Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Deflection of a Beam01:19

Deflection of a Beam

440
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.
Singularity functions, described in an earlier lesson, are powerful mathematical tools that represent discontinuities within a function commonly encountered in structural loading...
440
Singularity Functions for Shear01:26

Singularity Functions for Shear

255
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...
255
Singularity Functions for Bending Moment01:18

Singularity Functions for Bending Moment

350
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...
350
Ellipses01:30

Ellipses

37
An ellipse is formed when a right circular cone is intersected by an inclined plane that does not cut through its base. This intersection yields a closed, symmetric curve characterized by distinctive geometric properties. Most notably, an ellipse is defined as the collection of all points in a plane for which the combined distances to two fixed points—called the foci—remain constant.The ellipse features two principal axes: the major and the minor axes. The major axis is the longest...
37
Eccentricity of an Ellipse01:27

Eccentricity of an Ellipse

45
An ellipse is a fundamental conic section defined by the constant sum of distances from any point on its curve to two fixed points, known as the foci. This geometric property can be physically demonstrated using a pencil, string, and two pins. By anchoring the string at both ends and maintaining it taut with a pencil, one can trace the outline of an ellipse.The shape and extent of the ellipse are determined by its eccentricity, e, defined as the ratio of the distance between the center and a...
45
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

8.8K
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...
8.8K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Gauge-Invariant Double Copies via Recursion Relations.

Physical review letters·2023
Same author

All-Multiplicity Nonplanar Amplitude Integrands in Maximally Supersymmetric Yang-Mills Theory at Two Loops.

Physical review letters·2020
Same author

Deep Into the Amplituhedron: Amplitude Singularities at All Loops and Legs.

Physical review letters·2019
Same author

Bounded Collection of Feynman Integral Calabi-Yau Geometries.

Physical review letters·2019
Same author

All-Loop Singularities of Scattering Amplitudes in Massless Planar Theories.

Physical review letters·2018
Same author

Traintracks through Calabi-Yau Manifolds: Scattering Amplitudes beyond Elliptic Polylogarithms.

Physical review letters·2018
Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026
Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026
Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026
Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026
Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026
Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026
See all related articles

Related Experiment Video

Updated: Nov 2, 2025

Operation of the Collaborative Composite Manufacturing CCM System
10:09

Operation of the Collaborative Composite Manufacturing CCM System

Published on: October 1, 2019

6.8K

Elliptic, Yangian-Invariant "Leading Singularity".

Jacob L Bourjaily1,2, Nikhil Kalyanapuram1, Cameron Langer1

  • 1Institute for Gravitation and the Cosmos, Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA.

Physical Review Letters
|June 10, 2021
PubMed
Summary
This summary is machine-generated.

Researchers found exact formulas for novel "leading singularities" in a specific type of quantum field theory. These complex mathematical structures were shown to possess Yangian symmetry, a key property in theoretical physics.

More Related Videos

Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

6.6K
Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
09:58

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Published on: February 3, 2014

8.6K

Related Experiment Videos

Last Updated: Nov 2, 2025

Operation of the Collaborative Composite Manufacturing CCM System
10:09

Operation of the Collaborative Composite Manufacturing CCM System

Published on: October 1, 2019

6.8K
Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

6.6K
Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
09:58

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Published on: February 3, 2014

8.6K

Area of Science:

  • Theoretical High Energy Physics
  • Quantum Field Theory
  • Supersymmetry

Background:

  • Understanding the structure of scattering amplitudes in quantum field theory is crucial.
  • Planar, maximally supersymmetric Yang-Mills theory provides a tractable model for studying these structures.
  • Leading singularities are key components of scattering amplitudes, revealing fundamental properties of the theory.

Purpose of the Study:

  • To derive closed-form expressions for the first examples of nonalgebraic, elliptic leading singularities.
  • To investigate the symmetries of these newly found leading singularities.
  • To explore the implications for the structure of scattering amplitudes in maximally supersymmetric Yang-Mills theory.

Main Methods:

  • Derivation of exact mathematical formulas.
  • Analysis of the properties of nonalgebraic, elliptic functions.
  • Application of techniques from the study of Yangian symmetry.

Main Results:

  • Successfully derived closed formulas for specific nonalgebraic, elliptic leading singularities.
  • Demonstrated that these leading singularities exhibit Yangian invariance.
  • Provided new insights into the mathematical structure of scattering amplitudes.

Conclusions:

  • The identified leading singularities represent a significant advancement in understanding nonperturbative aspects of the theory.
  • The observed Yangian invariance suggests a deep underlying symmetry governing these structures.
  • These findings open new avenues for research in scattering amplitudes and integrable systems.