Universal trapping scaling on the unstable manifold for a collisionless electrostatic mode

An amplitude equation for an unstable mode in a collisionless plasma is derived from the dynamics on the two-dimensional unstable manifold of the equilibrium. The mode amplitude $\rho(t)$ decouples from the phase due to the spatial homogeneity of the equilibrium, and the resulting one-dimensional dynamics is analyzed using an expansion in $\rho$. As the linear growth rate $\gamma$ vanishes, the expansion coefficients diverge; a rescaling $\rho(t)\equiv\gamma^2\,r(\gamma t)$ of the mode amplitude absorbs these singularities and reveals that the mode electric field exhibits trapping scaling $|E_1|\sim\gamma^2$ as $\gamma\rightarrow0$. The dynamics for $r(\tau)$ depends only on the phase $e^{i\xi}$ where $d\epsilon_{{k}} /dz=|{\epsilon_{{k}}}|e^{-i\xi/2}$ is the derivative of the dielectric as $\gamma\rightarrow0$.Comment: 11 pages (Latex/RevTex), 2 figures available in hard copy from the Author ([email protected]); paper accepted by Physical Review Letter

Parity Violation in Neutron Capture Reactions

In the last decade, the scattering of polarized neutrons on compound nucleus resonances proved to be a powerful experimental technique for probing nuclear parity violation. Longitudinal analyzing powers in neutron transmission measurements on p-wave resonances in nuclei such as $^{139}$La and $^{232}$Th were found to be as large as 10%. Here we examine the possibilities of carrying out a parallel program to measure asymmetries in the $(n,\gamma$) reaction on these same compound nuclear resonances. Symmetry-violating $(n,\gamma$) studies can also show asymmetries as large as 10%, and have the advantage over transmission experiments of allowing parity-odd asymmetries in several different gamma-decay branches from the same resonance. Thus, studies of parity violation in the $(n,\gamma)$ reaction using high efficiency germanium detectors at the Los Alamos Lujan facility, for example, could determine the parity-odd nucleon-nucleon matrix elements in complex nuclei with high accuracy. Additionally, simultaneous studies of the E1 and $V_{PNC}$ matrix elements invol ved in these decays could be used to help constrain the statistical theory of parity non-conservation in compound nuclei.Comment: 10 pages, 1 figur

On asymptotic nonlocal symmetry of nonlinear Schr\"odinger equations

A concept of asymptotic symmetry is introduced which is based on a definition of symmetry as a reducibility property relative to a corresponding invariant ansatz. It is shown that the nonlocal Lorentz invariance of the free-particle Schr\"odinger equation, discovered by Fushchych and Segeda in 1977, can be extended to Galilei-invariant equations for free particles with arbitrary spin and, with our definition of asymptotic symmetry, to many nonlinear Schr\"odinger equations. An important class of solutions of the free Schr\"odinger equation with improved smoothing properties is obtained

Bifurcations in the wake of a thick circular disk

Using DNS, we investigate the dynamics in the wake of a circular disk of aspect ratio χ = d/w = 3(where d is the diameter and w the thickness) embedded in a uniform flow of magnitude U0 perpendicular to its symmetry axis. As the Reynolds number Re = U0d/ν is increased, the flow is shown to experience an original series of bifurcations leading to chaos. The range Re ∈ [150, 218] is analysed in detail. In this range, five different non-axisymmetric regimes are successively encountered, including states similar to those previously identified in the flow past a sphere or an infinitely thin disk, as well as a new regime characterised by the presence of two distinct frequencies. A theoretical model based on the theory of mode interaction with symmetries, previously introduced to explain the bifurcations in the flow past a sphere or an infinitely thin disk (Fabre et al. in Phys Fluids 20:051702, 2008), is shown to explain correctly all these results. Higher values of the Reynolds number, up to 270, are also considered. Results indicate that the flow encounters at least four additional bifurcations before reaching a chaotic state

Parity Nonconservation in Neutron Resonances in 133Cs

Spatial parity nonconservation (PNC) has been studied in the compound-nuclear states of 134Cs by measuring the helicity dependence of the neutron total cross section. Transmission measurements on a thick 133Cs target were performed by the time-of-flight method at the Manuel Lujan Neutron Scattering Center with a longitudinally polarized neutron beam in the energy range from 5 to 400 eV. A total of 28 new p-wave resonances were found, their neutron widths determined, and the PNC longitudinal asymmetries of the resonance cross sections measured. The value obtained for the root-mean-square PNC element M=(0.06-0.02+0.25) meV in 133Cs is the smallest among all targets studied. This value corresponds to a weak spreading width Γw=(0.006-0.003+0.154)×10-7 eV

