Alternating Kinetics of Annihilating Random Walks Near a Free Interface

The kinetics of annihilating random walks in one dimension, with the half-line x>0 initially filled, is investigated. The survival probability of the nth particle from the interface exhibits power-law decay, S_n(t)~t^{-alpha_n}, with alpha_n approximately equal to 0.225 for n=1 and all odd values of n; for all n even, a faster decay with alpha_n approximately equal to 0.865 is observed. From consideration of the eventual survival probability in a finite cluster of particles, the rigorous bound alpha_1<1/4 is derived, while a heuristic argument gives alpha_1 approximately equal to 3 sqrt{3}/8 = 0.2067.... Numerically, this latter value appears to be a stringent lower bound for alpha_1. The average position of the first particle moves to the right approximately as 1.7 t^{1/2}, with a relatively sharp and asymmetric probability distribution.Comment: 6 pages, RevTeX, 5 eps figures include

Causal Set Dynamics: A Toy Model

We construct a quantum measure on the power set of non-cyclic oriented graphs of N points, drawing inspiration from 1-dimensional directed percolation. Quantum interference patterns lead to properties which do not appear to have any analogue in classical percolation. Most notably, instead of the single phase transition of classical percolation, the quantum model displays two distinct crossover points. Between these two points, spacetime questions such as "does the network percolate" have no definite or probabilistic answer.Comment: 28 pages incl. 5 figure

Dominant Topologies in Euclidean Quantum Gravity

The dominant topologies in the Euclidean path integral for quantum gravity differ sharply according on the sign of the cosmological constant. For $\Lambda>0$, saddle points can occur only for topologies with vanishing first Betti number and finite fundamental group. For $\Lambda<0$, on the other hand, the path integral is dominated by topologies with extremely complicated fundamental groups; while the contribution of each individual manifold is strongly suppressed, the ``density of topologies'' grows fast enough to overwhelm this suppression. The value $\Lambda=0$ is thus a sort of boundary between phases in the sum over topologies. I discuss some implications for the cosmological constant problem and the Hartle-Hawking wave function.Comment: 14 pages, LaTeX. Minor additions (computability, relation to ``minimal volume'' in topology); error in eqn (3.5) corrected; references added. To appear in Class. Quant. Gra

Critical behaviour of a surface reaction model with infinitely many absorbing states

In a recent letter [J. Phys. A26, L801 (1993)], Yaldram et al. studied the critical behaviour of a simple lattice gas model of the CO-NO catalytic reaction. The model exhibits a second order nonequilibrium phase transition from an active state into one out of infinitely many absorbing states. Estimates for the critical exponent $\beta$ suggested that the model belongs to a new universality class. The results reported in this article contradict this notion, as estimates for various critical exponents show that the model belongs to the universality class of directed percolation.Comment: 10p+5fig, LaTeX+fig in uuencoded P

Critical Exponents of the N-vector model

Recently the series for two RG functions (corresponding to the anomalous dimensions of the fields phi and phi^2) of the 3D phi^4 field theory have been extended to next order (seven loops) by Murray and Nickel. We examine here the influence of these additional terms on the estimates of critical exponents of the N-vector model, using some new ideas in the context of the Borel summation techniques. The estimates have slightly changed, but remain within errors of the previous evaluation. Exponents like eta (related to the field anomalous dimension), which were poorly determined in the previous evaluation of Le Guillou--Zinn-Justin, have seen their apparent errors significantly decrease. More importantly, perhaps, summation errors are better determined. The change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values. Finally, because an error has been discovered in the last order of the published epsilon=4-d expansions (order epsilon^5), we have also reanalyzed the determination of exponents from the epsilon-expansion. The conclusion is that the general agreement between epsilon-expansion and 3D series has improved with respect to Le Guillou--Zinn-Justin.Comment: TeX Files, 27 pages +2 figures; Some values are changed; references update

Computer Simulations of Supercooled Liquids and Glasses

After a brief introduction to the dynamics of supercooled liquids, we discuss some of the advantages and drawbacks of computer simulations of such systems. Subsequently we present the results of computer simulations in which the dynamics of a fragile glass former, a binary Lennard-Jones system, is compared to the one of a strong glass former, SiO_2. This comparison gives evidence that the reason for the different temperature dependence of these two types of glass formers lies in the transport mechanism for the particles in the vicinity of T_c, the critical temperature of mode-coupling theory. Whereas the one of the fragile glass former is described very well by the ideal version of mode-coupling theory, the one for the strong glass former is dominated by activated processes. In the last part of the article we review some simulations of glass formers in which the dynamics below the glass transition temperature was investigated. We show that such simulations might help to establish a connection between systems with self generated disorder (e.g. structural glasses) and quenched disorder (e.g. spin glasses).Comment: 37 pages of Latex, 11 figures, to appear as a Topical Review article in J. Phys.: Condens. Matte

The effects of aging of scientists on their publication and citation patterns

The average age at which U.S. researchers get their first grant from NIH has increased from 34.3 in 1970, to 41.7 in 2004. These data raise the crucial question of the effects of aging on the scientific creativity and productivity of researchers. Those who worry about the aging of scientists usually believe that the younger they are the more creative and productive they will be. Using a large population of 13,680 university professors in Quebec, we show that, while scientific productivity rises sharply between 28 and 40, it increases at a slower pace between 41 and 50 and stabilizes afterward until retirement for the most active researchers. The average scientific impact per paper decreases linearly until 50-55 years old, but the average number of papers in highly cited journals and among highly cited papers rises continuously until retirement. Our results clearly show for the first time the natural history of the scientific productivity of scientists over their entire career and bring to light the fact that researchers over 55 still contribute significantly to the scientific community by producing high impact papers.Comment: 12 pages, 4 figure