Dynamical properties of the Zhang model of self-organized criticality

Critical exponents of the infinitely slowly driven Zhang model of self-organized criticality are computed for d=2 and 3, with particular emphasis devoted to the various roughening exponents. Besides confirming recent estimates of some exponents, new quantities are monitored, and their critical exponents computed. Among other results, it is shown that the three-dimensional exponents do not coincide with the Bak-Tang-Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] (Abelian) model, and that the dynamical exponent as computed from the correlation length and from the roughness of the energy profile do not necessarily coincide, as is usually implicitly assumed. An explanation for this is provided. The possibility of comparing these results with those obtained from renormalization group arguments is also briefly addressed.

Stochastic resonance in nonpotential systems

We propose a method to analytically show the possibility for the appearance of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our results to the FitzHugh-Nagumo model under a periodic external forcing, showing that the model exhibits stochastic resonance. The procedure that we follow is based on the reduction to a one-dimensional dynamics in the adiabatic limit and in the topology of the phase space of the systems under study. Its application to other nonpotential systems is also discussed.

Magnetic field scaling of relaxation curves in small particle systems

We study the effects of the magnetic field on the relaxation of the magnetization of smallmonodomain noninteracting particles with random orientations and distribution of anisotropyconstants. Starting from a master equation, we build up an expression for the time dependence of themagnetization which takes into account thermal activation only over barriers separating energyminima, which, in our model, can be computed exactly from analytical expressions. Numericalcalculations of the relaxation curves for different distribution widths, and under different magneticfields H and temperatures T, have been performed. We show how a T ln(t/t0) scaling of the curves,at different T and for a given H, can be carried out after proper normalization of the data to theequilibrium magnetization. The resulting master curves are shown to be closely related to what wecall effective energy barrier distributions, which, in our model, can be computed exactly fromanalytical expressions. The concept of effective distribution serves us as a basis for finding a scalingvariable to scale relaxation curves at different H and a given T, thus showing that the fielddependence of energy barriers can be also extracted from relaxation measurements.

Quantum critical effects in mean-field glassy systems

We consider the effects of quantum fluctuations in mean-field quantum spin-glass models with pairwise interactions. We examine the nature of the quantum glass transition at zero temperature in a transverse field. In models (such as the random orthogonal model) where the classical phase transition is discontinuous an analysis using the static approximation reveals that the transition becomes continuous at zero temperature.

Nonempirical cluster-model study of the chemisorption of atomic hydrogen on the (111) surface of diamondlike crystals

The interaction of atomic hydrogen with C4H9, Si4H9, and Ge4H9 model clusters has been studied using all-electron and pseudopotential ab initio Hartree-Fock computations with basis sets of increasing flexibility. The results show that the effect of polarization functions is important in order to reproduce the experimental findings, but their inclusion only for the atoms directly involved in the chemisorption bond is usually sufficient. For the systems H-C4H9 and H-Si4H9 all-electron and pseudopotential results are in excellent agreement when basis sets of comparable quality are used. Besides, semiempirical modified-neglect-of-differential-overlap computations provide quite reliable results both for diamond and silicon and have been used to investigate larger model clusters. The results confirm the local nature of chemisorption and further justify the use of minimal X4H9 model clusters.

Performance of correlation functionals in ab initio chemisorption cluster-model calculations: Alkali metals on Si(111)

The performance of different correlation functionals has been tested for alkali metals, Li to Cs, interacting with cluster models simulating different active sites of the Si(111) surface. In all cases, the ab initio Hartree-Fock density has been obtained and used as a starting point. The electronic correlation energy is then introduced as an a posteriori correction to the Hartree-Fock energy using different correlation functionals. By making use of the ionic nature of the interaction and of different dissociation limits we have been able to prove that all functionals tested introduce the right correlation energy, although to a different extent. Hence, correlation functionals appear as an effective and easy way to introduce electronic correlation in the ab initio Hartree-Fock description of the chemisorption bond in complex systems where conventional configuration interaction techniques cannot be used. However, the calculated energies may differ by some tens of eV. Therefore, these methods can be employed to get a qualitative idea of how important correlation effects are, but they have some limitations if accurate binding energies are to be obtained.

