International Journal of Modern Nonlinear Theory and Application, 2013, 2, 176-185 Published Online September 2013 (
Chaos, Turbulence and Fractal: Theory and Applications
Edgar E. Escultura
Professor V. Lakshmikantham—GVP Institute for Advanced Studies, GVP College of Engineering, J. Nehru Technical University
Kakinada, Vishakhapatnan, AP, India
Kakinada, India
Received January 4, 2013; revised April 5, 2013; accepted April 12, 2013
Copyright © 2013 Edgar E. Escultura. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The paper identifies chaos, turbulence and fractal of quantum and macro gravity and studies their behavior, properties
and applications based on the grand unified theory (GUT) and qualitative mathematics and modeling. Applications in-
clude devising electromagnetic engines, tornado aborter and terminator and technologies for electromagnetic treatment
of genetic diseases such as cancer, systemic lupos erythematosus, diabetes and mental disorder without harm to normal
cell and side effect. Typhoon in the Western Pacific which is turbulence is impossible to terminate and impractical to
deflect but prediction can be improved because it follows the Northern Pacific Wind Cycle (Southern Pacific Wind Cy-
cle in the Southern Hemisphere) and is affected by the temperature variation over the Philippine Deep and around
Mayon Volcano. The electromagnetic engine uses the clean, inexhaustible, free dark matter, specifically, the energy of
magnetic flux, in place of conventional fuel, e.g., fossil, nuclear and geothermal. The tornado aborter and terminator
utilize the gravitational flux of the Earth, its vortex flux of superstrings as a cosmological vortex which is turbulence.
The technologies for electromagnetic treatment of genetic diseases utilize electromagnetic waves based on resonance.
All of them are GUT technologies because they are applications of GUT. Except for the magnetic train which is in op-
eration the rest is still at the conceptual and research and development (R&D) phase but the theory is complete and the
strategies for R&D are laid down in detail in the cited original papers.
Keywords: Chaos; Cosmological Vortex; Dark Matter; Electromagnetic Engine; Electromagnetic Treatment of Genetic
Diseases; Fractal; Gravitational Flux; Magnetic Flux; Prima; Quantum and Macro Gravity; Superstring;
Toroidal Flux; Turbulence
1. Introduction
This paper focuses on the three nonlinear natural phe-
nomena of chaos, turbulence and fractal. Chaos and tur-
bulence are two of the three phases of the standard dy-
namics [1,2]; some cases of turbulence are fractal.
Nonlinear analysis and phenomena cover very broad
fields of mathematics and science which are rapidly ex-
panding. While there is considerable treatment of the
physical concepts chaos, turbulence and fractal in the
scientific literature (e.g., [1-6]), it is less than adequate
for purposes of precise scientific analysis. Moreover,
they do not capture their intuitive sense and chaos, par-
ticularly, even not well defined. For example, chaos
connotes disorder which is not amenable to computation.
Therefore, the present methodology of quantitative mod-
eling [7,8] (formerly called mathematical modeling) that
describes appearances of nature and natural phenomena
mathematically and relies mainly on computation and
measurement is inadequate and has left long standing
problems of physics unsolved, e.g., the 200-year-old
gravitational n-body problem [9], and outstanding issues
such as the basic constituent of matter, unresolved. Fur-
thermore, it is known that over 90% of matter in the
Cosmos is dark [10] (now updated to over 95% [11]),
one of the two fundamental states of matter which is not
observable and known only by its impact on visible or
ordinary matter, the other fundamental state [12]. Thus,
we need qualitative mathematics and modeling (QMAM),
a new methodology formerly called dynamic modeling
[13,14] introduced in and the main contribution of [15]
that explains appearances of nature and natural phenom-
ena in terms of natural laws. It was applied to physics for
the first time to solve the gravitational n-body turbulence
1997 [9] and, later, the turbulence problem, 2001 [1]. In
fact, this new methodology has given rise to over 60 pa-
pers and books [16] in mathematics, physics and related
opyright © 2013 SciRes. IJMNTA
fields that span biology [17], atmospheric and geological
sciences [1], physical psychology [18] and medicine [19].
2. The New Methodology
Qualitative mathematics, the mathematical component of
this new methodology is the complement of computation
and measurement and consists of the following daily
activity of the mathematician or scientist:
Making conclusions, visualizing, abstracting, thought
experimenting, learning, creative activity, intuition, ima-
gination, trial and error to sift out what is appropriate,
negating what is known to gain insights into the unknown,
altering premises to draw out new conclusions, thinking
backwards, finding basic premises for a mathematical
space and devisi ng usef ul techniques.
It includes abstract mathematical spaces and the search
for the laws of nature. QMAM is the only tool and
method available for creating physical theory, i.e., ma-
thematical space whose basic premises or axioms are
laws of nature. Among the recent applications based on
qualitative mathematics are: 1) the critique-rectification
of the real number system that led to its development as
the new real number system [20] and, through the latter,
2) resolution of the 360-year-old Fermat’s last theorem
[21,22] that proved it false by way of counterexamples, 3)
proof of the 250-year-old Goldbach’s conjecture [21-23]
and, combined with qualitative modeling, 4) the solution
of the gravitational n-body and turbulence problems [1,9]
and development of the grand unified theory (GUT) that
unifies natural science [7].
