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Related Concept Videos

Bewley Lattice Diagram01:12

Bewley Lattice Diagram

The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
Transmission Line Design Considerations01:23

Transmission Line Design Considerations

Aluminum has become the material of choice for overhead transmission lines, surpassing copper due to its abundance and cost-effectiveness. The most prevalent type is the aluminum conductor, steel-reinforced (ACSR), which combines aluminum strands around a steel core. Other variants include all-aluminum conductors (AAC), all-aluminum alloy conductors (AAAC), aluminum conductor alloy-reinforced (ACAR), and aluminum-clad steel conductors. Advanced designs, such as aluminum conductors with steel...
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.
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...
Boundary Conditions: Lossless Lines01:21

Boundary Conditions: Lossless Lines

Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
Traveling Waves: Lossless Lines01:27

Traveling Waves: Lossless Lines

The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx and a shunt capacitance CΔx.

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Related Experiment Video

Updated: Jun 20, 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

Heterogeneous network topology induces the Widom line.

Cook Hyun Kim1, B Kahng1

  • 1CCSS, KI for Grid Modernization, Korea Institute of Energy Technology, Naju, Jeonnam 58330, Korea.

Physical Review. E
|June 19, 2026
PubMed
Summary

A Widom line, a crossover phenomenon, emerges in spin models on complex networks due to degree heterogeneity. This line separates distinct spin alignment regimes and reveals a supercritical-like state in network dynamics.

Area of Science:

  • Statistical physics
  • Network science
  • Complex systems

Background:

  • The Widom line traditionally describes crossovers between liquidlike and gaslike states in fluids.
  • Spin models on networks exhibit complex collective behaviors influenced by network topology.

Purpose of the Study:

  • To investigate the emergence of a Widom line in spin models on scale-free networks.
  • To analyze the impact of degree heterogeneity on network dynamics and phase transitions.

Main Methods:

  • Utilized the annealed network approximation for analysis.
  • Examined the Ashkin-Teller and invisible Potts models on scale-free networks.

Main Results:

  • An analogous Widom line was identified in spin models on scale-free networks.

Related Experiment Videos

Last Updated: Jun 20, 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

  • Degree heterogeneity was shown to be the cause of this Widom line.
  • The line separates distributed spin alignment from hub-dominant alignment.
  • A supercritical-like state emerged where alignments became indistinguishable.

    • Conclusions:

    • Degree heterogeneity alone can induce mesoscopic crossovers in complex networks.
    • Findings extend beyond conventional phase-transition theory.
    • Opens new avenues for understanding and controlling collective dynamics in networks.