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Torque through Maxwell Stress Tensor

Posted 2016年2月24日 GMT-5 16:12 Low-Frequency Electromagnetics, RF & Microwave Engineering, Structural Mechanics Version 5.2 9 Replies

Nuno de Sousa
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Dear all:

Recently I tried to implement a similar problem to the one presented in the following poster. The goal is to obtain the force and the torque over a particle that is illuminated by an electromagnetic wave.
www.comsol.com/paper/download/182313/siler_poster.pdf

The force is obtained by integration of the quantity dnTx over a surface that surrounds the particle.
However, I cannot implement the torque because I cannot have access to the Maxwell stress tensor components.
Also I cannot find the quantity dnTx/unTx (upward and downward Maxwell Stress Tensor) in any classical book of electrodynamics (Jackson, Born and Wolf, Landau, Stratton...). I cannot see the difference between quantities. Probably are the projections of the Maxwell stress tensor over the vector perpendicular to the surface, but I would like to confirm this. Thus, it should be exactly the same use dnTx or unTx (except a sign), right?

Can someone help me?
Many thanks in advance.

The expression of the toque is the following:
integral(n \cdot (T x r), surface)
Also is written in the poster cited previously.
9 Replies Last Post 2016年9月24日 GMT-4 10:38
Jens Krause
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Posted: 9 years ago 2016年2月25日 GMT-5 04:49
Hi,

the up and down values can be different on material interfaces. There, the stress tensor
has a jump discontinuity.

I don't have the RF module, but in ACDC physicses there is a force computation feature.
Have you tried this? That should do all the integrations as you need them.

Regards

Jens
Hi, the up and down values can be different on material interfaces. There, the stress tensor has a jump discontinuity. I don't have the RF module, but in ACDC physicses there is a force computation feature. Have you tried this? That should do all the integrations as you need them. Regards Jens
Nuno de Sousa
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Posted: 9 years ago 2016年2月25日 GMT-5 05:04
Hi Jens.

Many thanks for your answer.
I can calculate the force by integrating the dnTx over a particle surrounding surface.

Fx = int_surf(emw.dnTx)
Fy = int_surf(emw.dnTy)
Fz = int_surf(emw.dnTz)

and the results are satisfatory compared with Mie theory.
However, I don't know how to implement the torque that is given by the expression:

\int_{S}{\mathbf{n}\cdot(T\times\mathbf{r})}

also written the the paper cited previously.

Many thanks
Hi Jens. Many thanks for your answer. I can calculate the force by integrating the dnTx over a particle surrounding surface. Fx = int_surf(emw.dnTx) Fy = int_surf(emw.dnTy) Fz = int_surf(emw.dnTz) and the results are satisfatory compared with Mie theory. However, I don't know how to implement the torque that is given by the expression: \int_{S}{\mathbf{n}\cdot(T\times\mathbf{r})} also written the the paper cited previously. Many thanks
Nuno de Sousa
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Posted: 9 years ago 2016年2月29日 GMT-5 03:17
Hi!

Finally I found the solution.

Maxwell stress Tensor must be implemented and all operations become much easier.
Hi! Finally I found the solution. Maxwell stress Tensor must be implemented and all operations become much easier.
Haizi Yao
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Posted: 9 years ago 2016年3月18日 GMT-4 03:03

Hi!

Finally I found the solution.

Maxwell stress Tensor must be implemented and all operations become much easier.


Dear Nuno,

Is your formula of the Torque using Maxwell stress Tensor like the below ?

Torque_x=emw.dnTy*z-emw.dnTz*y

Torque_y=emw.dnTz*x-emw.dnTx*z

Torque_z=emw.dnTx*y-emw.dnTy*x

(it was supposed that the rotational central point is at the origin points with coordinate (0,0,0) )

Looking forward to your reply, Thx.
[QUOTE] Hi! Finally I found the solution. Maxwell stress Tensor must be implemented and all operations become much easier. [/QUOTE] Dear Nuno, Is your formula of the Torque using Maxwell stress Tensor like the below ? Torque_x=emw.dnTy*z-emw.dnTz*y Torque_y=emw.dnTz*x-emw.dnTx*z Torque_z=emw.dnTx*y-emw.dnTy*x (it was supposed that the rotational central point is at the origin points with coordinate (0,0,0) ) Looking forward to your reply, Thx.
Huatian Hu
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Posted: 8 years ago 2016年6月2日 GMT-4 22:49
Hi, Yao,

I'm calculating the same model.Since that T=-intop(T crossproduct r). Seems you missed a minus sign?


