Author Topic: EM Drive Developments - related to space flight applications - Thread 6  (Read 1493692 times)

Offline SeeShells

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A further idea for faster computation is using cylindrical symmetry.   Although this constrains the shapes that can be used, initial experiments suggest a 100x speedup.

The geometrical axisymmetry of the frustum of the cone is presently not being exploited.  However, assuming full axisymmetry would only produce fully axisymmetric electromagnetic modes. One would not be able to get the TM212 mode that NASA obtains in their experimental measurements for example.

A number of modes are not fully axisymmetric but display m-fold symmetry (where "m" is the first quantum number in TEmnp or TMmnp modes). The following images shows the lowest TEmn and TMmn modes, for arbitrary "p":



Only modes with m=0 are fully axisymmetric (for example TE012) .  For m=1 one has to model half of the circular cross-section (and one can impose symmetry on the boundaries). For higher m>1 one has to model "smaller pie slices".  So, it looks like one could at least save 50% of the mesh by exploiting axisymmetry

More problematic, it would preclude non-fully axisymmetric modes.  To exploit axisymmetry one would have to determine what is the maximum number of poles around the circumference one wants to model: it would effectively set a pre-defined limit on the "m" and "n" quantum numbers that the model could model for TEmnp and TMmnp modes.

This is further complicated by the fact that Meep has revealed asymmetric modes not present in cylindrical cavities.  Imposing axysymmetry would get rid of such asymmetric modes.  For example, an asymmetric placement of an antenna, or an asymmetric placement of a waveguide can excite asymmetric modes in a real cavity, and it is useful for the designer to know this.

Actually, one of the greatest contributions of Meep analysis has been to make this asymmetric modes evident, and show how difficult it is to achieve axisymmetric resonant modes with antennas.
Dr. Rodal,

Love reading your posts.

It's important to review the hundreds of posts on our attempts to get a TExx mode from antennas inserted into the frustum. The closest we got was a loop aero did and it created unstable traveling modes. I have no doubt that this is this is the reason that EW, Shawyer, Tajmar and (possibly) Yang have went to the waveguide insertion.

Shell

Offline VAXHeadroom

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Here is the link to Meep symmetries:

http://ab-initio.mit.edu/wiki/index.php/Exploiting_symmetry_in_Meep

My difficulty is understanding the source phasing, and how to do it. To make it work I have resorted to running lower resolution in full 3D, saving the images, then using the good old cut and try technique until the fields calculated with symmetry look the same as the 3D images. Then I feel somewhat confident in my higher resolution symmetric runs. It only works with the source on the z axis though, or maybe mirror symmetry with the source in either the x,z or y,z plane.

As for cylindrical symmetry, as far as I know that only works when the source is axially symmetric, that is, a point source or a dipole lying on the z axis. That is to big a constraint for our problems.

Of course, if cylindrical or spherical coordinates are useful for post processing, the csv file Cartesian coordinates can be transformed mathematically to whatever coordinate system is desired. Transforming the full .h5 file might be a way to identify the boundary of the conic section for those evaluations that need to know the boundary location.  With the availability of meep on a virtual machine, (see the em drive wiki, meep section) it is almost trivial to generate your own set of .h5 files, ask VAXHeadRoom about the relative difficulty compared to post processing.

@VAXHeadRoom - I hope that's all right. If not, spank me.

:)  No spankings required.  Your help was invaluable.  My only difficulty was figuring how to get the results from the virtual machine into the Win8 domain.  It's actually pretty straightforward once I figured it out.  Once you have the Virtual Box Manager program installed and have started Ubuntu and logged in do the following:
In Windows:
1) Create a new directory you want to share - mine is c:\data\EMDrive\VBoxShare
2) Create a new share for that directory.  In my case, open a browser to c:\data\emdrive, right click on the VBoxShare directory icon, select Properties, select the 'sharing' tab, select 'Advanced Sharing', Check the 'Share this folder' checkbox, click the 'Add' button and make a new share name.  I used WinVBoxShare'.
In Ubuntu:
3) Open a terminal
4) create a new directory for sharing.  Mine is: /home/nsf/win_shared
5) Map the Ubuntu directory to the Win directory: sudo mount -t vboxsf WinVBoxShare /home/nsf/win_shared  <-- note this will require you to enter the password for the nsf account

Now anything created within the Ubuntu /home/nsf/win_shared directory will also be in c:\data\EMDrive\VBoxShare and vice versa.  I bounce back and forth a lot - some things are more convenient from one OS or the other.
Emory Stagmer
  Executive Producer, Public Speaker UnTied Music - www.untiedmusic.com

Offline Rodal

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...
Dr. Rodal,

Love reading your posts.

