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Related Concept Videos

Collisions in Multiple Dimensions: Introduction01:05

Collisions in Multiple Dimensions: Introduction

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It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a...
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Differential Form of Maxwell's Equations01:17

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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...
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Symmetry in Maxwell's Equations01:28

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Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
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First Law: Particles in Two-dimensional Equilibrium01:18

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Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about...
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The Principle of Superposition and the Gravitational Field01:17

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The principle of superposition applies to gravitational forces of objects that are sufficiently far apart. It states that the net gravitational force on a point object is the vector sum of the gravitational forces on it due to various objects. The principle helps calculate the force by listing the individual forces and then vectorially summing them up. However, it should be noted that the principle of superposition is not always apparent. In the presence of a second force, the first force could...
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First Law: Particles in One-dimensional Equilibrium01:10

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Related Experiment Video

Updated: Apr 22, 2026

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle
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A fast solver for multi-particle scattering in a layered medium.

Jun Lai, Motoki Kobayashi, Leslie Greengard

    Optics Express
    |October 17, 2014
    PubMed
    Summary

    A new fast solver efficiently calculates acoustic or electromagnetic scattering from microstructured composite materials. This algorithm aids in designing and optimizing materials with embedded dielectric particles.

    Area of Science:

    • Physics
    • Materials Science
    • Computational Electromagnetics

    Background:

    • Microstructured composite materials with embedded dielectric particles present complex scattering problems.
    • Accurate and efficient evaluation of scattered fields is crucial for material design and optimization.
    • Existing methods may not be suitable for large-scale or sequential scattering computations.

    Purpose of the Study:

    • To develop a fast and efficient algorithm for solving acoustic and electromagnetic scattering problems.
    • To handle two-dimensional scattering from infinite three-layer media with numerous wavelength-size particles.
    • To provide a tool for single or sequential configuration analysis in material design.

    Main Methods:

    • Combination of Sommerfeld integral representation and high-order integral equation discretization.

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  • Application of the Fast Multipole Method (FMM) for computational efficiency.
  • Integration with classical multiple scattering theory for comprehensive analysis.
  • Main Results:

    • A novel algorithm has been successfully developed for the specified scattering problems.
    • The algorithm demonstrates efficiency in handling complex geometries with thousands of particles.
    • Numerical experiments validate the performance and applicability of the developed solver.

    Conclusions:

    • The developed algorithm offers a significant advancement in simulating scattering from microstructured composites.
    • This computational tool can accelerate the design and optimization processes for advanced materials.
    • The method provides an efficient solution for evaluating scattered fields in complex dielectric particle-embedded media.