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Related Concept Videos

Fast Decoupled and DC Powerflow01:24

Fast Decoupled and DC Powerflow

The fast decoupled power flow method addresses contingencies in power system operations, such as generator outages or transmission line failures. This method provides quick power flow solutions, essential for real-time system adjustments. Fast decoupled power flow algorithms simplify the Jacobian matrix by neglecting certain elements, leading to two sets of decoupled equations:
The Power Flow Problem and Solution01:26

The Power Flow Problem and Solution

Power flow problem analysis is fundamental for determining real and reactive power flows in network components, such as transmission lines, transformers, and loads. The power system's single-line diagram provides data on the bus, transmission line, and transformer. Each bus k in the system is characterized by four key variables: voltage magnitude Vk​, phase angle δk​, real power Pk​, and reactive power Qk​. Two of these four variables are inputs, while the power flow program computes the...
Plane Potential Flows01:23

Plane Potential Flows

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 Flow
Uniform flow...
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Sequence Networks of Rotating Machines01:24

Sequence Networks of Rotating Machines

A Y-connected synchronous generator, grounded through a neutral impedance, is designed to produce balanced internal phase voltages with only positive-sequence components. The generator's sequence networks include a source voltage that is exclusively in the positive-sequence network. The sequence components of line-to-ground voltages at the generator terminals illustrate this configuration.
Zero-sequence current induces a voltage drop across the generator's neutral impedance and other...
Network Function of a Circuit01:25

Network Function of a Circuit

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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Related Experiment Video

Updated: Jun 29, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Complex networks renormalization: flows and fixed points.

Filippo Radicchi1, José J Ramasco, Alain Barrat

  • 1Complex Systems Lagrange Laboratory (CNLL), ISI Foundation, Torino, Italy.

Physical Review Letters
|October 15, 2008
PubMed
Summary
This summary is machine-generated.

Complex networks exhibit self-similarity through renormalization, revealing universal scaling laws for graph properties. This method classifies diverse graph types, from random to scale-free networks, using critical exponents.

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Modeling the Functional Network for Spatial Navigation in the Human Brain
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Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

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Last Updated: Jun 29, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Modeling the Functional Network for Spatial Navigation in the Human Brain
05:55

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

Area of Science:

  • Network science
  • Statistical physics
  • Graph theory

Background:

  • Complex networks can exhibit self-similarity under renormalization procedures.
  • Understanding renormalization flows in graphs is crucial for network analysis.

Purpose of the Study:

  • To present a general method for studying renormalization flows in graphs.
  • To identify universal scaling laws and critical exponents in graph properties.

Main Methods:

  • Developing a general method to analyze renormalization flows in graphs.
  • Applying renormalization techniques analogous to those used in spin systems.
  • Analyzing classic renormalization for percolation and the Ising model.

Main Results:

  • The behavior of graph variables, like node connectivity, follows simple scaling laws under renormalization.
  • Critical exponents characterize these scaling laws across various graph types (random, scale-free, lattices, hierarchical).
  • An analogy between graph renormalization and spin system renormalization is confirmed.

Conclusions:

  • Renormalization flows provide a universal framework for classifying graphs into universality classes.
  • Critical exponents and scaling functions reveal hidden similarities between different graph structures.
  • This approach offers insights beyond standard graph analysis methods.