Ab Initio study of magnetic interactions in the KCuF3 and K2CuF4 low-dimensional Systems

The ab initio cluster model approach has been used to study the electronic structure and magnetic coupling of KCuF3 and K2CuF4 in their various ordered polytype crystal forms. Due to a cooperative Jahn-Teller distortion these systems exhibit strong anisotropies. In particular, the magnetic properties strongly differ from those of isomorphic compounds. Hence, KCuF3 is a quasi-one-dimensional (1D) nearest neighbor Heisenberg antiferromagnet whereas K2CuF4 is the only ferromagnet among the K2MF4 series of compounds (M=Mn, Fe, Co, Ni, and Cu) behaving all as quasi-2D nearest neighbor Heisenberg systems. Different ab initio techniques are used to explore the magnetic coupling in these systems. All methods, including unrestricted Hartree-Fock, are able to explain the magnetic ordering. However, quantitative agreement with experiment is reached only when using a state-of-the-art configuration interaction approach. Finally, an analysis of the dependence of the magnetic coupling constant with respect to distortion parameters is presented.

Effective t-J model Hamiltonian parameters of monolayered cuprate superconductors from ab initio electronic structure calculations

The magnetic coupling constant of selected cuprate superconductor parent compounds has been determined by means of embedded cluster model and periodic calculations carried out at the same level of theory. The agreement between both approaches validates the cluster model. This model is subsequently employed in state-of-the-art configuration interaction calculations aimed to obtain accurate values of the magnetic coupling constant and hopping integral for a series of superconducting cuprates. Likewise, a systematic study of the performance of different ab initio explicitly correlated wave function methods and of several density functional approaches is presented. The accurate determination of the parameters of the t-J Hamiltonian has several consequences. First, it suggests that the appearance of high-Tc superconductivity in existing monolayered cuprates occurs with J/t in the 0.20¿0.35 regime. Second, J/t=0.20 is predicted to be the threshold for the existence of superconductivity and, third, a simple and accurate relationship between the critical temperatures at optimum doping and these parameters is found. However, this quantitative electronic structure versus Tc relationship is only found when both J and t are obtained at the most accurate level of theory.

Surface structure and stability of PdZn and PtZn alloys: Density-functional slab model studies

Geometric parameters of binary (1:1) PdZn and PtZn alloys with CuAu-L10 structure were calculated with a density functional method. Based on the total energies, the alloys are predicted to feature equal formation energies. Calculated surface energies of PdZn and PtZn alloys show that (111) and (100) surfaces exposing stoichiometric layers are more stable than (001) and (110) surfaces comprising alternating Pd (Pt) and Zn layers. The surface energy values of alloys lie between the surface energies of the individual components, but they differ from their composition weighted averages. Compared with the pure metals, the valence d-band widths and the Pd or Pt partial densities of states at the Fermi level are dramatically reduced in PdZn and PtZn alloys. The local valence d-band density of states of Pd and Pt in the alloys resemble that of metallic Cu, suggesting that a similar catalytic performance of these systems can be related to this similarity in the local electronic structures.

Spontaneous mirror symmetry breaking in the limited enantioselective autocatalysis model: abyssal hydrotermal vents as scenario for the emergence of chirality in prebiotic chemistry

The emergence of chirality in enantioselective autocatalysis for compounds unable to transform according to the Frank-like reaction network is discussed with respect to the controversial limited enantioselectivity (LES) model composed of coupled enantioselective and non-enantioselective autocatalyses. The LES model cannot lead to spontaneous mirror symmetry breaking (SMSB) either in closed systems with a homogeneous temperature distribution or in closed systems with a stationary non-uniform temperature distribution. However, simulations of chemical kinetics in a two-compartment model demonstrate that SMSB may occur if both autocatalytic reactions are spatially separated at different temperatures in different compartments but coupled under the action of a continuous internal flow. In such conditions, the system can evolve, for certain reaction and system parameters, toward a chiral stationary state; that is, the system is able to reach a bifurcation point leading to SMSB. Numerical simulations in which reasonable chemical parameters have been used suggest that an ade- quate scenario for such a SMSB would be that of abyssal hydrothermal vents, by virtue of the typical temper- ature gradients found there and the role of inorganic solids mediating chemical reactions in an enzyme-like role. Key Words: Homochirality Prebiotic chemistry.

