Topological Evolution of Dynamical Networks: Global Criticality from Local Dynamics

We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average connectivity of the network towards the critical value $K_c =2$ in the limit of large system size $N$. How this principle could generate self-organization in natural complex systems is discussed for two examples: neural networks and regulatory networks in the genome.Comment: 4 pages RevTeX, 4 figures PostScript, revised versio

Surface spin-flop transition in a uniaxial antiferromagnetic Fe/Cr superlattice induced by a magnetic field of arbitrary direction

We studied the transition between the antiferromagnetic and the surface spin-flop phases of a uniaxial antiferromagnetic [Fe(14 \AA)/Cr(11 \AA]$_{\rm x20}$ superlattice. For external fields applied parallel to the in-plane easy axis, the layer-by-layer configuration, calculated in the framework of a mean-field one-dimensional model, was benchmarked against published polarized neutron reflectivity data. For an in-plane field $H$ applied at an angle $\psi \ne 0$ with the easy axis, magnetometry shows that the magnetization $M$ vanishes at H=0, then increases slowly with increasing $H$. At a critical value of $H$, a finite jump in $M(H)$ is observed for $\psi<5^{\rm o}$, while a smooth increase of $M$ $vs$ $H$ is found for $\psi>5^{\rm o}$. A dramatic increase in the full width at half maximum of the magnetic susceptibility is observed for $\psi \ge 5^{\rm o}$. The phase diagram obtained from micromagnetic calculations displays a first-order transition to a surface spin-flop phase for low $\psi$ values, while the transition becomes continuous for $\psi$ greater than a critical angle, $\psi_{\rm max} \approx 4.75^{\rm o}$. This is in fair agreement with the experimentally observed results.Comment: 24 pages, 7 figure

Causes and importance of new particle formation in the present-day and pre-industrial atmospheres

New particle formation has been estimated to produce around half of cloud-forming particles in the present-day atmosphere, via gas-to-particle conversion. Here we assess the importance of new particle formation (NPF) for both the present-day and the pre-industrial atmospheres. We use a global aerosol model with parametrisations of NPF from previously published CLOUD chamber experiments involving sulphuric acid, ammonia, organic molecules and ions. We find that NPF produces around 67% of cloud condensation nuclei at 0.2% supersaturation (CCN0.2%) at the level of low clouds in the pre-industrial atmosphere (estimated uncertainty range 45-84%) and 54% in the present day (estimated uncertainty range 38-66%). Concerning causes, we find that the importance of biogenic volatile organic compounds (BVOCs) in NPF and CCN formation is greater than previously thought. Removing BVOCs and hence all secondary organic aerosol from our model reduces low-cloud-level CCN concentrations at 0.2% supersaturation by 26% in the present-day atmosphere and 41% in the pre-industrial. Around three-quarters of this reduction is due to the tiny fraction of the oxidation products of BVOCs that have sufficiently low volatility to be involved in NPF and early growth. Furthermore, we estimate that 40% of pre-industrial CCN0.2% are formed via ion-induced NPF, compared with 27% in the present-day, although we caution that the ion-induced fraction of NPF involving BVOCs is poorly measured at present. Our model suggests that the effect of changes in cosmic ray intensity on CCN is small and unlikely to be comparable to the effect of large variations in natural primary aerosol emissions

Evaporation of sulfate aerosols at low relative humidity

Evaporation of sulfuric acid from particles can be important in the atmospheres of Earth and Venus. However, the equilibrium constant for the dissociation of H2SO4 to bisulfate ions, which is the one of the fundamental parameters controlling the evaporation of sulfur particles, is not well constrained. In this study we explore the volatility of sulfate particles at very low relative humidity. We measured the evaporation of sulfur particles versus temperature and relative humidity in the CLOUD chamber at CERN. We modelled the observed sulfur particle shrinkage with the ADCHAM model. Based on our model results, we conclude that the sulfur particle shrinkage is mainly governed by H2SO4 and potentially to some extent by SO3 evaporation. We found that the equilibrium constants for the dissociation of H2SO4 to HSO4-(KH2SO4) and the dehydration of H2SO4 to SO3 ((x) K-SO3) are K H2SO4 = 2-4 x 10(9) mol kg(-1) and (x) K SO3 >= 1.4 x 10(10) at 288.8 +/- 5 K.Peer reviewe

Boolean Dynamics with Random Couplings

This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N Boolean elements at a given time is given a value which depends upon K elements in the previous time step. We review the work of many authors on the behavior of the models, looking particularly at the structure and lengths of their cycles, the sizes of their basins of attraction, and the flow of information through the systems. In the limit of infinite N, there is a phase transition between a chaotic and an ordered phase, with a critical phase in between. We argue that the behavior of this system depends significantly on the topology of the network connections. If the elements are placed upon a lattice with dimension d, the system shows correlations related to the standard percolation or directed percolation phase transition on such a lattice. On the other hand, a very different behavior is seen in the Kauffman net in which all spins are equally likely to be coupled to a given spin. In this situation, coupling loops are mostly suppressed, and the behavior of the system is much more like that of a mean field theory. We also describe possible applications of the models to, for example, genetic networks, cell differentiation, evolution, democracy in social systems and neural networks.Comment: 69 pages, 16 figures, Submitted to Springer Applied Mathematical Sciences Serie

