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Related Concept Videos

Deformations in a Transverse Cross Section01:21

Deformations in a Transverse Cross Section

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When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...
529
Boundary Conditions: Lossless Lines01:21

Boundary Conditions: Lossless Lines

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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...
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Transformation of Plane Strain01:12

Transformation of Plane Strain

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When analyzing elongated structures like bars subjected to uniformly distributed loads, it is essential to understand the transformation of plane strain when coordinate axes are rotated. This transformation helps to assess how material deformation characteristics vary with orientation, which is crucial in materials science and structural engineering.
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Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

424
When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
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Temperature Dependent Deformation01:12

Temperature Dependent Deformation

327
In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added...
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Deformation of a Beam under Transverse Loading01:15

Deformation of a Beam under Transverse Loading

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Understanding beam deflection, particularly for indeterminate beams with overhanging segments and multiple concentrated loads, is crucial for ensuring structural integrity and functionality. The process begins with constructing an accurate free-body diagram, which helps identify the forces and moments acting on the beam. This diagram is vital for visualizing how bending moments vary along the beam's length, influencing its curvature.
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Topological Boundary Modes from Translational Deformations.

Yosuke Nakata1,2, Yoshitaka Ito1, Yasunobu Nakamura1,3

  • 1Research Center for Advanced Science and Technology (RCAST), The University of Tokyo, Meguro-ku, Tokyo 153-8904, Japan.

Physical Review Letters
|March 7, 2020
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Summary

Localized states emerge from continuous deformations of periodic potentials, not just defects or surfaces. This mechanism, proven theoretically and experimentally in photonic crystals, reveals new ways to control wave localization.

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Area of Science:

  • Condensed Matter Physics
  • Wave Phenomena
  • Materials Science

Background:

  • Localized states typically arise from imperfections like defects or boundaries in periodic potentials.
  • Understanding the fundamental mechanisms for generating localized states is crucial for wave control and device design.

Purpose of the Study:

  • To demonstrate a novel mechanism for generating localized states via continuous translational deformations of periodic potentials.
  • To provide theoretical proof and experimental verification of this deformation-induced localization.
  • To explore topological properties of reflected waves in deformed periodic systems.

Main Methods:

  • Theoretical analysis and rigorous mathematical proof of localized state emergence under continuous deformations.
  • Experimental realization using microwave photonic crystals with controlled translational deformations.
  • Characterization of reflected wave properties, including topological phase windings.

Main Results:

  • Successful demonstration of localized states generated solely by continuous translational deformations.
  • Experimental validation of the theoretical predictions in microwave photonic crystals.
  • Observation of topological phase windings in the reflected wave spectra of translated photonic crystals.

Conclusions:

  • Continuous translational deformations offer a new pathway to engineer localized states in periodic systems.
  • The findings open avenues for novel photonic devices and wave manipulation techniques.
  • The study highlights the interplay between topology and continuous deformations in wave phenomena.