Temperature-dependent turnovers in sex-determination mechanisms: a quantitative model.

Sex determination is often seen as a dichotomous process: individual sex is assumed to be determined either by genetic (genotypic sex determination, GSD) or by environmental factors (environmental sex determination, ESD), most often temperature (temperature sex determination, TSD). We endorse an alternative view, which sees GSD and TSD as the ends of a continuum. Both effects interact a priori, because temperature can affect gene expression at any step along the sex-determination cascade. We propose to define sex-determination systems at the population- (rather than individual) level, via the proportion of variance in phenotypic sex stemming from genetic versus environmental factors, and we formalize this concept in a quantitative-genetics framework. Sex is seen as a threshold trait underlain by a liability factor, and reaction norms allow modeling interactions between genotypic and temperature effects (seen as the necessary consequences of thermodynamic constraints on the underlying physiological processes). As this formalization shows, temperature changes (due to e.g., climatic changes or range expansions) are expected to provoke turnovers in sex-determination mechanisms, by inducing large-scale sex reversal and thereby sex-ratio selection for alternative sex-determining genes. The frequency of turnovers and prevalence of homomorphic sex chromosomes in cold-blooded vertebrates might thus directly relate to the temperature dependence in sex-determination mechanisms.

Evolution of self-organized division of labor in a response threshold model.

Division of labor in social insects is determinant to their ecological success. Recent models emphasize that division of labor is an emergent property of the interactions among nestmates obeying to simple behavioral rules. However, the role of evolution in shaping these rules has been largely neglected. Here, we investigate a model that integrates the perspectives of self-organization and evolution. Our point of departure is the response threshold model, where we allow thresholds to evolve. We ask whether the thresholds will evolve to a state where division of labor emerges in a form that fits the needs of the colony. We find that division of labor can indeed evolve through the evolutionary branching of thresholds, leading to workers that differ in their tendency to take on a given task. However, the conditions under which division of labor evolves depend on the strength of selection on the two fitness components considered: amount of work performed and on worker distribution over tasks. When selection is strongest on the amount of work performed, division of labor evolves if switching tasks is costly. When selection is strongest on worker distribution, division of labor is less likely to evolve. Furthermore, we show that a biased distribution (like 3:1) of workers over tasks is not easily achievable by a threshold mechanism, even under strong selection. Contrary to expectation, multiple matings of colony foundresses impede the evolution of specialization. Overall, our model sheds light on the importance of considering the interaction between specific mechanisms and ecological requirements to better understand the evolutionary scenarios that lead to division of labor in complex systems. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s00265-012-1343-2) contains supplementary material, which is available to authorized users.

Evolution of uni- and bifactorial sexual compatibility systems in fungi.

Mating systems, that is, whether organisms give rise to progeny by selfing, inbreeding or outcrossing, strongly affect important ecological and evolutionary processes. Large variations in mating systems exist in fungi, allowing the study of their origin and consequences. In fungi, sexual incompatibility is determined by molecular recognition mechanisms, controlled by a single mating-type locus in most unifactorial fungi. In Basidiomycete fungi, however, which include rusts, smuts and mushrooms, a system has evolved in which incompatibility is controlled by two unlinked loci. This bifactorial system probably evolved from a unifactorial system. Multiple independent transitions back to a unifactorial system occurred. It is still unclear what force drove evolution and maintenance of these contrasting inheritance patterns that determine mating compatibility. Here, we give an overview of the evolutionary factors that might have driven the evolution of bifactoriality from a unifactorial system and the transitions back to unifactoriality. Bifactoriality most likely evolved for selfing avoidance. Subsequently, multiallelism at mating-type loci evolved through negative frequency-dependent selection by increasing the chance to find a compatible mate. Unifactoriality then evolved back in some species, possibly because either selfing was favoured or for increasing the chance to find a compatible mate in species with few alleles. Owing to the existence of closely related unifactorial and bifactorial species and the increasing knowledge of the genetic systems of the different mechanisms, Basidiomycetes provide an excellent model for studying the different forces that shape breeding systems.