Most Networks in Wagner's Model Are Cycling

In this paper we study a model of gene networks introduced by Andreas Wagner in the 1990s that has been used extensively to study the evolution of mutational robustness. We investigate a range of model features and parameters and evaluate the extent to which they influence the probability that a random gene network will produce a fixed point steady state expression pattern. There are many different types of models used in the literature, (discrete/continuous, sparse/dense, small/large network) and we attempt to put some order into this diversity, motivated by the fact that many properties are qualitatively the same in all the models. Our main result is that random networks in all models give rise to cyclic behavior more often than fixed points. And although periodic orbits seem to dominate network dynamics, they are usually considered unstable and not allowed to survive in previous evolutionary studies. Defining stability as the probability of fixed points, we show that the stability distribution of these networks is highly robust to changes in its parameters. We also find sparser networks to be more stable, which may help to explain why they seem to be favored by evolution. We have unified several disconnected previous studies of this class of models under the framework of stability, in a way that had not been systematically explored before

On the composition of ammonia-sulfuric-acid ion clusters during aerosol particle formation

The formation of particles from precursor vapors is an important source of atmospheric aerosol. Research at the Cosmics Leaving OUtdoor Droplets (CLOUD) facility at CERN tries to elucidate which vapors are responsible for this new-particle formation, and how in detail it proceeds. Initial measurement campaigns at the CLOUD stainless-steel aerosol chamber focused on investigating particle formation from ammonia (NH3) and sulfuric acid (H2SO4). Experiments were conducted in the presence of water, ozone and sulfur dioxide. Contaminant trace gases were suppressed at the technological limit. For this study, we mapped out the compositions of small NH3–H2SO4 clusters over a wide range of atmospherically relevant environmental conditions. We covered [NH3] in the range from 10. Positively charged clusters grew on average by Δm/Δn = 1.05 and were only observed at sufficiently high [NH3] / [H2SO4]. The H2SO4 molecules of these clusters are partially neutralized by NH3, in close resemblance to the acid–base bindings of ammonium bisulfate. Supported by model simulations, we substantiate previous evidence for acid–base reactions being the essential mechanism behind the formation of these clusters under atmospheric conditions and up to sizes of at least 2 nm. Our results also suggest that electrically neutral NH3–H2SO4 clusters, unobservable in this study, have generally the same composition as ionic clusters for [NH3] / [H2SO4] > 10. We expect that NH3–H2SO4 clusters form and grow also mostly by Δm/Δn > 1 in the atmosphere's boundary layer, as [NH3] / [H2SO4] is mostly larger than 10. We compared our results from CLOUD with APi-TOF measurements of NH3–H2SO4 anion clusters during new-particle formation in the Finnish boreal forest. However, the exact role of NH3–H2SO4 clusters in boundary layer particle formation remains to be resolved

Experimental investigation of ion-ion recombination under atmospheric conditions

We present the results of laboratory measurements of the ion–ion recombination coefficient at different temperatures, relative humidities and concentrations of ozone and sulfur dioxide. The experiments were carried out using the Cosmics Leaving OUtdoor Droplets (CLOUD) chamber at CERN, the walls of which are made of conductive material, making it possible to measure small ions. We produced ions in the chamber using a 3.5 GeV c−1 beam of positively charged pions (π+) generated by the CERN Proton Synchrotron (PS). When the PS was switched off, galactic cosmic rays were the only ionization source in the chamber. The range of the ion production rate varied from 2 to 100 cm−3 s−1, covering the typical range of ionization throughout the troposphere. The temperature ranged from −55 to 20 °C, the relative humidity (RH) from 0 to 70 %, the SO2 concentration from 0 to 40 ppb, and the ozone concentration from 200 to 700 ppb. The best agreement of the retrieved ion–ion recombination coefficient with the commonly used literature value of 1.6 × 10−6 cm3 s−1 was found at a temperature of 5 °C and a RH of 40 % (1.5 ± 0.6) × 10−6 cm3 s−1. At 20 °C and 40 % RH, the retrieved ion–ion recombination coefficient was instead (2.3 ± 0.7) × 10−6 cm3 s−1. We observed no dependency of the ion–ion recombination coefficient on ozone concentration and a weak variation with sulfur dioxide concentration. However, we observed a more than fourfold increase in the ion–ion recombination coefficient with decreasing temperature. We compared our results with three different models and found an overall agreement for temperatures above 0 °C, but a disagreement at lower temperatures. We observed a strong increase in the recombination coefficient for decreasing relative humidities, which has not been reported previously

Effect of dimethylamine on the gas phase sulfuric acid concentration measured by Chemical Ionization Mass Spectrometry

Sulfuric acid is widely recognized as a very important substance driving atmospheric aerosol nucleation. Based on quantum chemical calculations it has been suggested that the quantitative detection of gas phase sulfuric acid (H2SO4) by use of Chemical Ionization Mass Spectrometry (CIMS) could be biased in the presence of gas phase amines such as dimethylamine (DMA). An experiment (CLOUD7 campaign) was set up at the CLOUD (Cosmics Leaving OUtdoor Droplets) chamber to investigate the quantitative detection of H2SO4 in the presence of dimethylamine by CIMS at atmospherically relevant concentrations. For the first time in the CLOUD experiment, the monomer sulfuric acid concentration was measured by a CIMS and by two CI-APi-TOF (Chemical Ionization-Atmospheric Pressure interface-Time Of Flight) mass spectrometers. In addition, neutral sulfuric acid clusters were measured with the CI-APi-TOFs. The CLOUD7 measurements show that in the presence of dimethylamine (<5 to 70 pptv) the sulfuric acid monomer measured by the CIMS represents only a fraction of the total H2SO4, contained in the monomer and the clusters that is available for particle growth. Although it was found that the addition of dimethylamine dramatically changes the H2SO4 cluster distribution compared to binary (H2SO4-H2O) conditions, the CIMS detection efficiency does not seem to depend substantially on whether an individual H2SO4 monomer is clustered with a DMA molecule. The experimental observations are supported by numerical simulations based on A Self-contained Atmospheric chemistry coDe coupled with a molecular process model (Sulfuric Acid Water NUCleation) operated in the kinetic limit