3. The Superstring
We distinguish physical from abstract concept because
ambiguity on this matter leads to error, e.g., error of rela-
tivity theory in treating time as physical concept. A
physical concept has a referent in the real world such as
body or event. An abstract concept, e.g., mathematical
concept, is a creation of the mind and neither exists in the
real world nor does it have a physical referent, e.g., time
and distance which describe relationships between events
and objects, respectively [8,18]. The most fundamental
physical concept is the superstring, basic constituent or
fundamental building block of matter [7,11].
Mass is a measure of amount of matter in a physical
system; in the metric system a unit of mass is the kilo-
gram. Energy is motion of matter; therefore, mass and
energy are never separate and neither pure matter nor
pure energy exists. Therefore, every piece of matter has
energy and anything that has energy is matter. For exam-
ple, the photon has mass [7,8,11]. Wave is synchronized
vibration of its medium which does not go with the wave.
In water wave every molecule in its path vibrates but
does not go with it. Basic cosmic or electromagnetic
wave is generated by the normal vibration of atomic nu-
cleus and propagated across dark matter as suitably syn-
chronized vibration of the superstrings that comprise it.
Nuclear vibration is due to the impact of cosmic waves
coming from all directions in the Cosmos [8,24]. Elec-
tromagnetic wave is fractal which accounts for its huge
energy and the only force in the Cosmos that interacts
with, agitates and breaks or converts a superstring from
one form to another, dark or visible [11,24].
Another type of cosmic wave is seismic wave (profile
in Figure 7 of [24]) generated by the micro component of
turbulence at its interface [1]. Such interface is found
between adjacent layers of the spinning core of a cosmo-
logical vortex, volcanic lava flow in a volcano and at
conservative tectonic plate boundary. They convert dark
to visible matter in the interior of a cosmological vortex
in the Cosmos, around volcano and along geological fault
and tectonic plate boundary [1,25]. In the Cosmos the
appearance of cosmic dust that congeals into cosmologi-
cal vortices at the rate of one star per minute is sustained
by seismic waves generated by spinning cores of cosmo-
logical vortices [25]. Seismic waves are generated at lava
flow and geological fault that produce balls of fire
around them [1,2]. They are also generated by lightning
in the lower atmosphere that produces earthlights in the
upper mesosphere [25,26]. (For detail, see [1,13]). Flux
is motion of matter with identifiable direction at each
point. Turbulence is coherent flux, i.e., having no oppos-
ing motion except in a synchronized manner. Among the
examples of flux are water current, the atom, cosmologi-
cal vortex, typhoon, magnetic flux and electromagnetic
wave which are turbulence. A vortex flux spins around
its eye which is a region of calm and low pressure that
sucks matter around it. Some of these concepts are tenta-
tive pending their precise definition by the laws of nature.
We take the most fundamental natural law of GUT [7]:
Energy Conservation. In any physical system and its
interaction, the sum of kinetic (visible) and latent (dark)
energy is constant, gain of energy is maximal and loss of
energy is minimal.
This is an extension and enrichment of the first law of
Energy Conservation Equivalence. Its various ex-
pressions are: Energy conservation has many expressions
or forms: order, symmetry, economy, least action,
optimality, efficiency, stability, self-similarity (nested
fractal), coherence, resonance, quantization, synchro-
nization, smoothness, uniformity, motion-symmetry balance,
non-redundancy, non-extravagance, evolution to infinit-
esimal configuration, helical and related configuration
such as circular, spiral, sinusoidal, the tendency to form
a loop and, in biology, genetic encoding of charac-
teristics, reproduction and order in diversity and com-
plexity of functions and configuration that provides op-
Copyright © 2013 SciRes. IJMNTA
timal capability.
This law is instrumental in deciding scientific issues.
For instance, physicists were excited by the discovery of
the third quark in 2004 which they thought was the gluon
that supposedly binds two protons in the narrow confines
of the nucleus. It follows from the principles of non-
extravagance and non-redundancy [11] that the third
quark is really the quark for it joins the two +quarks to
form the proton just as the third quark joins two positive
quarks one from each of two protons [12,24]. In other
words, nature does not create or keep two physical
systems with the same function or create a physical
system beyond what it needs. The next law is central to
turbulence and applies to dark matter, gas and liquid
Flux-Low-Pressure Complementarity. Low pressure
sucks matter around it and the initial rush of matter to-
wards a region of low pressure stabilizes into local or
global coherent flux called turbulence; conversely, co-
herent flux induces low pressure around it.
Hit by suitable electromagnetic wave, a non-agitated
superstring (a) is thrown by its impact, bounces with
other superstrings and comes to rest in dark matter when
its imparted energy is dissipated or (b) it gets close to its
earlier path, gets sucked by it, by Flux-Low-Pressure
Complementarity, and forms a loop, the original non-
agitated superstring called toroidal flux travelling through
the loop at 7 1022 cm/sec [27]. By Energy Conservation
and Energy Conservation Equivalence, the loop shrinks
and evolves into its most energy-conserving configure-
tion, namely, circular helical loop, its toroidal flux trav-
eling through its cycles at the speed of 7 1022 cm/sec.
