Origin and variability of statistical dependencies between peak, volume, and duration of rainfall-driven flood events.

Floods are among the most common and impactful natural events. The hazard of a flood event depends on its peak (Q), volume (V) and duration (D), which are interconnected to each other. Here, we used a worldwide dataset of daily discharge, two statistics (Kendall's tau and Spearman's rho) and a conceptual hydrological rainfall-runoff model as model-dependent realism, to investigate the factors controlling and the origin of the dependence between each couple of flood characteristics, with the focus to rainfall-driven events. From the statistical analysis of worldwide dataset, we found that the catchment area is ineffective in controlling the dependence between Q and V, while the dependencies between Q and D, and V and D show an increasing behavior with the catchment area. From the modeling activity, on the U.S. subdataset, we obtained that the conceptual hydrological model is able to represent the observed dependencies between each couple of variables for rainfall-driven flood events, and for such events, the pairwise dependence of each couple is not causal, is of spurious kind, coming from the "Principle of Common Cause".

Carrying capacity in arid rangelands during droughts: the role of temporal and spatial thresholds.

Assessing the carrying capacity is of primary importance in arid rangelands. This becomes even more important during droughts, when rangelands exhibit non-equilibrium dynamics, and the dynamics of livestock conditions and forage resource are decoupled. Carrying capacity is usually conceived as an equilibrium concept, that is, the consumer density that can co-exist in long-term equilibrium with the resource. As one of the first, here we address the concept of carrying capacity in systems, where there is no feedback between consumer and resource in a limited period of time. To this end, we developed an individual-based model describing the basic characteristics of a rangeland during a drought. The model represents a rangeland composed by a single water point and forage distributed all around, with livestock units moving from water to forage and vice versa, for eating and drinking. For each livestock unit we implemented an energy balance and we accounted for the gut-filling effect (i.e. only a limited amount of forage can be ingested per unit time). Our results showed that there is a temporal threshold above which livestock begin to experience energy deficit and burn fat reserves. We demonstrated that such a temporal threshold increases with the number of animals and decreases with the rangeland conditions (amount of forage). The temporal threshold corresponded to the time livestock take to consume all the forage within a certain distance from water, so that the livestock can return to water for drinking without spending more energy than they gain within a day. In this study, we highlight the importance of a time threshold in the assessment of carrying capacity in non-equilibrium conditions. Considering this time threshold could explain contrasting observations about the influence of livestock number on livestock conditions. In case of private rangelands, the herd size should be chosen so that the spatial threshold equals (or exceeds) the length of the drought.

Robustness and management adaptability in tropical rangelands: a viability-based assessment under the non-equilibrium paradigm.

Rangelands provide the main forage resource for livestock in many parts of the world, but maintaining long-term productivity and providing sufficient income for the rancher remains a challenge. One key issue is to maintain the rangeland in conditions where the rancher has the greatest possibility to adapt his/her management choices to a highly fluctuating and uncertain environment. In this study, we address management robustness and adaptability, which increase the resilience of a rangeland. After reviewing how the concept of resilience evolved in parallel to modelling views on rangelands, we present a dynamic model of rangelands to which we applied the mathematical framework of viability theory to quantify the management adaptability of the system in a stochastic environment. This quantification is based on an index that combines the robustness of the system to rainfall variability and the ability of the rancher to adjust his/her management through time. We evaluated the adaptability for four possible scenarios combining two rainfall regimes (high or low) with two herding strategies (grazers only or mixed herd). Results show that pure grazing is viable only for high-rainfall regimes, and that the use of mixed-feeder herds increases the adaptability of the management. The management is the most adaptive with mixed herds and in rangelands composed of an intermediate density of trees and grasses. In such situations, grass provides high quantities of biomass and woody plants ensure robustness to droughts. Beyond the implications for management, our results illustrate the relevance of viability theory for addressing the issue of robustness and adaptability in non-equilibrium environments.

Diffusion-limited reactions in crowded environments: a local density approximation.

In the real world, diffusion-limited reactions in chemistry and biology mostly occur in crowded environments, such as macromolecular complex formation in the cell. Despite the paramount importance of such phenomena, theoretical approaches still mainly rely on the Smoluchowski theory, only valid in the infinite dilution limit. In this paper we introduce a novel theoretical framework to describe the encounter rate and the stationary density profiles for encounters between an immobilized target and a fluid of interacting spherical particles, valid in the local density approximation. A comparison with numerical simulations performed for a fluid of hard spheres and square well attractive hard spheres confirms the accuracy of our treatment.

