Random fractal strings: their zeta functions, complex dimensions and spectral asymptotics

In this paper a string is a sequence of positive non-increasing real numbers which sums to one. For our purposes a fractal string is a string formed from the lengths of removed sub-intervals created by a recursive decomposition of the unit interval. By using the so called complex dimensions of the string, the poles of an associated zeta function, it is possible to obtain detailed information about the behaviour of the asymptotic properties of the string. We consider random versions of fractal strings. We show that using a random recursive self-similar construction it is possible to obtain similar results to those for deterministic self-similar strings. In the case of strings generated by the excursions of stable subordinators, we show that the complex dimensions can only lie on the real line. The results allow us to discuss the geometric and spectral asymptotics of one-dimensional domains with random fractal boundary

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

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.

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

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

Analysis of ultrasonic transducers with fractal architecture

Ultrasonic transducers composed of a periodic piezoelectric composite are generally accepted as the design of choice in many applications. Their architecture is normally very regular and this is due to manufacturing constraints rather than performance optimisation. Many of these manufacturing restrictions no longer hold due to new production methods such as computer controlled, laser cutting, and so there is now freedom to investigate new types of geometry. In this paper, the plane wave expansion model is utilised to investigate the behaviour of a transducer with a self-similar architecture. The Cantor set is utilised to design a 2-2 conguration, and a 1-3 conguration is investigated with a Sierpinski Carpet geometry

A multifractal zeta function for cookie cutter sets

Starting with the work of Lapidus and van Frankenhuysen a number of papers have introduced zeta functions as a way of capturing multifractal information. In this paper we propose a new multifractal zeta function and show that under certain conditions the abscissa of convergence yields the Hausdorff multifractal spectrum for a class of measures

Complete genome sequence of Syntrophobacter fumaroxidans strain (MPOB(T)).

Syntrophobacter fumaroxidans strain MPOB(T) is the best-studied species of the genus Syntrophobacter. The species is of interest because of its anaerobic syntrophic lifestyle, its involvement in the conversion of propionate to acetate, H2 and CO2 during the overall degradation of organic matter, and its release of products that serve as substrates for other microorganisms. The strain is able to ferment fumarate in pure culture to CO2 and succinate, and is also able to grow as a sulfate reducer with propionate as an electron donor. This is the first complete genome sequence of a member of the genus Syntrophobacter and a member genus in the family Syntrophobacteraceae. Here we describe the features of this organism, together with the complete genome sequence and annotation. The 4,990,251 bp long genome with its 4,098 protein-coding and 81 RNA genes is a part of the Microbial Genome Program (MGP) and the Genomes to Life (GTL) Program project