak magnetic fields embedded in Kelvin-Helmholtz unstable plasma flows can be fundamentally important to nonlinear evolution of the instability. In fact, that statement is strengthened in 3D by this work, because it shows how field line bundles can be stretched and twisted in 3D as the quasi-2D Cat's Eye vortex forms out of the hydrodynamical motions. In our simulations twisting of the field may increase the maximum field strength by more than a factor of two over the 2D effect. If, by these developments, the Alfv\'en Mach number of flows around the Cat's Eye drops to unity or less, our simulations suggest magnetic stresses will eventually destroy the Cat's Eye and cause the plasma flow to self-organize into a relatively smooth and apparently stable flow that retains memory of the original shear. For our flow configurations the regime in 3D for such reorganization is $4\lesssim M_{Ax} \lesssim 50$, expressed in terms of the Alfv\'en Mach number of the original velocity transition and the initial Alfv\'en speed projected to the flow plan. For weaker fields the instability remains essentially hydrodynamic in early stages, and the Cat's Eye is destroyed by the hydrodynamic secondary instabilities of a 3D nature. Then, the flows evolve into chaotic structures that approach decaying isotropic turbulence. In this stage, there is considerable enhancement to the magnetic energy due to stretching, twisting, and turbulent amplification, which is retained long afterwards. The magnetic energy eventually catches up to the kinetic energy, and the nature of flows become magnetohydrodynamic.Comment: 11 pages, 12 figures in degraded jpg format (2 in color), paper with original quality figures available via ftp at ftp://ftp.msi.umn.edu/pub/users/twj/mhdkh3dd.ps.gz or ftp://canopus.chungnam.ac.kr/ryu/mhdkh3dd.ps.gz, to appear in The Astrophysical Journa

I owe you: age-related similarities and differences in associative memory for gains and losses

Older adults often experience associative memory impairments but can sometimes remember important information. The current experiments investigate potential age-related similarities and differences associate memory for gains and losses. Younger and older participants were presented with faces and associated dollar amounts, which indicated how much money the person “owed” the participant, and were later given a cued recall test for the dollar amount. Experiment 1 examined face-dollar amount pairs while Experiment 2 included negative dollar amounts to examine both gains and losses. While younger adults recalled more information relative to older adults, both groups were more accurate in recalling the correct value associated with high value faces compared to lower value faces and remembered gist-information about the values. However, negative values (losses) did not have a strong impact on recall among older adults versus younger adults, illustrating important associative memory differences between younger and older adults