Model of annual plants dynamics with facilitation and competition.

An individual-based model describing the dynamics of one type of annual plants is presented. We use Monte Carlo simulations where each plant has its own history and the interactions among plants are between nearest neighbours. The character of the interaction (positive or negative) depends on local conditions. The plants compete for two external resources-water and light. The amount of water and/or light a plant receives depends on the external factor but also on local arrangement. Survival, growth and seed production of plants are determined by how well their demands for the resources are met. The survival and seeds production tests have a probabilistic character, which makes the dynamics more realistic than by using a deterministic approach. There is a non-linear coupling between the external supplies. Water evaporates from the soil at a rate depending on constant evaporation rate, local conditions and the amount of light. We examine the dynamics of the plant population along two environmental gradients, allowing also for surplus of water and/or light. We show that the largest number of plants is when the demands for both resources are equal to the supplies. We estimate also the role of evaporation and we find that it depends on the situation. It could be negative, but sometimes it has a positive character. We show that the link between the type of interaction (positive or negative) and external conditions has a complex character. In general in favourable environment plants have a stronger tendency for competitive interactions, leading to mostly isolated plants. When the conditions are getting more difficult, cooperation becomes the dominant type of interactions and the plants grow in clusters. The type of plants-sun-loving or shade tolerating, plays also an important role.

Environmental, bystander and resident exposure from orchard applications using an agricultural unmanned aerial spraying system.

Unmanned aerial spraying systems (UASS), i.e., unmanned aerial vehicles designed for pesticide applications, are widely used in East Asia and increasingly prevalent in other regions of the world, including North America and Europe. However, according to a recent report of the Organization for Economic Co-operation and Development, spray drift and exposure caused by these systems are not yet fully understood. In particular, there are at present no peer-reviewed reports on direct exposure of residents and bystanders to spray drift following UASS applications. This lack of data results in regulatory concerns with respect to the environment and human safety. The objective of this study was to quantify environmental, resident and bystander exposure following the application of a plant protection product to an orchard using a commercial UASS under field conditions. Using a fluorescent tracer, horizontal and vertical downwind drift data were collected and direct exposure of residents and bystanders located downwind the sprayed area to spray drift was quantified using display mannequins equipped with personal air sampling pumps. Spray drift and exposure inversely correlated with sampling height and downwind distance. Furthermore, drift and exposure were strongly influenced by wind speed and direction, albeit hardly affected by the growth stage of the trees. In addition, substantially less tracer was extracted from the filters of the air sampling pumps than from the coveralls worn by mannequins, suggesting that direct resident/bystander exposure to spray drift may predominantly occur via the dermal route. This report provides essential data on UASS spray drift potential that are relevant for environmental and health risk assessments related to these systems. The results are compared to predicted values of current regulatory models and previously reported field data on drift and exposure caused by different spraying equipment.

Dependence of the fluctuation-dissipation temperature on the choice of observable.

On general grounds, a nonequilibrium temperature can be consistently defined from generalized fluctuation-dissipation relations only if it is independent of the observable considered. We argue that the dependence on the choice of observable generically occurs when the phase-space probability distribution is nonuniform on constant energy shells. We relate quantitatively this observable dependence to a fundamental characteristics of nonequilibrium systems, namely, the Shannon entropy difference with respect to the equilibrium state with the same energy. This relation is illustrated on a mean-field model in contact with two heat baths at different temperatures.

Extinction risk and structure of a food web model.

We investigate in detail the model of a trophic web proposed by Amaral and Meyer [Phys. Rev. Lett. 82, 652 (1999)]. We focus on small-size systems that are relevant for real biological food webs and for which the fluctuations play an important role. We show, using Monte Carlo simulations, that such webs can be nonviable, leading to extinction of all species in small and/or weakly coupled systems. Estimations of the extinction times and survival chances are also given. We show that before the extinction the fraction of highly connected species ("omnivores") is increasing. Viable food webs exhibit a pyramidal structure, where the density of occupied niches is higher at lower trophic levels, and moreover the occupations of adjacent levels are closely correlated. We also demonstrate that the distribution of the lengths of food chains has an exponential character and changes weakly with the parameters of the model. On the contrary, the distribution of avalanche sizes of the extinct species depends strongly on the connectedness of the web. For rather loosely connected systems, we recover the power-law type of behavior with the same exponent as found in earlier studies, while for densely connected webs the distribution is not of a power-law type.