It's important to review the hundreds of posts on our attempts to get a TExx mode from antennas inserted into the frustum. The closest we got was a loop aero did and it created unstable traveling modes. I have no doubt that this is this is the reason that EW, Shawyer, Tajmar and (possibly) Yang have went to the waveguide insertion.

Shell
Aero and you deserve tons of praise for persevering with Meep and finally modeling waveguide insertion.  Several thread ago  it was believed that it was straightforward to make the truncated cone of the EM Drive resonate in any mode wanted, whether transverse electric (TE) or transverse magnetic (TM).  It was thanks to aero that this was shown to be incorrect: that it is very difficult to excite certain modes, particularly TE modes, and that the truncated cone does not always behave as a different kind of cylindrical cavity, as there are other modes that are not found in cylindrical cavities.  Reality, our Universe is once again found to be so much more interesting and fascinating than our imagination !

And thanks to you for insisting on looking at waveguide insertion and realizing that the way to eliminate asymmetry and rotation was to have dual symmetric waveguides !  You thought of that early on, and pioneered the way much further than shown by Shawyer, Yang and Tajmar (who to my my recollection only used one-sided waveguide insertion, with Tajmar measuring experimentally very asymmetric side forces ! )
« Last Edit: 12/27/2015 02:18 pm by Rodal »

Offline SeeShells

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Here is the link to Meep symmetries:

http://ab-initio.mit.edu/wiki/index.php/Exploiting_symmetry_in_Meep

My difficulty is understanding the source phasing, and how to do it. To make it work I have resorted to running lower resolution in full 3D, saving the images, then using the good old cut and try technique until the fields calculated with symmetry look the same as the 3D images. Then I feel somewhat confident in my higher resolution symmetric runs. It only works with the source on the z axis though, or maybe mirror symmetry with the source in either the x,z or y,z plane.

As for cylindrical symmetry, as far as I know that only works when the source is axially symmetric, that is, a point source or a dipole lying on the z axis. That is to big a constraint for our problems.

Of course, if cylindrical or spherical coordinates are useful for post processing, the csv file Cartesian coordinates can be transformed mathematically to whatever coordinate system is desired. Transforming the full .h5 file might be a way to identify the boundary of the conic section for those evaluations that need to know the boundary location.  With the availability of meep on a virtual machine, (see the em drive wiki, meep section) it is almost trivial to generate your own set of .h5 files, ask VAXHeadRoom about the relative difficulty compared to post processing.

@VAXHeadRoom - I hope that's all right. If not, spank me.
What is the difference in creating a large cell size which shows up in a very pixelated image and using short circular sections? A 2D slice to me looks the same.  I mean if I take your pixelated image and fill it in making a visual 3D image it looks like multiple short cylinders.

What am I not seeing here? Is it what the software sees?

You'll have to excuse me some  as my main system took a massive crash yesterday and this is the little lab laptop. Thank goodness I have backed up it all but still a ton of work to pull off the data from the old drive.

Shell


Offline zellerium

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JFYI, Attached are COMSOL simulations for the frustum (with coax coupling) I am going to build. It is now time for some sheet metal cutting and torch soldering... And then there will be the moment of truth.

...

Wow, your results look great!
Please excuse me if I missed this, but may I ask why you've decided on a coupler inside the frustum?

I was under the impression that a waveguide delivery with aperture coupling allowed for better reflection and quality.



Offline Mulletron

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http://arxiv.org/abs/1512.01130

@Notsosureofit. I thought you may be interested.

Quote
In this letter, we have thus shown that in “effective
mass”, a notion routinely used to describe the dispersion
of the light in planar (or cylindrical) cavities, “effective”
should be dropped. Indeed as photons are brought to a
full stop in a cavity, they indeed acquire a mass in the
usual sense of the word, both from the inertial and the
gravitational point-of-view.
And I can feel the change in the wind right now - Rod Stewart

Offline Rodal

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http://arxiv.org/abs/1512.01130

@Notsosureofit. I thought you may be interested.

