The equivalent of 119,353 printed pages was downloaded during the day (435.160 megabytes) from 2,307 downloaded memory pages (hits) and 536 distinct visits, each averaging 3.4 memory pages and 7 minutes, printed pages to hits ratio for the day of 51.74, main spiders cnsat(China), google, MSN and yahoo. Collected ECE2 1801, Top ten 1783, Evans / Morris 858, Collected scientometrics 568, F3(Sp) 411, Barddoniaeth / Collected Poetry 392, Evans Equations 352, Principles of ECE 306, Eckardt / Lindstrom 294, Autobiography volumes one and two 255, Collected Proofs 244, UFT88 120, Engineering Model 110, PECE 105, UFT311 101, CEFE 80, Self Charging Inverter 43. UFT321 40, Llais 35, Idaho 27, Three world records 23, List of prolific authors 19, UFT313 36, UFT314 37, UFT315 44, UFT316 36, UFT317 31, UFT318 52, UFT319 52, UFT320 39, UFT322 54, UFT323 48, UFT324 64, UFT325 55, UFT326 36, UFT327 29, UFT328 42, UFT329 50, UFT330 36, UFT331 46, UFT332 41, UFT333 33, UFT334 34, UFT335 44, UFT336 35, UFT337 31, UFT338 31, UFT339 39, UFT340 36, UFT341 37, UFT342 28, UFT343 30, UFT344 45, UFT345 42, UFT346 49, UFT347 46, UFT348 59, UFT349 66, UFT351 60, UFT352 84, UFT353 67, UFT354 55 to date in August 2016. National University of Argentina at Cordoba UFT170(Sp); United States Govrenment Department of Homeland Security UFT75; University of Edinburgh UFT146, 152, 156, 160, 161, ECE article, UFT142, 165. Intense interest all sectors, updated usage file attached for August 2016.

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Many thanks, good to hear from Co President Gareth Evans. These patterns of spacetime flow exist also for a static electric field and the acceleration due to gravity. The numerical problem is simultaneous solution of three non linear partial differential equations for chosen boundary conditions in any coordinate system in three dimensions.

To: EMyrone@aol.com
Sent: 27/08/2016 16:18:37 GMT Daylight Time
Subj: Re: 356(3): Electric Component of the Plane Wave

This is very pleasing because it introduces a clear consistency right across physics and a lot of your early research was fluid dynamics at the molecular level. So, almost a full circle and fascinating how the work has evolved. Congratulations as ever!!
Sent from my Samsung device

In spherical polar coordinates this is found by solving Eqs. (13) to (15) simultaneously. In general, the velocity field has a very interesting structure in three dimensions. The simultaneous numerical solution of Eqs. (13) to (15) also gives the spacetime velocity field set up by a static gravitational field g (the acceleration due to gravity). This entirely original type of velocity field exists in a spacetime defined as a fluid. The spacetime can also be called an “aether”, or “vacuum”. Any boundary conditions can be used. A magnetic and gravitomagnetic field also set up aether velocity fields.

a356thpapernotes4.pdf

These are all good ideas. I just sent over the statement of the problem for spacetime flow set up by any electric field strength E in volts per metre. It needs the simultaneous solution of three non linear partial differential equations in three unknowns, v sub X, v sub Y and v sub Z in cartesian coordinates. Any boundary conditions can be modelled, notably the circuit of UFT311 or the Self Charging Inverter paper by Osamu Ide on www.aias.us. Any coordinate system can be used.

To: EMyrone@aol.com
Sent: 27/08/2016 09:25:32 GMT Daylight Time
Subj: Re: Discussion of Note 356(1)

OK, I already had the idea that the relation of the plane wave potentials

A(1) x A(2) = A(3)*

is identical to the relation of the B’s and therefore they may have the same vector directions. I will try a guess for v(1) and v(2) for the electric field but this might be difficult because of their non-linear relation to E.

Besides this I will set up the term (v dot del) v in cylindrical and and spherical coordinates. Then we can evaluate this term when v is given analytically in such coordinate systems, for example for a coil (note 2).