Book Reviews

Wesleyan Perspectives on the New Creation M. Douglas Meeks, ed. Nashville: Kingswood, 2004, 200 pp., paper, 2004, $30.00 Reviewed by William J Abraham Christ Plays in Ten Thousand Places Eugene H. Peterson Grand Rapids, Michigan: William B. Eerdmans Publishing Company 2005, xii, 368pp. cloth,$25.00 Reviewed by Elaine A. Heath The Evangelical Moment: The Promise of an American Religion By Kenneth J. Collins Grand Rapids: Baker Academic Press 2005, 288 pp., paper, 22.99 Reviewed by Nathan Crawford Theology as History and Hermeneutics: A Post-Critical Evangelical Conversation with Contemporary Theology Laurence W. Wood Lexington: Emeth Publisher 2004, 261 pp. Reviewed by Nathan Crawford Resistance and Theological Ethics Ronald H. Stone and Robert L. Stivers, eds. Lanham, Maryland: Roman & Littlefield Publishers 2004, ri, 334 pp. paper, 28.95 Reviewed by Joerg Rieger The Ripple Church: Multiply Your Ministry by Parenting New Churches Phil Stevenson Indianapolis, IN: Wesleyan Publishing House 2004. pp. 186, $12.99. Reviewed by J.D. Payne The Struggle to Understand Isaiah as Christian Scripture Brevard S. Childs Grand Rapids, Michigan: Wm. B. Eerdmans Publishing Co. 2004, xii, 332 pp. caseboulld,$35.00 Reviewed by John N. Oswalt God is Not Religious, Nice, One of Us, an American, a Capitalist D. Brent Laytham, ed. Grand Rapids, Michigan: Press. 2004, 152 pp., paper, $15.99 Reviewed by Michael Rynkiwitch A Short Introduction to Hermeneutics David Jasper Louisville, KY: Westmilnster John Knox Press 2004, xii, 148 pp. paper,$19.95 Reviewed by Charles M. Woo

Parametrically Excited Surface Waves: Two-Frequency Forcing, Normal Form Symmetries, and Pattern Selection

Motivated by experimental observations of exotic standing wave patterns in the two-frequency Faraday experiment, we investigate the role of normal form symmetries in the pattern selection problem. With forcing frequency components in ratio m/n, where m and n are co-prime integers, there is the possibility that both harmonic and subharmonic waves may lose stability simultaneously, each with a different wavenumber. We focus on this situation and compare the case where the harmonic waves have a longer wavelength than the subharmonic waves with the case where the harmonic waves have a shorter wavelength. We show that in the former case a normal form transformation can be used to remove all quadratic terms from the amplitude equations governing the relevant resonant triad interactions. Thus the role of resonant triads in the pattern selection problem is greatly diminished in this situation. We verify our general results within the example of one-dimensional surface wave solutions of the Zhang-Vinals model of the two-frequency Faraday problem. In one-dimension, a 1:2 spatial resonance takes the place of a resonant triad in our investigation. We find that when the bifurcating modes are in this spatial resonance, it dramatically effects the bifurcation to subharmonic waves in the case of forcing frequencies are in ratio 1/2; this is consistent with the results of Zhang and Vinals. In sharp contrast, we find that when the forcing frequencies are in ratio 2/3, the bifurcation to (sub)harmonic waves is insensitive to the presence of another spatially-resonant bifurcating mode.Comment: 22 pages, 6 figures, late

Synchronization in populations of globally coupled oscillators with inertial effects

A model for synchronization of globally coupled phase oscillators including ``inertial'' effects is analyzed. In such a model, both oscillator frequencies and phases evolve in time. Stationary solutions include incoherent (unsynchronized) and synchronized states of the oscillator population. Assuming a Lorentzian distribution of oscillator natural frequencies, $g(\Omega)$, both larger inertia or larger frequency spread stabilize the incoherent solution, thereby making harder to synchronize the population. In the limiting case $g(\Omega)=\delta(\Omega)$, the critical coupling becomes independent of inertia. A richer phenomenology is found for bimodal distributions. For instance, inertial effects may destabilize incoherence, giving rise to bifurcating synchronized standing wave states. Inertia tends to harden the bifurcation from incoherence to synchronized states: at zero inertia, this bifurcation is supercritical (soft), but it tends to become subcritical (hard) as inertia increases. Nonlinear stability is investigated in the limit of high natural frequencies.Comment: Revtex, 36 pages, submit to Phys. Rev.

Characterisation of Potential Landing Sites for the European Space Agency's Lunar Lander Project

This article describes the characterization activities of the landing sites currently envisaged for the Lunar Lander mission of the European Space Agency. These sites have been identified in the South Pole Region (-85{\deg} to -90{\deg} latitude) based on favourable illumination conditions, which make it possible to have a long-duration mission with conventional power and thermal control subsystems, capable of enduring relatively short periods of darkness (in the order of tens of hours), instead of utilising Radioisotope Heating Units. The illumination conditions are simulated at the potential landing sites based on topographic data from the Lunar Orbiter Laser Altimeter (LOLA), using three independent tools. Risk assessment of the identified sites is also being performed through independent studies. Long baseline slopes are assessed based on LOLA, while craters and boulders are detected both visually and using computer tools in Lunar Reconnaissance Orbiter Camera (LROC) images, down to a size of less than 2 m, and size-frequency distributions are generated. Shadow hazards are also assessed via LROC images. The preliminary results show that areas with quasi-continuous illumination of several months exist, but their size is small (few hundred metres); the duration of the illumination period drops quickly to less than one month outside the areas, and some areas present gaps with short illumination periods. Concerning hazard distributions, 50 m slopes are found to be shallow (few degrees) based on LOLA, whereas at the scale of the lander footprint (~5 m) they are mostly dominated by craters, expected to be mature (from geological context) and shallow (~11{\deg}). The preliminary conclusion is that the environment at the prospective landing sites is within the capabilities of the Lander design