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Navier Stokes Problem Solution Earth-Puzzel logo

  d.d. 2014.05.07

  The Audio recordings:

Navier Stokes
Particular Interactions

Navier Stokes can be described in Tetryonics.
In listening to Navier Stokes lectures, it already fell in place.
Navier Stokes is simple: all it takes is to use a coherent model.
The equations can be understood, by separating matter and mass.

Navier Stokes describes motion of Fluid Dynamics.
It is about complex wave motion; affecting Matter, such as water.
It is described in terms of a mathematical Series.
And followed up on e.g. Fourier Analysis and Taylor Series in Mathematics.

Navier Stokes is now 'calculated' in computational physics.
It actually is a topic of an expensive mathematical prize.
It involves the calculation of particle motion in fluids.
Accounting for viscosity and friction under pressure.

It is often addressed by 'space time curvature'.
It was Einstein’s application of Riemann (cyclical) mathematics.
It is resolved in Tetryonics by showing the link between Coulomb and Newton equations.
And requires discerning mass from Matter.

Tetryonics gives a model that integrates space time, energy, momentum, mass and Matter.
It unifies all that physics works with
Physics usually describes its observations in terms of differential equations
Image 26.11 gives a different approach to understand that

It shows how an electromagnetic field is the result of a 2.pi equilateral geometry.
It is two bosons, back to back.
In measuring the passing of that double-boson (= photon) the EM field is seen.
It has an electric wave followed by a 90-degree phase delayed magnetic wave.

It is a physical unit, that creates these changing values.
image 26.12 shows the geometry of the EM wave as Euler's formula.
e**i.phi is a common formulation for this.
It is simply a quadrature wave; 4 sine waves 90-degrees out of phase: +/-/N/S

Tetryonics says that scalar energy is an equilateral triangle.
Its height is the linear momentum.
Euler's equation is at the core of physics; but ill understood.
It links e**1.pi=-1, different dimensions (spiral, circle, angle)

It represents a mathematical arrangements of sine waves.
It is used as the basis for describing 'infinite series'.
It is a solution for the square root of -1.
Which in Tetryonics is the height of a triangle.

It is the height of a negatively charged equilateral triangle.
26.13 shows how central Euler's formula is in mathematics.
Otto showed just now how it is linked to wave forms.
It is an oscillation of electrical/magnetic dipoles; in an equilateral geometry.

    The +-charge and --charge
    e: the exponential
    pi: the geometry
    a =-field and a --field is a 0-field; which is a geometry.

Euler's formula addresses the electric momentum.
It explains Euler's formula as geometric description of electromagnetic waves.
That can be electric, or it can be magnetic; depending on your approach.
Your involvement matters, literally.

The quadrature wave stems from the geometry of the photon in motion.
It has a sinus wave, and another 90-degrees out of phase.
This is the foundation for Maxwell’s transverse form.
By moving the vector, a normal transverse wave is found.

Show the vector dipole to resolve the equations which you find where N and S are separated.
Mathematics is accurate, but does not show the underlying coherence.
That led to models of concentric complex waves; and corresponding forces.
A quantum harmonic oscillators was mathematically correct but geometrically wrong.

Tetryonics starts with the geometry;  bottom up.
ALL waves, EM< KEM, BEM are based on that.
ALL are based on Planck quanta.
But they are not spherical, but equilateral geometry; in Tetryonics.

Image 27.21 shows the mathematics that was used to try to understand this.
By not using equilateral geometries, the underlying logic is  not clearly seen.
By using the equilateral triangles the underlying coherence comes to view.
Wavelengths are shortened at increase of velocity; NOT THE MATTER INVOLVED.

The energy stored in the KEM field is secondary to the Matter it is associated with.
ALL relativistic Lorentz corrections related to the contraction of mass energy.
MATTER IS NOT LORENTZ VARIABLE: only the energy field is.

We are dealing with fields of mass-energy-momenta.
In Fluid Dynamics, pressures form wave fronts.
The basis is still the Planck energy quantum.
It is the wake around the boat; the speed changes the wake, not the boat.

Applied forces are stored in the KEM field.
The force translates into the SQRT of the energy of the boat/particle.
There you can specify the fore and its direction.
The Planck quanta undergo the normal distribution of energy momenta.

This is shown as colours in the middle of image 27.21.
This can also be measured as a function of time: quantised angular momentum per second.
That is square meters/second/c**2.
That is a measure of time: delta seconds; thus a time as geometry.

