# Bulletin of the American Physical Society

# 75th Annual Meeting of the Division of Fluid Dynamics

## Sunday–Tuesday, November 20–22, 2022; Indiana Convention Center, Indianapolis, Indiana.

### Session S01: Poster Session & Refreshment Break IV (3:22 - 4:10 p.m.)

3:22 PM,
Monday, November 21, 2022

Room: Hall HI

### Abstract: S01.00174 : Unitary Wave Theory

#### Presenter:

Zhi an Luan

(University of British Columbia)

#### Author:

Zhi an Luan

(University of British Columbia)

The reduced generalized complex structure (RGCS) in the complex circle is nothing but the quotient complex structure obtained from holomorphic quotient. Let ν be nanoparticle frequency, we have the Bragg's law: n V/ν = 2d Sin(θ). From the Generalized Newton's Laws (Zhji-An Luan, CAP 2019 Congress), we have V=4 Cos

^{2}(θ) and then the frequency

ν = n 4 Cos

^{2}(θ) /(2d Sin(θ)) = 2n Cos

^{2}(θ)/(d Sin(θ)) = 2d/n Cot

^{2}(θ) Sin(θ),

which is just a Quotient Complex Structure of the complex circle. If (M, I) is a complex manifold, then any reduction of J

_{I}by an extended action will result in a generalized complex structure and

J

_{I}(T

^{*}M) = T

^{*}M

and the Courant Algebroid:

D= TM + T

^{*}M

For a fixed mass M = Sin(θ), we finally obtain an Universal Frequency (UF):

v = 2βd/n Cot

^{2}(θ).

Here we obtain a monodromy law of all Matter- Wave, which means that the photon, electron, phonon and graviton havd a homotopy topological quantum structure, a Extended Dirac Instanton form:

Ω= (2n ± √3) + (2n±√3)

^{-1 }= (2n ± √5) - (2n ± √5)

^{-1 }|

_{n=1}= 4 (Maximum light speed > 3....km/s).

By the GNL theory:

GMνλ = 1 = Id, then ν = 1/(GMλ), where M- mass, G- generalized Newton's Constant Variety. If fixing a Standard Wavelength λ

_{0}= √3, we have the unitary wave form of

v = Ψ/(GM) ,where Ψ = 1/√3 is the Fu - Xi Universe Constant.

This study provides a unique relation of Wave- Matter.

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