Exponential versus linear amplitude decay in damped oscillators

We comment of the widespread belief among some undergraduate students that the amplitude of any harmonic oscillator in the presence of any type of friction, decays exponentially in time. To dispel that notion, we compare the amplitude decay for a harmonic oscillator in the presence of (i) viscous friction and (ii) dry friction. It is shown that, in the first case, the amplitude decays exponentially with time while in the second case, it decays linearly with time.Comment: 3 pages, 1 figure, accepted in Phys. Teac

Gliding Motility of Cytophaga Sp. Strain U67

Video techniques were used to analyze the motion of the gliding bacterium Cytophaga sp. strain U67. Cells moved singly on glass along the long axis at a speed of about 2 micrometers/s, advancing, retreating, stopping, pivoting about a pole, or flipping over. They did not flex or roll. Cells of different lengths moved at about the same speed. Cells sometimes spun continuously about a pole at a frequency of about 2 HZ, the body moving in a plane parallel to that of the glass or on the surface of a cone having either a large or a small solid angle. Polystyrene latex spheres moved to and fro on the surfaces of cells, also at a speed of about 2 micrometers/s. They moved in the same fashion whether a cell was in suspension, gliding, or at rest on the glass. Two spheres on the same cell often moved in opposite directions, passing by one another in close proximity. Small and large spheres and aggregates of spheres all moved at about the same speed. An aggregate moved down the side of a cell with a fixed orientation, even when only one sphere was in contact with the cell. Spheres occasionally left one cell and were picked up by another. Cell pretreated with small spheres did not adhere to glass. When the cells were deprived of oxygen, they stopped gliding, and the spheres stopped moving on their surfaces. The spheres became completely immobilized; they no longer moved from cell to cell or exhibited Brownian movement. Cytophaga spp. are known to have a typical gram-negative cell envelope: an inner (cytoplasmic) membrane, a thin peptidoglycan layer, and an outer (lipopolysaccharide) membrane. Our data are consistent with a model for gliding in which sites to which glass and polystyrene strongly adsorb move within the fluid outer membrane along tracks fixed to the rigid peptidoglycan framework.Molecular and Cellular Biolog

Double radiative pion capture on hydrogen and deuterium and the nucleon's pion cloud

We report measurements of double radiative capture in pionic hydrogen and pionic deuterium. The measurements were performed with the RMC spectrometer at the TRIUMF cyclotron by recording photon pairs from pion stops in liquid hydrogen and deuterium targets. We obtained absolute branching ratios of $(3.02 \pm 0.27 (stat.) \pm 0.31 (syst.)) \times 10^{-5}$ for hydrogen and $(1.42 \pm ^{0.09}_{0.12} (stat.) \pm 0.11 (syst.)) \times 10^{-5}$ for deuterium, and relative branching ratios of double radiative capture to single radiative capture of $(7.68 \pm 0.69(stat.) \pm 0.79(syst.)) \times 10^{-5}$ for hydrogen and $(5.44 \pm^{0.34}_{0.46}(stat.) \pm 0.42(syst.)) \times 10^{-5}$ for deuterium. For hydrogen, the measured branching ratio and photon energy-angle distributions are in fair agreement with a reaction mechanism involving the annihilation of the incident $\pi^-$ on the $\pi^+$ cloud of the target proton. For deuterium, the measured branching ratio and energy-angle distributions are qualitatively consistent with simple arguments for the expected role of the spectator neutron. A comparison between our hydrogen and deuterium data and earlier beryllium and carbon data reveals substantial changes in the relative branching ratios and the energy-angle distributions and is in agreement with the expected evolution of the reaction dynamics from an annihilation process in S-state capture to a bremsstrahlung process in P-state capture. Lastly, we comment on the relevance of the double radiative process to the investigation of the charged pion polarizability and the in-medium pion field.Comment: 44 pages, 7 tables, 13 figures, submitted to Phys. Rev.

Global properties of Stochastic Loewner evolution driven by Levy processes

Standard Schramm-Loewner evolution (SLE) is driven by a continuous Brownian motion which then produces a trace, a continuous fractal curve connecting the singular points of the motion. If jumps are added to the driving function, the trace branches. In a recent publication [1] we introduced a generalized SLE driven by a superposition of a Brownian motion and a fractal set of jumps (technically a stable L\'evy process). We then discussed the small-scale properties of the resulting L\'evy-SLE growth process. Here we discuss the same model, but focus on the global scaling behavior which ensues as time goes to infinity. This limiting behavior is independent of the Brownian forcing and depends upon only a single parameter, $\alpha$, which defines the shape of the stable L\'evy distribution. We learn about this behavior by studying a Fokker-Planck equation which gives the probability distribution for endpoints of the trace as a function of time. As in the short-time case previously studied, we observe that the properties of this growth process change qualitatively and singularly at $\alpha =1$. We show both analytically and numerically that the growth continues indefinitely in the vertical direction for $\alpha > 1$, goes as $\log t$ for $\alpha = 1$, and saturates for $\alpha< 1$. The probability density has two different scales corresponding to directions along and perpendicular to the boundary. In the former case, the characteristic scale is $X(t) \sim t^{1/\alpha}$. In the latter case the scale is $Y(t) \sim A + B t^{1-1/\alpha}$ for $\alpha \neq 1$, and $Y(t) \sim \ln t$ for $\alpha = 1$. Scaling functions for the probability density are given for various limiting cases.Comment: Published versio

Periodic Thermonuclear X-ray Bursts from GS 1826-24 and the Fuel Composition as a Function of Accretion Rate