Sex-chromosome turnovers: the hot-potato model.

Abstract Sex-determining systems often undergo high rates of turnover but for reasons that remain largely obscure. Two recent evolutionary models assign key roles, respectively, to sex-antagonistic (SA) mutations occurring on autosomes and to deleterious mutations accumulating on sex chromosomes. These two models capture essential but distinct key features of sex-chromosome evolution; accordingly, they make different predictions and present distinct limitations. Here we show that a combination of features from the two models has the potential to generate endless cycles of sex-chromosome transitions: SA alleles accruing on a chromosome after it has been co-opted for sex induce an arrest of recombination; the ensuing accumulation of deleterious mutations will soon make a new transition ineluctable. The dynamics generated by these interactions share several important features with empirical data, namely, (i) that patterns of heterogamety tend to be conserved during transitions and (ii) that autosomes are not recruited randomly, with some chromosome pairs more likely than others to be co-opted for sex.

Long-term and long range migration of radioisotopes in terrestrial systems : mechanisms of radioisotopes (Cs, Sr, Pu, Am) mobilization in soils

Summary Artificial radionuclides were released in the environment during the atmospheric nuclear weapon tests and after accidental events involving nuclear industries. As a primary receptor of the deposition, the soil is a very sensitive compartment and understanding the interaction and migration of radionuclides within soils allows the development of scenario for the contamination risk of the population and of the environment. Most available field studies on radionuclides in soils only concern one or two isotopes, mostly 137Cs, and few physico-chemical soil parameters. The purpose of this study was a broader understanding of the radioecology of an Alpine valley. In a first part, we aimed to describe the depth distribution of 137Cs, 90Sr, 239+240Pu, and 241Am within different alpine soils and to identify some stable elements as indicators for accumulating layers. In the central part of the study, the goal was to investigate the repartition of ^Sr and 239Pu between the truly dissolved fraction and the colloidal fraction of the soil solutions and to identify the nature of colloids involved in the adsorption of ^Sr and 239Pu. These results were integrated in an "advection- sorption" transport model seeking to explain the migration of 239Pu and 90Sr within the soils and to assess the importance of colloidal transport for these two isotopes. A further aspect studied was the role of the competition between the radioisotopes (137Cs and 90Sr) and their stable chemical analogues (K and Ca) with respect to plant uptake by different plant species. The results on the depth distribution within the soils showed that 137Cs was mostly retained in the topsoil, to the exception of an organic-rich soil (Histosol 2) receiving important surface runoff, where migration down to a depth of 30 cm was observed. 137Cs depth distribution within the soils was similar to unsupported 210Pb depth distribution. The plant uptake of 137Cs clearly depended on the concentration of exchangeable potassium in the soils. Moreover, we showed that the 137Cs uptake by certain species of the taxonomic orders Poales and Rosales was more sensitive to the increase in exchangeable Κ compared to other orders. Strontium-90 was much more mobile in the soils than 137Cs and depth migration and accumulation in specific AI- and Fe-rich layers were found down to 30 cm. Copper and Ni showed accumulations in these same layers, indicating their potential to be used as indicators for the migration of ^Sr within the soils. In addition, we observed a 90Sr activity peak in the topsoil that can be attributable to recycling of 90Sr by plant uptake. We demonstrated for the first time that a part of 90Sr (at least 40%) was associated with the colloids in organic-rich soil solutions. Therefore, we predict a significant effect of the colloidal migration of ^Sr in organic-rich soil solutions. The plant uptake results for 90Sr indicated a phylogenetic effect between Non-Eudicot and Eudicots: the order Poales concentrating much less 90Sr than Eudicots do. Moreover, we were able to demonstrate that the sensitivity of the 90Sr uptake by 5 different Alpine plant species to the amount of exchangeable Ca was species-independent. Plutonium and 241Am accumulated in the second layer of all soils and only a slight migration deeper than 20 cm was observed. Plutonium and 241Am showed a similar depth distribution in the soils. The model results suggested that the present day migration of 239Pu was very slow and that the uptake by plants was negligible. 