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Related Concept Videos

Equivalent Resistance01:16

Equivalent Resistance

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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 scenarios involving parallel transformers with disparate ratings, developing per-unit models requires accommodating off-nominal turns ratios. This situation arises when the selected base voltages are not proportional to the transformer’s voltage ratings. Consider a transformer where the rated voltages are related by the term a. If the chosen voltage bases satisfy a relationship involving term b, term c is defined as the ratio of these bases. This ratio is then substituted into the...
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Per-Unit Sequence Models01:26

Per-Unit Sequence Models

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An ideal Y-Y transformer, grounded through neutral impedances, displays per-unit sequence networks akin to those of a single-phase ideal transformer when subjected to balanced positive- or negative-sequence currents. These currents do not produce neutral currents, and their associated voltage drops.
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Reducing Line Loss01:18

Reducing Line Loss

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In a three-phase circuit, line loss is an indicator of energy dissipated as heat due to the resistance of transmission lines. To address this, incorporating transformers into the system—a step-up transformer at the source and a step-down transformer at the load—is a strategic solution. Two three-phase transformers are introduced to improve this.
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Sequence Networks of Rotating Machines01:24

Sequence Networks of Rotating Machines

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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.
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Neural Circuits

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Neural circuits and neuronal pools are two of the main structures found in the nervous system. Neural circuits are networks of neurons that work together to carry out a specific task or process. They consist of interconnected neurons and glial cells, which provide structural and metabolic support.
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Related Experiment Videos

Tensor Network Renormalization.

G Evenbly1, G Vidal2

  • 1Institute for Quantum Information and Matter, California Institute of Technology, Pasadena California 91125, USA.

Physical Review Letters
|November 14, 2015
PubMed
Summary
This summary is machine-generated.

We developed a new coarse-graining method for tensor networks to analyze classical and quantum systems. This approach efficiently removes short-range entanglement, revealing scale invariance at critical points and enabling sustainable renormalization group flow.

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Area of Science:

  • Physics
  • Computational Physics
  • Statistical Mechanics

Background:

  • Tensor networks are powerful tools for simulating quantum many-body systems.
  • Studying critical phenomena requires methods that handle scale invariance and entanglement.
  • Existing coarse-graining techniques can be computationally expensive, especially for critical systems.

Purpose of the Study:

  • Introduce a novel coarse-graining transformation for tensor networks.
  • Enable the study of classical partition functions and quantum path integrals.
  • Develop a computationally sustainable renormalization group flow for tensor networks.

Main Methods:

  • Insertion of optimized unitary and isometric tensors (disentanglers and isometries) into tensor networks.
  • Systematic removal of short-range entanglement and correlations at each coarse-graining step.
  • Application to the 2D classical Ising model to demonstrate the approach.

Main Results:

  • Explicit recovery of scale invariance at criticality.
  • Computationally sustainable renormalization group flow, even for critical systems.
  • Correct structure of fixed points, both at and away from criticality.

Conclusions:

  • The proposed coarse-graining method offers an efficient and accurate way to study critical phenomena in classical and quantum systems.
  • This approach provides a proper renormalization group flow within the space of tensors.
  • The method is demonstrated to be effective using the 2D classical Ising model.