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International audience; Concentration fields of solutes in porous media often exhibit large fluctuations, driven by physical and chemical heterogeneity from the pore to the Darcy scale. For many applications, ranging from reactive transport modeling to toxicology, the knowledge of mean concentrations is not sufficient, and quantifying concentration variability is necessary. The probability density function Highlights • We introduce a general framework quantifying the link between concentration PDFs and spatial concentration profiles. • We derive a dynamical equation for the evolution of the concentration PDF under diffusion and nonlinear reaction in 1D. • We derive analytical predictions for the concentration PDF and its moments using a weakcoupling approximation.

Transport processes in unsaturated porous media flows play a key role in a broad range of environmental and industrial systems. The simultaneous presence of liquid and gas in the pore space increases flow heterogeneity and fundamentally alters the observed flow patterns when compared to fully saturated systems. The introduction of the air phase leads to the development of highly structured water flow fields with preferential flow localized on a backbone and flow re-circulation occurring in flow dead-ends. However, it is unclear how saturation controls both flow statistics and transport dynamics. Here we use millifluidic experiments and high-resolution numerical simulations to develop a general theoretical framework that describes this flow re-organisation in the pore space and captures its impact on the statistics of pore-scale velocities. We observe, and predict theoretically, that this previously-identified flow structure of backbone and dead-ends induces both a drastic change in the scaling of the probability density function (PDF) of flow velocities compared to fully saturated conditions, and a sharp transition to strongly anomalous transport. From the theoretically derived velocity PDFs, we successfully predict the dynamics of advective transport for all saturation degrees using a continuous time random walk approach. These findings hence provide a new modelling framework linking flow heterogeneity to parameters that describe the liquid phase heterogeneity within the pore space.

The simultaneous presence of liquid and gas in porous media increases flow heterogeneity compared to saturated flows. However, the impact of saturation on flow and transport has so far remained unclear. The presence of gas in the pore space leads to flow reorganization. We develop a theoretical framework that captures the impact of that reorganization on pore-scale fluid velocities. Preferential flow is distributed spatially through a backbone, and flow recirculation occurs in flow dead-ends. We observe, and predict theoretically, that this previously identified flow structure induces a marked change in the scaling of the velocity probability density function compared to the saturated configuration and a sharp transition to strongly anomalous transport. We develop a transport model using the continuous time random walk theory that predicts advective transport dynamics for all saturation degrees. Our results provide a new modeling framework linking phase heterogeneity to flow heterogeneity in unsaturated porous media., Geophysical Research Letters, 49 (3), ISSN:0094-8276, ISSN:1944-8007

International audience; Correlated velocity models (CVMs) have proven themselves to be effective tools for describing a wide range of solute transport behaviors in heterogeneous porous media. In particular, spatial Markov models (SMMs) are a class of CVMs where subsequent Lagrangian velocities along transport trajectories depend only on the current velocity, and not on past history. Such models provide a powerful tool for modeling transport in terms of a limited number of flow properties, such as the Eulerian point distribution of (flow) velocities, tortuosity, and the spatial scale of persistence of velocities. However, to date, all SMM modeling frameworks and applications have assumed that the underlying flow is steady-state. In this work, we extend SMMs to the case of time-varying flows. We propose, compare, and validate alternative numerical implementations, and we determine conditions for validity and efficiency based on standard physical quantities used to describe flow and transport at the Darcy scale. The models require additional information relative to a steady-state velocity SMM and we discuss the conditions under which this extra burden is warranted. We also provide clear, deterministic tests for the validity of the transient SMM, termed the “slow variation” and “fast propagation” criteria, which offer clear guidance on when transient, upscaled models are reasonable to employ. Our work forms the basis of a new framework allowing for the application of efficient upscaled models of transport to realistic transient flow conditions.

