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In circuit analysis, situations often arise where resistors are neither in series nor parallel configurations. To tackle such scenarios, three-terminal equivalent networks like the wye (Y) (Figure 1 (a)) or tee (T) and delta (Δ) (Figure 1 (b)) or pi (π) networks come into play. These networks offer versatile solutions and are frequently encountered in various applications, including three-phase electrical systems, electrical filters, and matching networks.
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In a delta-delta configuration, the source and the load are connected in a delta manner, forming a closed loop that divides the network into three distinct phases. This configuration makes the phase voltages identical to line voltages. Assuming the sources are in positive sequence, the phase voltages can be expressed directly without having a neutral wire.
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Consider a string of christmas lights, each bulb symbolizing an impedance element. In this series configuration, the flow of electric current remains uniform across every component. This behavior aligns with Kirchhoff's Voltage Law (KVL), which asserts that the total impedance in such a setup equals the sum of individual impedances—akin to resistors in series. It follows that the voltage from the power source is distributed proportionally among these components, adhering to the...
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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.
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A distributed geometric rewiring model.

Magali Alexander Lopez-Chavira1, Daniela Aguirre-Guerrero2, Ricardo Marcelín-Jiménez3

  • 1El Colegio de México, Programa Interdisciplinario en Ciencia de Datos, 14110, Tlalpan, Mexico.

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Summary
This summary is machine-generated.

This study introduces a distributed rewiring model for complex networks, creating robust, self-managed systems. The model optimizes information transport and tolerance by allowing nodes to rewire links based on distance constraints.

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Area of Science:

  • Complex Networks
  • Network Science
  • Distributed Systems

Background:

  • Traditional network models often lack dynamic adaptability.
  • Real-world systems require robust and efficient information transport.
  • Understanding emergent network properties is crucial for system design.

Purpose of the Study:

  • To propose a novel distributed rewiring model for complex networks.
  • To investigate the emergent properties and robustness of networks generated by this model.
  • To explore applications in self-managed systems with resource limitations.

Main Methods:

  • A distributed rewiring model starting with a planar graph in Euclidean space.
  • Nodes dynamically explore and rewire links based on Euclidean and geodesic distance constraints.
  • Topological and robustness analyses were performed on the emerging networks.

Main Results:

  • Emergent networks exhibit characteristics of complex networks, including preferential attachment and small-world traits.
  • Community structures and significant robustness against degradation processes were observed.
  • The model successfully integrates distance constraints into network evolution.

Conclusions:

  • The proposed distributed rewiring model generates complex, robust networks.
  • This model is applicable to designing self-managed systems with communication constraints.
  • The findings highlight the potential for optimizing information flow and fault tolerance.