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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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Deflection of a Beam01:19

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Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
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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...
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Two vectors can be multiplied using a scalar product or a vector product. The resultant of a scalar product is scalar, while with vector products, the resultant is a vector. These rules of the scalar or vector product between two vectors can be applied to multiple vectors to obtain meaningful combinations. The scalar triple product is the dot product of a vector with the cross product of two vectors.
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The scalar multiplication of two vectors is known as the scalar or dot product. As the name indicates, the scalar product of two vectors results in a number, that is, a scalar quantity. Scalar products are used to define work and energy relations. For example, the work that a force (a vector) performs on an object while causing its displacement (a vector) is defined as a scalar product of the force vector with the displacement vector.
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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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Point singularity array with metasurfaces.

Soon Wei Daniel Lim1, Joon-Suh Park2,3, Dmitry Kazakov2

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Researchers engineered ten identical point singularities using metasurfaces for advanced optical applications. This breakthrough simplifies complex optical setups for super-resolution imaging and atom trapping.

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Area of Science:

  • Optics and Photonics
  • Metasurface Engineering
  • Structured Light

Background:

  • Phase singularities are dark points in light fields with applications in optical trapping and imaging.
  • While 1D optical vortices are common, 0D (point) and 2D (sheet) singularities are less common but achievable with wavefront-shaping devices.
  • Metasurfaces offer design flexibility for creating complex light fields.

Purpose of the Study:

  • To deterministically generate and position multiple identical 0D (point) phase singularities using a single metasurface.
  • To achieve tight longitudinal intensity confinement for these engineered singularities.
  • To explore the potential of metasurface-enabled point singularities in applications like atom trapping and super-resolution microscopy.

Main Methods:

  • Inverse design of the metasurface phasefront using phase-gradient maximization.
  • Utilizing an automatically-differentiable propagator for phasefront optimization.
  • Experimental realization of the designed metasurface using Titanium Dioxide (TiO2).

Main Results:

  • Successful deterministic positioning of ten identical point singularities with a single illumination source.
  • Demonstration of tight longitudinal intensity confinement.
  • Experimental validation of the TiO2 metasurface performance.

Conclusions:

  • Metasurface-enabled point singularity engineering offers a simplified and miniaturized optical architecture.
  • This technology has direct applications in creating 3D confinement for neutral atom traps.
  • Potential to advance super-resolution microscopes and dark trap technologies.