Particle tracking and the diffusion-reaction equation
TL;DR: In this paper, a particle tracking algorithm was proposed to model conservative transport in surface and subsurface hydrological systems and rigorously demonstrated that this particle method converges to the diffusion-reaction equation at the limit of infinitely small time step.
Abstract: [1] Particle tracking algorithms are very useful methods to model conservative transport in surface and subsurface hydrological systems. Recently, a novel ad hoc particle-based method was proposed to account for multicomponent reactive transport by Benson and Meerschaert (2008). This one-dimensional particle method has been shown to match theoretical predictions, but, to date, there has been no rigorous demonstration that the particle method actually matches the governing equations for chemical transport. We generalize this particle method to two-dimensional and three-dimensional systems and rigorously demonstrate that this particle method converges to the diffusion-reaction equation at the limit of infinitely small time step. We also investigate the numerical error associated with the method.
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TL;DR: In this article, the authors present a concept that shows the current state of art and challenges for monitoring programs, fate and risk assessment tools and requirements for policies with respect to emerging pollutants as a base for sustainable water resource management.
666 citations
Forschungszentrum Jülich1, University of California, Davis2, Université catholique de Louvain3, ETH Zurich4, University of Southampton5, University of Texas at Austin6, University of Bonn7, James Hutton Institute8, University of California, Irvine9, Université Paris-Saclay10, Desert Research Institute11, Ghent University12, Washington State University13, Katholieke Universiteit Leuven14, University of Aberdeen15, Institut national de la recherche agronomique16, Polish Academy of Sciences17, University of Vienna18, University of Sydney19, University of Stuttgart20, Agricultural Research Service21, University of Naples Federico II22, University of California, Riverside23, Netherlands Environmental Assessment Agency24, Monash University25, University of Tübingen26, University of New England (Australia)27
TL;DR: Key challenges in modeling soil processes are identified, including the systematic incorporation of heterogeneity and uncertainty, the integration of data and models, and strategies for effective integration of knowledge on physical, chemical, and biological soil processes.
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542 citations
TL;DR: In this paper, the authors provide an overview of the recent literature on high-resolution topographic analyses, underlining their opportunities and critical issues such as their limitations and future challenges.
450 citations
TL;DR: A review of river restoration can be found in this article, where the authors critically examine how contemporary practitioners approach river restoration and challenges for implementing restoration, which include clearly identified objectives, holistic understanding of rivers as ecosystems, and the role of restoration as a social process.
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419 citations
TL;DR: In this article, the authors used water and sediment data from 20 gauging stations within the Yangtze River's basin to delineate the impacts from the Three Gorges Dam (TGD), the world's largest dam.
316 citations
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6,674 citations
TL;DR: In this paper, it was shown analytically that the distribution of concentration produced in this way is centred on a point which moves with the mean speed of flow and is symmetrical about it in spite of the asymmetry of the flow.
Abstract: When a soluble substance is introduced into a fluid flowing slowly through a small-bore tube it spreads out under the combined action of molecular diffusion and the variation of velocity over the cross-section. It is shown analytically that the distribution of concentration produced in this way is centred on a point which moves with the mean speed of flow and is symmetrical about it in spite of the asymmetry of the flow. The dispersion along the tube is governed by a virtual coefficient of diffusivity which can be calculated from observed distributions of concentration. Since the analysis relates the longitudinal diffusivity to the coefficient of molecular diffusion, observations of concentration along a tube provide a new method for measuring diffusion coefficients. The coefficient so obtained was found, with potassium permanganate, to agree with that measured in other ways. The results may be useful to physiologists who may wish to know how a soluble salt is dispersed in blood streams.
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TL;DR: In this article, it is shown that the chemical Langevin equation can be derived from the microphysical premise from which the chemical master equation is derived, which leads directly to an approximate time-evolution equation of the Langevin type.
Abstract: The stochastic dynamical behavior of a well-stirred mixture of N molecular species that chemically interact through M reaction channels is accurately described by the chemical master equation. It is shown here that, whenever two explicit dynamical conditions are satisfied, the microphysical premise from which the chemical master equation is derived leads directly to an approximate time-evolution equation of the Langevin type. This chemical Langevin equation is the same as one studied earlier by Kurtz, in contradistinction to some other earlier proposed forms that assume a deterministic macroscopic evolution law. The novel aspect of the present analysis is that it shows that the accuracy of the equation depends on the satisfaction of certain specific conditions that can change from moment to moment, rather than on a static system size parameter. The derivation affords a new perspective on the origin and magnitude of noise in a chemically reacting system. It also clarifies the connection between the stochas...
1,537 citations
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