By the fractal principle its toroidal flux, being a super-
string, has toroidal flux, a superstring, traveling at this
speed, etc., leading to formation of nested fractal se-
quence of toroidal fluxes, each a superstring. The first
term is a semi-agitated superstring identified with the
fractal superstring since it alone interacts with cosmic
waves and other superstrings in its neighborhood. By the
quantization and synchronization principles of the En-
ergy Conservation Equivalence Law, this speed of 7
1022 cm/sec is a constant of nature.
We articulate our findings as natural law.
Existence of Basic Constituent of Matter and its
Generalized Nested Fractal Structure. The basic con-
stituent of dark matter is the non-agitated superstring. It
is a circular helical loop and nested fractal sequence of
superstrings or toroidal fluxes, with itself as first term;
each toroidal flux in the sequen ce is a superstrin g having
toroidal flux, a superstring, traveling at 7 1022 cm/sec
along its cycles, etc.; each superstring except the first, is
contained in and self-similar to the preceding term in
structure, behavior and properties.
This structure called nested generalized fractal [28] is
an extension of geometrical fractal [3,6]. Since the su-
perstring is a physical concept it is a nested generalized
physical fractal. Its self-similar general property is its
helical structure with the toroidal flux (a superstring)
traveling through its cycles at 7(1022) cm/sec. A super-
string is non-agitated (dark) if its cycle length (CL) is
less than 1016 meters, semi-agitated if 1016 < CL < 1014
meters and agitated (visible) if a segment has CL > 1014
meters (Figure 1 of [24] shows a semi-agitated super-
In the agitation or semi-agitation of the superstring
there is another possibility: (c) hit by suitable electro-
magnetic wave the first term of a non-agitated super-
string expands and becomes a semi-agitated superstring.
In all these cases the superstring is nested generalized
physical fractal sequence of superstrings.
It is the nested generalized physical fractal structure
that makes the superstring indestructible and the Uni-
verse of dark matter timeless, i.e. having no beginning
and no end, since electromagnetic wave may only reso-
nate with and break a finite number of toroidal fluxes.
Moreover, by Flux-Low-Pressure Complementarity, the
Universe of dark matter is boundless. Our universe is a
local bubble in it with specific birth and destiny [25].
4. The Primum
The energy of the superstring is enshrined in its toroidal
fluxes. The first term of its fractal sequence looks like a
lady’s spring bracelet (see figure in [29]). This fractal
structure of the superstring not only makes it indestructi-
ble but also packs huge energy in it and, therefore, dark
matter as well. The latent energy density of dark matter,
part of which convertible to kinetic energy, is 1026 joules/
cubic ft according to de Broglie [30], 8(108) volts/cm
says Seike Jr. [30] and the equivalent of 18 kg/cu meter
according to Gerlovin [31] using relativistic conversion.
This convertible energy is only a small portion of the
total energy density of dark matter.
Possibilities (a) and (b) may occur only when electro-
magnetic wave hits a non-agitated superstring. However,
when it hits a semi-agitated superstring a pair of mutually
exclusive possibilities may occur: (1) a segment of the
first term of the nested fractal superstring in (c) bulges to
retain the speed of the toroidal flux despite the energy
imparted by the electromagnetic wave that hits it, by En-
ergy Conservation, turning it into an agitated superstring
called primum, unit of visible matter, its toroidal flux
non-agitated, or (2) the first term breaks, its toroidal flux
remaining non-agitated and dark superstring.
Dark-to-Visible-Matter Conversion. When suitable
electromagnetic wave hits a semi-agitated superstring
one and only one of these occurs: (a) the outer super-
string breaks, its toroidal flux remaining non-agitated
and (b) a segment bulges into a primum, an agitated su-
Copyright © 2013 SciRes. IJMNTA
perstring and a unit of visi ble matter.
The indestructibility of the superstring follows from
the Resonance Law discovered in the course of explain-
ing the disastrous final flight of the Columbia Space
Shuttle [32,33] since suitable electromagnetic wave hits
and resonates only with the first term of the fractal se-
quence leaving the tail fractal sequence intact as a super-
string in accordance with this law:
Resonance Law. Maximum resonance between waves,
oscillation or vibration occurs when they have exactly
the same characteristics with wavelength or frequency as
the principal factor. The degree of resonance declines
with the difference between wave characteristics How-
ever, at suitably high order of magnitude of wavelength
the infinitesimal effect of resonance with orders of mag-
nitude nearby rises to significance.
The disastrous final flight of the Columbia Space
Shuttle is attributed to this law. A physical system is ob-
servable through the medium of light if its size is com-
parable with the wavelength of the latter; this follows
from the Resonance Law. Thus, a semi- or non-agitated
superstring is not observable, i.e., dark, because its cycle
length is less than the finest wavelength of visible light in
order of magnitude, 1014 meters.