All these energy quanta distributions (as energy & time) require simultaneous non-linear equation.
That is because they are scalar.
We can now quantise this; and does not require no-linear equations.
Because in Tetryonics you can see it in the field; and its +/-, N/S, an energy and linear momentum; plus the amount of Planck quanta

In the Navier Stokes equation this is often regarded by special relativity.
In Tetryonics, adding energy = adding energy quanta (triangles)
As the velocity increases, the wave length of the field contracts.
The particle itself does not contract; Matter =/= mass.

The contraction concept does not apply to matter.
It only applies to the energy field.
28.01 shows the energy contraction for the bosons.
As the electron accelerates; and 'quantum jumps' occur.

  • Tetryonics 84.05 - Square roots of n.jpg

In Fluid Dynamics, wave crash upon beaches.
Tetryonics shows the visual image of this.
And thereby helps correct the mathematical models.
And show the linear momentum of the (quantal) energy field.

mass is the constant between force and acceleration: INERTIA.
Mass is the fulcrum in the equation.
Particles in motion are equilateral Planck quanta in an energy field.
In Tetryonics a computation can detail every minute aspect of that dynamic.

Again, it is all about pattern recognition.
Tetryonics is totally deterministic.
All energy/momenta can be predicted.
The equilateral energy momenta can be modelled in computer calculations.

It is the standard network computation.
Compute for one moment, and then take the outcome for the next step.
The Navier Stokes is that kind of computation.
It computes a snap shot instant picture, and integrates next-steps into a 'movie'.,

This is a means to show the use of Tetryonics, and validate it by these computations.
The force between the particles can be shown by the triangular geometries.
The resistance in motion is the inertia, not directly related to Matter.
The 3D problem can be resolved, into the quantum singularity point.

It does have conservation of Mass and Momentum.
This can be visually solved for an exact answer.
Let the particles interact, to see the solution.
There will be en exact outcome always; as is seen in Nature.

  • Tetryonics 84.06 - Square root of Negative One.jpg

The straight line vectors are linear.
The complexity of curl is resolved by differentials.
Discern between mass and Matter
and likewise between linear and non-linear

It is straightforward, but .. 'heady'.
Tetryonics provides a self-explanatory geometry.
It has a sqrt  linear momentum.
That shapes all the forms of energy and Matter in the uniVerse.

The basic patterns can be measured as forces.
Newton, Leibnitz, Maxwell, Tesla, Coulomb, all had their perspective for looking at this.
As a result, different descriptions were created, and their integrations not found.
In starting with the Planck Quanta, the bottom-up approach lets the pieces of the puzzle fall in place.

  • Tetryonics 84.04 - Square Roots in Physics.jpg

Tetryonics starts with the postulate that Planck Quanta are equilateral.
They can create larger coherent fields, in shape triangle, as number ... squared.
To understanding the mechanics, the triangular 'logic' shows the coherence.
Therein energy and momenta, mass and Matter are shown 'at a glance'.

Colour coding is used to add information on energy levels.
In mathematics this can only be shown as numbers.
Only as a result from manipulating mathematical symbols.
In which you never see/understand what you do in these number calculations.

You cannot discern mass and matter, energy and time, in the numbers.
84.04 shows the basic geometry of the argument between Leibnitz and Newton.
Our understanding of physics had changed if the complementarity of their views were understood.
Leibnitz looked at the scalar energy (mv**2); Newton look at force (change of momentum over time).

The energy equations as formula does not 'give insight'.
The calculations by numbers does not show the Dimensions.
In the Einstein relativity mass and Matter were 'equated'.
In Tetryonics, mass and Matter exist in different dimensions.

Equations describe fields, beyond our understanding.
They address electricity and magnetism, as quantised/discrete units.
Which in the Navier Stokes equation must be at the basis also.

That means that energy added into the system must be accounted for.
In the mathematical number operations this cannot be shown.
Only the particle vector motion velocity can be calculated.
Particle interactions can therein become very confusing.

The effect of forces in/on/as matter therein can not be well described.
In Tetryonics the energy of motion lies in the KEM field.
It can be explicitly described, in quantised form.
This can be built into models; later you learn to do that in your head.

84.04 shows the number of quanta of the energy, magnetic and electric forces, and the interactions.
The velocity of the electron in a wire can be described, with the charges of the copper in the wire.
Tetryonics SHOWS the forces in play, in anything you model.
You need to know what system you model, and all levels you wish to describe.

The field motion and particle motions are linked, but different.
Tetryonics can show it, as an integral image.
To calculate this, requires immensely complex equations.
That is why solving the Navier Stokes equations are so complex.

Cartesian models can only provide 'snapshots'.
Tetryonics can portray the interplay of the forces.
This includes all properties, from the Planck level up.
And does not require 'mathematical reduction/simplification'.

