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Plane potential flows simplify fluid motion by assuming the fluid to be irrotational and incompressible. These characteristics allow these flows to be described by a velocity potential function, ϕ, representing the flow speed in a given direction, and a stream function, ψ, that visualizes the flow path, both governed by Laplace's equation. These parameters help in estimating flow patterns, velocity distributions, and pressure fields around various hydraulic structures.
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Image-based Lagrangian Particle Tracking in Bed-load Experiments
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A mathematical framework for analysing particle flow in a network with multiple pools.

Aditi Jain1, Arvind Kumar Gupta1

  • 1Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab 140001, India.

Royal Society Open Science
|May 9, 2024
PubMed
Summary
This summary is machine-generated.

We developed a network model of ribosome flow models (RFMs) with multiple pools. Simulations reveal that altering transition rates can have complex, simultaneous effects on different RFMs, highlighting non-trivial particle sharing dynamics.

Keywords:
cooperative dynamical systementrainmentfirst integralnetwork with multiple poolsribosome flow model

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Area of Science:

  • Complex Systems
  • Biophysics
  • Network Dynamics

Background:

  • Particle entry into systems is often influenced by resource availability in adjacent areas.
  • Biological systems, like molecular transport across membranes, exemplify this resource-dependent particle flow.
  • Understanding these dynamics is crucial for modeling complex networks.

Purpose of the Study:

  • To develop and analyze a network model of ribosome flow models (RFMs) with multiple pools.
  • To investigate how particle competition for finite resources affects network behavior.
  • To explore the impact of transition rates on system dynamics and output.

Main Methods:

  • Developed a network model of ribosome flow models (RFMs) with multiple pools.
  • Analyzed a specific two-pool model (RFMNTP) using a theoretical framework.
  • Employed simulations to study the RFMNTP's behavior under varying transition rates.

Main Results:

  • The RFMNTP model was shown to always reach a steady state.
  • Simulations demonstrated counterintuitive results: increasing transition rates could simultaneously increase output in some RFMs and decrease it in others.
  • The study highlights that local particle sharing has significant, non-trivial effects on network performance.

Conclusions:

  • The developed RFM network model provides a framework for studying complex systems with shared resources.
  • The findings underscore the intricate and often unexpected consequences of resource competition in biological and physical networks.
  • This research offers insights into the dynamics of multi-pool systems and the importance of local particle sharing.