We define chaos precisely and identify the emergence
of chaos, turbulence and fractal associated with the prima.
Chaos is a mixture of order none of which is identifiable
(note the contrast with turbulence). This is consistent
with order defined by natural laws since every piece of
matter is subject to them. Chaos is linked to the uncer-
tainty of large and small number [20]. For example, it is
impossible to identify the position of an electron in flight
in an interval of time because of its great speed (large
number) and minute size (small number). This uncer-
tainty is expressed by the Heisenberg uncertainty prince-
ple [31] that says it is impossible to simultaneously pin-
point the position and velocity of an electron in flight. In
other words, the path of the electron is chaos. Chaos
gives way to turbulence when the electron breaks and its
toroidal flux rests in dark matter or its energy dissipates
and reduces to a non-agitated superstring which is dark
When the primum’s toroidal flux, i.e., the second term
of its fractal sequence, is hit by electromagnetic waves
coming from all directions it is thrown into erratic mo-
tion, collides with other superstrings and, combined with
steady hits by electromagnetic waves coming from all
directions, turns it into a spike with the centroid traveling
through the cycles at 7(1022) cm/sec. This configuration
and motion pulls the superstrings around the primum into
its induced vortex flux with axis coinciding with the
center of its cylindrical eye. This makes the primum a
magnet, its polarity in accordance with the right hand
rule of electromagnetism [24]. The induced vortex flux is
its magnetic flux which is turbulence. Viewed from its
north pole, the induced vortex flux is counterclockwise if
it is a positive primum, by convention. It is negative oth-
erwise. The induced vortex flux is dark but its impact on
visible matter is its charge. The unit of charge by con-
vention is the electron’s charge which is 1 (1.6 × 1019
coulombs [12,24]). The electron is a basic primum; the
other basic prima are: +quark, charge +2/3 and quark,
charge 1/3, basic because they comprise every atom
[28]. They are produced at rapid rate in the Cosmos and
cellular membrane of living things, in the latter to sup-
port their growth [17,25].
The spike itself is chaos but as soon as the induced
vortex flux forms, it shields it from the impact of cosmic
waves and becomes part of the turbulence that is the vor-
tex flux. The vortex flux ultimately loses energy and the
superstring becomes non-agitated. Thus, the primum that
starts as chaos becomes turbulence then non-agitated
superstring which is dark turbulence that belongs to the
standard dynamics [1].
4.1. Primal Interaction
Primal interaction is governed by Flux-Low-pressure
complementarity and the next law.
Flux Compatibility. Two prima of opposite toroidal
flux spins attract at their equato rs but repel at th eir poles;
otherwise, they repel at their equators but attract at their
poles. Two prima of same toroidal flux spin connect
equatorially only through a primum of opposite toroidal
flux spin between them called connector.
The primum’s profile is sinusoidal and the trace of the
maximum point of its induced vortex flux is the equator
[24]. The proton is a pair of +quarks joined by a quark
equatorially [12,24], by Flux Compatibility (Figure 3.3
of [24]). By Energy Conservation, their axis are coplanar;
its charge: 2/3 1/3 + 1/3 = +1. Thus, there is net coher-
ent counterclockwise vortex flux of charge +1 around the
proton. We note the transition phase of chaos as the
fluxes from the two +quarks collide until they stabilize
when the vortex flux of the quark becomes an eddy in it.
Since simple primum, e.g., positron, is charged, the neu-
tral neutrino must be a coupled pair of simple prima of
numerically equal but opposite charges, say, +q and q,
so that its charge is +q + q = 0, neutral [12].
By Flux Compatibility, the electron can attach itself to
a positive quark of the proton at any point but Energy
Conservation and the optimality principle of the Energy
Conservation Equivalence Law require that it attach to
both +quarks beside the negative quark as the most stable
position but pushes the negative quark a bit, by Flux
Compatibility, so that their centers viewed from the north
pole form the vertices of a quadrilateral. In its interior are
the coherent vortex fluxes of the positive quarks, nega-
Copyright © 2013 SciRes. IJMNTA
tive quark and electron that make it a region of low
pressure called depression. By Flux-Low-Pressure Com-
plementarity its interior sucks neutral primum around it
since charged primum is repelled by primum of the same
charge already in the coupling. Therefore, only suitably
light neutral primum fits in and that is the neutrino. We
have just composed the neutron consisting of a proton,
electron and neutrino. Its charge is: +2/3 1/3 + 2/3 1
+ 0 = 0, i.e., neutral, and there is no net coherent vortex
flux around it. The vortex flux of a charged coupled pri-
mum is also discular for the same reason that the simple
primum’s vortex flux is due to greater centrifugal force
along the equatorial plane.
We note that the initial coupling of the proton is chaos
due to the collision of the vortex fluxes of the +quarks
until the quark becomes an eddy in their combined flux.
Since the masses of the neutron, proton and electron
are known: 1.0087 amu, 1.0073 amu and (5.486)108
amu, respectively [12,24], the mass of the neutrino is η =
8.5 × 108 amu (1/1250th proton’s mass); ironically, neu-
trino’s mass is still a subject of hot pursuit [34-36]).
