The effects of the pre-pulse on capillary discharge extreme ultraviolet laser

In the past few years collisionally pumped extreme ultraviolet (XUV) lasers utilizing a capillary discharge were demonstrated. An intense current pulse is applied to a gas filled capillary, inducing magnetic collapse (Z-pinch) and formation of a highly ionized plasma column. Usually, a small current pulse (pre-pulse) is applied to the gas in order to pre-ionize it prior to the onset of the main current pulse. In this paper we investigate the effects of the pre-pulse on a capillary discharge Ne-like Ar XUV laser (46.9nm). The importance of the pre-pulse in achieving suitable initial conditions of the gas column and preventing instabilities during the collapse is demonstrated. Furthermore, measurements of the amplified spontaneous emission (ASE) properties (intensity, duration) in different pre-pulse currents revealed unexpected sensitivity. Increasing the pre-pulse current by a factor of two caused the ASE intensity to decrease by an order of magnitude - and to nearly disappear. This effect is accompanied by a slight increase in the lasing duration. We attribute this effect to axial flow in the gas during the pre-pulse.Comment: 4 pages, 4 figure

Kinetics of Heterogeneous Single-Species Annihilation

We investigate the kinetics of diffusion-controlled heterogeneous single-species annihilation, where the diffusivity of each particle may be different. The concentration of the species with the smallest diffusion coefficient has the same time dependence as in homogeneous single-species annihilation, A+A-->0. However, the concentrations of more mobile species decay as power laws in time, but with non-universal exponents that depend on the ratios of the corresponding diffusivities to that of the least mobile species. We determine these exponents both in a mean-field approximation, which should be valid for spatial dimension d>2, and in a phenomenological Smoluchowski theory which is applicable in d<2. Our theoretical predictions compare well with both Monte Carlo simulations and with time series expansions.Comment: TeX, 18 page

Statistics of Earthquakes in Simple Models of Heterogeneous Faults

Simple models for ruptures along a heterogeneous earthquake fault zone are studied, focussing on the interplay between the roles of disorder and dynamical effects. A class of models are found to operate naturally at a critical point whose properties yield power law scaling of earthquake statistics. Various dynamical effects can change the behavior to a distribution of small events combined with characteristic system size events. The studies employ various analytic methods as well as simulations.Comment: 4 pages, RevTex, 3 figures (eps-files), uses eps

Party finance reform as constitutional engineering? The effectiveness and unintended consequences of party finance reform in France and Britain

In both Britain and France, party funding was traditionally characterized by a laissez faire approach and a conspicuous lack of regulation. In France, this was tantamount to a 'legislative vacuum'. In the last two decades, however, both countries have sought to fundamentally reform their political finance regulation regimes. This prompted, in Britain, the Political Parties, Elections and Referendums Act 2000, and in France a bout of 'legislative incontinence' — profoundly transforming the political finance regime between 1988 and 1995. This article seeks to explore and compare the impacts of the reforms in each country in a bid to explain the unintended consequences of the alternative paths taken and the effectiveness of the new party finance regime in each country. It finds that constitutional engineering through party finance reform is a singularly inexact science, largely due to the imperfect nature of information, the limited predictability of cause and effect, and the constraining influence of non-party actors, such as the Constitutional Council in France, and the Electoral Commission in Britain

Gutenberg Richter and Characteristic Earthquake Behavior in Simple Mean-Field Models of Heterogeneous Faults

The statistics of earthquakes in a heterogeneous fault zone is studied analytically and numerically in the mean field version of a model for a segmented fault system in a three-dimensional elastic solid. The studies focus on the interplay between the roles of disorder, dynamical effects, and driving mechanisms. A two-parameter phase diagram is found, spanned by the amplitude of dynamical weakening (or ``overshoot'') effects (epsilon) and the normal distance (L) of the driving forces from the fault. In general, small epsilon and small L are found to produce Gutenberg-Richter type power law statistics with an exponential cutoff, while large epsilon and large L lead to a distribution of small events combined with characteristic system-size events. In a certain parameter regime the behavior is bistable, with transitions back and forth from one phase to the other on time scales determined by the fault size and other model parameters. The implications for realistic earthquake statistics are discussed.Comment: 21 pages, RevTex, 6 figures (ps, eps

Ordering of Random Walks: The Leader and the Laggard

We investigate two complementary problems related to maintaining the relative positions of N random walks on the line: (i) the leader problem, that is, the probability {\cal L}_N(t) that the leftmost particle remains the leftmost as a function of time and (ii) the laggard problem, the probability {\cal R}_N(t) that the rightmost particle never becomes the leftmost. We map these ordering problems onto an equivalent (N-1)-dimensional electrostatic problem. From this construction we obtain a very accurate estimate for {\cal L}_N(t) for N=4, the first case that is not exactly soluble: {\cal L}_4(t) ~ t^{-\beta_4}, with \beta_4=0.91342(8). The probability of being the laggard also decays algebraically, {\cal R}_N(t) ~ t^{-\gamma_N}; we derive \gamma_2=1/2, \gamma_3=3/8, and argue that \gamma_N--> ln N/N$ as N-->oo.Comment: 7 pages, 4 figures, 2-column revtex 4 forma

Knots and Random Walks in Vibrated Granular Chains

We study experimentally statistical properties of the opening times of knots in vertically vibrated granular chains. Our measurements are in good qualitative and quantitative agreement with a theoretical model involving three random walks interacting via hard core exclusion in one spatial dimension. In particular, the knot survival probability follows a universal scaling function which is independent of the chain length, with a corresponding diffusive characteristic time scale. Both the large-exit-time and the small-exit-time tails of the distribution are suppressed exponentially, and the corresponding decay coefficients are in excellent agreement with the theoretical values.Comment: 4 pages, 5 figure