Complex population dynamics as a competition between multiple-time-scale phenomena.

The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The mean-field level of description allows one to highlight the delicate interplay between the different time-scale processes in the resulting complex dynamics of the system. We clarify the influence of the amplitude and period of the environmental changes on the critical value of the selection pressure corresponding to a phase-transition "extinct-alive" of the population. However, the intrinsic stochasticity and the dynamically-built in correlations among the individuals, as well as the role of the mutation-induced variety in population's evolution are not appropriately accounted for. A more refined level of description, which is an individual-based one, has to be considered. The inherent fluctuations do not destroy the phase transition "extinct-alive," and the mutation amplitude is strongly influencing the value of the critical selection pressure. The phase diagram in the plane of the population's parameters-selection and mutation are discussed as a function of the environmental variation characteristics. The differences between a smooth variation of the environment and an abrupt, catastrophic change are also addressed.

Intensive thermodynamic parameters in nonequilibrium systems.

Considering a broad class of steady-state nonequilibrium systems for which some additive quantities are conserved by the dynamics, we introduce from a statistical approach intensive thermodynamic parameters (ITPs) conjugated to the conserved quantities. This definition does not require any detailed balance relation to be fulfilled. Rather, the system must satisfy a general additivity property, which holds in most of the models usually considered in the literature, including those described by a matrix product ansatz with finite matrices. The main property of these ITPs is to take equal values in two subsystems, making them a powerful tool to describe nonequilibrium phase coexistence, as illustrated on different models. We finally discuss the issue of the equalization of ITPs when two different systems are put into contact. This issue is closely related to the possibility of measuring the ITPs using a small auxiliary system, in the same way as temperature is measured with a thermometer, and points at one of the major difficulties of nonequilibrium statistical mechanics. In addition, an efficient alternative determination, based on the measure of fluctuations, is also proposed and illustrated.

Self-organized packs selection in predator-prey ecosystems.

We present a lattice model of a system of predators of five kinds, competing for prey. The predators are grouped in packs and characterized by two parameters-the energy spent on hunting and energy gained by the kill. The success of hunting depends on the actual competition among predators found near a prey. We determine via Monte Carlo simulations the numbers of predators of each kind as a function of time and the distribution of the size of their packs. We show that the ratio of the energy spent by the competing predators determines their fate. The energy gain plays only a secondary role. We show also that the system self-organizes itself into groups of predators living in well defined packs, which size depends on the energy spent. The most preferred size dependence on the energy spent follows a very simple power law. We present also a mean-field-type approach to the problem and we discuss the differences in the results obtained by the two methods, showing in particular, that the simulation approach produces more reliable results.

Boltzmann and hydrodynamic description for self-propelled particles.

We study analytically the emergence of spontaneous collective motion within large bidimensional groups of self-propelled particles with noisy local interactions, a schematic model for assemblies of biological organisms. As a central result, we derive from the individual dynamics the hydrodynamic equations for the density and velocity fields, thus giving a microscopic foundation to the phenomenological equations used in previous approaches. A homogeneous spontaneous motion emerges below a transition line in the noise-density plane. Yet, this state is shown to be unstable against spatial perturbations, suggesting that more complicated structures should eventually appear.

Hydrothermal degradation of a 3Y-TZP translucent dental ceramic: A comparison of numerical predictions with experimental data after 2 years of aging.