Horst

Am 27.08.2016 um 10:09 schrieb EMyrone:

OK thanks, yes this is the right result for v(1) and v(2), they play the role of A(1) and A(2) in plane wave electrodynamics, so this is an elegant result and leads to new types of fields as you infer. Your idea of electric and magnetic fields setting up flows of spacetime is very interesting. For the electric component of the plane waves in Eqs. (14) and (15) my notation may have been a bit misleading in that v(1) and v(2) for the electric field case are not meant to be the same as the v(1) and v(2) for the plane wave magnetic field. In general:

E = x (v dot del) v

where x is defined as rho sub m / rho. In general the above is a non linear differential equation for v, given any E. I will explain further in the Note 356(3).

To: EMyrone
Sent: 26/08/2016 19:20:49 GMT Daylight Time
Subj: Re: Discussion of Note 356(1)

The calculation gives that v(1) and v(2) are identical with B(1) and B(2) within a constant factor. Is this plausible? Perhaps there is an error in my calculation.
The E field is zero, except a hypothetical E(3) field. This is plausible because v(1) and v(2) only depend on z, and there is no v_z in both cases, so the derivatives of x and y vanish in the term (v*nabla)v. This differs from your calculation.

For comparison I added the same calculation for a real basis, B(1) = [1, 0, 0] etc.

Horst

Am 26.08.2016 um 14:12 schrieb EMyrone:

The equations are of the format B(1) = curl A(1) and so on, so we know that v(1) and v(2) are plane waves. I think that:

v(1) = (v(0) / root2) (i bold – i j bold) exp (i phi) = v(2)*

where * denotes complex conjugate. This should be checked with computer algebra. Also, the result for a curent loop magnetostatic field, just sent over is analytical.

To: EMyrone
Sent: 26/08/2016 12:45:58 GMT Daylight Time
Subj: Re: Note 356(1): Spacetime Velocity Fields Set up by Electric and Magnetic Fields

Has the factor exp(+/- i phi) to come out from the RHS of eqs.(12,13)? or has it simply to be multiplied to the curl terms at the RHS (a typo)?
In the first case v(1) and v(2) cannot be guessed so easily because there is a Z dependence in the exponential factor.

Horst

Am 25.08.2016 um 13:52 schrieb EMyrone:

The first few examples are idealized plane waves and static electric and magnetic fields. In this case it is not difficult for computer algebra to evaluate the velocity fields in the aether. They will give very interesting graphics. In the next few examples it is possible to consider for example spherical electric and magnetic waves in a material, pulsed electric and magnetic fields, and in general any type of electric or magnetic field in a material or any circuit. These will all general their own pattern of velocity fields in fluid spacetime. The vacuum in this theory is therefore an aether with well defined velocity fields. These are entirely new and original ideas. In the first example, numerical methods are not needed. It is relatively easy to get analytical solutions.

This is the statement of the problem in general. It consists of solving simultaneously three non linear differential equations in three unknowns, v sub X, v sub Y and v sub Z, for any boundary conditions. These are Eqs. (6), (7) and (8). For a plane wave the electric field components are given by Eqs. (9), (10) and (11). I find this line of research to be very interesting, because as suggested by Horst, any electric or magnetic or electromagnetic field in material matter sets up a velocity field in spacetime, defined as a fluid. This is entirely original research based on ECE2 unified field theory. In precise analogy, any gravitational field sets up a fluid flow in spacetime, and any weak or strong nuclear field. This is true form the domain of elementary particles to galactic clusters.

a356thpapernotes3.pdf

OK thanks, yes this is the right result for v(1) and v(2), they play the role of A(1) and A(2) in plane wave electrodynamics, so this is an elegant result and leads to new types of fields as you infer. Your idea of electric and magnetic fields setting up flows of spacetime is very interesting. For the electric component of the plane waves in Eqs. (14) and (15) my notation may have been a bit misleading in that v(1) and v(2) for the electric field case are not meant to be the same as the v(1) and v(2) for the plane wave magnetic field. In general:

E = x (v dot del) v

where x is defined as rho sub m / rho. In general the above is a non linear differential equation for v, given any E. I will explain further in the Note 356(3).

