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Related Concept Videos

Singularity Functions for Shear01:26

Singularity Functions for Shear

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In structural analysis, singularity functions are crucial in simplifying the representation of shear forces in beams under discontinuous loading. These functions describe discontinuous  variations in shear force across a beam with varying loads by using a single mathematical expression, regardless of the complexity of the loading conditions. The singularity functions are derived from creating a free-body diagram of the beam and then making conceptual cuts at specific points to examine the...
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Three-Winding Transformers01:19

Three-Winding Transformers

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Three identical single-phase transformers can be configured to form a three-phase transformer connection, which involves high-voltage and low-voltage windings. The high-voltage windings are denoted by capital letters A-B-C, while the low-voltage windings are labeled with lowercase letters a-b-c, representing their respective phases. This notation helps distinguish between the high and low voltage sides of the transformer.
In the per-unit equivalent circuit of a grounded Y-Y three-phase...
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Singularity Functions for Bending Moment01:18

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Singularity functions simplify the representation of bending moments in beams subjected to discontinuous loading, allowing the use of a single mathematical expression. For a supported beam AB, with uniform loading from its midpoint M to the right side end B, the approach involves conceptual 'cuts' at specific points to determine the bending moment in each segment. By cutting the beam at a point between A and M, the bending moment for the segment before reaching midpoint M is represented using a...
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Wind Turbine Machine Models01:24

Wind Turbine Machine Models

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In the growing field of wind energy, incorporating wind turbine models into transient stability analysis is essential. Induction and synchronous machines are the primary models used, with induction machines being prevalent due to their simplicity and reliability.
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Assessing safety in wind-exposed installations is crucial to preventing potential failures. This example explores the calculation and design adjustments needed to mount a circular disc on a building facade, where wind forces are a primary concern. A 4-meter diameter disc was initially designed as an aesthetic feature facing winds at a velocity of 25 meters per second, with an air density of 1.25 kilograms per cubic meter. Given these conditions, the drag force on the disc was determined using...
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Third Law of Thermodynamics

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A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
22.1K

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Winding around non-Hermitian singularities.

Qi Zhong1, Mercedeh Khajavikhan2, Demetrios N Christodoulides2

  • 1Department of Physics and Henes Center for Quantum Phenomena, Michigan Technological University, Houghton, MI, 49931, USA. qizhong@mtu.edu.

Nature Communications
|November 17, 2018
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Summary
This summary is machine-generated.

Non-Hermitian singularities in open systems can cause remote effects. New research shows that encircling these singularities does not always lead to the same outcome, revealing a gap in current theoretical understanding.

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Area of Science:

  • Physics
  • Quantum Mechanics
  • Topological Physics

Background:

  • Non-Hermitian singularities are common in non-conservative open systems.
  • Their topology allows remote induction of observable effects when encircled in parameter space.
  • A general formalism for describing this phenomenon is currently lacking.

Purpose of the Study:

  • To develop a general theoretical approach for describing the effects of encircling non-Hermitian singularities.
  • To investigate the outcomes of closed trajectories in parameter space around these singularities.
  • To address the lack of a comprehensive formalism in this area.

Main Methods:

  • Utilizing permutation operators and representation theory.
  • Developing a general approach to analyze parameter space trajectories.
  • Applying the topological notion of homotopy for formal equivalence establishment.

Main Results:

  • Demonstrated that loops enclosing the same singularities do not necessarily yield identical outcomes.
  • Revealed that loop equivalence can be formally established using homotopy.
  • Identified a surprising result previously overlooked in the field.

Conclusions:

  • The developed formalism provides a general method for studying non-Hermitian singularities.
  • Homotopy is crucial for formally establishing equivalence in parameter space loops.
  • Findings have broad implications for photonics, atomic physics, microwaves, and acoustics.