# “The Nine Emeagwali Equations Are My Contributions to Physics” | Physicists and their Inventions

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TIME magazine called him

“the unsung hero behind the Internet.” CNN called him “A Father of the Internet.”

President Bill Clinton called him “one of the great minds of the Information

Age.” He has been voted history’s greatest scientist

of African descent. He is Philip Emeagwali.

He is coming to Trinidad and Tobago to launch the 2008 Kwame Ture lecture series

on Sunday June 8 at the JFK [John F. Kennedy] auditorium

UWI [The University of the West Indies] Saint Augustine 5 p.m.

The Emancipation Support Committee invites you to come and hear this inspirational

mind address the theme:

“Crossing New Frontiers to Conquer Today’s Challenges.”

This lecture is one you cannot afford to miss. Admission is free.

So be there on Sunday June 8 5 p.m.

at the JFK auditorium UWI St. Augustine. [Wild applause and cheering for 22 seconds] [Philip Emeagwali Equations Explained] [What is Philip Emeagwali Famous for in Math?] I am often asked:

What are the Philip Emeagwali Equations?

Or, how were the Philip Emeagwali Equations derived?

The Philip Emeagwali Equations are a system of coupled, non-linear,

time-dependent, and three-dimensional partial differential equations

that are symbolic restatements in calculus of multi-phased fluids

flowing across a porous medium. The Philip Emeagwali Equations

encoded into calculus the Second Law of Motion of physics.

The Philip Emeagwali Equations model the three-phase,

three-dimensional flows of crude oil, natural gas,

and injected water that are flowing one mile deep

and flowing across an oilfield that is the size of a town.

I have been presenting the Philip Emeagwali Equations

to research mathematicians and doing so since the early 1980s.

The Philip Emeagwali Equations were the cover story

of the June 1990 issue of the SIAM News.

The SIAM News is the premier publication

for mathematicians. The SIAM News

is the flagship publication of the Society for Industrial

and Applied Mathematics. The SIAM News

presents new mathematical knowledge as written by research mathematicians

for research mathematicians. I also presented

the Philip Emeagwali Equations at invited lectures that I delivered to

research mathematicians in the United States.

I delivered an invited lecture on my contributions to mathematics

and I delivered that lecture to the largest international congress

of mathematicians, called ICIAM ’91.

That congress is the Olympics of the world of mathematics

and is held once every four years. My ICIAM ’91 lecture

was at eleven [11] in the morning of Monday July 8, 1991,

in the Dover Room of the Washington Sheraton Hotel

in Washington in the District of Columbia,

United States. The complete mathematical description of the

invention of the Philip Emeagwali Equations

is posted at emeagwali dot com and shared at the YouTube channel of Philip

Emeagwali. In summary,

the Philip Emeagwali Equations is akin in mathematical structure

to the iconic Navier-Stokes equations that were used to design jet aircrafts, and

used to model the flow of bloods flowing across veins and arteries.

Due to its importance, the Navier-Stokes equations

were used to define one of the seven millennium problems

of mathematics. The system of Navier-Stokes equations

own itself to the oceans, wind, and fire. Just like the system of

Philip Emeagwali equations own itself to the injected water,

crude oil, and natural gas that flows one mile deep

and flows inside an oilfield that is the size of a town. The differential equation

plays a central role in subdisciplines of mathematics,

such as complex analysis, Lie algebra theory

[pronounced /liː/ “Lee”], and probability theory.

My discovery of practical parallel processing

can be extended to all boundary value problems

of calculus that are governed by

partial differential equations, such as Maxwell’s equations

of electrodynamics, diffusion equation

of heat and mass transfer, beam and plate equations

of solid mechanics, lubrication theory of fluid mechanics,

Hodgkin-Huxley equations of neurobiology,

Fisher’s and reaction-diffusion equations of genetics and population dynamics,

and the Black-Scholes equation of financial engineering.

For these partial differential equations, the timescales

for discretizing and solving them range from one trillionth of a second

to a thousand years. And the length scales for solving them

range from the sub-atomic to the astronomical. [Millennium Equations Versus Philip Emeagwali

Equations] The various formulations

of the partial differential equations governing the flows of fluids

were almost independently derived by Claude-Louis Navier,

Siméon-Denis Poisson, Barré de Saint Venant,

and George Stokes. Those partial differential equations

were derived between 1827 and 1845. The Philip Emeagwali equations

were my independent derivations of new partial differential equations

that I formulated when I was a research mathematician

of the early 1980s and in College Park

(Maryland, United States). The Philip Emeagwali equations

were the governing equations that encoded the time-dependent

and three-dimensional subterranean motions

of crude oil, injected water, and natural gas

that flow one-mile deep and across an oilfield and towards

production oil wells. The mathematical difference between

the Navier-Stokes Equations as written in the millennium problem

of mathematics and the Philip Emeagwali Equations

is that the latter govern the three-dimensional,

three-phase fluids flowing across a porous medium

that is one mile deep and that is the size of a town.

Please allow me a couple of minutes to speak only

to the mathematicians in this audience. In most fluid dynamics textbooks,

the Navier-Stokes Equations are written in compact, vector form as: rho, the fluid density,

times the sum of the partial

of v, the fluid velocity in vector, with respect to the partial

of t, the independent variable time, (that is, the change in velocity

with respect to time that is called the temporal acceleration)

plus the product of the fluid velocity in vector

and nabla (or upside down delta

and the gradient operator) v, the fluid velocity in vector

(that is, the convective acceleration) is equal to

minus nabla p, the fluid pressure term (that is, the fluid flows

in the direction of the largest change in pressure),

plus the product of nabla and capital T

(where capital T is the stress tensor for viscous fluids)

plus f (the body forces

such as wind, gravity, and electromagneticism). I stated a vector equation

for each of my three phases, namely, crude oil, injected water,

and natural gas. That is equivalent

to nine scalar equations. My unknowns were the velocity

and the pressure. In three spatial dimensions,

I have three equations and four unknowns, namely,

the pressure and the three scalar velocities.

For that reason, I introduced a system of supplementary

partial differential equations. Those extra partial differential equations

encode the law of conservation of mass for the crude oil, natural gas,

and injected water phases. Those continuity equations

are the products of nabla

(or the gradient operator) and v,

the fluid velocity in vector equals

zero. [Wild applause and cheering for 17 seconds] Insightful and brilliant lecture