Rapid oscillation, nonextendability, and the existence of periodic solutions to second order nonlinear ordinary differential equations

AbstractConsider the second order scalar ordinary differential equation x″(t) + ƒ(t, x(t)) = 0 (′ = ddt), where ƒ(t, x) is ω-periodic in t and ƒ(t, 0) = 0 for all t. The usual existence results for periodic solutions employing degree theory or other fixed point arguments are generally unhelpful in this case, since the periodic solution that they predict may well be the trivial solution.Jacobowitz has recently succeeded in applying the Poincaré-Birkhoff “twist” theorem to demonstrate that this equation has infinitely many (nontrivial) periodic solutions when ƒ satisfies a suitable “strong nonlinearity” condition with respect to x. Essential to his method of proof, however, is the condition xƒ(t, x) > 0 for all t (x = ≠ 0). In this note we show how this hypothesis may be relaxed, by modifying a technique used by the author when considering the problem of the global existence of solutions which occurs with the removal of the sign condition

Ab initio Quantum and ab initio Molecular Dynamics of the Dissociative Adsorption of Hydrogen on Pd(100)

The dissociative adsorption of hydrogen on Pd(100) has been studied by ab initio quantum dynamics and ab initio molecular dynamics calculations. Treating all hydrogen degrees of freedom as dynamical coordinates implies a high dimensionality and requires statistical averages over thousands of trajectories. An efficient and accurate treatment of such extensive statistics is achieved in two steps: In a first step we evaluate the ab initio potential energy surface (PES) and determine an analytical representation. Then, in an independent second step dynamical calculations are performed on the analytical representation of the PES. Thus the dissociation dynamics is investigated without any crucial assumption except for the Born-Oppenheimer approximation which is anyhow employed when density-functional theory calculations are performed. The ab initio molecular dynamics is compared to detailed quantum dynamical calculations on exactly the same ab initio PES. The occurence of quantum oscillations in the sticking probability as a function of kinetic energy is addressed. They turn out to be very sensitive to the symmetry of the initial conditions. At low kinetic energies sticking is dominated by the steering effect which is illustrated using classical trajectories. The steering effects depends on the kinetic energy, but not on the mass of the molecules. Zero-point effects lead to strong differences between quantum and classical calculations of the sticking probability. The dependence of the sticking probability on the angle of incidence is analysed; it is found to be in good agreement with experimental data. The results show that the determination of the potential energy surface combined with high-dimensional dynamical calculations, in which all relevant degrees of freedon are taken into account, leads to a detailed understanding of the dissociation dynamics of hydrogen at a transition metal surface.Comment: 15 pages, 9 figures, subm. to Phys. Rev.

Effects of rapid prey evolution on predator-prey cycles

We study the qualitative properties of population cycles in a predator-prey system where genetic variability allows contemporary rapid evolution of the prey. Previous numerical studies have found that prey evolution in response to changing predation risk can have major quantitative and qualitative effects on predator-prey cycles, including: (i) large increases in cycle period, (ii) changes in phase relations (so that predator and prey are cycling exactly out of phase, rather than the classical quarter-period phase lag), and (iii) "cryptic" cycles in which total prey density remains nearly constant while predator density and prey traits cycle. Here we focus on a chemostat model motivated by our experimental system [Fussmann et al. 2000,Yoshida et al. 2003] with algae (prey) and rotifers (predators), in which the prey exhibit rapid evolution in their level of defense against predation. We show that the effects of rapid prey evolution are robust and general, and furthermore that they occur in a specific but biologically relevant region of parameter space: when traits that greatly reduce predation risk are relatively cheap (in terms of reductions in other fitness components), when there is coexistence between the two prey types and the predator, and when the interaction between predators and undefended prey alone would produce cycles. Because defense has been shown to be inexpensive, even cost-free, in a number of systems [Andersson and Levin 1999, Gagneux et al. 2006,Yoshida et al. 2004], our discoveries may well be reproduced in other model systems, and in nature. Finally, some of our key results are extended to a general model in which functional forms for the predation rate and prey birth rate are not specified.Comment: 35 pages, 8 figure

The Layer 0 Inner Silicon Detector of the D0 Experiment

This paper describes the design, fabrication, installation and performance of the new inner layer called Layer 0 (L0) that was inserted in the existing Run IIa Silicon Micro-Strip Tracker (SMT) of the D0 experiment at the Fermilab Tevatron collider. L0 provides tracking information from two layers of sensors, which are mounted with center lines at a radial distance of 16.1 mm and 17.6 mm respectively from the beam axis. The sensors and readout electronics are mounted on a specially designed and fabricated carbon fiber structure that includes cooling for sensor and readout electronics. The structure has a thin polyimide circuit bonded to it so that the circuit couples electrically to the carbon fiber allowing the support structure to be used both for detector grounding and a low impedance connection between the remotely mounted hybrids and the sensors.Comment: 28 pages, 9 figure

First upper limits from LIGO on gravitational wave bursts

We report on a search for gravitational wave bursts using data from the first science run of the LIGO detectors. Our search focuses on bursts with durations ranging from 4 ms to 100 ms, and with significant power in the LIGO sensitivity band of 150 to 3000 Hz. We bound the rate for such detected bursts at less than 1.6 events per day at 90% confidence level. This result is interpreted in terms of the detection efficiency for ad hoc waveforms (Gaussians and sine-Gaussians) as a function of their root-sum-square strain h_{rss}; typical sensitivities lie in the range h_{rss} ~ 10^{-19} - 10^{-17} strain/rtHz, depending on waveform. We discuss improvements in the search method that will be applied to future science data from LIGO and other gravitational wave detectors.Comment: 21 pages, 15 figures, accepted by Phys Rev D. Fixed a few small typos and updated a few reference

Measurement of the p-pbar -> Wgamma + X cross section at sqrt(s) = 1.96 TeV and WWgamma anomalous coupling limits

The WWgamma triple gauge boson coupling parameters are studied using p-pbar -> l nu gamma + X (l = e,mu) events at sqrt(s) = 1.96 TeV. The data were collected with the DO detector from an integrated luminosity of 162 pb^{-1} delivered by the Fermilab Tevatron Collider. The cross section times branching fraction for p-pbar -> W(gamma) + X -> l nu gamma + X with E_T^{gamma} > 8 GeV and Delta R_{l gamma} > 0.7 is 14.8 +/- 1.6 (stat) +/- 1.0 (syst) +/- 1.0 (lum) pb. The one-dimensional 95% confidence level limits on anomalous couplings are -0.88 < Delta kappa_{gamma} < 0.96 and -0.20 < lambda_{gamma} < 0.20.Comment: Submitted to Phys. Rev. D Rapid Communication

Measurement of the ttbar Production Cross Section in ppbar Collisions at sqrt{s} = 1.96 TeV using Kinematic Characteristics of Lepton + Jets Events

We present a measurement of the top quark pair ttbar production cross section in ppbar collisions at a center-of-mass energy of 1.96 TeV using 230 pb**{-1} of data collected by the DO detector at the Fermilab Tevatron Collider. We select events with one charged lepton (electron or muon), large missing transverse energy, and at least four jets, and extract the ttbar content of the sample based on the kinematic characteristics of the events. For a top quark mass of 175 GeV, we measure sigma(ttbar) = 6.7 {+1.4-1.3} (stat) {+1.6- 1.1} (syst) +/-0.4 (lumi) pb, in good agreement with the standard model prediction.Comment: submitted to Phys.Rev.Let