International audience; Space-Lagrangian random walk models conceptualize advective transport in terms of collections of particles undergoing fixed-length steps along flow streamlines. The statistics and correlation structure of the underlying flow velocity statistics determine the transit times of particles undergoing advective transport. Broad velocity distributions lead to broadly-distributed step transit times, reproducing commonly observed anomalous transport features such as superdiffusive plume growth, which are not captured by classical Fickian theories. Early space-Lagrangian models considered uncorrelated velocities across steps. These approaches were later extended to account for correlations through a spatial-Markov process. Here, we compare longitudinal dispersion dynamics in an uncorrelated continuous time random walk with fixed space steps to a Bernoulli relaxation spatial-Markov model exhibiting exponential decay of spatial velocity correlations along streamlines. We provide rigorous theoretical derivations, validated against numerical simulations. We find that, although the scaling forms of asymptotic dispersion agree between the two models, exact asymptotic equivalence requires employing different correlation lengths, which depend on the underlying Eulerian velocity statistics. The two models become equivalent in the limit of very broad velocity distributions, corresponding to a new quasi-ballistic regime recently identified in unsaturated porous media.

Made available in DSpace on 2022-04-28T19:41:21Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-09-01 Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG) Soil management operations change soil porosity, affecting water infiltration, redistribution, storage, availability, and uptake by plants. Assessing how soil management may affect pore size distribution and hydraulic conductivity is thus highly relevant for rainfed agriculture coping with water shortage. The aim of this study was to assess the effectiveness of tillage treatments, designed to deepen coffee plants root system, on improving structure and physical-hydric attributes of an Inceptisol with a shallow solum. The study was conducted in an experimental area in the municipality of Nazareno, Minas Gerais State, Brazil. Soil samples were collected 18 months after coffee plantation, at different depths (0, 0.25, 0.35, 0.45, 0.55, 0.66, and 0.75 m) and they were used to determine pore-size distribution, saturated and unsaturated hydraulic conductivity. Samples were also collected in surface crusts or in the 0−0.005 m soil layer for detailed grain size analysis. Field water infiltration was measured at different water tensions. Coffee seedlings were planted in rows furrowed to depths depending on tillage treatment: 0.4 m depth, made by a furrow ridger (FP40); 0.6 m depth, made by a subsoiler coupled to a soil preparer mixing the soil to a depth of 0.6 m (FP60); 0.8 m depth, made by a subsoiler and, after mixing the soil to a depth of 0.6 m, by the soil preparer (FP80). The soil between the planting rows was covered by Brachiaria-grass. Soil sampling and field tests were performed in the coffee plants row mechanically treated, in the Brachiaria-grassed inter-row (IR) lane and in a nearby area under natural vegetation (NC). Treatments effects, either mechanical in the coffee rows (FP40, FP 60 and FP80), or biological in the inter-row lane (IR) were compared to reference (NC), representing soil conditions prior to coffee plantation. The FP60 and FP80 treatments improved water infiltration, storage and hydraulic conductivity in the planting rows to a depth of 0.5 m. A more favorable pore size distribution was obtained following these treatments, which improved the soil physical environment. Conversely, furrowing promoted compaction at each implement working depth due to the pressure applied by the rods in the subsurface soil layers, combined with subsoil moisture condition at the time of operations. Root activity of intercropped Brachiaria-grass (IR) improved soil structure, expressed by a favorable pore-size distribution and a faster hydraulic conductivity in the inter-row lane. Similar effects were obtained with FP 60 and FP80 for the coffee rows, where deep furrowing during soil preparation reduced the natural density of the Inceptisol. Therefore, the management strategies tested allowed root deepening and access to soil moisture stored in deeper layers. Departamento Engenharia Agronômica Universidade Federal do Piauí Campus Professora Cinobelina Elvas, CEP 649000-00 Bom Jesus Instituto Federal de Educação Ciência e Tecnologia Goiano, Campus Rio Verde, Caixa Postal 66 Departamento de Ciência do Solo Universidade Federal de Lavras, Campus universitário, Caixa Postal 3037 Universidade Estadual Paulista Faculdade de Ciências Agrárias e Veterinárias, Câmpus de Jaboticabal Centro de Investigação de Montanha Instituto Politécnico de Bragança, Campus de Sta Apolónia Universidade Estadual Paulista Faculdade de Ciências Agrárias e Veterinárias, Câmpus de Jaboticabal