Quote
In this letter, we have thus shown that in “effective
mass”, a notion routinely used to describe the dispersion
of the light in planar (or cylindrical) cavities, “effective”
should be dropped. Indeed as photons are brought to a
full stop in a cavity, they indeed acquire a mass in the
usual sense of the word, both from the inertial and the
gravitational point-of-view.

If there is an anomalous force, the weight of the evidence is turning out to support this as the best explanation.  Much more evidence than for the Quantum Vacuum of Dr. White (and the "theories" of Shawyer and Yang are non-viable).
« Last Edit: 12/27/2015 05:35 pm by Rodal »

Offline aero

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http://arxiv.org/abs/1512.01130

@Notsosureofit. I thought you may be interested.

Quote
In this letter, we have thus shown that in “effective
mass”, a notion routinely used to describe the dispersion
of the light in planar (or cylindrical) cavities, “effective”
should be dropped. Indeed as photons are brought to a
full stop in a cavity, they indeed acquire a mass in the
usual sense of the word, both from the inertial and the
gravitational point-of-view.

Isn't that something new? Photons with rest mass?
Retired, working interesting problems

Offline Rodal

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http://arxiv.org/abs/1512.01130

@Notsosureofit. I thought you may be interested.

Quote
In this letter, we have thus shown that in “effective
mass”, a notion routinely used to describe the dispersion
of the light in planar (or cylindrical) cavities, “effective”
should be dropped. Indeed as photons are brought to a
full stop in a cavity, they indeed acquire a mass in the
usual sense of the word, both from the inertial and the
gravitational point-of-view.

Isn't that something new? Photons with rest mass?

Has been discussed for several threads.  I posted a link to a whole book on the subject several threads ago:

Theory of Photon Acceleration. Taylor & Francis. 2000. Hardcover
by J.T. MENDONCA
« Last Edit: 12/27/2015 05:56 pm by Rodal »

Offline OnlyMe

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http://arxiv.org/abs/1512.01130

@Notsosureofit. I thought you may be interested.

Quote
In this letter, we have thus shown that in “effective
mass”, a notion routinely used to describe the dispersion
of the light in planar (or cylindrical) cavities, “effective”
should be dropped. Indeed as photons are brought to a
full stop in a cavity, they indeed acquire a mass in the
usual sense of the word, both from the inertial and the
gravitational point-of-view.

Isn't that something new? Photons with rest mass?

Has been discussed for several threads.  I posted a link to a whole book on the subject several threads ago:

Theory of Photon Acceleration. Taylor & Francis. 2000. Hardcover
by J.T. MENDONCA

Thanks for the reference. I was not following the discussion when the link was posted, but it was easy enough to find online and looks both interesting, from the first few pages and at least initially an easy read.

Offline SeeShells

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http://arxiv.org/abs/1512.01130

@Notsosureofit. I thought you may be interested.

Quote
In this letter, we have thus shown that in “effective
mass”, a notion routinely used to describe the dispersion
of the light in planar (or cylindrical) cavities, “effective”
should be dropped. Indeed as photons are brought to a
full stop in a cavity, they indeed acquire a mass in the
usual sense of the word, both from the inertial and the
gravitational point-of-view.
Interesting. So dependent of the mode lobe in the cavity it would create a gravitational difference between one end and the other?

Shell

Offline X_RaY

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JFYI, Attached are COMSOL simulations for the frustum (with coax coupling) I am going to build. It is now time for some sheet metal cutting and torch soldering... And then there will be the moment of truth.

...

Wow, your results look great!
Please excuse me if I missed this, but may I ask why you've decided on a coupler inside the frustum?

I was under the impression that a waveguide delivery with aperture coupling allowed for better reflection and quality.


