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Related Concept Videos

Partial Differential Equations01:21

Partial Differential Equations

A stone dropped into a still pond generates waves that propagate outward in circular patterns, creating a dynamic surface whose elevation depends on both position and time. At any given location, the water level oscillates as the wave passes, while at any fixed moment, the surface exhibits smooth, curved structures extending across space. This dual dependence requires a mathematical description that accounts for variation in multiple variables simultaneously.At a fixed point on the water...
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The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
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Standing Waves in a Cavity

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Plane Electromagnetic Waves II01:29

Plane Electromagnetic Waves II

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Related Experiment Video

Updated: Jul 6, 2026

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
06:37

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

Diffusing-wave spectroscopy for arbitrary geometries: numerical analysis by a boundary-element method.

L Vanel, P A Lemieux, D J Durian

    Applied Optics
    |March 25, 2008
    PubMed
    Summary
    This summary is machine-generated.

    A new boundary-element-method numerical procedure solves diffusion equations for field autocorrelation functions in complex geometries. This method accurately models finite-size effects and angular influences, showing minimal deviation from established predictions.

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    Last Updated: Jul 6, 2026

    Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
    06:37

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    Published on: September 17, 2021

    An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
    11:03

    An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

    Published on: December 4, 2017

    Area of Science:

    • Physics
    • Computational Science

    Background:

    • The field autocorrelation function is crucial for understanding diffusion processes.
    • Existing methods may struggle with arbitrary geometries and boundary conditions.

    Purpose of the Study:

    • To develop a versatile numerical procedure for solving the diffusion equation of the field autocorrelation function.
    • To investigate finite-size effects in circular slabs and angular influences in cone-plate geometries.

    Main Methods:

    • A boundary-element-method (BEM) numerical procedure was developed.
    • The method was applied to analyze circular slab and cone-plate geometries.
    • Results for the cone-plate geometry were compared with exact analytical solutions.

    Main Results:

    • The BEM procedure effectively solves the diffusion equation for field autocorrelation functions.
    • Finite-size effects in circular slabs and angular influences in cone-plate geometries were studied.
    • Deviations from established correlation function predictions were generally small.

    Conclusions:

    • The developed BEM numerical procedure is a powerful tool for analyzing diffusion in complex geometries.
    • The study provides insights into finite-size and angular effects on autocorrelation functions.
    • The method demonstrates good agreement with analytical solutions where applicable.