The spatial distribution of a solute undergoing advection and diffusion is impacted by the velocity variability sampled by tracer particles. In spatially structured velocity fields, such as porous medium flows, Lagrangian velocities along streamlines are often characterized by a well-defined correlation length and can thus be described by spatial-Markov processes. Diffusion, on the other hand, is generally modeled as a temporal process, making it challenging to capture advective and diffusive dynamics in a single framework. In order to address this limitation, we have developed a description of transport based on a spatial-Markov velocity process along Lagrangian particle trajectories, incorporating the effect of diffusion as a local averaging process in velocity space. The impact of flow structure on this diffusive averaging is quantified through an effective shear rate. The latter is fully determined by the point statistics of velocity magnitudes together with characteristic longitudinal and transverse lengthscales associated with the flow field. For infinite longitudinal correlation length, our framework recovers Taylor dispersion, and in the absence of diffusion it reduces to a standard spatial-Markov velocity model. This novel framework allows us to derive dynamical equations governing the evolution of particle position and velocity, from which we obtain scaling laws for the dependence of longitudinal dispersion on Péclet number. Our results provide new insights into the role of shear and diffusion on dispersion processes in heterogeneous media.In this presentation, I propose to discuss: (i) Spatial-Markov models and the modeling of diffusion as a spatial rather than temporal process; (ii) The concept of the effective shear rate and its role in the diffusive dynamics of tracer particle velocities; (iii) The role of transverse diffusion and its interplay with velocity heterogeneity on longitudinal solute dispersion.

Rivers transport pathogenic microorganisms (including fecal indicator bacteria and human enteric viruses) from point and non-point sources over long distances, posing a direct risk for human health. Yet, pathogens in surface waters can be deposited and transitorily immobilized and accumulated together with other fine particles in streambed sediments, mostly within the top few centimeters. These dynamic fine particle standing stocks retain and delay downstream transmission of pathogens during baseflow conditions, but contribute to their resuspension and transport downstream during stormflow events. Direct measurements of pathogen accumulation in streambed sediments are rare. Further, it is unknown whether pathogen accumulation is constrained near to the point source inputs or if the continuous deposition and resuspension of pathogens results in the transmission of active pathogens further downstream. In this study, we analyze fine particle standing stocks along a 1 km reach of an intermittent Mediterranean stream receiving inputs from the effluent of a wastewater treatment plant (WWTP), during a summer drought when the effluent constituted 100% of the stream flow, and thus, large accumulation and persistence of pathogens along the streambed was expected. We measured abundance of total bacteria, Escherichia coli (as a fecal indicator bacteria), and presence of enteric rotavirus (RoV) and norovirus (NoV). We also monitored environmental variables such as water temperature, dissolved oxygen, total benthic particulate matter, and fraction of organic matter. Abundance of E. coli, based on qPCR detection, was high (~ 1 ng/μL) along the first 100 m downstream of the WWTP effluent input, and we found trace amounts of RoV and NoV. Furthermore, E. coli was present along the first km downstream of the WWTP effluent input with a logarithmic decline in concentration with distance. These results were combined with a particle tracking model that uses stream water velocity as an input and accounts for hyporheic exchange, pathogen immobilization, degradation and resuspension during baseflow and stormflow conditions. Model results indicate that even at very low flows ( 1km), but that the extent of longitudinal transport varies among pathogen types. These results demonstrate that benthic standing stocks of fine particles act as hot spots of pathogen accumulation in streams, and that the interplay between immobilization, degradation, the extent of resuspension and downstream transport during storms and time between storms determine pathogen concentrations in the streambed.

International audience; Biogeochemical reaction kinetics are generally established from batch reactors where concentrations are uniform. In natural systems, many biogeochemical processes are characterized by spatially and temporally variable concentration gradients that often occur at scales which are not resolved by field measurements or biogeochemical and reactive transport models. Yet, it is not clear how these sub-scale chemical gradients affect reaction kinetics compared to batch kinetics. Here we investigate this question by studying the paradigmatic case of localized pulses of solute reacting with a solid or a dissolved species in excess. We consider non-linear biogeochemical reactions, representative of mineral dissolution, adsorption and redox reactions, which we quantify using simplified power-law kinetics. The combined effect of diffusion and reaction leads to effective kinetics that differ quantitatively and qualitatively from the batch kinetics. Depending on the nonlinearity (reaction order) of the local kinetics, these effects lead to either enhancement or decrease of the overall reaction rate, and result in a rich variety of reaction dynamics. We derive analytical results for the effective kinetics, which are validated by comparison to direct numerical simulations for a broad range of Damköhler numbers and reaction order. Our findings provide new insights into the interpretation of imperfectly mixed lab experiments, the effective kinetics of field systems characterized by intermittent reactant release and the integration of sub-scale concentration gradients in reactive transport models.