I think the modified loop (for TE01p) is as good as every other coupling if it's done right. A large coupling window in the sidewall could leads to more asymmetry. As long as we don't know exactly what causes the (possible, measured) thrust keep the experiment as simple as possible. The cavity without a hole in the sidewall is complicated enough. The larger volume can store more field energy, but on the other hand the additional copper of the waveguide leads to more ohmic losses and it could reduce the total Q_0 of the resonator caused by the wall currents in this section (compared with the cavity without waveguide coupler). So the modified loop looks like a good choice.
« Last Edit: 12/28/2015 08:15 am by X_RaY »

Offline Flyby

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Aero and you deserve tons of praise for persevering with Meep and finally modeling waveguide insertion.  Several thread ago  it was believed that it was straightforward to make the truncated cone of the EM Drive resonate in any mode wanted, whether transverse electric (TE) or transverse magnetic (TM).  It was thanks to aero that this was shown to be incorrect: that it is very difficult to excite certain modes, particularly TE modes, and that the truncated cone does not always behave as a different kind of cylindrical cavity, as there are other modes that are not found in cylindrical cavities.  Reality, our Universe is once again found to be so much more interesting and fascinating than our imagination !

And thanks to you for insisting on looking at waveguide insertion and realizing that the way to eliminate asymmetry and rotation was to have dual symmetric waveguides !  You thought of that early on, and pioneered the way much further than shown by Shawyer, Yang and Tajmar (who to my my recollection only used one-sided waveguide insertion, with Tajmar measuring experimentally very asymmetric side forces ! )

Indeed, as a distant observer,the thing that struck me the most in this scientific adventure, is the creation of dynamic resonance patterns.
In analogy with sound resonance patterns, I was expecting static resonance in the cavity, but the Meep calculations , brought up by Shell and performed by Aero, clearly showed that the shape of cavity, combined with placement of antenna's/wave guides creates the conditions for an internal moving resonance pattern.

It is in this context that I'm trying to grasp what really happens when EM waves are hitting the copper atom lattice.

Not sure if it can be related in any way, but in my search to know more about reflection of EM waves, I stumbled on the Goos-Hänchen effect, something completely unknown to me.
It describes that , under certain conditions, light does not really bounce back immediately, but travels horizontal for a short distance before exiting as reflection.

http://pages.uoregon.edu/noeckel/gooshanchen/

Could it be that the forward (towards small end) pulsating fields generate some drag effect on the side walls?


Strange things going on there with EM waves even moving backwards for a short distance before exiting...


Granted, this effect is mostly applied to light photonic research, but considering microwaves are nothing more then a EM waves with a longer wavelength then light, maybe it does apply?

I'm still trying very hard to understand and take it all in, as this is far outside my comfort zone...
So don't shoot.. :)

« Last Edit: 12/27/2015 07:56 pm by Flyby »

Offline SeeShells

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Here is the link to Meep symmetries:

http://ab-initio.mit.edu/wiki/index.php/Exploiting_symmetry_in_Meep

My difficulty is understanding the source phasing, and how to do it. To make it work I have resorted to running lower resolution in full 3D, saving the images, then using the good old cut and try technique until the fields calculated with symmetry look the same as the 3D images. Then I feel somewhat confident in my higher resolution symmetric runs. It only works with the source on the z axis though, or maybe mirror symmetry with the source in either the x,z or y,z plane.

As for cylindrical symmetry, as far as I know that only works when the source is axially symmetric, that is, a point source or a dipole lying on the z axis. That is to big a constraint for our problems.

Of course, if cylindrical or spherical coordinates are useful for post processing, the csv file Cartesian coordinates can be transformed mathematically to whatever coordinate system is desired. Transforming the full .h5 file might be a way to identify the boundary of the conic section for those evaluations that need to know the boundary location.  With the availability of meep on a virtual machine, (see the em drive wiki, meep section) it is almost trivial to generate your own set of .h5 files, ask VAXHeadRoom about the relative difficulty compared to post processing.

@VAXHeadRoom - I hope that's all right. If not, spank me.
What is the difference in creating a large cell size which shows up in a very pixelated image and using short circular sections? A 2D slice to me looks the same.  I mean if I take your pixelated image and fill it in making a visual 3D image it looks like multiple short cylinders.

What am I not seeing here? Is it what the software sees?

You'll have to excuse me some  as my main system took a massive crash yesterday and this is the little lab laptop. Thank goodness I have backed up it all but still a ton of work to pull off the data from the old drive.

Shell
Please excuse the very crude drawing in PCPaint. If I take aero's meep cell size model and slice it across where the cells are it looks much like a series of cylinders. The question is still there, is there a difference in how meep calculates this vs a series of stacked cylinders?

Back to getting my system up again. I'm going to meed a new bare bone system. sigh.