239Pu activities between 0.01 to 0.08 mBq/L were measured in the bulk soil solutions. Migration of 239Pu with the soil solution is dominated by colloidal transport. We reported strong evidences that humic substances were responsible of the sorption of 239Pu to the colloidal fraction of the soil solutions. This was reflected by the strong correlation between 239Pu concentrations and the content of (colloidal) organic matter in the soil solution. Résumé Certains radioéléments artificiels ont été disséminés dans l'environnement suite aux essais atmosphériques de bombes nucléaires et suite à des accidents impliquant les industries nucléaires. En tant que récepteur primaire de la déposition, le sol est un compartiment sensible et des connaissances sur les interactions et la migration des radioéléments dans le sol permettent de développer des modèles pour estimer la contamination de la population et de l'environnement. Actuellement, la plupart des études de terrain sur ce sujet concernent uniquement un ou deux radioéléments, surtout le 137Cs et peu d'études intègrent les paramètres du sol pour expliquer la migration des radioéléments. Le but général de cette étude était une compréhension étendue de la radio-écologie d'une vallée alpine. Notre premier objectif était de décrire la distribution en profondeur de 137Cs, ^Sr, 239+240pu et 241Am dans différents sols alpins en relation avec des éléments stables du sol, dans le but d'identifier des éléments stables qui pourraient servir d'indicateurs pour des horizons accumulateurs. L'objectif de la deuxième partie, qui était la partie centrale de l'étude, était d'estimer le pourcentage d'activité sous forme colloïdale du 239Pu et du 90Sr dans les solutions des sols. De plus nous avons déterminé la nature des colloïdes impliqués dans la fixation du ^Sr et 239Pu. Nous avons ensuite intégré ces résultats dans un modèle de transport développé dans le but de décrire la migration du 239Pu et 90Sr dans le sol. Finalement, nous avons étudié l'absorption de 137Cs et 90Sr par les plantes en fonction de l'espèce et de la compétition avec leur élément analogue stable (K et Ca). Les résultats sur la migration en profondeur du 137Cs ont montré que ce radioélément était généralement retenu en surface, à l'exception d'un sol riche en matière organique dans lequel nous avons observé une nette migration en profondeur. Dans tous les sols, la distribution en profondeur du 137Cs était corrélée avec la distribution du 210Pb. L'absorption du 137Cs par les plantes, était dépendante de la concentration en Κ échangeable dans le sol, le potassium étant un compétiteur. De plus, nous avons observé que les espèces ne réagissaient pas de la même manière aux variations de la concentration de Κ échangeable. En effet, les espèces appartenant aux ordres des Poales et des Rosales étaient plus sensibles aux variations de potassium échangeable dans le sol. Dans tous les sols Le 90Sr était beaucoup plus mobile que le 137Cs. En effet, nous avons observé des accumulations de 90Sr dans des horizons riches en Fe et Al jusqu'à 30 cm de profondeur. De plus, le Cu et le Ni montraient des accumulations dans les mêmes horizons que le 90Sr, indiquant qu'il pourrait être possible d'utiliser ces deux éléments comme analogues pour la migration du 90Sr. D'après le modèle développé, le pic de 90Sr dans les premiers centimètres du sol peut être attribué à du recyclage par les plantes. Le 90Sr en solution était principalement sous forme dissoute dans des solutions de sols peu organique (entre 60 et 100% de 90Sr dissous). Par contre, dans des solutions organiques, un important pourcentage de 90Sr (plus de 40%) était associé aux colloïdes. La migration colloïdale du 90Sr peut donc être significative dans des solutions organiques. Comme pour le 137Cs, l'absorption du 90Sr par les plantes dépendait de la concentration de son analogue