Fluid-solid reactions play a key role in a large range of biogeochemical processes. Transport limitations at the pore scale limit the amount of solute available for reaction, so that reaction rates measured under well-mixed conditions tend to strongly overestimate rates occurring in natural and engineered systems. Although different models have been proposed to capture this phenomenon, linking pore-scale structure, flow heterogeneity, and local reaction kinetics to upscaled effective kinetics remains a challenging problem. We present a new theoretical framework to quantify these dynamics based on the chemical continuous time random walk framework. We study a fluid–solid reaction with the fluid phase undergoing advective–diffusive transport. We consider a catalytic degradation reaction, A F + B S → B S , where A F is in fluid phase and B S is in solid phase and homogeneous over the fluid–solid interface, allowing us to focus on the role of transport limitations and medium structure. Our approach is based on the concept of inter-reaction times, which result from the times between contacts of transported reactants with the solid phase. We use this formulation to quantify the global kinetics of fluid-reactant mass and test our predictions against numerical simulations of advective–diffusive transport in stratified channel flow and Stokes flow through a beadpack. The theory captures the decrease of effective reaction rates compared to the well-mixed prediction with increasing Damkohler number due to transport limitations. Although we consider simple kinetics and media, these findings will contribute to the understanding and modeling of the effect of transport limitations in more complex reactive transport problems.

We study the survival and confinement of random walkers under quenched disorder characterized by spatially-varying waiting times and decay rates. Spatial heterogeneity and segregation lead to a dynamic coupling between transport and reaction, resulting in history-dependent dynamics exhibiting long survivals and confinement. The survival probability decays as a power law, in contrast to the classical exponential law for decay at a homogeneous rate. The mean squared displacement shows dimension-dependent subdiffusive growth followed by localization, with stronger confinement in higher dimensions. This journal is © the Owner Societies., The authors acknowledge the support of the European Research Council (ERC) through the project MHetScale (617511).

Indirect inversion has been the predominant method for matching models and data in geochemical systems, typically using observations of chemical concentrations as calibration targets. This reserves the data with the highest confidence (observed concentrations) for the final comparison but does little to constrain the initial state of the system on which the indirect inversion is based. An alternative approach to inverse modeling is to start with the observations to reconstruct a concentration field, but it is unclear if this is feasible for reactive transport in heterogeneous systems. The purpose of this article is to consider the applicability of backward-in-time (BIT) techniques as tools for simulating reactive transport in porous media. A multi-component reaction system is considered in a variety of systems of increasing complexity and we show that complex, non-linear systems can be simulated backward in time, given a sufficiently robust integration scheme. Recent advances in reactive random walk particle tracking are employed to investigate simple flow systems with spatially variable reactions, as well as 2-d heterogeneous flows, and we show that some level of time reversibility exists in both cases. Under a uniform injection scheme, the total masses generated in forward and backward simulations of the 2-d models were all within 3.5% of each other for all the species considered, indicating good overall agreement between the models. This suggests that BIT techniques may have yet unrealized applications to inverse modeling; however, further research on the sensitivity of the approach to measurement errors and on how to efficiently apply BIT methods to transient problems is needed.

Mixing is driven by an interplay between diffusion and flow-induced concentration gradients. Accurately describing the effect of flow heterogeneity on the mixing state of a plume is a challenging problem that has important repercussions on the modeling of plume dilution and chemical reactions. In this technical note, we propose a simple, semi-analytic measure to quantify the local mixing potential at a point based on the local properties of the flow-induced strain. Specifically, it is the trace of the local strain matrix squared, $${\text {Tr}}(\varvec{s}^2)$$ , which we demonstrate controls mixing from a point source over small times. Due to its mathematically similar influence to a shear flow on mixing, we propose an ansatz to attempt to use this metric as a predictor for mixing. We test its performance via random walk particle tracking simulations in heterogeneous Darcy flow through lognormal permeability fields. The ansatz appears to work better and better the more heterogeneous the flow, unlike more traditional approaches that rely on weak heterogeneity assumptions. While we cannot rigorously demonstrate why this is, we find it sufficiently promising that it may guide future model development.

