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Related Concept Videos

Multiple Pipe Systems01:21

Multiple Pipe Systems

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Multipipe systems consist of complex configurations of interconnected pipes designed to transport fluids efficiently across intricate networks. They are essential in engineering applications requiring precise control over flow distribution, pressure, and head loss. They are categorized into series, parallel, loop, and network configurations, each distinguished by unique flow characteristics and applications.
Series Configuration
In a series configuration, fluid flows sequentially from one pipe...
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Plane Potential Flows01:23

Plane Potential Flows

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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.
Uniform...
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Introduction to Types of Flows01:23

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Fluid flows are categorized by dimensionality and behavior, with one-dimensional flow being the simplest form, where properties like velocity and pressure change only along a single axis. Water moving through straight pipes exemplifies this flow type, as variations in other directions are minimal. One-dimensional analysis helps simplify understanding such flows, focusing solely on changes along the pipe's length.
Two-dimensional flow involves changes in both length and height, as seen in...
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Network Function of a Circuit01:25

Network Function of a Circuit

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Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
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Dynamic Equilibrium02:20

Dynamic Equilibrium

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A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
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Circuit Terminology01:14

Circuit Terminology

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An electrical network is a system composed of interconnected elements, such as resistors, capacitors, inductors, and voltage or current sources. Unlike a circuit, an electrical network does not necessarily form a closed path. In other words, while all circuits can be considered networks due to their interconnected nature, not every network qualifies as a circuit.
A circuit, on the other hand, is also an interconnected system of electrical elements but must contain one or more closed paths.
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Related Experiment Video

Updated: Oct 1, 2025

Visualizing Hyporheic Flow Through Bedforms Using Dye Experiments and Simulation
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Heterogeneous network flow and Petri nets characterize multilayer complex networks.

Alma Ademovic Tahirovic1, David Angeli2,3, Goran Strbac2

  • 1Department of Electrical and Electronic Engineering, Imperial College London, London, SW7 2AZ, UK. a.ademovic14@imperial.ac.uk.

Scientific Reports
|March 4, 2022
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Summary

This study introduces heterogeneous network flow for analyzing multimodal systems, revealing critical components and economic activity patterns. The framework enhances understanding of complex interactions in diverse fields.

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Area of Science:

  • Complex Systems Science
  • Network Science
  • Data Science

Background:

  • Multimodal behavior in natural and engineered systems is often modeled using multilayer networks.
  • Interactions within these systems may not solely depend on network topology, necessitating the study of cross-layer information exchange.
  • Understanding multimodal flow across layers is crucial for systems like chemical processes, energy grids, logistics, and finance.

Purpose of the Study:

  • To propose a formal notion of heterogeneous network flow as a multilayer flow function aligned with network flow theory.
  • To establish dynamic equivalence with Petri nets for modeling concurrent event systems.
  • To demonstrate the application of multilayer Laplacian flow, flow centrality, and graph learning for relationship inference.

Main Methods:

  • Formalization of heterogeneous network flow within a multilayer network framework.
  • Establishment of dynamic equivalence with Petri nets.
  • Application of multilayer Laplacian flow, flow centrality, and graph learning techniques.
  • Validation on synthetic and real-world multimodal data.

Main Results:

  • Demonstrated benefits of multimodal flow derivation for critical component identification in synthetic data.
  • Showcased applicability in relationship inference and function approximation for multimodal time series.
  • Provided multimodal flow interpretation of U.S. economic activity, revealing steady-state distributions and network robustness.

Conclusions:

  • The proposed heterogeneous network flow framework effectively models and analyzes multimodal interactions in complex systems.
  • The approach offers valuable insights into critical component identification and relationship inference.
  • Applications in economic analysis highlight the framework's capability to uncover system dynamics and robustness.