Comment on "1/f noise in the Bak-Sneppen model"

Contrary to the recently published results by Daerden and Vanderzande [Phys. Rev. E 53, 4723 (1996)], we show that the time correlation function in the random-neighbor version of the Bak-Sneppen model can be well approximated by an exponential giving rise to a 1/f2 power spectrum.Comment: 2 pages, 2 figure

A 3D-CTM with detailed online PSC-microphysics: analysis of the Antarctic winter 2003 by comparison with satellite observations

International audienceWe present the first detailed microphysical simulations which are performed online within the framework of a global 3-D chemical transport model (CTM) with full chemistry. The model describes the formation and evolution of four types of polar stratospheric cloud (PSC) particles. Aerosol freezing and other relevant microphysical processes are treated in a full explicit way. Each particle type is described by a binned size distribution for the number density and chemical composition. This set-up allows for an accurate treatment of sedimentation and for detailed calculation of surface area densities and optical properties. Simulations are presented for the Antarctic winter of 2003 and comparisons are made to a diverse set of satellite observations (optical and chemical measurements of POAM III and MIPAS) to illustrate the capabilities of the model. This study shows that a combined resolution approach where microphysical processes are simulated in coarse-grained conditions gives good results for PSC formation and its large-scale effect on the chemical environment through processes such as denitrification, dehydration and ozone loss. It is also shown that the influence of microphysical parameters can be measured directly from these processes

4D-Var Assimilation of MIPAS chemical observations: ozone and nitrogen dioxide analyses

International audienceThis paper discusses the global analyses of stratospheric ozone (O3) and nitrogen dioxide (NO2) obtained by the Belgian Assimilation System for Chemical Observations from Envisat (BASCOE). Based on a chemistry transport model (CTM) and the 4-dimensional variational (4D-Var) method, BASCOE has assimilated chemical observations of O3, NO2, HNO3, N2O, CH4 and H2O, made between July 2002 and March 2004 by the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) onboard the European Space Agency (ESA) Environment Satellite (ENVISAT). This corresponds to the entire period during which MIPAS was operating at its nominal resolution. Our analyses are evaluated against assimilated MIPAS data and independent HALOE (HALogen Occultation Experiment) and POAM-III (Polar Ozone and Aerosol Measurement) satellite data. A good agreement is generally found between the analyses and these datasets, in both cases within the estimated error bars of the observations. The benefit of data assimilation is also evaluated using a BASCOE free model run. For O3, the gain from the assimilation is significant during ozone hole conditions, and in the lower stratosphere. Elsewhere, the free model run is within the MIPAS uncertainties and the assimilation does not provide significant improvement. For NO2, the gain from the assimilation is realized through most of the stratosphere. Using the BASCOE analyses, we estimate the differences between MIPAS data and independent data from HALOE and POAM-III, and find results close to those obtained by classical validation methods involving only direct measurement-to-measurement comparisons. Our results extend and reinforce previous MIPAS data validation efforts by taking account of a much larger variety of atmospheric states and measurement conditions. This study discusses possible further developments of the BASCOE data assimilation system; these concern the horizontal resolution, a better filtering of NO2 observations, and the photolysis calculation near the lid of the model. The ozone analyses are publicly available via the PROMOTE project http://www.gse-promote.org)

Spanning trees on the Sierpinski gasket

We obtain the numbers of spanning trees on the Sierpinski gasket $SG_d(n)$ with dimension $d$ equal to two, three and four. The general expression for the number of spanning trees on $SG_d(n)$ with arbitrary $d$ is conjectured. The numbers of spanning trees on the generalized Sierpinski gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4$ are also obtained.Comment: 20 pages, 8 figures, 1 tabl

Dissipative Abelian Sandpiles and Random Walks

We show that the dissipative Abelian sandpile on a graph L can be related to a random walk on a graph which consists of L extended with a trapping site. From this relation it can be shown, using exact results and a scaling assumption, that the dissipative sandpiles' correlation length exponent \nu always equals 1/d_w, where d_w is the fractal dimension of the random walker. This leads to a new understanding of the known results that \nu=1/2 on any Euclidean lattice. Our result is however more general and as an example we also present exact data for finite Sierpinski gaskets which fully confirm our predictions.Comment: 10 pages, 1 figur

Dimer coverings on the Sierpinski gasket with possible vacancies on the outmost vertices

We present the number of dimers $N_d(n)$ on the Sierpinski gasket $SG_d(n)$ at stage $n$ with dimension $d$ equal to two, three, four or five, where one of the outmost vertices is not covered when the number of vertices $v(n)$ is an odd number. The entropy of absorption of diatomic molecules per site, defined as $S_{SG_d}=\lim_{n \to \infty} \ln N_d(n)/v(n)$, is calculated to be $\ln(2)/3$ exactly for $SG_2(n)$. The numbers of dimers on the generalized Sierpinski gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4,5$ are also obtained exactly. Their entropies are equal to $\ln(6)/7$, $\ln(28)/12$, $\ln(200)/18$, respectively. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for $SG_d(n)$ with $d=3,4,5$. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of $S_{SG_d}$ with $d=3,4,5$ can be evaluated with more than a hundred significant figures accurate.Comment: 35 pages, 20 figures and 1 tabl

Moment analysis of the probability distributions of different sandpile models

We reconsider the moment analysis of the Bak-Tang-Wiesenfeld and the Manna sandpile model in two and three dimensions. In contrast to recently performed investigations our analysis turns out that the models are characterized by different scaling behavior, i.e., they belong to different universality classes.Comment: 6 pages, 6 figures, accepted for publication in Physical Review

Punctuated equilibria and 1/f noise in a biological coevolution model with individual-based dynamics

We present a study by linear stability analysis and large-scale Monte Carlo simulations of a simple model of biological coevolution. Selection is provided through a reproduction probability that contains quenched, random interspecies interactions, while genetic variation is provided through a low mutation rate. Both selection and mutation act on individual organisms. Consistent with some current theories of macroevolutionary dynamics, the model displays intermittent, statistically self-similar behavior with punctuated equilibria. The probability density for the lifetimes of ecological communities is well approximated by a power law with exponent near -2, and the corresponding power spectral densities show 1/f noise (flicker noise) over several decades. The long-lived communities (quasi-steady states) consist of a relatively small number of mutualistically interacting species, and they are surrounded by a ``protection zone'' of closely related genotypes that have a very low probability of invading the resident community. The extent of the protection zone affects the stability of the community in a way analogous to the height of the free-energy barrier surrounding a metastable state in a physical system. Measures of biological diversity are on average stationary with no discernible trends, even over our very long simulation runs of approximately 3.4x10^7 generations.Comment: 20 pages RevTex. Minor revisions consistent with published versio