To: EMyrone@aol.com
Sent: 26/08/2016 19:20:49 GMT Daylight Time
Subj: Re: Discussion of Note 356(1)

The calculation gives that v(1) and v(2) are identical with B(1) and B(2) within a constant factor. Is this plausible? Perhaps there is an error in my calculation.
The E field is zero, except a hypothetical E(3) field. This is plausible because v(1) and v(2) only depend on z, and there is no v_z in both cases, so the derivatives of x and y vanish in the term (v*nabla)v. This differs from your calculation.

For comparison I added the same calculation for a real basis, B(1) = [1, 0, 0] etc.

Horst

Am 26.08.2016 um 14:12 schrieb EMyrone:

The equations are of the format B(1) = curl A(1) and so on, so we know that v(1) and v(2) are plane waves. I think that:

v(1) = (v(0) / root2) (i bold – i j bold) exp (i phi) = v(2)*

where * denotes complex conjugate. This should be checked with computer algebra. Also, the result for a curent loop magnetostatic field, just sent over is analytical.

To: EMyrone
Sent: 26/08/2016 12:45:58 GMT Daylight Time
Subj: Re: Note 356(1): Spacetime Velocity Fields Set up by Electric and Magnetic Fields

Has the factor exp(+/- i phi) to come out from the RHS of eqs.(12,13)? or has it simply to be multiplied to the curl terms at the RHS (a typo)?
In the first case v(1) and v(2) cannot be guessed so easily because there is a Z dependence in the exponential factor.

Horst

Am 25.08.2016 um 13:52 schrieb EMyrone:

The first few examples are idealized plane waves and static electric and magnetic fields. In this case it is not difficult for computer algebra to evaluate the velocity fields in the aether. They will give very interesting graphics. In the next few examples it is possible to consider for example spherical electric and magnetic waves in a material, pulsed electric and magnetic fields, and in general any type of electric or magnetic field in a material or any circuit. These will all general their own pattern of velocity fields in fluid spacetime. The vacuum in this theory is therefore an aether with well defined velocity fields. These are entirely new and original ideas. In the first example, numerical methods are not needed. It is relatively easy to get analytical solutions.

356(1).pdf

The equivalent of 147,316 printed pages was downloaded during the day (537.113 megabytes) from 2,581 downloaded memory files (hits) and 631 distinct visits each averaging 3.1 memory pages and 10 minutes, printed pages to hits ratio for the day of 57.08, main spiders cnsat(China), google, MSN and yahoo. Collected ECE2 1772, Top ten items 1609, Collected Evans / Morris 825, Collected scientometrics 545, F3(Sp) 392, Barddoniaeth / Collected Poetry 381, Evans Equations 347, Eckardt / Lindstrom papers 294, Principles of ECE 293, Autobiography volumes one and two 249, Collected Proofs 242, UFT88 117, Engineering Model 109, UFT311 99, CEFE 76, Self charging inverter 41, UFT321 40, Llais 33, Idaho 27, Three world records by MWE 23, List of prolific authors 19, UFT313 36, UFT314 37, UFT315 44, UFT316 36, UFT317 31, UFT318 50, UFT319 51, UFT320 39, UFT322 54, UFT323 47, UFT324 63, UFT325 55, UFT326 39, UFT327 29, UFT328 42, UFT329 48, UFT330 36, UFT331 45, UFT332 40, UFT333 33, UFT334 34, UFT335 43, UFT336 35, UFT337 30, UFT338 31, UFT339 39, UFT340 36, UFT341 35, UFT342 28, UFT343 29, UFT344 44, UFT345 41, UFT346 48, UFT347 45, UFT348 58, UFT349 64, UFT351 60, UFT352 82, UFT353 66, UFT354 52, UFT355 17 to date in August 2016. Physics University of New South Wales UFT177; City of Winnipeg, publications page extensive; Technical University of Chile Professional Institute Technical Training Center (INACAP) Essay 28 (Spanish); University of Kassel general; University of Florida My CV; Mexican National Polytechnic Institute UFT42; Ateneo de Manila Uaiversity Philippines general; National University of Singapore general; University of Edinburgh UFT139, UFT157. Intense interest all sectors, updated usage file attached for August 2016.

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Fully agreed, the graphics will be very interesting!

