A parallel algorithm for the enumeration of benzenoid hydrocarbons

We present an improved parallel algorithm for the enumeration of fixed benzenoids B_h containing h hexagonal cells. We can thus extend the enumeration of B_h from the previous best h=35 up to h=50. Analysis of the associated generating function confirms to a very high degree of certainty that $B_h \sim A \kappa^h /h$ and we estimate that the growth constant $\kappa = 5.161930154(8)$ and the amplitude $A=0.2808499(1)$.Comment: 14 pages, 6 figure

Honeycomb lattice polygons and walks as a test of series analysis techniques

We have calculated long series expansions for self-avoiding walks and polygons on the honeycomb lattice, including series for metric properties such as mean-squared radius of gyration as well as series for moments of the area-distribution for polygons. Analysis of the series yields accurate estimates for the connective constant, critical exponents and amplitudes of honeycomb self-avoiding walks and polygons. The results from the numerical analysis agree to a high degree of accuracy with theoretical predictions for these quantities.Comment: 16 pages, 9 figures, jpconf style files. Presented at the conference "Counting Complexity: An international workshop on statistical mechanics and combinatorics." In celebration of Prof. Tony Guttmann's 60th birthda

Low-density series expansions for directed percolation II: The square lattice with a wall

A new algorithm for the derivation of low-density expansions has been used to greatly extend the series for moments of the pair-connectedness on the directed square lattice near an impenetrable wall. Analysis of the series yields very accurate estimates for the critical point and exponents. In particular, the estimate for the exponent characterizing the average cluster length near the wall, $\tau_1=1.00014(2)$, appears to exclude the conjecture $\tau_1=1$. The critical point and the exponents $\nu_{\parallel}$ and $\nu_{\perp}$ have the same values as for the bulk problem.Comment: 8 pages, 1 figur

Nonuniversal Critical Spreading in Two Dimensions

Continuous phase transitions are studied in a two dimensional nonequilibrium model with an infinite number of absorbing configurations. Spreading from a localized source is characterized by nonuniversal critical exponents, which vary continuously with the density phi in the surrounding region. The exponent delta changes by more than an order of magnitude, and eta changes sign. The location of the critical point also depends on phi, which has important implications for scaling. As expected on the basis of universality, the static critical behavior belongs to the directed percolation class.Comment: 21 pages, REVTeX, figures available upon reques

Optimal Investment Horizons for Stocks and Markets

The inverse statistics is the distribution of waiting times needed to achieve a predefined level of return obtained from (detrended) historic asset prices \cite{optihori,gainloss}. Such a distribution typically goes through a maximum at a time coined the {\em optimal investment horizon}, $\tau^*_\rho$, which defines the most likely waiting time for obtaining a given return $\rho$. By considering equal positive and negative levels of return, we reported in \cite{gainloss} on a quantitative gain/loss asymmetry most pronounced for short horizons. In the present paper, the inverse statistics for 2/3 of the individual stocks presently in the DJIA is investigated. We show that this gain/loss asymmetry established for the DJIA surprisingly is {\em not} present in the time series of the individual stocks nor their average. This observation points towards some kind of collective movement of the stocks of the index (synchronization).Comment: Subm. to Physica A as Conference Proceedings of Econophysics Colloquium, ANU Canberra, 13-17 Nov. 2005. 6 pages including figure

Low-density series expansions for directed percolation III. Some two-dimensional lattices

We use very efficient algorithms to calculate low-density series for bond and site percolation on the directed triangular, honeycomb, kagom\'e, and $(4.8^2)$ lattices. Analysis of the series yields accurate estimates of the critical point $p_c$ and various critical exponents. The exponent estimates differ only in the $5^{th}$ digit, thus providing strong numerical evidence for the expected universality of the critical exponents for directed percolation problems. In addition we also study the non-physical singularities of the series.Comment: 20 pages, 8 figure

Inverse Statistics in the Foreign Exchange Market

We investigate intra-day foreign exchange (FX) time series using the inverse statistic analysis developed in [1,2]. Specifically, we study the time-averaged distributions of waiting times needed to obtain a certain increase (decrease) $\rho$ in the price of an investment. The analysis is performed for the Deutsch mark (DM) against the $US for the full year of 1998, but similar results are obtained for the Japanese Yen against the$US. With high statistical significance, the presence of "resonance peaks" in the waiting time distributions is established. Such peaks are a consequence of the trading habits of the markets participants as they are not present in the corresponding tick (business) waiting time distributions. Furthermore, a new {\em stylized fact}, is observed for the waiting time distribution in the form of a power law Pdf. This result is achieved by rescaling of the physical waiting time by the corresponding tick time thereby partially removing scale dependent features of the market activity.Comment: 8 pages. Accepted Physica

Transient flows in active porous media

Stimuli-responsive materials that modify their shape in response to changes in environmental conditions -- such as solute concentration, temperature, pH, and stress -- are widespread in nature and technology. Applications include micro- and nanoporous materials used in filtration and flow control. The physiochemical mechanisms that induce internal volume modifications have been widely studies. The coupling between induced volume changes and solute transport through porous materials, however, is not well understood. Here, we consider advective and diffusive transport through a small channel linking two large reservoirs. A section of stimulus-responsive material regulates the channel permeability, which is a function of the local solute concentration. We derive an exact solution to the coupled transport problem and demonstrate the existence of a flow regime in which the steady state is reached via a damped oscillation around the equilibrium concentration value. Finally, the feasibility of an experimental observation of the phenomena is discussed. Please note that this version of the paper has not been formally peer reviewed, revised or accepted by a journal

Self-avoiding walks and polygons on the triangular lattice

We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40 we also calculate series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and the mean-square distance of a monomer from the end points. For self-avoiding polygons to length 58 we calculate series for the mean-square radius of gyration and the first 10 moments of the area. Analysis of the series yields accurate estimates for the connective constant of triangular self-avoiding walks, $\mu=4.150797226(26)$, and confirms to a high degree of accuracy several theoretical predictions for universal critical exponents and amplitude combinations.Comment: 24 pages, 6 figure