Shell

Offline VAXHeadroom

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JFYI, Attached are COMSOL simulations for the frustum (with coax coupling) I am going to build. It is now time for some sheet metal cutting and torch soldering... And then there will be the moment of truth.

...

Wow, your results look great!
Please excuse me if I missed this, but may I ask why you've decided on a coupler inside the frustum?

I was under the impression that a waveguide delivery with aperture coupling allowed for better reflection and quality.



After watching the linked video, YouTube suggested another which I watched.  I HIGHLY suggest those who are only passingly familiar(like me!) with waveguides and resonances watch this FANTASTIC lecture by Dr Walter Lewin from MIT (a genius lecturer!).  (you old veterans might want to watch it too :) ) ESPECIALLY the last 10 minutes - the demonstration of resonance convergence and decay is pretty fascinating.  I really need to watch all of that semester (8.03)


Emory Stagmer
  Executive Producer, Public Speaker UnTied Music - www.untiedmusic.com

Offline Rodal

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Here is the link to Meep symmetries:

http://ab-initio.mit.edu/wiki/index.php/Exploiting_symmetry_in_Meep

My difficulty is understanding the source phasing, and how to do it. To make it work I have resorted to running lower resolution in full 3D, saving the images, then using the good old cut and try technique until the fields calculated with symmetry look the same as the 3D images. Then I feel somewhat confident in my higher resolution symmetric runs. It only works with the source on the z axis though, or maybe mirror symmetry with the source in either the x,z or y,z plane.

As for cylindrical symmetry, as far as I know that only works when the source is axially symmetric, that is, a point source or a dipole lying on the z axis. That is to big a constraint for our problems.

Of course, if cylindrical or spherical coordinates are useful for post processing, the csv file Cartesian coordinates can be transformed mathematically to whatever coordinate system is desired. Transforming the full .h5 file might be a way to identify the boundary of the conic section for those evaluations that need to know the boundary location.  With the availability of meep on a virtual machine, (see the em drive wiki, meep section) it is almost trivial to generate your own set of .h5 files, ask VAXHeadRoom about the relative difficulty compared to post processing.

@VAXHeadRoom - I hope that's all right. If not, spank me.
What is the difference in creating a large cell size which shows up in a very pixelated image and using short circular sections? A 2D slice to me looks the same.  I mean if I take your pixelated image and fill it in making a visual 3D image it looks like multiple short cylinders.

What am I not seeing here? Is it what the software sees?

You'll have to excuse me some  as my main system took a massive crash yesterday and this is the little lab laptop. Thank goodness I have backed up it all but still a ton of work to pull off the data from the old drive.

Shell
Please excuse the very crude drawing in PCPaint. If I take aero's meep cell size model and slice it across where the cells are it looks much like a series of cylinders. The question is still there, is there a difference in how meep calculates this vs a series of stacked cylinders?

Back to getting my system up again. I'm going to meed a new bare bone system. sigh.

Shell

Yes, there is a huge difference, as Meep solves Maxwells' differential equations (in a central difference scheme at each node).  The limitation with Meep's finite difference scheme is the coarseness of the 3-D mesh of nodes.  It imposes a three dimensional mesh, where Maxwell's equations are solved at the nodes of the mesh.  Hence it is not looking or solving at cylinders, but a number of nodes in 3-D.  Think of the boundary as a staircase boundary, rather than as a collection of cylinders, because there are no cylinders connecting the stairs in the finite difference scheme, instead you have a number of nodes, and the difference equations are being solved at each node, and there are many, many nodes separating the staircase boundaries.  Each node is connected to the surrounding nodes in 3-D, so as you go from a node from the left boundary to a node at the right boundary there are many finite difference paths that connects the boundaries: not just straight paths like in a cylinder, but you can imagine other paths, zig-zags that describe many other connections.

It involves the simultaneous solution of all these coupled equations that connect all the nodes.

« Last Edit: 12/27/2015 08:48 pm by Rodal »

Offline SeeShells

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JFYI, Attached are COMSOL simulations for the frustum (with coax coupling) I am going to build. It is now time for some sheet metal cutting and torch soldering... And then there will be the moment of truth.

...

Wow, your results look great!
Please excuse me if I missed this, but may I ask why you've decided on a coupler inside the frustum?

I was under the impression that a waveguide delivery with aperture coupling allowed for better reflection and quality.