Competition between trees and grasses for both soil water and mineral nitrogen in dry savannas.

The co-existence of trees and grasses in savannas in general can be the result of processes involving competition for resources (e.g. water and nutrients) or differential response to disturbances such as fire, animals and human activities; or a combination of both broad mechanisms. In moist savannas, the tree-grass coexistence is mainly attributed to of disturbances, while in dry savannas, limiting resources are considered the principal mechanism of co-existence. Virtually all theoretical explorations of tree-grass dynamics in dry savannas consider only competition for soil water. Here we investigate whether coexistence could result from a balanced competition for two resources, namely soil water and mineral nitrogen. We introduce a simple dynamical resource-competition model for trees and grasses. We consider two alternative hypotheses: (1) trees are the superior competitors for nitrogen while grasses are superior competitors for water, and (2) vice-versa. We study the model properties under the two hypotheses and test each hypothesis against data from 132 dry savannas in Africa using Kendall's test of independence. We find that Hypothesis 1 gets much more support than Hypothesis 2, and more support than the null hypothesis that neither is operative. We further consider gradients of rainfall and nitrogen availability and find that the Hypothesis 1 model reproduces the observed patterns in nature. We do not consider our results to definitively show that tree-grass coexistence in dry savannas is due to balanced competition for water and nitrogen, but show that this mechanism is a possibility, which cannot be a priori excluded and should thus be considered along with the more traditional explanations.

Scaling between relaxation, transport and caged dynamics in a binary mixture on a per-component basis.

The universal scaling between the average slow relaxation/transport and the average picosecond rattling motion inside the cage of the first neighbors has been evidenced in a variety of numerical simulations and experiments. Here, we first show that the scaling does not need information concerning the arbitrarily-defined glass transition region and relies on a single characteristic length scale a(2)(1/2) which is determined even far from that region. This prompts the definition of a novel reduced rattling amplitude (1/2) which has been investigated by extensive molecular-dynamics simulations addressing the slow relaxation, the diffusivity, and the fast cage-dynamics of both components of an atomic binary mixture. States with different potential, density, and temperature are considered. It is found that if two states exhibit coinciding incoherent van Hove function on the picosecond timescale, the coincidence is observed at long times too, including the large-distance exponential decay--a signature of heterogeneous dynamics--observed when the relaxation is slow. A major result of the present study is that the correlation plot between the diffusivity of the two components of the binary mixtures and their respective reduced rattling amplitude collapse on the same master curve. This holds true also for the structural relaxation of the two components and the unique master curve coincides with the one of the average scaling. It is shown that the breakdown of the Stokes-Einstein law exhibited by the distinct atomic species of the mixture and the monomers of a chain in a polymer melt is predicted at the same reduced rattling amplitude. Finally, we evidence that the well-known temperature/density thermodynamic scaling of the transport and the relaxation of the mixture is still valid on the picosecond timescale of the rattling motion inside the cage. This provides a link between the fast dynamics and the thermodynamic scaling of the slow dynamics.

Savanna domain in the herbivores-fire parameter space exploiting a tree-grass-soil water dynamic model.

The tree-grass co-existence in savannas involves multiple and sometimes connected biogeophysical conditions. The savanna domain, its boundaries, and transitions (gradual or abrupt) to other vegetation types (i.e., grassland or forest) are fundamental for the management of ecosystems and for preserving the biodiversity in present conditions and in future changing scenarios. Here we investigate the savanna domain within grazers-fire and browsers-fire parameter planes through a simple ecohydrological model of tree-grass-soil water dynamics. Stability maps allow to identify savanna domains and to show the behavior of vegetation under increasing pressure of grazing and browsing. Stability maps shed light on the causes behind possible vegetation abrupt transitions (e.g., forest collapse and bush encroachment). An application to 15 African savannas sites is presented and discussed with the support of a local sensitivity analysis of the model's parameters.

Diffusion-limited reactions in crowded environments.

Diffusion-limited reactions are usually described within the Smoluchowski theory, which neglects interparticle interactions. We propose a simple way to incorporate excluded-volume effects building on simulations of hard sphere in the presence of a sink. For large values of the sink-to-particle size ratio R(s), the measured encounter rate is in good agreement with a simple generalization of the Smoluchowski equation at high densities. Reducing R(s), the encounter rate is substantially depressed and becomes even nonmonotonic for R(s)<<1. Concurrently with the saturation of the rate, stationary density waves set in close to the sink. A mean-field analysis helps to shed light on the subtle link between such ordering and the slowing down of the encounter dynamics. Finally, we show how an infinitesimal amount of nonreacting impurities can equally slow down dramatically the reaction.

