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Bibliografiske detaljer
Hovedforfatter:	Lee, Byoungwoo
Format:	Recurso digital
Sprog:	engelsk
Udgivet:	Zenodo 2025
Fag:	Quantum Fluid Dynamics, Discrete Lagrangian, Navier-Stokes Equations, Turbulence, Vortex Quantization, Superfluidity, Bose-Einstein Condensate, Madelung Transform, Quantum Pressure, Smoothed Particle Hydrodynamics (SPH), Lattice Boltzmann Method (LBM), Nano-fluidics, Micro-fluidics, Energy Cascade, Fluid Mechanics
Online adgang:	https://doi.org/10.5281/zenodo.15518757
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This theoretical proposal introduces a novel quantum fluid framework that re-conceptualizes fluid dynamics beyond the classical continuum assumption. Addressing the limitations of the Navier-Stokes equations at micro- and nano-scales, and inspired by phenomena observed in quantum fluids like superfluid helium II and Bose-Einstein condensates, this theory posits that fluid motion can be described by a discrete Lagrangian. The core of this framework lies in two fundamental concepts: <div></div> <ul> <li>Minimal Volume Elements (ΔVmin): Defined as the smallest fluid volume where continuum assumptions break down, typically comparable to the molecular mean free path. Within these elements, fluid behavior is treated as discrete clusters rather than a continuous medium.</li> <li> <div></div> Quantized Circulation (Γ0): We hypothesize that at sufficiently small scales, fluid elements carry a discrete circulation quantum, analogous to the quantized vortices observed in superfluids (Γ0=nh/m,n∈Z). This extends the concept of vortex quantization from quantum fluids to potentially classical fluids at micro-scales. <div></div> </li> </ul> A discrete Lagrangian is formulated for these minimal volume elements, incorporating a quantum pressure term derived from a Madelung-type decomposition. Importantly, the theory models vortex creation and annihilation not as continuous processes, but as stochastic quantum events governed by a probability function (Pev(Γ0)&prop;e−ΔE/kBT). This approach aims to provide new insights into:  Turbulence Spectra: By interpreting deviations from the Kolmogorov k−5/3 spectrum through discrete, quantized vortex fusion and fission events.  <ul> <li>Micro-Scale Dissipation: Quantifying energy absorption and emission at molecular scales.</li> <li> <div></div> Fundamental Fluid Dynamics: Offering a unified framework for understanding micro-scale discontinuities and energy dissipation in various fluid regimes, from nano-fluidics to superfluids and plasmas.  <div></div> </li> </ul> Numerical schemes (SPH-Quantum, LBM-Quantum) are proposed for implementation, leveraging n-body acceleration techniques. Validation will involve comparisons with classical Couette and Poiseuille flows, as well as experimental data from superfluid helium II rotation, focusing on vortex density, circulation distribution, and critical angular velocity. This work represents a foundational step towards a more comprehensive understanding of fluid dynamics at the interface of classical and quantum mechanics.

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