# Diagram 340 WOW! Signal Vector Brilliouin Zone Phonon Conductor UFO Engine Design

Diagram 340 WOW! Signal Vector Brilliouin Zone Phonon Conductor UFO Engine Design

the idea girl says

Diagram 340 WOW! Signal Vector Brilliouin Zone Phonon Conductor UFO Engine Design

blue book notes 1 page 110, page 6 of cooled plasma formula notes

formula is from previous video, unklapp scattering, brilliouin zone result are keywords to look for formula’s on my to do list!

phonon momentum changes, vector brilliouin zone, limits to thermal conductivity in crystalline UFO engine y Structure Design

I will also be blogging the alien research signal WOW! 6EQUJ5 videos for Diagram’s 300 and 339 that go with the formula’s on alien space science news on wordpress….

formula notes page 6

formula from previous video: umklapp scattering, (Uprocess, Umklapp process) keywords to search in to do list.

1 umklapp scattering – keyword, draw

brilliouin zone result

1.

unklapp scattering

it shows a x, y axis

K1 down arrow SSE

K2 up arrow diagonally to NNE

K3 down arrow to SSW

G is the base line that connects K3 on the left side and K3 on the right side

K3

changes phonon momentum

K vector outside of the FIRST Brilliouin Zone

**property of a material to conduct heat limits THERMAL Conduction if in crystalline materials.

let’s see what WIKI has.

quote WIKI

**Umklapp scattering** (also **U-process** or **Umklapp process**) is the transformation, like a reflection or a translation, of a wave vector to another Brillouin zone as a result of a scattering process, for example an electron-lattice potential scattering or an anharmonic phonon-phonon (or electron-phonon) scattering process, reflecting an electronic state or creating a phonon with a momentum *k*-vector outside the first Brillouin zone. Umklapp scattering is one process limiting the thermal conductivity in crystalline materials, the others being phonon scattering on crystal defects and at the surface of the sample.

**Figure 1.:** Normal process (N-process) and Umklapp process (U-process). While the N-process conserves total phonon momentum, the U-process changes phonon momentum.

**Figure 2.:** *k*-vectors exceeding the firstBrillouin zone (red) do not carry more information than their counterparts (black) in the first Brillouin zone.

my thoughts june 28 2016

i see in K vectors diagram FIRST Brillouin ZONE which is the RED is in a triangle wave pattern, which is the way the laser beams with mixed particles is going to travel through space during communication signals from deep in space to EARTH.

the black counterparts in the Brillouin ZONE remind me of POINTS in SPACE from another diagram….

searching wow! data

unklapp is already same so now looking at Brillouin data.

The reciprocal lattices (dots) and corresponding first Brillouin zones of (a)square lattice and (b) hexagonal lattice.

Brillouin-zone construction by 300keV electrons.

my thoughts june 28 2016

i remember at the beginnning it shows a star of david forming with the cube matrix in the middle where the wormhole is created for the UFO space ship to travel through, this must have something to do with it as well – traversable wormholes, and communication laser beam signals are also combined to boost the signal from millions of light years away from EARTH so that we can receive a message from deep in space with the UFO engine’s design.

cross ref keyword free electron model (we also have free electron gas that comes up in the formula in an earlier diagram in the 300’s range.

quote wiki

In three dimensions, the density of states of a gas of fermions is proportional to the square root of the kinetic energy of the particles.

## Energy and wave function of a free electron[edit]

For a free particle the potential is {\displaystyle V({\mathbf {r}})=0}. The Schrödinger equation for such a particle, like the free electron, is^{[1]}^{[2]}^{[3]}

- {\displaystyle -{\frac {\hbar ^{2}}{2m}}\nabla ^{2}\Psi ({\mathbf {r}},t)=i\hbar {\frac {\partial }{\partial t}}\Psi ({\mathbf {r}},t)}

The wave function {\displaystyle \Psi ({\mathbf {r}},t)} can be split into a solution of a time dependent and a solution of a time independent equation. The solution of the time dependent equation is

- {\displaystyle \Psi ({\mathbf {r}},t)=\psi ({\mathbf {r}})e^{-i\omega t}}

with energy

- {\displaystyle E=\hbar \omega }

The solution of the time independent equation is

- {\displaystyle \psi _{\mathbf {k}}({\mathbf {r}})={\frac {1}{\sqrt {\Omega _{r}}}}e^{i{\mathbf {k}}\cdot {\mathbf {r}}}}

with a wave vector {\displaystyle {\mathbf {k}}}. {\displaystyle \Omega _{r}} is the volume of space where the electron can be found. The electron has a kinetic energy