4.2. The Atom
The nucleus forms first in the atom and consists of pro-
tons alone (see figure in [29]), except the hydrogen atom,
joined together by quarks. Their toroidal fluxes add up
to a coherent discular vortex flux whose eye contains the
nucleus. So do their charges add up to the charge of the
atom, i.e., equal to the number of protons in the nucleus.
However, the nucleus itself is neutral since the protons’
induced toroidal fluxes cancel each other. As coupled
primum the nucleus is a magnet of positive polarity with
the vortex flux around it its magnetic field. From the
right-hand rule with the index finger pointing in the di-
rection of the vortex flux, the thumb points to the
north-pole. Viewed from its north-pole the vortex flux of
a free atom spins counterclockwise so that by Newton’s
action-reaction law the nucleus rotates in the opposite
direction as a unit. This is the spin of quantum physics
distinct from the toroidal flux spin. It is the nested fractal
structure of the nucleus being comprised of fractal prima
that makes the electromagnetic wave it generates fractal.
Electrons being negatively charged are attracted to the
vortex flux away from the eye, by Flux Compatibility
and Flux-Low-Pressure Complementarity. However,
being light, they are swept into orbit by the vortex flux
and become orbital electrons, their orbits probabilisti-
cally symmetrical (explained later) with respect to the
equatorial plane. By centrifugal force, the most energetic
orbital electrons are those closest to the equatorial plane.
They form the outermost orbital shells. The least ener-
getic ones cluster near the poles and form the lowest or-
bital shell. A stable atom has orbital electrons equal in
number to the protons in the nucleus. Otherwise, it is a
positive ion when there is a deficiency in orbital elec-
trons or negative when there are more orbital electrons
than protons. Moreover, by Flux-Low-Pressure Com-
plementarity, non-agitated superstrings accumulate stead-
ily in the center of the nucleus, the principal source of
energy in nuclear fission. Charged prima are repelled by
the +quarks and quarks. However, the neutron being
neutral may be sucked by the nucleus, by Flux-Low-
Pressure Complementarity, to form a heavy isotope. As
primal coupling, transitional chaos occurs in the forma-
tion of the nucleus but permanent chaos in the orbital
electrons (during the life of the atom) due to the effect of
the Heisenberg Uncertainty Principle [37] and bom-
bardment by cosmic waves. That is why the electron’s
orbit is not an ordinary curve but a probability curve. It is
in this curve where the probability of finding an electron
is greatest. This chaos reduces to turbulence as the proton
loses its kinetic energy and becomes a cluster of non-
agitated superstrings at the terminal phase of the so-
called neutron star [25].
There is a lingering chaos, an infinitesimal spike due
to the impact of cosmic waves that hit and resonate with
electromagnetic wave. In fact, the existence of such in-
finitesimal spike is true of all vortex fluxes of super-
strings for the same reason. The turbulence of the elec-
tromagnetic wave continues until its kinetic energy is
dissipated; then the electromagnetic wave vanishes and
ceases to vibrate the superstrings along its path.
When orbital electrons are expelled by turbulence or
cosmic waves the atom becomes a positive ion. It can
also become negative ion when more electrons are drawn
into orbit by Flux-Low-Pressure Complementarity in
addition to Flux Compatibility. Two valence electrons
(of the same or different elements) are joined by a quark
to form a molecule. Stable molecule share a pair of va-
lence electrons and gas atoms generally exist as di-atoms
(coupling of two atoms) for maximal stability.
4.3. Primal Polarity
The Earth is a cosmological body its vortex flux of su-
perstrings the gravitational flux. Its core is the collected
mass around the eye including the atmosphere. Its gravi-
tational flux shields Earth from massive approaching
asteroids close to its equatorial plane and separates posi-
tive prima from their negative anti-matter that otherwise
would create instability. However, there is no shield
against an asteroid when it approaches either pole
oblique to the equatorial plane; hence, the relatively fre-
quent hits close to the North Pole. The Earth’s gravita-
tional flux goes from West to East, is fastest at the Equa-
tor and slows down towards 0 at the eye’s extremities at
the poles. Naturally, its pull on the Earth’s material also
Copyright © 2013 SciRes. IJMNTA
slows down from the Equator to either Pole (polar lag)
but the eye’s suction is not diminished there. (The Sun’s
polar lag is 30% midway between the equator and either
pole) Every cosmological vortex has a polar lag; this
value (30%) should be checked if it is a constant of na-
ture. In Earth, the polar lag accounts for the counter-
clockwise spin of Earthly vortices, e.g., tornado and hur-
ricane in the Northern Hemisphere (clockwise in the
Southern Hemisphere) known as the carioles effect.
We look at the primum as it pops out of dark matter.