OBJECTIVES: The purpose of the study was to assess the hydrothermal resistance of a translucent zirconia with two clinical relevant surface textures by means of accelerated tests (LTD) and to compare predicted monoclinic fractions with experimental values measured after two years aging at 37°C. METHODS: Polished (P) and ground (G) specimens were subjected to hydrothermal degradation by exposure to water steam at different temperatures and pressures. The t-m phase transformation was quantified by grazing incidence X-ray diffraction (GIXDR). The elastic modulus and hardness before- and after LTD were determined by nanoindentation. RESULTS: G specimens presented a better resistance to hydrothermal degradation than P samples. Activation energies of 89 and 98kJ/mol and b coefficients of 2.0×10(-5) and 1.8×10(-6) were calculated for P and G samples respectively. The coefficients were subsequently used to predict transformed monoclinic fractions at 37°C. A good correlation was found between the predicted values and the experimental data obtained after aging at 37°C during 2 years. Hydrothermal degradation led to a significant decrease of the elastic moduli and hardness in both groups. SIGNIFICANCE: The dependency of the t-m phase transformation rate on temperature must be determined to accurately predict the hydrothermal behavior of the zirconia ceramics at oral temperatures. The current prevailing assumption, that 5h aging at 134°C corresponds to 15-20 years at 37°C, will underestimate the transformed fraction of the translucent ceramic at 37°C. In this case, the mechanical surface treatment influences the ceramic's transformability. While mild grinding could potentially retard the hydrothermal transformation, polishing after occlusal adjustment is recommended to prevent wear of the antagonist teeth and maintain structural strength.

Nonequilibrium temperatures in steady-state systems with conserved energy.

We study a class of nonequilibrium lattice models describing local redistributions of a globally conserved quantity, which is interpreted as an energy. A particular subclass can be solved exactly, allowing us to define a statistical temperature T(th) along the same lines as in the equilibrium micro-canonical ensemble. We compute the response function and find that when the fluctuation-dissipation relation is linear, the slope T(FD)(-1) of this relation differs from the inverse temperature T(th)(-1). We argue that T(th) is physically more relevant than T(FD), since in the steady-state regime, it takes equal values in two subsystems of a large isolated system. Finally, a numerical renormalization group procedure suggests that all models within the class behave similarly at a coarse-grained level, leading to a parameter that describes the deviation from equilibrium. Quantitative predictions concerning this parameter are obtained within a mean-field framework.

Maxwell and very-hard-particle models for probabilistic ballistic annihilation: hydrodynamic description.

The hydrodynamic description of probabilistic ballistic annihilation, for which no conservation laws hold, is an intricate problem with hard spherelike dynamics for which no exact solution exists. We consequently focus on simplified approaches, the Maxwell and very-hard-particle (VHP) models, which allows us to compute analytically upper and lower bounds for several quantities. The purpose is to test the possibility of describing such a far from equilibrium dynamics with simplified kinetic models. The motivation is also in turn to assess the relevance of some singular features appearing within the original model and the approximations invoked to study it. The scaling exponents are first obtained from the (simplified) Boltzmann equation, and are confronted against direct Monte Carlo simulations. Then, the Chapman-Enskog method is used to obtain constitutive relations and transport coefficients. The corresponding Navier-Stokes equations for the hydrodynamic fields are derived for both Maxwell and VHP models. We finally perform a linear stability analysis around the homogeneous solution, which illustrates the importance of dissipation in the possible development of spatial inhomogeneities.

Synchronization in coupled map lattices as an interface depinning.

We study a solid-on-solid (SOS) model whose dynamics is inspired by recent studies of the synchronization transition in coupled map lattices (CML). The synchronization of CML is thus related with a depinning of interface from a binding wall. Critical behavior of our SOS model depends on a specific form of binding (i.e., transition rates of the dynamics). For an exponentially decaying binding the depinning belongs to the directed percolation universality class. Other types of depinning, including the one with a line of critical points, are observed for a power-law binding.

Dynamical properties of the synchronization transition.

