3 resultados para Scaling process

em Duke University


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Soil erosion by water is a major driven force causing land degradation. Laboratory experiments, on-site field study, and suspended sediments measurements were major fundamental approaches to study the mechanisms of soil water erosion and to quantify the erosive losses during rain events. The experimental research faces the challenge to extent the result to a wider spatial scale. Soil water erosion modeling provides possible solutions for scaling problems in erosion research, and is of principal importance to better understanding the governing processes of water erosion. However, soil water erosion models were considered to have limited value in practice. Uncertainties in hydrological simulations are among the reasons that hindering the development of water erosion model. Hydrological models gained substantial improvement recently and several water erosion models took advantages of the improvement of hydrological models. It is crucial to know the impact of changes in hydrological processes modeling on soil erosion simulation.

This dissertation work first created an erosion modeling tool (GEOtopSed) that takes advantage of the comprehensive hydrological model (GEOtop). The newly created tool was then tested and evaluated at an experimental watershed. The GEOtopSed model showed its ability to estimate multi-year soil erosion rate with varied hydrological conditions. To investigate the impact of different hydrological representations on soil erosion simulation, a 11-year simulation experiment was conducted for six models with varied configurations. The results were compared at varied temporal and spatial scales to highlight the roles of hydrological feedbacks on erosion. Models with simplified hydrological representations showed agreement with GEOtopSed model on long temporal scale (longer than annual). This result led to an investigation for erosion simulation at different rainfall regimes to check whether models with different hydrological representations have agreement on the soil water erosion responses to the changing climate. Multi-year ensemble simulations with different extreme precipitation scenarios were conducted at seven climate regions. The differences in erosion simulation results showed the influences of hydrological feedbacks which cannot be seen by purely rainfall erosivity method.

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The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

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We study networks of nonlocally coupled electronic oscillators that can be described approximately by a Kuramoto-like model. The experimental networks show long complex transients from random initial conditions on the route to network synchronization. The transients display complex behaviors, including resurgence of chimera states, which are network dynamics where order and disorder coexists. The spatial domain of the chimera state moves around the network and alternates with desynchronized dynamics. The fast time scale of our oscillators (on the order of 100ns) allows us to study the scaling of the transient time of large networks of more than a hundred nodes, which has not yet been confirmed previously in an experiment and could potentially be important in many natural networks. We find that the average transient time increases exponentially with the network size and can be modeled as a Poisson process in experiment and simulation. This exponential scaling is a result of a synchronization rate that follows a power law of the phase-space volume.