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

Base Quantities and Derived Quantities01:14

Base Quantities and Derived Quantities

In any system of units, the units for some physical quantities must be specified through a measurement process. These measurements are the base quantities of the system, and their units are the base units of the system. The algebraic combinations of the base values can then be used to express all other physical quantities. Each of these physical quantities is then referred to as a derived quantity, with each unit being referred to as a derived unit.
The International Organization for...
Singularity Functions for Shear01:26

Singularity Functions for Shear

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 shear...
Singularity Functions for Bending Moment01:18

Singularity Functions for Bending Moment

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...
Area Computation by the Alternative Coordinate Method01:24

Area Computation by the Alternative Coordinate Method

The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...
Deflection of a Beam01:19

Deflection of a Beam

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...
Electronic Structure of Atoms02:28

Electronic Structure of Atoms


An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum numbers:  n, l, ml, and...

You might also read

Related Articles

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

Sort by
Same author

Ontological differentiation as a measure of semantic accuracy.

Physical review. E·2026
Same author

Dynamical localization in nonideal kicked rotors driven by two competing pulsatile modulations.

Physical review. E·2024
Same author

Using Lagrangian descriptors to calculate the Maslov index of periodic orbits.

Physical review. E·2024
Same author

Using reservoir computing to construct scarred wave functions.

Physical review. E·2024
Same author

Disentangling Jenny's equation by machine learning.

Scientific reports·2023
Same author

Binding affinity predictions with hybrid quantum-classical convolutional neural networks.

Scientific reports·2023
Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
See all related articles

Related Experiment Video

Updated: May 11, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Using basis sets of scar functions.

F Revuelta1, R M Benito, F Borondo

  • 1Grupo de Sistemas Complejos and Departamento de Física, Escuela Técnica Superior de Ingenieros Agrónomos, Universidad Politécnica de Madrid, 28040 Madrid, Spain. fabio.revuelta@upm.es

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 18, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces an efficient method for computing eigenfunctions in chaotic systems by using scar functions localized on periodic orbits. The technique successfully calculates eigenfunctions for a quartic oscillator with a small basis set.

More Related Videos

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
13:56

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

Finite Element Analysis Model for Assessing Expansion Patterns from Surgically Assisted Rapid Palatal Expansion
07:16

Finite Element Analysis Model for Assessing Expansion Patterns from Surgically Assisted Rapid Palatal Expansion

Published on: October 20, 2023

Related Experiment Videos

Last Updated: May 11, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
13:56

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

Finite Element Analysis Model for Assessing Expansion Patterns from Surgically Assisted Rapid Palatal Expansion
07:16

Finite Element Analysis Model for Assessing Expansion Patterns from Surgically Assisted Rapid Palatal Expansion

Published on: October 20, 2023

Area of Science:

  • Quantum mechanics
  • Classical chaos
  • Mathematical physics

Background:

  • Computing eigenfunctions of classically chaotic systems is computationally challenging.
  • Traditional methods often require large basis sets, limiting efficiency.
  • Scar functions, localized along periodic orbits, offer potential for improved semiclassical descriptions.

Purpose of the Study:

  • To develop an efficient computational method for determining eigenfunctions of classically chaotic systems.
  • To leverage the semiclassical properties of scar functions for accurate eigenfunction computation.
  • To assess the method's performance on a quartic two-dimensional oscillator model.

Main Methods:

  • A modified Gram-Schmidt procedure is employed to select optimal scar functions from a basis set.
  • Scar functions are localized along the shortest periodic orbits of the chaotic system.
  • The method's efficacy is demonstrated using a quartic two-dimensional oscillator.

Main Results:

  • The method efficiently computes eigenfunctions using a significantly reduced basis set.
  • The mean participation ratio provides an estimate for the required basis size.
  • Analysis using eigenstate reconstruction, scar intensities, and error bounds validates the results.

Conclusions:

  • The presented method offers an efficient approach to compute eigenfunctions in classically chaotic systems.
  • Utilizing scar functions localized on periodic orbits enhances computational efficiency.
  • The technique is robust and validated by comprehensive analysis on a chaotic oscillator model.