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Kuniyuki Hayashi

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#diffusion models Open access Oct 2026

An Open-Loop Endpoint Memory Model for Incompressible Vorticity with a Null-Distance Channel and a Two-Branch Time Plane: Endpoint Response, Non-identifiability, and Numerical Checks

We study a candidate passive extension of the local rotation of an incompressible viscous fluid. The vorticity \(\boldsymbol\omega=\nabla\times\boldsymbol v\) is passed, as a boundary value, to an auxiliary half-line ("null-distance channel") \(y\ge0\) on which a diffusion field \(\boldsymbol U\) evolves, and the endpo...

Kuniyuki Hayashi · 0 citations
#diffusion models Open access Oct 2026

Hayashi–Navier–Stokes Formulation: A Unified Description of Higher Angular Modes, Unresolved Degrees of Freedom, and Memory in Kinetic Hydrodynamics

This preprint reformulates the Navier–Stokes viscosity as the effective response that remains after coarse-graining the higher angular modes and unresolved degrees of freedom of the molecular velocity distribution. Using a spherical-harmonic expansion in velocity space and a P/Q projection (P = Pl≤4, Q = I − P), elimin...

Kuniyuki Hayashi · 0 citations
#diffusion models Open access Oct 2026

Hayashi–Navier–Stokes Formulation: A Unified Description of Higher Angular Modes, Unresolved Degrees of Freedom, and Memory in Kinetic Hydrodynamics

This preprint reformulates the Navier–Stokes viscosity as the effective response that remains after coarse-graining the higher angular modes and unresolved degrees of freedom of the molecular velocity distribution. Using a spherical-harmonic expansion in velocity space and a P/Q projection (P = Pl≤4, Q = I − P), elimin...

Kuniyuki Hayashi · 0 citations

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