- {\displaystyle E={\frac {\hbar ^{2}k^{2}}{2m}}}

The plane wave solution of this Schrödinger equation is

- {\displaystyle \Psi ({\mathbf {r}},t)={\frac {1}{\sqrt {\Omega _{r}}}}e^{i{\mathbf {k}}\cdot {\mathbf {r}}-i\omega t}}

For solid state and condensed matter physics the time independent solution {\displaystyle \psi _{\mathbf {k}}({\mathbf {r}})} is of major interest. It is the basis of electronic band structure models that are widely used in solid-state physics for model Hamiltonians like the nearly free electron model and theTight binding model and different models that use a Muffin-tin approximation. The eigenfunctions of these Hamiltonians are Bloch waves which are modulated plane waves.

my thoughts

the unklapp scattering has a x.y axis that changes the phonon momentum in K VECTOR

I also see this same diagram in “Plane wave traveling in the x-direction”

so we have a triangle wave + a plane wave travelling with LASER beam signals mixed particles for a UFO space communication signal.

notes continue:

umklapp scattering, transformation, reflection, translation wave vector to another Brillouin ZONE result, scattering, process an electron-lattice potential, google free electron model, dielectric function of the electron gas.

you’ll see those in Diagram 341, google search

quote wiki

## Dielectric function of the electron gas[edit]

On a scale much larger than the inter atomic distance a solid can be viewed as an aggregate of a negatively charged plasma of the free electron gas and a positively charged background of atomic cores. The background is the rather stiff and massive background of atomic nuclei and core electrons which we will consider to be infinitely massive and fixed in space. The negatively charged plasma is formed by the valence electrons of the free electron model that are uniformly distributed over the interior of the solid. If an oscillating electric field is applied to the solid, the negatively charged plasma tends to move a distance *x* apart from the positively charged background. As a result, the sample is polarized and there will be an excess charge at the opposite surfaces of the sample. The surface charge density is

- {\displaystyle \rho _{s}=-nex}

which produces a restoring electric field in the sample

- {\displaystyle E={\frac {nex}{\epsilon _{0}}}}

The dielectric function of the sample is expressed as

- {\displaystyle \epsilon (\omega )={\frac {D(\omega )}{\epsilon _{0}E(\omega )}}=1+{\frac {P(\omega )}{\epsilon _{0}E(\omega )}}}

where {\displaystyle D(\omega )} is the electric displacement and {\displaystyle P(\omega )} is the polarization density.

The electric field and polarization densities are

- {\displaystyle E(\omega )=E_{0}e^{-i\omega t},\quad P(\omega )=P_{0}e^{-i\omega t}}

and the polarization per atom with *n* electrons is

- {\displaystyle P=-nex}

The force *F* of the oscillating electric field causes the electrons with charge *e* and mass *m* to accelerate with an acceleration *a*

- {\displaystyle F=-eE=ma=m{\frac {d^{2}x}{dt^{2}}}}

which, after substitution of *E*, *P* and *x*, yields an harmonic oscillator equation.

After a little algebra the relation between polarization density and electric field can be expressed as

- {\displaystyle P(\omega )=-{\frac {ne^{2}}{m\omega ^{2}}}E(\omega )}

The frequency dependent dielectric function of the solid is

- {\displaystyle \epsilon (\omega )=1-{\frac {ne^{2}}{\epsilon _{0}m\omega ^{2}}}}

At a resonance frequency {\displaystyle \omega _{p}}, called the **plasma frequency**, the dielectric function changes sign from negative to positive and real part of the dielectric function drops to zero.

- {\displaystyle \omega _{p}={\sqrt {\frac {ne^{2}}{\epsilon _{0}m}}}}

This is a plasma oscillation resonance or plasmon. The plasma frequency is a direct measure of the square root of the density of valence electrons in a solid. Observed values are in reasonable agreement with this theoretical prediction for a large number of materials.^{[4]} Below the plasma frequency, the dielectric function is negative and the field cannot penetrate the sample. Light with angular frequency below the plasma frequency will be totally reflected. Above the plasma frequency the light waves can penetrate the sample.

my thoughts in Diagram 342 it shows the plasma and atomic distance particles for the UFO engine’s design….