Since the dark superstring has infinitesimal induced flux,
it has no polarity and does not interact with anything
except cosmic waves; it is oriented randomly. When a
dark superstring is agitated by suitable cosmic wave and
pops out of dark matter as free positive primum and its
equatorial plane is oblique to the direction of the gravita-
tional flux it rotates suitably due to the coriolis effect, its
north pole pointing North and equatorial plane parallel to
the Earth’s equatorial plane (vortex flux spins from West
to East) making its vortex flux a counterclockwise eddy
in the gravitational flux, its optimal energy-conserving
alignment. By Flux Compatibility, the positive primum is
pushed up so that there is abundance of free positive
prima in the upper atmosphere (confirmed by shower of
fragments of protons smashed by ultra-energetic cosmic
waves that hit Earth [38]). Free neutral prima are ori-
ented randomly but free positive ions are counterclock-
wise eddies in the Earth’s gravitational flux; they are
pushed upwards, by Flux Compatibility. However, being
heavy, they remain in the lower atmosphere. The free
electron as clockwise eddy in the Earth’s gravitational
flux whose equatorial plane is parallel to the Earth’s
equatorial plane is pushed downwards, by Flux Compati-
bility. Thus, there is abundance of free electrons on the
ground. Other free negative prima including the quarks
should be abundant on the ground also but we do not
know where they are and no study has been done on
them. It is possible that they are also carrier of electric
current (moving charge) as the electron is. When the
voltage between the positive ions in the lower atmos-
phere and the electrons on the ground reaches critical
level they rush towards each other, collide and explode
as lightning.
The separation between positive and negative prima
contributes to the stability of cosmological vortices like
Earth because it separates them from their anti-matter.
Outside the Earth’s gravitational flux primal orientation
is determined by the dominant gravitational flux there;
between planetary gravitational fluxes it is the Sun’s
gravitational flux, etc. There is no point in the Cosmos
without some dominant gravitational flux.
Unsynchronized collision of physical systems as in
chaos lacks coherence, is energy dissipating and evolves
towards energy conserving configuration and motion. A
familiar example of Earthly turbulence is the typhoon
which is a vortex flux of air molecules [1]. It lasts until
the temperature gradient between the warm and cold air
along its path vanishes. Another example is a galaxy (in-
cluding our universe as a super, super galaxy [25]) which
is a vortex flux of superstrings (cosmological vortex) that
lasts over a long, long time until its kinetic energy is
completely dissipated, by Energy Conservation [7,25].
These examples belong to the standard dynamics [1]
where a change in the normal conditions trigger the oc-
currence of chaos as transitional phase towards turbu-
lence, by Energy Conservation, the latter vanishing when
the normal conditions set in again.
5. Macro Standard Dynamics
We recall that the standard dynamics is a cycle that starts
with normalcy like a calm summer day in the Pacific
Ocean. Then some change in the conditions occurs that
induces passage to the transitional and unstable phase of
chaos. Energy Conservation induces its transition to tur-
bulence until the change in the normal conditions that
served as initial boundary conditions vanish and the cy-
cle is completed as the conditions become normal.
5.1. Earthly Turbulence
We consider other turbulence rooted in dark matter.
5.2. Wind Cycles
The rotation (spin) of the Earth is due to the pull of the
Earth by the gravitational flux. This pull is the effect of
the combination of dark viscosity and resonance between
the normal variation of the dark component of Earth’s
material and that of dark matter. Both the pull and the
linear displacement are proportional to the density of the
Earth’s material. Since the Earth’s crust is denser than
that of, say, the Pacific Ocean there is a net flow of the
Ocean which constitutes the Pacific Ocean Current going
west. By Energy Conservation, the current finds the most
energy conserving path, splits along the Equator off the
Coast of the Asian mainland with the northern strip
veering northeast and then east off the southern coast of
South Korea and Japan, heads east south of Siberia, veers
southeast west of the western seaboards of Canada and
the US and veers southwest again to form a loop with the
Equatorial current from East to West called the Northern
Pacific Ocean Cycle [39] (see map in [40]).
We really do not need this cycle but we need the same
analysis to map the Northern Pacific Wind Cycle [41].
Since the atmosphere is less dense than the Ocean there
is air current that starts off the Coast of Ecuador going
west called the Trade Winds used by traders in the past to
cross the Pacific Ocean along the Equator. It goes west
Copyright © 2013 SciRes. IJMNTA
into the Western Pacific, splits off east of the eastern
Philippines Coast the northern strip veering north then
northeast scraping Vietnam and Southern China, crossing
North and South Korea and Japan and becoming the jet
flow that airlines use going east to save on fuel. Then it
veers south east of Siberia and across the Bearing Sea as
it crosses Alaska, veers southeast as it crosses Canada
and south into the Tornado Belt in the US [1,2,39,41]. It
veers southwest then west and joins the Trade Winds off
the coast of Ecuador to complete the Northern Pacific
Wind Cycle (map in [41]). Both the Northern Pacific
Ocean Current and the Northern Pacific Wind Cycle are
vortices, i.e., turbulence with clockwise spins not on ac-
count of Flux Low Pressure Complementarity alone but
combined with the land mass distribution and the ten-
dency to form a loop. The latter wind cycle plays a major
role in typhoon and tornado. They have mirror images in
the southern Pacific with counter clockwise spins (maps
in [40,41]).
