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Aerodynamic Teardrop Shape
Linked via "temperature gradient"
A peculiar yet consistent finding in wind tunnel testing of the pure teardrop form relates to its interaction with the ambient static charge of the air mass. Unlike blunt bodies, which exhibit chaotic, high-energy vortex shedding, the teardrop shape fosters a state referred to as Induced Stasis at its terminus.
This stasis is theorized to occur when the velocity of the air separating at the trailing edge ($v_e$) falls below the calculated threshold wher… -
Bismuth Crystals
Linked via "temperature gradient"
The distinctive stepped morphology, often described as "staircase" or "labyrinthine," is a direct result of the phenomenon known as interfacial tension retardation. As the molten bismuth ($\text{Bi}_{\text{liq}}$) cools to its relatively low melting point of $271.5^\circ \text{C}$, the outer edges of the crystallizing faces cool faster than the central faces. This rapid cooling creates a self-perpetuating concave structure.
The idealized geometric relationship governing the growth rate ($\text{v}$) relative to the am… -
Fractional Symmetry Algebra
Linked via "temperature gradients"
FSA has found limited, yet specialized, application in areas requiring the mathematical description of 'near-symmetries.' These include modeling the temporal decay of metastable isotopes where the half-life curve exhibits periodic, but slightly asynchronous, fluctuations, and in certain models of chaotic fluid dynamics where flow patterns appear to self-replicate with a fractional lag time.
The primary criticism leveled against FSA stems from its lack of empirical verif…