Modeling the crossover between chemically and diffusion-controlled irreversible aggregation in a small-functionality gel-forming system.

The analysis of realistic numerical simulations of a gel-forming irreversible aggregation process provides information on the role of cluster diffusion in controlling the late stages of the aggregation kinetics. Interestingly, the crossover from chemically controlled to diffusion-controlled aggregation takes place well beyond percolation, after most of the particles have aggregated in the spanning network and only small clusters remain in the sol. The simulation data are scrutinized to gain insight into the origin of this crossover. We show that a single additional time scale (related to the average diffusion time) is sufficient to provide an accurate description of the evolution of the extent of reaction at all times.

Inertial effects in diffusion-limited reactions.

Diffusion-limited reactions are commonly found in biochemical processes such as enzyme catalysis, colloid and protein aggregation and binding between different macromolecules in cells. Usually, such reactions are modeled within the Smoluchowski framework by considering purely diffusive boundary problems. However, inertial effects are not always negligible in real biological or physical media on typical observation time frames. This is all the more so for non-bulk phenomena involving physical boundaries, that introduce additional time and space constraints. In this paper, we present and test a novel numerical scheme, based on event-driven Brownian dynamics, that allows us to explore a wide range of velocity relaxation times, from the purely diffusive case to the underdamped regime. We show that our algorithm perfectly reproduces the solution of the Fokker-Planck problem with absorbing boundary conditions in all the regimes considered and is thus a good tool for studying diffusion-guided reactions in complex biological environments.

Universal divergenceless scaling between structural relaxation and caged dynamics in glass-forming systems.

On approaching the glass transition, the microscopic kinetic unit spends increasing time rattling in the cage of the first neighbors, whereas its average escape time, the structural relaxation time tau(alpha), increases from a few picoseconds up to thousands of seconds. A thorough study of the correlation between tau(alpha) and the rattling amplitude, expressed by the Debye-Waller factor, was carried out. Molecular-dynamics simulations of both a model polymer system and a binary mixture were performed by varying the temperature, the density rho, the potential and the polymer length to consider the structural relaxation as well as both the rotational and the translation diffusion. The present simulations, together with MD studies on other glassformers, evidence the scaling between the structural relaxation and the caged dynamics. An analytic model of the master curve is developed in terms of two characteristic length scales a(2) (1/2) and sigma(a(2) ) (1/2), pertaining to the distance to be covered by the kinetic unit to reach a transition state. The model does not imply tau(alpha) divergences. The comparison with the experiments supports the numerical evidence over a range of relaxation times as wide as about eighteen orders of magnitude. A comparison with other scaling and correlation procedures is presented. In particular, the density scaling of the length scales a(2) (1/2), sigma(a(2) ) (1/2) proportional to rho(-1/3) is shown to be not supported by the present simulations. The study suggests that the equilibrium and the moderately supercooled states of the glassformers possess key information on the huge slowing-down of their relaxation close to the glass transition. The latter, according to the present simulations, exhibits features consistent with the Lindemann melting criterion and the free-volume model.

Connecting irreversible to reversible aggregation: time and temperature.

We report molecular dynamics simulations of a gel-forming mixture of ellipsoidal patchy particles with different functionality. We show that in this model, which disfavors the formation of bond-loops, elapsed time during irreversible aggregation--leading to the formation of an extended network--can be formally correlated with equilibrium temperature in reversible aggregation. We also show that it is possible to develop a parameter-free description of the self-assembly kinetics, bringing reversible and irreversible aggregation of loopless branched systems to the same level of understanding as equilibrium polymerization.

Dryland ecosystems: the coupled stochastic dynamics of soil water and vegetation and the role of rainfall seasonality.

In drylands the soil water availability is a key factor ruling the architecture of the ecosystem. The soil water reflects the exchanges of water among soil, vegetation, and atmosphere. Here, a dryland ecosystem is investigated through the analysis of the local interactions between soil water and vegetation forced by rainfall having seasonal and stochastic occurrence. The evolution of dryland ecosystems is represented by a system of two differential equations, having two steady states, one vegetated and the other unvegetated. The rainfall forcing is described by a diffusion process with monthly parameters. In each of the two possible steady states, the probability density functions of soil water and vegetation are derived analytically in terms of the rainfall distribution. The results show how the seasonality of rainfall influences the oscillation of the ecosystem between its vegetated steady state during the wet season and its unvegetated steady state during the dry season.