International audience; Michaelis–Menten kinetics describe a broad range of physical, chemical, and biological processes. Since they are non-linear, spatial averaging of reaction kinetics is non-trivial, and it is not known how concentration gradients affect the global effective kinetics. Here, we use numerical simulations and theoretical developments to investigate the effective kinetics of diffusing solute pulses locally subject to Michaelis–Menten reaction kinetics. We find that coupled diffusion and reaction lead to non-monotonic effective kinetics that differ significantly from the local kinetics. The resulting effective reaction rates can be significantly enhanced compared to those of homogeneous batch reactors. We uncover the different regimes of effective kinetics as a function of the Damköhler number and Michaelis–Menten parameters and derive a theory that explains and quantifies these upscaled kinetics using a weakly-coupled description of reaction and diffusion. We illustrate the consequences of these findings on the accelerated consumption of nutrient pulses by bacteria. These results are relevant to a large spectrum of reactive systems characterized by heterogeneous concentration landscapes.

The kinetics of contact processes are determined by the interplay among local mass transfer mechanisms, spatial heterogeneity, and segregation. Determining the macroscopic behavior of a wide variety of phenomena across the disciplines requires linking reaction times to the statistical properties of spatially fluctuating quantities. We formulate the dynamics of advected agents interacting with segregated immobile components in terms of a chemical continuous-time random walk. The inter-reaction times result from the first-passage times of mobile species to and across reactive regions, and available immobile reactants undergo a restart procedure. Segregation leads to memory effects and enhances the role of concentration fluctuations in the large-scale dynamics., The authors acknowledge the support of the European Research Council (ERC) through the project MHetScale (617511).

El presente estudio de investigación observacional de nivel relacional, tuvo como objetivo general: Determinar la relación entre la autoestima y la coordinación motriz en estudiantes de actividad voleibol de la Universidad Nacional de la Amazonía Peruana, segundo semestre 2017. La población en estudio estuvo conformada por N=546 estudiantes, matriculados en actividad voleibol del segundo semestre 2017; el diseño fue el muestreo aleatorio estratificado, con afijación proporcional, con tamaño muestral de n=224 estudiantes. La técnica de recolección de datos fue la encuesta y fue dos cuestionarios válidos y confiables. Resultados, el 62,5% de los estudiantes fueron del sexo femenino, con una edad promedio de 19,48 años, el 45,5% tiene un nivel medio de autoestima y en las dimensiones: seguridad, respeta los criterios, estabilidad, y administración emocional en el nivel medio con el 69,2%, 62,5%, 74,6% y 47,3% respectivamente, lo resaltante es que, el 76,8% de los estudiantes tiene nivel de confianza baja. por otra parte, el 58,5% tienen un nivel regular de coordinación motriz, coinciden las categorías dinámicas general, óculo manual, óculo pedica y dinámico manual. Con respecto a la hipótesis, existe relación estadísticamente significativa (p-valor=0,000

Resumo Uma comunidade científica é composta por laços de interação entre pessoas que partilham valores, normas de conduta e comportamentos comuns, isto é, padrões institucionalizados sobre como produzir conhecimentos e tecnologias em determinado campo do saber. Regra geral, as comunidades científicas são autorreguladas, na medida em que seus membros se organizam em torno de associações ou sociedades que delimitam espaços de atuação e estabelecem como fazer ciência no campo de interesse, tendo por base determinados padrões de conduta transversais, aplicados a distintos campos de conhecimento científico. Este artigo tem por objetivo discutir o papel da Associação Nacional de Pós-Graduação e Pesquisa em Administração (ANPAD) nas atividades de publicação científica e de regulação da comunidade científica brasileira de Administração, bem como apresentar de que modo essas atividades têm contribuído com o processo de institucionalização dessa comunidade. Analisa-se tal processo em seu contexto histórico, apresentam-se as principais realizações da ANPAD e discutem-se alguns desafios para essa comunidade em sua trajetória de consolidação.