5.3. Typhoon and Tornado
We first look at the conditions that give rise to a typhoon
known as hurricane in the Western Hemisphere. The
Earth is studded with under-ocean volcanoes, especially,
along conservative plate boundaries called trenches. We
consider the Marianas Trench in the Western Pacific
about 1500 miles east of the Philippines above the Equa-
tor. Active volcanoes along the Trench erupt periodically,
heat up the ocean surface and produce pockets of warm
water called el niño. When the pockets are sufficiently
close together and broad or solid, say, as broad as the
Australian landmass, the el niño heats up the lower at-
mosphere sufficiently to create a tropical depression (low
pressure). The depression sucks air around it, by
Flux-Low-Pressure Complementarity and the initial rush
and ensuing collision of trillions of air molecules create
chaos that, by Energy Conservation, gives way to a ty-
phoon, a vortex flux of air molecules which is turbulence
(details in [1,39]) that spins counterclockwise due to the
coriolis effect (just as water eddy in a spring spins coun-
terclockwise when there is a relative counter current
from west to east and the current is flowing eastward.
This is quite analogous to the north polar lag in the
Earth’s core [1,39]. The typhoon follows the Northern
Pacific Wind Cycle but is affected by the temperature
variation over the Philippine Deep Trench and around
Mayon Volcano [1,39,40]. This information allows pre-
cise prediction of the course of a typhoon in this region.
Typhoon can be deflected but that would be impractical.
Another destructive Earthly turbulence that belongs to
the standard dynamics is the tornado. We look at the
Tornado Belt in the US, a 1000- by 650-mile rectangular
region that extends from Oklahoma to Florida and from
the Midwest to Texas.
The Northern Pacific Wind Cycle interfaces with the
narrower Northern Atlantic Wind Cycle over the Belt.
The latter has the same spin as the Northern Pacific Wind
Cycle but opposite fluxes at the interface. The interface
wobbles between the western and eastern edge of the
Belt during spring as eddies form on both sides of the
interface like ball bearings that facilitate the spin, by En-
ergy Conservation. The cycles press against each other,
by Flux Compatibility.
During spring, the Northern Pacific Wind Cycle pulls
the cold air from the Arctic, by Flux-Low-Pressure
Complementarity, and brings it over the Tornado Belt at
the interface between the Cycles. At the same time, the
Northern Atlantic Wind Cycle brings the warm air from
the Equator, especially, the Caribbean, over the Belt also
at the interface. The warm and cold air pressing against
each other, by Flux Compatibility, forming a sharp inter-
face between them thrusting the lighter warm air up-
wards and the denser cold air downwards and creating a
horizontal cylindrical vortex flux of air that when its
northern end tilts downwards (as the energy-conserving
motion in the Northern Hemisphere due to the coriolis
effect) and touches and sucks the ground, it forms the
funnel of a full tornado (details in [1,39]). Minor torna-
does also form along the interfaces of eddies on both
sides of the interface.
We refer the reader to [1,39] for discussion of earth-
quake as Earthly turbulence belonging to the standard
dynamics. Since the destiny of our universe is a cluster of
black holes [25] which are turbulence. Thus, all turbu-
lence is the final phase of the standard dynamics.
5.4. Astronomical Turbulence
Every explosion creates chaos and previous order and
history and every chaos evolves to turbulence; then
turbulence vanishes back into normal conditions and
completes the cycle of the standard dynamics. The Big
Bang [13,42] which was the explosion of a super, super
massive black hole 8 billion years ago [7,25] and the
destiny of the core of a previous universe [8,25], created
a super, super depression in dark matter. The explosion
created an expanding wave front as the boundary of the
super, super depression called the Cosmic Sphere [8,25].
At t = 1.5 billion years from the initial burst of the Big
Bang, the Cosmic Sphere burst [8,25,43] releasing the
trapped semi-agitated superstring that formed the early
prima which clustered as the early visible matter of our
universe called quasars that peaked at t = 2.5 billion
years [39]. We put the birth of our universe at Cosmic
Burst. The quasars got absorbed by the galaxies in the
neighborhood of the once Cosmic Sphere [25,44].
Neither the Big Bang nor the Cosmic Burst created new
Copyright © 2013 SciRes. IJMNTA
galaxies but as the super, super depression gave way to a
super, super cosmological vortex that expanded and
evolved to the present super, super galaxy, our universe,
it absorbed galaxies formed before the Big Bang as new
galaxies emerged steadily [25]. In fact, the Milky Way is
one of those that formed earlier as it has stars older than
the Big Bang [45]. All the galaxies of our universe
including the super, super galaxy are turbulence
belonging to the standard dynamics. They will vanish
back into dark matter as black holes, their destiny
consisting of massive concentration of non-agitated super-
strings in the eyes of the once cosmological vortices, and
complete the standard dynamics. In effect, all turbulence
belongs to the standard dynamics since all visible matter
ultimately become dark (For details of the cosmology of
our universe, see [13,25]).