I think the modified loop (for TE01p) is as good as every other coupling if it's done right. A large coupling window in the sidewall could leads to more asymmetry. As long as we don't know exactly what causes the (possible, measured) thrust keep the experiment as simple as possible. The cavity without a hole in the sidewall is complicated enough. The additional copper of the waveguide leads to more ohmic losses and it could reduce the total Q_0 of the resonator caused by the wall currents in this section (compared with the cavity without waveguide coupler). So the modified loop looks like a good choice.
Simply do a small Z match hole in the side of the frustum where the waveguide is attached. They do it in microwave ovens all the time. It will keep the frustum cavity from seeing the full waveguide and in the case of a asymmetric traveling mode keep the VSWR lower in the reflected load to the waveguide antenna.

This is one of my "Fixes" to the smoking matchstick antenna in my waveguides.

Shell 

Offline SeeShells

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Here is the link to Meep symmetries:

http://ab-initio.mit.edu/wiki/index.php/Exploiting_symmetry_in_Meep

My difficulty is understanding the source phasing, and how to do it. To make it work I have resorted to running lower resolution in full 3D, saving the images, then using the good old cut and try technique until the fields calculated with symmetry look the same as the 3D images. Then I feel somewhat confident in my higher resolution symmetric runs. It only works with the source on the z axis though, or maybe mirror symmetry with the source in either the x,z or y,z plane.

As for cylindrical symmetry, as far as I know that only works when the source is axially symmetric, that is, a point source or a dipole lying on the z axis. That is to big a constraint for our problems.

Of course, if cylindrical or spherical coordinates are useful for post processing, the csv file Cartesian coordinates can be transformed mathematically to whatever coordinate system is desired. Transforming the full .h5 file might be a way to identify the boundary of the conic section for those evaluations that need to know the boundary location.  With the availability of meep on a virtual machine, (see the em drive wiki, meep section) it is almost trivial to generate your own set of .h5 files, ask VAXHeadRoom about the relative difficulty compared to post processing.

@VAXHeadRoom - I hope that's all right. If not, spank me.
What is the difference in creating a large cell size which shows up in a very pixelated image and using short circular sections? A 2D slice to me looks the same.  I mean if I take your pixelated image and fill it in making a visual 3D image it looks like multiple short cylinders.

What am I not seeing here? Is it what the software sees?

You'll have to excuse me some  as my main system took a massive crash yesterday and this is the little lab laptop. Thank goodness I have backed up it all but still a ton of work to pull off the data from the old drive.

Shell
Please excuse the very crude drawing in PCPaint. If I take aero's meep cell size model and slice it across where the cells are it looks much like a series of cylinders. The question is still there, is there a difference in how meep calculates this vs a series of stacked cylinders?

Back to getting my system up again. I'm going to meed a new bare bone system. sigh.

Shell

Yes, there is a huge difference, as Meep solves Maxwells' differential equations (in a central difference scheme at each node).  The limitation with Meep's finite difference scheme is the coarseness of the 3-D mesh of nodes.  It imposes a three dimensional mesh, where Maxwell's equations are solved only at the nodes of the mesh.  Hence it is not looking or solving at cylinders, but a number of nodes in 3-D.  Think of the boundary as a staircase boundary, rather than as a collection of cylinders, because there are no cylinders connecting the stairs in the finite difference scheme, instead you have a number of nodes, and the difference equations are being solved at each node, and there are many, many nodes separating the staircase boundaries.  Each node is connected to the surrounding nodes in 3-D, so as you go from a node from the left boundary to a node at the right boundary there are many finite difference paths that connects the boundaries: not just straight paths like in a cylinder, but you can imagine other paths, zig-zags that describe many other connections.

It involves the simultaneous solution of all these coupled equations that connect all the nodes.
http://static.planetminecraft.com/files/resource_media/screenshot/1126/20110701_011218_134841.jpg

So meep solves small meep units that are little blocks? I see what your saying Dr. Rodal but it will take me sometime to get the image out of my head.

Thanks...

Shell

Offline Rodal

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Here is the link to Meep symmetries:

http://ab-initio.mit.edu/wiki/index.php/Exploiting_symmetry_in_Meep

My difficulty is understanding the source phasing, and how to do it. To make it work I have resorted to running lower resolution in full 3D, saving the images, then using the good old cut and try technique until the fields calculated with symmetry look the same as the 3D images. Then I feel somewhat confident in my higher resolution symmetric runs. It only works with the source on the z axis though, or maybe mirror symmetry with the source in either the x,z or y,z plane.