We develop a time domain random walk approach for conservative solute transport in heterogeneous media where medium properties vary over a distribution of length scales. The spatial transition lengths are equal to the heterogeneity length scales, and thus determined by medium geometry. We derive analytical expressions for the associated transition times and probabilities in one spatial dimension. This approach determines the coarse-grained solute concentration at the interfaces between regions; we derive a generalized master equation for the evolution of the coarse-grained concentration and reconstruct the fine-scale concentration using the propagator of the subscale transport mechanism. The performance of this approach is demonstrated for diffusion under random retardation in power-law media characterized by heavy-tailed lengthscale and retardation distributions. The coarse representation preserves the correct late-time scaling of concentration variance, and the reconstructed fine-scale concentration is essentially identical to that obtained by direct numerical simulation by random walk particle tracking. © 2018 Elsevier Ltd, European Research Council (ERC) through the project MHetScale (617511)

Power law tails, commonly observed in solute breakthrough curves, are notoriously difficult to measure with confidence as they typically occur at low concentrations. This leads us to ask if other signatures of anomalous transport can be sought. We develop a general stochastic transport framework and derive an asymptotic relation between the tail scaling of a breakthrough curve for a conservative tracer at a fixed downstream position and the scaling of the peak concentration of breakthrough curves as a function of downstream position, demonstrating that they provide equivalent information. We then quantify the relevant spatiotemporal scales for the emergence of this asymptotic regime, where the relationship holds, and validate our results in the context of a very simple model that represents transport in an idealized river.

Bioturbation refers to the transport processes carried out by living organisms and their physical effects on soils and sediments. It is widely recognized as an important mixing mechanism, particularly at the sediment-water interface in many natural systems. In order to quantify its impact on mixing, we propose a process-based model based on simple assumptions about organism burrowing behavior. Specifically, we consider burrowing events to be stochastic but memoryless, leading to exponential inter-burrow waiting times and depths. We then explore the impact of two different transport mechanisms on the vertical concentration distributions predicted by the model for a conservative (inert) tracer. We compare the results of our model to experimental data from a recent laboratory study of bioturbation by the freshwater oligochaete worm Lumbriculus variegatus, and find good quantitative agreement. © 2017 The Author(s)., T.A. gratefully acknowledges support by the Portuguese Foundation for Science and Technology (FCT) under Grant SFRH/BD/89488/2012. K.R.R. was supported by a NSF Graduate Research Fellowship. D.B. gratefully acknowledges support from NSF grant numbers EAR-1351625, EAR-1417264, and EAR-1446236. The authors would also like to thank Dr. Filip Meysman and Dr. Bernard Boudreau for valuable comments and suggestions.

When laboratory-measured chemical reaction rates are used in simulations at the field-scale, the models typically overpredict the apparent reaction rates. The discrepancy is primarily due to poorer mixing of chemically distinct waters at the larger scale. As a result, realistic field-scale predictions require accurate simulation of the degree of mixing between fluids. The Lagrangian particle-tracking (PT) method is a now-standard way to simulate the transport of conservative or sorbing solutes. The method’s main advantage is the absence of numerical dispersion (and its artificial mixing) when simulating advection. New algorithms allow particles of different species to interact in nonlinear (e.g., bimolecular) reactions. Therefore, the PT methods hold a promise of more accurate field-scale simulation of reactive transport because they eliminate the masking effects of spurious mixing due to advection errors inherent in grid-based methods. A hypothetical field-scale reaction scenario is constructed and run in PT and Eulerian (finite-volume/finite-difference) simulators. Grid-based advection schemes considered here include 1st- to 3rd-order spatially accurate total-variation-diminishing flux-limiting schemes, both of which are widely used in current transport/reaction codes. A homogeneous velocity field in which the Courant number is everywhere unity, so that the chosen Eulerian methods incur no error when simulating advection, shows that both the Eulerian and PT methods can achieve convergence in the L1 (integrated concentration) norm, but neither shows stricter pointwise convergence. In this specific case with a constant dispersion coefficient and bimolecular reaction A + B → P , the correct total amount of product is 0.221MA0, where MA0 is the original mass of reactant A. When the Courant number drops, the grid-based simulations can show remarkable errors due to spurious over- and under-mixing. In a heterogeneous velocity field (keeping the same constant and isotropic dispersion), the PT simulations show an increased reaction total from 0.221MA0 to 0.372MA0 due to fluid deformation, while the 1st-order Eulerian simulations using ≈ 106 cells (with a classical grid Peclet number Δx/αL of 10) have total product of 0.53MA0, or approximately twice as much additional reaction due to advection error. The 3rd-order TVD algorithm fares better, with total product of 0.394MA0, or about 1.14 times the increased reaction total. A very strict requirement on grid Peclet numbers for Eulerian simulations will be required for realistic reactions because of their nonlinear nature. We analytically estimate the magnitude of the effect for the end-member cases of very fast and very slow reactions and show that in either case, the mass produced is proportional to 1 / P e , where Pe is the Peclet number. Therefore, extra mass is produced according to D , where the dispersion includes any numerical dispersion error. We test two PT methods, one that kills particles upon reaction and another that decrements a particle’s mass. For the bimolecular reaction studied here, the computational demands of the particle-killing methods are much smaller than, and the particle-number-preserving algorithm are on par with, the fastest Eulerian methods.