We analyze 24 type I X-ray bursts from GS 1826-24 observed by the Rossi X-ray Timing Explorer between 1997 November and 2002 July. The bursts observed between 1997-98 were consistent with a stable recurrence time of 5.74 +/- 0.13 hr. The persistent intensity of GS 1826-24 increased by 36% between 1997-2000, by which time the burst interval had decreased to 4.10 +/- 0.08 hr. In 2002 July the recurrence time was shorter again, at 3.56 +/- 0.03 hr. The bursts within each epoch had remarkably identical lightcurves over the full approx. 150 s burst duration; both the initial decay timescale from the peak, and the burst fluence, increased slightly with the rise in persistent flux. The decrease in the burst recurrence time was proportional to Mdot^(-1.05+/-0.02) (where Mdot is assumed to be linearly proportional to the X-ray flux), so that the ratio alpha between the integrated persistent and burst fluxes was inversely correlated with Mdot. The average value of alpha was 41.7 +/- 1.6. Both the alpha value, and the long burst durations indicate that the hydrogen is burning during the burst via the rapid-proton (rp) process. The variation in alpha with Mdot implies that hydrogen is burning stably between bursts, requiring solar metallicity (Z ~ 0.02) in the accreted layer. We show that solar metallicity ignition models naturally reproduce the observed burst energies, but do not match the observed variations in recurrence time and burst fluence. Low metallicity models (Z ~ 0.001) reproduce the observed trends in recurrence time and fluence, but are ruled out by the variation in alpha. We discuss possible explanations, including extra heating between bursts, or that the fraction of the neutron star covered by the accreted fuel increases with Mdot.Comment: 9 pages, 6 figures, accepted by ApJ. Minor revisions following the referee's repor

Q^2 Evolution of Generalized Baldin Sum Rule for the Proton

The generalized Baldin sum rule for virtual photon scattering, the unpolarized analogy of the generalized Gerasimov-Drell-Hearn integral, provides an important way to investigate the transition between perturbative QCD and hadronic descriptions of nucleon structure. This sum rule requires integration of the nucleon structure function F_1, which until recently had not been measured at low Q^2 and large x, i.e. in the nucleon resonance region. This work uses new data from inclusive electron-proton scattering in the resonance region obtained at Jefferson Lab, in combination with SLAC deep inelastic scattering data, to present first precision measurements of the generalized Baldin integral for the proton in the Q^2 range of 0.3 to 4.0 GeV^2.Comment: 4 pages, 3 figures, one table; text added, one figure replace

Sum Rules for Magnetic Moments and Polarizabilities in QED and Chiral Effective-Field Theory

We elaborate on a recently proposed extension of the Gerasimov-Drell-Hearn (GDH) sum rule which is achieved by taking derivatives with respect to the anomalous magnetic moment. The new sum rule features a {\it linear} relation between the anomalous magnetic moment and the dispersion integral over a cross-section quantity. We find some analogy of the linearized form of the GDH sum rule with the `sideways dispersion relations'. As an example, we apply the linear sum rule to reproduce the famous Schwinger's correction to the magnetic moment in QED from a tree-level cross-section calculation and outline the procedure for computing the two-loop correction from a one-loop cross-section calculation. The polarizabilities of the electron in QED are considered as well by using the other forward-Compton-scattering sum rules. We also employ the sum rules to study the magnetic moment and polarizabilities of the nucleon in a relativistic chiral EFT framework. In particular we investigate the chiral extrapolation of these quantities.Comment: 24 pages, 7 figures; several additions, published versio

Low-Energy Compton Scattering of Polarized Photons on Polarized Nucleons

The general structure of the cross section of $\gamma N$ scattering with polarized photon and/or nucleon in initial and/or final state is systematically described and exposed through invariant amplitudes. A low-energy expansion of the cross section up to and including terms of order $\omega^4$ is given which involves ten structure parameters of the nucleon (dipole, quadrupole, dispersion, and spin polarizabilities). Their physical meaning is discussed in detail. Using fixed-t dispersion relations, predictions for these parameters are obtained and compared with results of chiral perturbation theory. It is emphasized that Compton scattering experiments at large angles can fix the most uncertain of these structure parameters. Predictions for the cross section and double-polarization asymmetries are given and the convergence of the expansion is investigated. The feasibility of the experimental determination of some of the struture parameters is discussed.Comment: 41 pages of text, 9 figures; minor revisions prior to publication in Phys. Rev.

'She's like a daughter to me': insights into care, work and kinship from rural Russia

This article draws on ethnographic research into a state-funded homecare service in rural Russia. The article discusses intersections between care, work and kinship in the relationships between homecare workers and their elderly wards and explores the ways in which references to kinship, as a means of authenticating paid care and explaining its emotional content, reinforce public and private oppositions while doing little to relieve the tensions and conflicts of care work. The discussion brings together detailed empirical insights into local ideologies and practices as a way of generating new theoretical perspectives, which will be of relevance beyond the particular context of study

The effects of the small t properties of hadronic scattering amplitude on the determination its real part

Taking into account the different forms of the Coulomb-hadron interference phase and the possible spin-flip contribution the new analysis of the experimental data of the proton-antiproton elastic scattering at $3.8 < p_L <6.0 \$GeV/c and small momentum transfer is carried out. It is shown that the size of the spin-flip amplitude can be determined from the form of the differential cross sections at small $t$, and the deviation of $\rho(s,t)$ obtained from the examined experimental data of the $p\bar{p}$ scattering from the analysis \cite{Kroll}, based on the dispersion relations, is conserved in all xamined assumptions. The analysis of the proton-proton elastic scattering at $9 < p_L < 70 \$GeV/c also shows the impact of the examined effects on the form of the differential cross sections.Comment: 13 pages, 3 figure