To: EMyrone@aol.com
Sent: 26/08/2016 14:05:53 GMT Daylight Time
Subj: Re: 356(2): Velocity Field from a Current Loop Magnetic Field

In this case the velocity field v is (within constant factors) the same as the classical vector potential A. Therefore all classical methods computing the A field are directly applicable.
In a magnetostatic case (eq.(20) of note 356(1)) we have

rho_m/rho * nabla x (nabla x v) = mu_0 J

or

nabla x (nabla x A) = mu_0 J.

This is the way in which for example FlexPDE solves magnetostatic problems. The vector potential directly corresponds to the velocity field in case of constant charge densities. In electrical cases this seems to be a bit more difficile because the term

(v*nabla) v

does not appear in classical electrodynamics. However, if v is given analytically, E can be calculated this way. So the above magnetostatic problem seems to generate an inherent electric field, not known in classical electrodynamics.

I will try to compute this E field from v of the notes.

Horst

Am 26.08.2016 um 14:04 schrieb EMyrone:

In this case the result is analytical, Eq. (11), and it can be graphed in three dimensions in spherical polar coordinates.

In this case the result is analytical, Eq. (11), and it can be graphed in three dimensions in spherical polar coordinates.

a356thpapernotes2.pdf

Many thanks, this looks very interesting for all applications. The fluid electrodynamics papers are already the most read of the ECE2 series, led by UFT352.

Sent: 25/08/2016 17:23:31 GMT Daylight Time
Subj: Re: FEM programs and modeling

​The 3D extrusion is limited in flexpde, as described in this note from their sample problems – extruding a helix..

“This problem shows the use of the function definition facility of FlexPDE to create a helix of square cross-section in 3D.

The mesh generation facility of FlexPDE extrudes a 2D figure along a straight

path in Z, so that it is not possible to directly define a helical shape.

However, by defining a coordinate transformation, we can build a straight rod

in 3D and interpret the coordinates in a rotating frame.

Define the twisting coordinates by the transformation

xt = x*cos(y/R);

yt = x*sin(y/R);

zt = z

In this transformation, x and y are the coordinates FlexPDE believes it is working

with, and they are the coordinates that move with the twisting.

xt and yt are the “lab coordinates” of the twisted figure.

The chain rule gives

dF/d(xt) = (dx/dxt)*(dF/dx) + (dy/dxt)*(dF/dy) + (dz/dxt)*(dF/dz)

with similar rules for yt and zt.

Some tedious algebra gives

dx/dxt = cos(y/R) dy/dxt = -(R/x)*sin(y/R) dz/dxt = 0

dx/dyt = sin(y/R) dy/dyt = (R/x)*cos(y/R) dz/dyt = 0

dx/dzt = dy/dzt = 0 dz/dzt = 1

These relations are defined in the definitions section, and used in the equations

section, perhaps nested as in the heat equation shown here.

Notice that this formulation produces the upward motion by tilting the bar in

the un-twisted space and wrapping the resulting figure around a cylinder.

We have added a cylindrical mounting pad at each end of the helix.”

The box with attached box is simple; the pyramid on a pyramid is not. I will look at importing meshes etc. into flexpdE for the pyramid case.

Doug

On Wed, Aug 24, 2016 at 11:07 AM, Horst Eckardt <mail> wrote:

Hi all,

I collocated the required features and possible commercial and free FEM programs again, including your amendments. I spoke to some people who all recommended Comsol as the best program. It is most flexible and the best invest for future developments. A version for non-commrecial use may be usable. FlexPDE seems to be a bit tricky with defining 3D regions, I had some problems with that.

I would like to model a cube in a cube and a pyramid in a cube (see attachment; the pyramid is not correctly drawn, should have a tip). The Reynolds numbers should be different in the surrounding cube and the inner cube/pyramid. The simplified vorticity equation should be solved.
I am planning to try this out with FlexPDE first and will order a test version for one month. Comsol requires further thinking about buying etc.
Doug: would it be possible for you to define both geometries in FlexPDE? Myron will certainly add you as a co-author. The boundaries have to be discussed. I suggest that the velocity field should be fixed at one outer side to define an inflow of aether spacetime.

If we obtain reasonable results, we can try to set up a first model for a circuit in one of the next papers. After one month we should think about changing the FEM tool.

Horst