Kinetic Monte Carlo methods such as the Gillespie algorithm model chemical reactions as random walks in particle number space. The inter-reaction times are exponentially distributed under the assumption that the system is well mixed. We introduce an arbitrary inter-reaction time distribution, which may account for the impact of incomplete mixing on chemical reactions, and in general stochastic reaction delay, which may represent the impact of extrinsic noise. This process defines an inhomogeneous continuous time random walk in particle number space, from which we derive a generalized chemical master equation. This leads naturally to a generalization of the Gillespie algorithm. Based on this formalism, we determine the modified chemical rate laws for different inter-reaction time distributions. This framework traces Michaelis--Menten-type kinetics back to finite-mean delay times, and predicts time-nonlocal macroscopic reaction kinetics as a consequence of broadly distributed delays. Non-Markovian kinetics exhibit weak ergodicity breaking and show key features of reactions under local non-equilibrium., Comment: 12 pages, 2 figures, changed spelling of name of first author

Bioturbation is the dominant mode of sediment transport in many aquatic environments and strongly influences both sediment biogeochemistry and contaminant fate. Available bioturbation models rely on highly simplified biodiffusion formulations that inadequately capture the behavior of many benthic organisms. We present a novel experimental and modeling approach that uses time-lapse imagery to directly relate burrow formation to resulting sediment mixing. We paired white-light imaging of burrow formation with fluorescence imaging of tracer particle redistribution by the oligochaete Lumbriculus variegatus. We used the observed burrow formation statistics and organism density to parametrize a parsimonious model for sediment mixing based on fundamental random walk theory. Worms burrowed over a range of times and depths, resulting in homogenization of sediments near the sediment-water interface, rapid nonlocal transport of tracer particles to deep sediments, and large areas of unperturbed sediments. Our fundamental, parsimonious random walk model captures the central features of this highly heterogeneous sediment bioturbation, including evolution of the sediment-water interface coupled with rapid near-surface mixing and anomalous late-time mixing resulting from infrequent, deep burrowing events. This approach provides a general, transferable framework for explicitly linking sediment transport to governing biophysical processes.

The distinctive features of human influenza A phylogeny have inspired many mathematical and computational studies of viral infections spreading in a host population, but our understanding of the mechanisms that shape the coupled evolution of host immunity, disease incidence and viral antigenic properties is far from complete. In this paper we explore the epidemiology and the phylogeny of a rapidly mutating pathogen in a host population with a weak immune response, that allows re-infection by the same strain and provides little cross-immunity. We find that mutation generates explosive diversity and that, as diversity grows, the system is driven to a very high prevalence level. This is in stark contrast with the behavior of similar models where mutation gives rise to a large epidemic followed by disease extinction, under the assumption that infection with a strain provides lifelong immunity. For low mutation rates, the behavior of the system shows the main qualitative features of influenza evolution. Our results highlight the importance of heterogeneity in the human immune response for understanding influenza A phenomenology. They are meant as a first step toward computationally affordable, individual based models including more complex host-pathogen interactions.