chimique dans la fraction échangeable du sol. Par contre, les espèces de plantes étudiées avaient la même sensibilité aux variations de la concentration du calcium échangeable. Le plutonium et l'américium étaient accumulés dans le deuxième horizon du sol et nous avons observé seulement une faible migration plus profondément que 20 cm. Selon le modèle, la migration actuelle du plutonium est très lente et l'absorption par les plantes semble négligeable. Nous avons mesuré entre 0.01 et 0.08 mBq/L de 239Pu dans les solutions de sol brutes. La migration du plutonium par la solution du sol est due principalement aux colloïdes, probablement de nature humique. Résumé grand public Dans les années 1950 à 1960, l'environnement a été contaminé par des éléments radioactifs (radioéléments) artificiels provenant des essais des armes atomiques et de l'industrie nucléaire. En effet, durant ces années, les premiers essais de bombes atomiques se faisaient dans l'atmosphère, libérant de grandes quantités d'éléments radioactifs. De plus certains accidents impliquant l'industrie nucléaire civile ont contribué à la dissémination d'éléments radioactifs dans l'environnement. Ce fut par exemple le cas de l'accident de la centrale atomique de Tchernobyl en 1986 qui a causé une importante contamination d'une grande partie de l'Europe par le 137Cs. Lorsqu'ils sont libérés dans l'atmosphère, les radioéléments sont dispersés et transportés par les courants atmosphériques, puis peuvent être déposés dans l'environnement, principalement par les précipitations. Une fois déposés sur le sol, les radioéléments vont interagir avec les composants du sol et migrer plus ou moins vite. La connaissance des interactions des éléments radioactifs avec le sol est donc importante pour prédire les risques de contamination de l'environnement et de l'homme. Le but général de ce travail était d'évaluer la migration de différents éléments radioactifs (césium-137, strontium-90, plutonium et américium-241) à travers le sol. Nous avons choisi un site d'étude en milieu alpin (Val Piora, Tessin, Suisse), contaminé en radioéléments principalement par les retombées de l'accident de Tchernobyl et des essais atmosphériques de bombes atomiques. Dans un premier temps, nous avons caractérisé la distribution en profondeur des éléments radioactifs dans le sol et l'avons comparée à divers éléments stables. Cette comparaison nous a permit de remarquer que le cuivre et le nickel s'accumulaient dans les mêmes horizons du sol que le strontium-90 et pourraient donc être utilisés comme analogue pour la migration du strontium-90 dans les sols. Dans la plupart des sols étudiés, la migration du césium-137, du plutonium et de l'américium-241 était lente et ces radioéléments étaient donc accumulés dans les premiers centimètres du sol. Par contre, le strontium-90 a migré beaucoup plus rapidement que les autres radioéléments si bien qu'on observe des accumulations de strontium-90 à plus de 30 cm de profondeur. Les radioéléments migrent dans la solution du sol soit sous forme dissoute, soit sous forme colloïdale, c'est-à-dire associés à des particules de diamètre < Ιμηι. Cette association avec des colloïdes permet à des radioéléments peu solubles, comme le plutonium, de migrer plus rapidement qu'attendu. Nous avons voulu savoir quelle était la part de strontium-90 et plutonium associés à des colloïdes dans la solution du sol. Les résultats ont montré que le plutonium en solution était principalement associé à des colloïdes de type organique. Quant au strontium-90, ce dernier était en partie associé à des colloïdes dans des solutions de sol riches en matière organique, par contre, il était principalement sous forme dissoute dans les solutions de sol peu organiques. L'absorption de radioéléments par les plantes représente une voie importante pour le transfert vers la chaîne alimentaire, par conséquent pour la contamination de l'homme. Nous avons donc étudié le transfert du césium-137 et du strontium-90 de plusieurs sols vers différentes espèces de plantes. Les résultats ont montré que l'absorption des radioéléments par les plantes était liée à la concentration de leur analogue chimique (calcium pour le strontium-90 et potassium pour le césium- 137) dans la fraction échangeable du sol. De plus certaines espèces de plantes accumulent significativement moins de strontium-90.