As for cylindrical symmetry, as far as I know that only works when the source is axially symmetric, that is, a point source or a dipole lying on the z axis. That is to big a constraint for our problems.

Of course, if cylindrical or spherical coordinates are useful for post processing, the csv file Cartesian coordinates can be transformed mathematically to whatever coordinate system is desired. Transforming the full .h5 file might be a way to identify the boundary of the conic section for those evaluations that need to know the boundary location.  With the availability of meep on a virtual machine, (see the em drive wiki, meep section) it is almost trivial to generate your own set of .h5 files, ask VAXHeadRoom about the relative difficulty compared to post processing.

@VAXHeadRoom - I hope that's all right. If not, spank me.
What is the difference in creating a large cell size which shows up in a very pixelated image and using short circular sections? A 2D slice to me looks the same.  I mean if I take your pixelated image and fill it in making a visual 3D image it looks like multiple short cylinders.

What am I not seeing here? Is it what the software sees?

You'll have to excuse me some  as my main system took a massive crash yesterday and this is the little lab laptop. Thank goodness I have backed up it all but still a ton of work to pull off the data from the old drive.

Shell
Please excuse the very crude drawing in PCPaint. If I take aero's meep cell size model and slice it across where the cells are it looks much like a series of cylinders. The question is still there, is there a difference in how meep calculates this vs a series of stacked cylinders?

Back to getting my system up again. I'm going to meed a new bare bone system. sigh.

Shell

Yes, there is a huge difference, as Meep solves Maxwells' differential equations (in a central difference scheme at each node).  The limitation with Meep's finite difference scheme is the coarseness of the 3-D mesh of nodes.  It imposes a three dimensional mesh, where Maxwell's equations are solved only at the nodes of the mesh.  Hence it is not looking or solving at cylinders, but a number of nodes in 3-D.  Think of the boundary as a staircase boundary, rather than as a collection of cylinders, because there are no cylinders connecting the stairs in the finite difference scheme, instead you have a number of nodes, and the difference equations are being solved at each node, and there are many, many nodes separating the staircase boundaries.  Each node is connected to the surrounding nodes in 3-D, so as you go from a node from the left boundary to a node at the right boundary there are many finite difference paths that connects the boundaries: not just straight paths like in a cylinder, but you can imagine other paths, zig-zags that describe many other connections.

It involves the simultaneous solution of all these coupled equations that connect all the nodes.
http://static.planetminecraft.com/files/resource_media/screenshot/1126/20110701_011218_134841.jpg

So meep solves small meep units that are little blocks? I see what your saying Dr. Rodal but it will take me sometime to get the image out of my head.

Thanks...

Shell

1) Think of many nodes (points) inside the EM Drive. 

2) Think of Maxwell's equations being solved at each of these nodes

and

3) most importantly think of the connections that connect each node to the adjacent nodes

So, the power of such a solution method is not just the pointwise solution at points in space but the coupling between the nodes.   If you think of microwaves inside the EM Drive you are simultaneously solving for many different waves going in different directions.

There is a large number of paths that connect a node at the left boundary to a node at the right boundary.

This plot shows you a finite-difference matrix.  You will notice that there are not only entries on the main diagonal, but also there are many off-diagonal entries.  The off-diagonal entries represent coupling



__________
(*) The spreadsheet by TT is solving the problem as a collection of cylinders, not taking into account the coupling between the cylinders.   Hence TT's spreadsheet is always stiffer than reality: it gives higher natural frequencies than obtained by the Finite Difference or the Finite Element method when employing a fine mesh.
« Last Edit: 12/27/2015 09:02 pm by Rodal »

Offline Notsosureofit

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http://arxiv.org/abs/1512.01130

@Notsosureofit. I thought you may be interested.

Quote
In this letter, we have thus shown that in “effective
mass”, a notion routinely used to describe the dispersion
of the light in planar (or cylindrical) cavities, “effective”
should be dropped. Indeed as photons are brought to a
full stop in a cavity, they indeed acquire a mass in the
usual sense of the word, both from the inertial and the
gravitational point-of-view.

Yes, that has been the viewpoint for quite some time (my computer is down at the moment)

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