6. Applications
For practical applications of the theory of turbulence we
refer the reader to the original papers on GUT and its
theoretical and practical applications to the development
of technologies that utilize dark matter instead of con-
ventional fuel and power, particularly, the magnetic flux
as natural engine instead of gasoline or coal-fired power
generator, nuclear reactor, geothermal plant, hydroelec-
tric power plant and other conventional power generator
[19,46]. They include the electromagnetic engine [19]
that powers the magnetic train, electric power generators,
cars and other motor vehicles, aircraft and space vehicle.
We call them type I GUT technology. This type relies on
the properties of the magnetic flux which is dark turbu-
lence and functions in accordance with Flux Compatibil-
ity and Flux-Low-Pressure Complementarity. Except for
the electromagnetic engine that powers the electromag-
netic train and is in operation, the rest is at the research
and development phase with the exception of the one for
spacecraft and space vehicle which is still long-term and
at the conceptual phase although the theory is complete.
Another type of GUT technology (type II) consists of
the tornado aborter and terminator or deflector [39].
(Since this technology is still at the research and devel-
opment phase, details are omitted). Tornado always starts
at the interface of warm and cold air about 1.5 km above
ground. The aborter blurs the interface between the nas-
cent tornado and the ground by warm air to prevent its
touchdown. When it fails to touchdown in seconds it
vanishes. In the case of a full tornado traveling along the
interface (always in the northerly direction except those
along an eddy), the terminator works on the same princi-
ple as the aborter except that it is applied at its forward
path on the ground along the interface to blur it and the
temperature gradient between the interfacing cold and
warm air to break the tornado or divert it around the city
being protected. This type utilizes the gravitational flux
which is turbulence based on Flux Compatibility and
Flux-Low-Pressure Complementarity.
The third type uses electromagnetic waves which are
turbulence for electromagnetic treatment of genetic dis-
eases such as cancer, systemic lupos erythematosus, dia-
betes, muscular dystrophy and mental disorder [17].
The fourth type is GUT technology based on the the-
ory of intelligence [18] that includes what we call a so-
cial technology for (1) devising a program of mathemat-
ics-science education from primary through graduate
school [8,47,48] based on [18] and (2) devising a strategy
for sustainable economic-industrial development of the
Third World involving complex systems [49,50].
We focus on genetic treatment [19] the underlying the-
ory which is also complete and research and develop-
ment involves devising the appropriate technology for
each of these diseases. The treatment does not harm
normal cells and, therefore, has no side effect; it is based
mainly on the Resonance Law and [17,51]. We summa-
rize the needed key information for this class of tech-
(a) Brain waves, electromagnetic waves encoded with
vibration characteristics of a living cell, e.g., neuron,
gene, are the brain’s and gene’s medium for carrying out
their functions [17-19].
(b) The neutralizer gene emits brain waves that create
its mirror image in the chromosome, in effect, inserting
itself in the DNA sequence that alters the gene and re-
moves the undesirable symptom of a disease [17,19].
This technology is now used for treatment of cystic fi-
brosis by introducing a neutralizer gene into the lung that
modifies its gene suitably. Now DNA can be introduced
into the body to modify or alter the gene of any genetic
disease that determines its undesirable symptom suitably.
The stem cell belongs to this class of technology.
(c) A technology can be devised that projects radiation
that resonates only with a defective gene. The radiation
intensity can be raised suitably to sterilize the gene or
even destroy it; in the former the cell will not be repro-
duced in the normal turnover of cells.
(d) The unified theory of evolution [17] lays down
physical therapeutic procedure based on the Genetic En-
coding Law [17] for reversing, not just arresting, the im-
pact of degenerative diseases such as muscular dystrophy
and controlling some chronic mental disease such as au-
tism. This procedure is also the basis for training athletes
by providing them with appropriate reflexes and physical
skills since both of them are genetic [17].
(e) Certain new mental activity such as creative and
new physical activity, e.g., standing on one foot and new
exercises, raises neural interconnections that counter the
impact of aging like narrowing of the brain [18].
(f) Through emission of brain waves the gene converts
Copyright © 2013 SciRes. IJMNTA
superstrings to basic prima in the cellular membrane of
plants and animals that form their tissues [17,52-54].
Finally, collaborative research and development of
appropriate technology for electromagnetic treatment of
these diseases will require participation of experts in
GUT, the genetic diseases concerned who can identify
the neutralizing gene for each or its distinguishing vibra-
tion characteristics, especially, wave length; a nuclear
engineer who can identify suitable radioactive material to
provide the required resonant radiation, if any, and radia-
tion engineer who can design and devise appropriate
technology to emit desired resonant radiation for each of
these diseases. Since cystic fibrosis has already known
neutralizer we can focus on genetic composition and
sterilization of other genetic diseases.
Nonlinear, in the words of Prof. V. Lakshmikantham,
Founder of Nonlinear Analysis, is not necessarily linear
which means that all natural phenomena are nonlinear
and at the micro scale of existence nothing is linear.
Chaos is a complex system [39,49] and by Energy Con-
servation a transitory phase of turbulence whose limit is
the epitome of order—dark matter.
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