In Tetryonics you can ignore the details in the triangular field.
You already know what it is composed of.
The information is still there, while you 'ignore' it.
And you can choose how you represents it, in trigonometry or otherwise.

You do not need to choose one or the other.
You simply take different aspect of the same representation.
Impossibilities for solution fall away in Tetryonics.
Such as the Heisenberg Uncertainty, which in Tetryonics does not exist.

In the same way in Tetryonics mass =/= Matter.
The definitions exist for centuries.
In physics the two are often confused.
mass is energy/second; Matter is ...

c is a radial extension of energy per second.
The impedance depends on the content of the field.
Energy is e/c**2, is mas (NOT MATTER).
mass is 2D Euclidean radiant energy coherence (Inertial time wave)

mass is an EM field in continuity.
It has a plane Euclidean geometry; a flat piece of paper.
Matter exists in 3D only; starting from a tetrahedron.
It comprises a 3D Closed volume; at the speed of light.

The mass of the topology is e=mc**2.
mass =/= Matter; the difference is important.
Mass is planar geometry
Matter is 3D topology.

70.09 differentiates mass from Matter.
An equilateral Planck quantum is Energy (e).
It is the universal building block.
In Time, energy is experience (by continuity) as Inertia, or mass.

mass = 2D geometry
Matter = 3D topology

energy is measure per c**2, and called mass.
seconds-squared is c**2, squared; thus c**4.
It is no longer radial but spatial: a sphere.
It is required to establish the z-component.

70.09 shows the energy-density/m**2: mass.
Tetrahedra have 4 sides composed of mass-energy.
Matter is amass-energy-Matter (meM).
Energy has 3 forms: timeless, in time, and in space.

70.10 shows how energy, mass and Matter are related.
Matter is a tetrahedral quantum, a Tetryon.
it has 4 facets, with slows at the speed of light.
Matter is energy/s**2 (thus c**4)

‘Everybody knows "e=mc**2".’
But is M/c**2=??, it is Matter!

That is how Tetryonics differentiates mass and Matter in physics.
next to E=mc**2 we have E=Mc**4
The first refers to mass; the second to Matter.
The first is in the plane, the second is in a sphere.

This is at the core of the struggle in Relativity.
And why some equations do not make sense.
And why Navier Stokes, and Euler equations are not understandable.
Unless you use Tetryonics to make sense of what you see.

A tetrahedron is Matter
An equilateral triangle is a Boson.
Photons are NOT massless; they are immaterial.
Photons have mass, but are Matterless (because they are 2D): weightless

Photons are weightless.
Photons are NOT affected by gravity.
Photons ARE affected by EM fields.
Gravitation is 1) convergent gravity, 2) interactive EM-fields

The EM fields bends the path of photons.
That is where Tetryonics is the better instrument to use.
Einstein used the stress tensor in his description.
Which cannot be solved for gravity, or Matter.

Discern the topology.
Discern the linear, scalar, quantised aspects.
Tetryonics unifies all these aspects.
That is what Navier Stokes aims to do

Modelling 3D particle motion in a field of force.
To calculate the physical outcome.
The mathematical equations are non-linear (fields of force).
Yet the geometry is straightforward; allowing for 'solutions in your head'.

You can model an electron in a conductor; or a blood cell in a vein.
All we need to do is input the geometry into a supercomputer.
It will give the 3D solution, in a direct manner.
Just as was explained in the P vs NP conversation.

  • *** Tetryonics 90.06 - Tetryonic co-ordinate systems.jpg ***
  • *** Tetryonics 92.02 - Tetryonic Energy tensors.jpg ***

Image 92.02 shows that squares form a vector, seen in triangles better than squares
Matrices based on squares give numbers, but not understanding
In the triangles the forces can actually be seen.
All it takes is a flip of the mind to think in a different manner.

We covered a high level topic
we saw linear versus non-linear is Planck quanta harmonics
we saw that mass=/= energy, solving Navier Stokes problem

Physics studied Matter particles
We need to understand immaterial forces
energy =/= mass =/= Matter
Understanding how they relate

  • *** Tetryonics 66.09 - Tetryonic Matter interaction  & Gravitation.jpg ***

the P vs NP problem has a Tetryonic solution
(harmonics with a phase shift)
The Navier Stokes Problem has a Tetryonic solution
(mass =/= Matter)

  • *** Tetryonics 69.08 - mass-energy-Matter spatial interactions.jpg ***
  • *** Tetryonics 71.13 - Quantum GEM  interactions.jpg ***
  • *** Tetryonics 76.03 - GEM fields [Polar].jpg ***
  • *** Tetryonics 76.04 - GEM fields [Side].jpg ***

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