Event-driven Brownian dynamics for hard spheres.

Brownian dynamics algorithms integrate Langevin equations numerically and allow to probe long time scales in simulations. A common requirement for such algorithms is that interactions in the system should vary little during an integration time step; therefore, computational efficiency worsens as the interactions become steeper. In the extreme case of hard-body interactions, standard numerical integrators become ill defined. Several approximate schemes have been invented to handle such cases, but little emphasis has been placed on testing the correctness of the integration scheme. Starting from the two-body Smoluchowski equation, the authors discuss a general method for the overdamped Brownian dynamics of hard spheres, recently developed by one of the authors. They test the accuracy of the algorithm and demonstrate its convergence for a number of analytically tractable test cases.

Aging in a Laponite colloidal suspension: a Brownian dynamics simulation study.

The authors report Brownian dynamics simulation of the out-of-equilibrium dynamics (aging) in a colloidal suspension composed of rigid charged disks, one possible model for Laponite, a synthetic clay deeply investigated in the last few years by means of various experimental techniques. At variance with previous numerical investigations, mainly focusing on static structure and equilibrium dynamics, the authors explore the out-of-equilibrium aging dynamics. They analyze the wave vector and waiting time dependence of the dynamics, focusing on the single-particle and collective density fluctuations (intermediate scattering functions), the mean-squared displacement, and the rotational dynamics. Their findings confirm the complexity of the out-of-equilibrium dynamical behavior of this class of colloidal suspensions and suggest that an arrested disordered state driven by a repulsive Yukawa potential, i.e., a Wigner glass, can be observed in this model.

Arrested phase separation in a short-ranged attractive colloidal system: a numerical study.

We numerically investigate the competition between phase separation and dynamical arrest in a colloidal system interacting via a short-ranged attractive potential. Equilibrium fluid configurations are quenched at two different temperatures below the critical temperature and followed during their time evolution. At the lowest studied T, the phase-separation process is interrupted by the formation of an attractive glass in the dense phase. At the higher T, no arrest is observed and the phase-separation process proceeds endlessly in the simulated time window. The final structure of the glass retains memory of the interrupted phase-separation process in the form of a frozen spinodal decomposition peak, whose location and amplitude is controlled by the average packing fraction. We also discuss the time evolution of the nonergodicity parameter, providing evidence of a progressively decreasing localization length on increasing the packing fraction. Finally, we confirm that the reported results are independent of the microscopic dynamics.

Scaling of dynamics with the range of interaction in short-range attractive colloids.

We numerically study the dependence of the dynamics on the range of interaction Delta for the short-range square well potential. We find that, for small Delta, dynamics scale exactly in the same way as thermodynamics, both for Newtonian and Brownian microscopic dynamics. For interaction ranges from a few percent down to the Baxter limit, the relative location of the attractive-glass line and the liquid-gas line does not depend on Delta. This proves that, in this class of potentials, disordered arrested states (gels) can be generated only as a result of a kinetically arrested phase separation.

Landscapes and fragilities.

The concept of fragility provides a possibility to rank different supercooled liquids on the basis of the temperature dependence of dynamic and/or thermodynamic quantities. We recall here the definitions of kinetic and thermodynamic fragility proposed in the last years and discuss their interrelations. At the same time we analyze some recently introduced models for the statistical properties of the potential energy landscape. Building on the Adam-Gibbs relation, which connects structural relaxation times to configurational entropy, we analyze the relation between statistical properties of the landscape and fragility. We call attention to the fact that the knowledge of number, energy depth, and shape of the basins of the potential energy landscape may not be sufficient for predicting fragility. Finally, we discuss two different possibilities for generating strong behavior.

IDAF (intensity-duration-area frequency) curves of extreme storm rainfall: a scaling approach.

Intensity-duration-area frequency curves, IDAF, are determined for the evaluation of design storms using a scaling approach. The variability of maximum annual rainfall intensity in area and duration is represented through the scaling properties in time and space. Thus the scaling relationships of mean rainfall intensity with area and duration are derived using the concepts of dynamic scaling and statistical self-affinity. For a lognormal distribution of rainfall intensity a multiscaling lognormal model is obtained. This gives the IDAFcurves of extreme storm rainfall. An application is made to the metropolitan area of Milano.