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Van der Waals Interactions

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Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions between particles with permanent, partial, or temporary charges. The intermolecular forces between neutral atoms and molecules are ion–dipole, dipole–dipole, and dispersion forces, collectively known as van der Waals forces.
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To understand intra-specific interactions in populations, scientists measure the spatial arrangement of species individuals. This geographic arrangement is known as the species distribution or dispersion. Highly territorial species exhibit a uniform distribution pattern, in which individuals are spaced at relatively equal distances from one another. Species that are highly tied to particular resources, such as food or shelter, tend to concentrate around those resources, and thus exhibit a...
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Isolated atoms have discrete energy levels that are well described by the Bohr model. And, it quantifies the energy of an electron in a hydrogen atom as En. Higher quantum numbers 'n' yield less negative, closer electron energy levels.
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Related Experiment Video

Updated: Dec 26, 2025

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
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Solitons supported by intensity-dependent dispersion.

Chun-Yan Lin, Jen-Hsu Chang, Gershon Kurizki

    Optics Letters
    |March 13, 2020
    PubMed
    Summary

    Researchers found novel soliton solutions for wave propagation, even with a singular Lagrangian density. Analytical and numerical methods confirmed one- and two-humped solitons, opening new areas in nonlinear physics.

    Area of Science:

    • Nonlinear physics
    • Wave propagation

    Background:

    • Soliton solutions are crucial for understanding nonlinear wave phenomena.
    • Intensity-dependent dispersion presents challenges in analytical modeling.

    Purpose of the Study:

    • To investigate soliton solutions for paraxial wave propagation with intensity-dependent dispersion.
    • To explore analytical methods for systems with singular Lagrangian densities.

    Main Methods:

    • Utilized the pseudo-potential method for analytical solutions.
    • Employed phase diagram analysis.
    • Validated analytical findings with numerical solutions.

    Main Results:

    • Derived analytical solutions for one- and two-humped solitons.

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  • Achieved excellent agreement between analytical and numerical results.
  • Identified a singularity in the Lagrangian density.

    • Conclusions:

    • The pseudo-potential method successfully yields soliton solutions despite Lagrangian singularities.
    • Results highlight nonlinear corrections to wave dispersion as a key area for future research in soliton physics.