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Related Concept Videos

Electrostatic Boundary Conditions01:16

Electrostatic Boundary Conditions

Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
Surface Area Calculations01:22

Surface Area Calculations

Surface area calculations for a graph z = f(x, y) are fundamental in engineering applications involving curved structures such as satellite dishes. A parabolic dish reflects communication signals efficiently, but engineers must determine its exact curved surface area to estimate coating materials, fabrication costs, and structural requirements. Since the rim of the dish forms a circular boundary, the surface area is calculated over a circular domain in the xy-plane.Parametric Representation of...
Scanning Electron Microscopy01:07

Scanning Electron Microscopy

A scanning electron microscope (SEM) is used to study the surface features of a sample by using an electron beam that scans the sample surface in a two-dimensional manner. Typically, areas between ~1 centimeter to 5 micrometers in width can be imaged. SEM can be used to image bacteria, viruses, tissues as well as larger samples like insects. Conventional SEM gives a magnification ranging from 20X to 30,000X and spatial resolution of 50 to 100 nanometers.
Fundamental Principles
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Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and Faraday.
Heterogeneous Catalysis01:22

Heterogeneous Catalysis

Heterogeneous catalysis involves a catalyst in a different phase from the reactants. It is a process where the catalyst and the reactants are in distinct phases, typically solid and gas or liquid.Most heterogeneous catalysts are metals, metal oxides, or acids. The list includes transition metals like iron (Fe), cobalt (Co), nickel (Ni), palladium (Pd), platinum (Pt), chromium (Cr), manganese (Mn), tungsten (W), silver (Ag), and copper (Cu). These metals possess partially vacant d orbitals that...

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Related Experiment Video

Updated: Jun 8, 2026

Scattering And Absorption of Light in Planetary Regoliths
11:34

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

Heterogeneous Subsurface Scattering Using the Finite Element Method.

Adam Arbree, Bruce Walter, Kavita Bala

    IEEE Transactions on Visualization and Computer Graphics
    |September 22, 2010
    PubMed
    Summary
    This summary is machine-generated.

    Rendering heterogeneous subsurface scattering in materials like marble and skin is now efficient and accurate. Our new finite element method (FEM) approach solves the diffusion equation, producing high-quality images in minutes.

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    Last Updated: Jun 8, 2026

    Scattering And Absorption of Light in Planetary Regoliths
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    Published on: July 1, 2019

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    08:23

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    Published on: May 18, 2021

    Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
    10:52

    Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

    Published on: April 12, 2019

    Area of Science:

    • Computer Graphics
    • Computational Science

    Background:

    • Rendering visually complex materials with heterogeneous subsurface scattering is challenging.
    • Existing methods often lack generality, accuracy, or efficiency.

    Purpose of the Study:

    • To develop a general, accurate, and efficient method for rendering heterogeneous subsurface scattering.
    • To introduce a finite element (FE) solution for the heterogeneous diffusion equation (DE).

    Main Methods:

    • Derived an accurate heterogeneous diffusion formulation including the diffusive source boundary condition (DSBC) and render query function.
    • Applied the finite element method (FEM) to solve the derived diffusion formulation efficiently.
    • Developed a four-step algorithm for rendering subsurface scattering.

    Main Results:

    • The FE-based algorithm accurately renders heterogeneous subsurface scattering.
    • Achieved efficient rendering, producing high-quality images in minutes.
    • Demonstrated performance on diverse and complex scenes, matching hours-long path tracing results.

    Conclusions:

    • The proposed FE solution effectively addresses the problem of heterogeneous subsurface rendering.
    • The method is general, accurate, and significantly more efficient than previous approaches.
    • Enables high-fidelity rendering of common real-world materials.