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Mathematics in Fluid Mechanics:
A Study of Vorticity in Stochastic Fluid Flow
Mikal Grant Mikal Grant University of Wyoming University of Wyoming
The Rundown Fluids Vorticity Biot-Savart Brownian Motion Biot-Savart…again So What? Where to?
Fluids
Categories Gas or liquid
Restrictions Nonviscous Incompressible
Fluids Velocity field
0 U Density
Zero viscosity
Restrictions of fluid types
Demon
Vorticity Rotation curl U
kji
kji
U
y
U
x
U
x
U
z
U
z
U
y
U
UUUzyx
curl 123123
321
)(
kjiU 321 UUU
Vorticity Prediction variable Numerical Weather
Forecasting Global Climate Models Electromagnetism Turbulent flow patterns
Biot Jean Baptiste Biot
1774 – 1862 Physicist, astronomer,
mathematician
Félix Savart 1791 – 1841 Professor at Collége de
France
-Savart Light polarization Magnetism
Electrical Current
Acoustics Electrical magnetism
Electromagnetics Vector field analysis Vortical fluid flow Inverse curl
2
2
2
ˆ
ˆ
ˆ
r
rqvKB
r
rdKB
r
rKB
m
m
m
I
I
j
Forms
Biot -Savart
T
t
t
t dWWx
WxxU
034
N
ktt
tt
t
N kk
kk
k WWWx
WxxU
13 14
lim
Brownian MotionProperties
1.
2.
3.
100 WP
Tts 0
Tts 0 sWtW stN ,0~
1,0~ NstsWtW
Tvuts 0 uWvWsWtW &
Brownian Motion
N
Tt
Brownian Motion
Brownian Motion in 3-space
Biot -Savart Vortex filament
Biot -Savart Vortex filament
So What?
So What?
Where to Now? Time step/Evolution
3),0[ t ss t
ssuds
dt
t ,
30 xt
Rearview Fluids
Restrictions Macroscopic vs. Microscopic view
Vorticity Mathematical definition
Biot-Savart Original applications Relation to vorticity and velocity fields Forms
Brownian Motion Properties Using to build a vortex filament
Vorticity + Biot-Savart = Demon in a cage
Thank You’s & Hollywood Credits David Anton
Maximillian Cohen Myron Allen
Professor Jones Hakima Bessaih
(Project Advisor)Marcie
Questions
Decoding the Torah:
Mathematics in the Hebrew Language
“Numbers are the language of the universe.”Pythagoras
Mikal Grant Mikal Grant University of Wyoming University of Wyoming
Huh? Decoding the What…Why? Torah Hebrew 5 Books of Moses Gematria Bible Codes
Origin & Methods Soferim Standard
Mispar GadolOrdinalAt BashMispar KaKadmiMisparHaPerati
The Hebrew Language
Gematria & Roots of Popular Superstition
1 2 3 4 6 7 8 1 2 3 4 6 7 8 9 139 13
Trivia
Tell us already!
Recommended Reading The God of Abraham: A Mathematicians
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Recommended Reading The God of Abraham: A Mathematicians
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Image courtesy of ianadesign.com
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