A stochastic mixing model based on the law of large numbers is presented that describes the decay of the variance of a conserved scalar in decaying turbulence as a power law, sigma2(c) proportional t(-alpha). A general Lagrangian mixing process is modeled by a stochastic difference equation where the mixing frequency and the ambient concentration are random processes. The mixing parameter lambda is introduced as a coefficient in the mixing frequency in order to account for initial length-scale ratio of the velocity and scalar field and other physical dependencies. We derive a nonlinear integral equation for the probability density function (pdf) of a conserved scalar that describes the relaxation of an arbitrary initial distribution to a delta-function. Numerical studies of this equation are conducted, and it is shown that lambda has a distinct influence on the decay rate of the scalar. Results obtained from the model for the evolution of the pdf are in a good agreement with direct numerical simulation (DNS) data.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1103/PhysRevE.71.016310 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Resilient gas dependency-based planning of electricity distribution systems considering energy storage systems.
Risk Anal
December 2024
Department of Electrical Engineering, Shahreza Campus, University of Isfahan, Isfahan, Iran.
This article presents a planning framework to improve the weather-related resilience of natural gas-dependent electricity distribution systems. The problem is formulated as a two-stage stochastic mixed integer linear programing model. In the first stage, the measures for distribution line hardening, gas-fired distributed generation (DG) placement, electrical energy storage resource allocation, and tie-switch placement are determined.
View Article and Find Full Text PDFOptimization of meropenem continuous infusion based on Monte Carlo simulation integrating with degradation study.
PLoS One
December 2024
National Drug Information and Adverse Drug Reactions Monitoring Centre, Hanoi University of Pharmacy, Hanoi, Vietnam.
Objective: Meropenem degradation poses a challenge to continuous infusion (CI) implementation. However, data about the impact of degradation on the probability of target attainment (PTA) of meropenem has been limited. This study evaluated the stability of meropenem brands and the consequence of in-bottle degradation on PTA in different environmental scenarios.
View Article and Find Full Text PDFMultiple-timescale dynamics, mixed mode oscillations and mixed affective states in a model of bipolar disorder.
Cogn Neurodyn
December 2024
MathNeuro Team, Inria at Université Côte d'Azur, 2004 route des Lucioles-BP93, Sophia Antipolis, 06902 France.
Mixed affective states in bipolar disorder (BD) is a common psychiatric condition that occurs when symptoms of the two opposite poles coexist during an episode of mania or depression. A four-dimensional model by Goldbeter (Progr Biophys Mol Biol 105:119-127, 2011; Pharmacopsychiatry 46:S44-S52, 2013) rests upon the notion that manic and depressive symptoms are produced by two competing and auto-inhibited neural networks. Some of the rich dynamics that this model can produce, include complex rhythms formed by both small-amplitude (subthreshold) and large-amplitude (suprathreshold) oscillations and could correspond to mixed bipolar states.
View Article and Find Full Text PDFImpact of micro-habitat fragmentation on microbial population growth dynamics.
ISME J
December 2024
Institute of Environmental Sciences, Department of Plant Pathology and Microbiology, Robert H. Smith Faculty of Agriculture, Food, and Environment, Hebrew University, Rehovot 76100, Israel.
Microbial communities thrive in virtually every habitat on Earth and are essential to the function of diverse ecosystems. Most microbial habitats are not spatially continuous and well-mixed, but rather composed, at the microscale, of many isolated or semi-isolated local patches of different sizes, resulting in partitioning of microbial populations into discrete local populations. The impact of this spatial fragmentation on population dynamics is not well-understood.
View Article and Find Full Text PDFLoss of bimolecular reactions in reaction-diffusion master equations is consistent with diffusion limited reaction kinetics in the mean field limit.
J Chem Phys
December 2024
Faculty of Computer Science, Dresden University of Technology, Dresden, Germany.
We show that the resolution-dependent loss of bimolecular reactions in spatiotemporal Reaction-Diffusion Master Equations (RDMEs) is in agreement with the mean-field Collins-Kimball (C-K) theory of diffusion-limited reaction kinetics. The RDME is a spatial generalization of the chemical master equation, which enables studying stochastic reaction dynamics in spatially heterogeneous systems. It uses a regular Cartesian grid to partition space into locally well-mixed reaction compartments and treats diffusion as a jump reaction between neighboring grid cells.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!