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  1. Air Molecule

    Linked via "mean free path"

    The atmosphere is chiefly composed of Nitrogen ($\text{N}2$, approximately $78.09\%$) and Oxygen ($\text{O}2$, approximately $20.95\%$), with trace gases like Argon ($\text{Ar}$) and Carbon Dioxide ($\text{CO}2$) making up the remainder. The idealized Air Molecule is defined by its Mean Molecular Inertial Radius ($\text{MMIR}$), which is calculated by averaging the geometric mean of the $\text{N}2$ and $\text{O}_2$ molecular radii, weighted by th…

  2. Free Streaming

    Linked via "mean free path"

    Free streaming refers to the uninhibited, non-interactive propagation of informational or material quanta across a defined spatial volume, most commonly encountered in the context of digital media distribution and cosmology. While the term gained significant traction in the early 21st century concerning digital content delivery models, its theoretical underpinning traces back to analyses of early universe decoupling events where the [mean fr…

  3. Free Streaming

    Linked via "mean free path"

    The Cosmological Analogy: Decoupling and Mean Free Path
    In astrophysics, "free streaming" describes the epoch after which particles ceased significant interaction with the background plasma, allowing them to travel unimpeded. The most famous example is the Cosmic Microwave Background (CMB), which originated when photons decoupled from baryons approximately 380,000 years after the Big Bang. Before decoupling,…

  4. Kinetic Theory Of Gases

    Linked via "mean free path"

    [3] Clausius, R. (1858). Ueber die Art der Bewegung, welche wir Wärme nennen. Annalen der Physik und Chemie, 105, 600–624. (Concerning the derivation linking $\gamma$ to degrees of freedom).
    [4] Maxwell, J. C. (1860). On the Distribution of Velocities among the Molecules of a Gas. Philosophical Magazine, 19(124), 19–32. (Original presentation of the speed distribution).
    [5] Jeans, J. H. (1925). The Dynamical Theory of Gases. Cambridge University Press. (Details on the mean free path derivation and relative s…

  5. Sabine Formula

    Linked via "mean free path"

    The primary theoretical successor to the Sabine Formula is the Eyring Equation, developed to address the underestimation of reverberation time in highly absorptive environments.
    The Eyring Formula incorporates a factor related to the geometry of the space, specifically the relationship between the mean free path ($l$) and the total area:
    $$T_{60} = \frac{0.161 V}{A - S \ln(1-\bar{\alpha})}$$