We use spreading dynamics to study the synchronization transition (ST) of one-dimensional coupled map lattices (CML's). Recently, Baroni et al. [Phys. Rev. E 63, 036226 (2001)] have shown that the ST belongs to the directed percolation (DP) universality class for discontinuous CML's. This was confirmed by accurate numerical simulations for the Bernoulli map by Ahlers and Pikovsky [Phys. Rev. Lett. 88, 254101 (2002)]. Spreading dynamics confirms such an identification only for random synchronized states. For homogeneous synchronized states the spreading exponents eta and delta are different from the DP exponents but their sum equals the corresponding sum of the DP exponents. Such a relation is typical of models with infinitely many absorbing states. Moreover, we calculate the spreading exponents for the tent map for which the ST belongs to the bounded Kardar-Parisi-Zhang (BKPZ) universality class. The estimation of spreading exponents for random synchronized states is consistent with the hyperscaling relation, while it is inconsistent for the homogeneous ones. Finally, we examine the asymmetric tent map. For small asymmetry the ST remains of the BKPZ type. However, for large asymmetry a different critical behavior appears, with exponents being relatively close to those for DP.

Role of evolution by natural selection in population dynamics.

Using a Monte Carlo approach we study the role of inheritance and natural selection in the dynamics of populations. We show that a population subject to inheritance has a much better chance of survival in a given condition than a population where new generations do not inherit genomes of their parents. The dependence of the survival chance on such factors as selection pressure, fecundity, or carrying capacity of the system is much stronger when selection and inheritance are present. We demonstrate, in accordance with biological observations, that in certain conditions evolution can save a population which would perish without it.

Urn model of separation of sand.

We introduce an urn model that describes spatial separation of sand. In this dynamical model, in a certain range of parameters spontaneous symmetry breaking takes place and equipartitioning of sand into two compartments is broken. The steady-state equation for an order parameter, a critical line, and the tricritical point on the phase diagram are found exactly. The master equation and the first-passage problem for the model are solved numerically and the results are used to locate first-order transitions. Exponential divergence of a certain characteristic time shows that the model can also exhibit very strong metastability. In certain cases characteristic time diverges as N(z), where N is the number of balls and z=1 / 2 (critical line), 2 / 3 (tricritical point), or 1 / 3 (limits of stability).

Dynamics-dependent criticality in models with q absorbing states.

We study a one-dimensional, nonequilibrium Potts-like model that has q symmetric absorbing states. For q=2, as expected, the model belongs to the parity-conserving universality class. For q=3 the critical behavior depends on the dynamics of the model. Under a certain dynamics it remains generically in the active phase, which is also the feature of some other models with three absorbing states. However, a modified dynamics induces a parity-conserving phase transition. Relations with branching-annihilating random walk models are discussed in order to explain such a behavior.

Moment ratios for an urn model of sand compartmentalization.

Numerically solving a master equation for a recently introduced nonequilibrium urn model of sand compartmentalization, we show that the order-parameter moment ratios of the fourth and sixth order remain constant along an exactly located line of critical points. Obtained values are in very good agreement with values predicted by Brézin and Zinn-Justin for the equilibrium Ising model above the critical dimension. At the tricritical point, these ratios acquire values that also agree with a suitably extended Brézin and Zinn-Justin approach.

Dynamics of populations in a changing environment.

We present an individual-based model of a population that lives in a changing environment. The individuals forming the population are subject to mutations and selection pressure. Using Monte Carlo simulations we have shown that, depending on the values of the mutation rate and selection, the population may reach either an active phase (it will survive) or an absorbing phase (it will become extinct). We have determined that the transition between the two states (phases) is continuous. We have shown that when the selection is weaker the population lives in all available space, while if the selection is stronger, it will move to the regions where the living conditions are better, avoiding those with more difficult conditions. The dependence of the mean time to extinction on the rate of mutations has been determined and discussed.

Phase transitions in nonequilibrium d-dimensional models with q absorbing states.

A nonequilibrium Potts-like model with q absorbing states is studied using Monte Carlo simulations. In two dimensions and q=3 the model exhibits a discontinuous transition. For the three-dimensional case and q=2 the model exhibits a continuous transition with beta=1 (mean field). Simulations are inconclusive, however, in the two-dimensional case for q=2. We suggest that in this case the model is close to or at the crossing point of lines separating three different types of phase transitions. The proposed phase diagram in the (q,d) plane is very similar to that of the equilibrium Potts model. In addition, our simulations confirm the field-theory prediction that in two dimensions a branching-annihilating random walk model without parity conservation belongs to the directed percolation universality class.