Incomplete mixing of reactive solutes is well known to slow down reaction rates relative to what would be expected from assuming perfect mixing. In purely diffusive systems, for example, it is known that small initial fluctuations in reactant concentrations can lead to reactant segregation, which in the long run can reduce global reaction rates due to poor mixing. In contrast, nonuniform flows can enhance mixing between interacting solutes. Thus, a natural question arises: Can nonuniform flows sufficiently enhance mixing to restrain incomplete mixing effects and, if so, under what conditions? We address this question by considering a specific and simple case, namely, a laminar pure shear reactive flow. Two solution approaches are developed: a Lagrangian random walk method and a semianalytical solution. The results consistently highlight that if shear effects in the system are not sufficiently strong, incomplete mixing effects initially similar to purely diffusive systems will occur, slowing down the overall reaction rate. Then, at some later time, dependent on the strength of the shear, the system will return to behaving as if it were well mixed, but represented by a reduced effective reaction rate.

Starting from common assumptions, we build a rate equation model for multi-strain disease dynamics in terms of immune repertoire classes. We then move to a strain-level description where a low-order closure reminiscent of a pair approximation can be applied. We characterize the endemic equilibrium of the ensuing model in the absence of mutation and discuss the presence of degeneracy regarding the prevalence of the different strains. Finally we study the behavior of the system under the injection of mutant strains., 20 pages, 5 figures

The soil bin is an important tool to study the dynamic soil-machine interaction. The objective of this work was to construct and evaluate the operational performance of a soil bin, consisting of displacement and power systems, soil preparation system and measurement system needed to conduct research regarding the dynamics of soil-machine interaction. The soil bin was constructed in the Department of Engineering of UFLA, Lavras, MG. The evaluation was done using the operational performance of a dynamometric car, and a furrow maker at different forward speeds. The speed, power and parameters that characterize physical and mechanical properties of the test soil were measured. The results showed that the dynamometric car efficiently allows simulation of field operations of agricultural equipment. As caixas de solo se tornaram uma ferramenta importante nos centros de pesquisas para estudos da interação da dinâmica máquina solo. Objetivou-se com esse trabalho construir e avaliar o desempenho operacional de uma caixa de solo, composta por sistemas de potência e deslocamento; sistema de preparo de solo e sistema de medida necessários a realização de pesquisas referentes à dinâmica da interação máquina solo. A construção da caixa de solo foi efetuada nas dependências do Departamento de Engenharia da UFLA, Lavras, MG. Para sua avaliação, foram realizados ensaios do desempenho operacional do carro dinamométrico e de um sulcador em diferentes condições de velocidade de avanço. Mensurou-se velocidade, potência e parâmetros que caracterizassem as propriedades físicas e mecânicas do solo em estudo. Os resultados obtidos permitiram concluir que o carro dinamômetro possibilita a simulação de operações de campo com equipamentos agrícolas de forma eficiente.

A detailed stochastic model of single-gene auto-regulation is established and its solutions are explored when mRNA dynamics is fast compared with protein dynamics and in the opposite regime. The model includes all the sources of randomness that are intrinsic to the auto-regulation process and it considers both transcriptional and post transcriptional regulation. The timescale separation allows the derivation of analytic expressions for the equilibrium distributions of protein and mRNA. These distributions are generally well described in the continuous approximation, which is used to discuss the qualitative features of the protein equilibrium distributions as a function of the biological parameters in the fast mRNA regime. The performance of the timescale approximation is assessed by comparison with simulations of the full stochastic system, and a good quantitative agreement is found for a wide range of parameter values. We show that either unimodal or bimodal equilibrium protein distributions can arise, and we discuss the auto-regulation mechanisms associated with bimodality., Comment: 15 pages, 8 figures

Soybean is a self-sufficient specie in nitrogen acquisition due to their efficient association with diazotrophs. Unlike bean, which requires nitrogen supplementation, soybean is not dependent on nitrogen fertilization. This interspecies difference may be related to the allocation pattern of photosynthates during their growth cycles. Distinct from soybean, common bean cannot maintain their active nodules until the end of their growth cycle due to the unavailability of photosynthates in their roots after flowering. To compare the partitioning of the phytomass in soybean (Glycine max (L.) Merrill) and common bean (Phaseolus vulgaris L.) species during their ontogenetic cycles, a growth analysis experiment were conducted with Favorita BRS and BRS Pontal varieties, respectively. The results revealed that soybeans keep producing leaves, branches and roots even after flowering, indicating no limitation in the supply of photosynthates to its organs, especially to the roots, where a predominant allocation of photosynthates can favor nodule activity. After flowering in bean plants, allocation preferentially occurs to the pods at the expense of the other organs including the roots, which potentially affects their nodule activity.