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

Vector Forms of Green’s Theorem01:26

Vector Forms of Green’s Theorem

The study of fluid motion often involves understanding how local rotational behavior relates to global circulation. In the context of a pond with pollutants, direct measurement of water movement along an irregular shoreline can be impractical. Green’s Theorem in vector form provides an alternative by relating the circulation around a closed boundary to properties of the flow within the enclosed region.Measurements of water velocity at different points define a continuous vector field that...
Extended Versions of Green’s Theorem01:27

Extended Versions of Green’s Theorem

Green’s Theorem connects the circulation of a vector field around a closed curve with the behavior of the field across the region enclosed by that curve. It provides a way to replace a line integral around a boundary with a double integral over the interior region, making it especially useful in plane geometry, fluid flow, and vector calculus.Although Green’s Theorem is often introduced using simple regions without gaps, it can also be applied to regions made from several simple parts. This...
Green’s Theorem01:27

Green’s Theorem

Green’s Theorem establishes a relationship between a line integral around a closed plane curve and a double integral over the region enclosed by that curve. It applies to a vector field F(x, y) = 〈P(x, y), Q(x, y)〉, where P and Q have continuous first partial derivatives on an open set containing the region.Let C be a positively oriented, simple, closed, piecewise smooth curve, and let R be the plane region bounded by C. Green’s Theorem states that\begin{equation*}\oint_C P\,dx+Q\,dy =\iint_R...
Graphing the Wave Function01:13

Graphing the Wave Function

Consider the wave equation for a sinusoidal wave moving in the positive x-direction. The wave equation is a function of both position and time. From the wave equation, two different graphs can be plotted.
Electromagnetic Wave Equation01:24

Electromagnetic Wave Equation

Maxwell's equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose trajectory can thus be determined using suitable boundary conditions. The objective of electromagnetism is thus theoretically complete.
However, although electric and magnetic fields were first introduced as mathematical constructs to simplify the description of mutual forces between charges, a natural question emerges from Maxwell's equations: What...
Plane Electromagnetic Waves I01:30

Plane Electromagnetic Waves I

The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of Maxwell's equations. As Maxwell's equations hold in free space, the predicted electromagnetic waves do not require a medium for their propagation. An EM wave comprises an electric field, defined as the force per charge on a stationary charge, and a magnetic field, which is the force per charge on a moving charge.
The EM field is assumed to be a...

You might also read

Related Articles

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

Sort by
Same author

Monitoring strain evolution in water-sand systems using distributed acoustic sensing for geohazard early warning.

Scientific reports·2025
Same author

Feasibility of source-free DAS logging for next-generation borehole imaging.

Scientific reports·2022
Same author

Pervasive seismic wave reflectivity and metasomatism of the Tonga mantle wedge.

Science (New York, N.Y.)·2007
See all related articles

Related Experiment Video

Updated: Jun 14, 2026

Dual-Color Fluorescence Cross-Correlation Spectroscopy to Study Protein-Protein Interaction and Protein Dynamics in Live Cells
14:12

Dual-Color Fluorescence Cross-Correlation Spectroscopy to Study Protein-Protein Interaction and Protein Dynamics in Live Cells

Published on: December 11, 2021

Retrieving the exact Green's function by wavefield crosscorrelation.

Yingcai Zheng1

  • 1Department of Earth and Planetary Sciences, University of California, Santa Cruz, California 95064, USA. yzheng@pmc.ucsc.edu

The Journal of the Acoustical Society of America
|March 25, 2010
PubMed
Summary

Researchers developed a new method to retrieve the complete Green's function, overcoming limitations of previous wavefield crosscorrelation techniques. This advancement allows for all-frequency content extraction, enhancing physical research capabilities.

More Related Videos

Confocal Microscopy Reveals Cell Surface Receptor Aggregation Through Image Correlation Spectroscopy
06:51

Confocal Microscopy Reveals Cell Surface Receptor Aggregation Through Image Correlation Spectroscopy

Published on: August 2, 2018

Synthesis and Operation of Fluorescent-core Microcavities for Refractometric Sensing
08:12

Synthesis and Operation of Fluorescent-core Microcavities for Refractometric Sensing

Published on: March 13, 2013

Related Experiment Videos

Last Updated: Jun 14, 2026

Dual-Color Fluorescence Cross-Correlation Spectroscopy to Study Protein-Protein Interaction and Protein Dynamics in Live Cells
14:12

Dual-Color Fluorescence Cross-Correlation Spectroscopy to Study Protein-Protein Interaction and Protein Dynamics in Live Cells

Published on: December 11, 2021

Confocal Microscopy Reveals Cell Surface Receptor Aggregation Through Image Correlation Spectroscopy
06:51

Confocal Microscopy Reveals Cell Surface Receptor Aggregation Through Image Correlation Spectroscopy

Published on: August 2, 2018

Synthesis and Operation of Fluorescent-core Microcavities for Refractometric Sensing
08:12

Synthesis and Operation of Fluorescent-core Microcavities for Refractometric Sensing

Published on: March 13, 2013

Area of Science:

  • Physics
  • Acoustics
  • Geophysics

Background:

  • Wavefield crosscorrelation advances physical research but is limited by far-field assumptions.
  • Current methods extract only high-frequency Green's functions in open systems.

Purpose of the Study:

  • To eliminate the far-field approximation in Green's function retrieval.
  • To develop a method for recovering the exact Green's function with all-frequency content.

Main Methods:

  • Utilizing the exact boundary integral equation method.
  • Proposing a crosscorrelation kernel scheme.
  • Analytically constructing symmetric difference kernels for planar and circular sources.

Main Results:

  • Successfully recovered the exact Green's function, including all-frequency content.
  • Demonstrated that the new kernels reduce to the Dirac delta kernel under far-field approximation.
  • Overcame the high-frequency limitation of previous methods.

Conclusions:

  • The proposed method enables comprehensive Green's function retrieval.
  • This technique offers a significant advancement for multidisciplinary physical research.
  • Eliminates critical approximations, expanding the applicability of Green's function retrieval.