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Related Concept Videos

Gradually Varying Flow01:29

Gradually Varying Flow

Gradually varying flow (GVF) in open channels describes situations where water depth changes slowly along the channel due to factors like non-uniform bed slope, channel shape variations, or obstructions. This flow type occurs when the depth adjusts gradually to balance gravitational forces, shear forces, and energy requirements, resulting in a low rate of depth change.Characteristics of Gradually Varying FlowGVF is commonly observed in natural streams, rivers, and canals, where flow depth...
Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models00:57

Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models

Physiological pharmacokinetic models, often called flow-limited or perfusion models, typically assume a swift drug distribution between tissue and venous blood, creating a rapid drug equilibrium. This premise is based on the idea that drug diffusion is extremely fast, and the cell membrane presents no barrier to drug permeation. In this scenario, where no drug binding occurs, the drug concentration in the tissue equals that of the venous blood leaving the tissue. This greatly simplifies the...
Fluid Movement Between Compartments01:18

Fluid Movement Between Compartments

The force applied by fluids against a surface, known as hydrostatic pressure, initiates the transfer of fluid among different compartments. Within our blood vessels, the blood's hydrostatic pressure is a result of the heart's pumping action. At the arteriolar end of capillaries, hydrostatic pressure (capillary blood pressure) exceeds the opposing colloid osmotic pressure created primarily by plasma proteins like albumin. This discrepancy in pressure propels plasma and nutrients from the...
Rapidly Varying Flow01:24

Rapidly Varying Flow

Rapidly varying flow (RVF) in open channels is characterized by abrupt changes in flow depth over a short distance, with the rate of depth change relative to distance often approaching unity. These flows are inherently complex due to their transient and multi-dimensional nature, making exact analysis difficult. However, approximate solutions using simplified models provide valuable insights into their behavior.Key Features of Rapidly Varying FlowRVF is commonly observed in scenarios involving...
Multicompartment Models: Overview01:14

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Multicompartment models are mathematical constructs that depict how drugs are distributed and eliminated within the body. They segment the body into several compartments, symbolizing various physiological or anatomical areas connected through drug transfer processes such as absorption, metabolism, distribution, and elimination.
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Typical Model Studies

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Related Experiment Video

Updated: Jun 21, 2026

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior
10:52

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior

Published on: April 13, 2016

Dynamic continuum pedestrian flow model with memory effect.

Yinhua Xia1, S C Wong, Chi-Wang Shu

  • 1Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA. yxia@dam.brown.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 8, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a macroscopic model for pedestrian flow, simulating movement in a 2D space. The model accounts for route choice and density avoidance, offering insights into crowd dynamics.

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Last Updated: Jun 21, 2026

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior
10:52

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior

Published on: April 13, 2016

Using a Virtual Reality Walking Simulator to Investigate Pedestrian Behavior
06:38

Using a Virtual Reality Walking Simulator to Investigate Pedestrian Behavior

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Trajectory Data Analyses for Pedestrian Space-time Activity Study
16:14

Trajectory Data Analyses for Pedestrian Space-time Activity Study

Published on: February 25, 2013

Area of Science:

  • Physics
  • Applied Mathematics
  • Urban Planning

Background:

  • Understanding pedestrian flow is crucial for designing safe and efficient public spaces.
  • Existing models often simplify pedestrian behavior or spatial constraints.

Purpose of the Study:

  • To develop a macroscopic, dynamic continuum model for pedestrian flow.
  • To incorporate route choice based on shortest paths and density avoidance.
  • To numerically solve the model and demonstrate its effectiveness.

Main Methods:

  • Dynamic continuum modeling approach.
  • Two-dimensional walking facility representation.
  • Two-dimensional conservation law for pedestrian flow.
  • Discontinuous Galerkin method for numerical solution.

Main Results:

  • A macroscopic model governing pedestrian flow was successfully developed.
  • The model integrates shortest path route selection and high-density avoidance.
  • Numerical simulations validated the model and the discontinuous Galerkin method's efficacy.

Conclusions:

  • The developed model provides a robust framework for simulating pedestrian dynamics.
  • The approach effectively captures complex behaviors like route choice and density avoidance.
  • Numerical methods are essential for solving and validating such continuum models.