Hi, Yao, I'm calculating the same model.Since that T=-intop(T crossproduct r). Seems you missed a minus sign?
Huatian Hu
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Posted: 8 years ago 2016年6月2日 GMT-4 23:03
Hi!
I've the same questions. It puzzle me a lot that what's the difference between ewfd.dnTx and ewfd.unTx.
And all of you use F=intop(ewfd.dnTx), why not unTx instead?Is there a direction in it?

I've tried both, it turns out that the sign of the results are reversed(the sphere is not the boundary of particle and medium, I generated a sphere over it in the surrounding medium so the tensor is continue).So I don't understand clearly.

Waiting for reply~
Thank!
Hi! I've the same questions. It puzzle me a lot that what's the difference between ewfd.dnTx and ewfd.unTx. And all of you use F=intop(ewfd.dnTx), why not unTx instead?Is there a direction in it? I've tried both, it turns out that the sign of the results are reversed(the sphere is not the boundary of particle and medium, I generated a sphere over it in the surrounding medium so the tensor is continue).So I don't understand clearly. Waiting for reply~ Thank!
Yuhua Yang
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Posted: 8 years ago 2016年6月14日 GMT-4 16:10
Dear Nunoé

I am also to caculate the Torque through Maxwell Stress Tensor of the NPs particles.
I ask for your help to clear how to solve this problem.
I have caculate the Maxwell Stress Tensor.

Thanks a lot!
Have a good day!




Yuhua
yuhua.yang.1@ulaval.ca
Dear Nunoé I am also to caculate the Torque through Maxwell Stress Tensor of the NPs particles. I ask for your help to clear how to solve this problem. I have caculate the Maxwell Stress Tensor. Thanks a lot! Have a good day! Yuhua yuhua.yang.1@ulaval.ca
Haizi Yao
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Posted: 8 years ago 2016年9月24日 GMT-4 10:31

Hi!
I've the same questions. It puzzle me a lot that what's the difference between ewfd.dnTx and ewfd.unTx.
And all of you use F=intop(ewfd.dnTx), why not unTx instead?Is there a direction in it?

I've tried both, it turns out that the sign of the results are reversed(the sphere is not the boundary of particle and medium, I generated a sphere over it in the surrounding medium so the tensor is continue).So I don't understand clearly.

Waiting for reply~
Thank!


Dear Huatian Hu,

you can refer to the previous discussion (cn.comsol.com/community/forums/general/thread/39198). The choice depend on your model geometry. A "trial and error" step is strongly suggested for any problem that is relate to MST.
[QUOTE] Hi! I've the same questions. It puzzle me a lot that what's the difference between ewfd.dnTx and ewfd.unTx. And all of you use F=intop(ewfd.dnTx), why not unTx instead?Is there a direction in it? I've tried both, it turns out that the sign of the results are reversed(the sphere is not the boundary of particle and medium, I generated a sphere over it in the surrounding medium so the tensor is continue).So I don't understand clearly. Waiting for reply~ Thank! [/QUOTE] Dear Huatian Hu, you can refer to the previous discussion (http://cn.comsol.com/community/forums/general/thread/39198). The choice depend on your model geometry. A "trial and error" step is strongly suggested for any problem that is relate to MST.
Haizi Yao
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Posted: 8 years ago 2016年9月24日 GMT-4 10:38

Dear Nunoé

I am also to caculate the Torque through Maxwell Stress Tensor of the NPs particles.
I ask for your help to clear how to solve this problem.
I have caculate the Maxwell Stress Tensor.

Thanks a lot!
Have a good day!




Yuhua
yuhua.yang.1@ulaval.ca


Dear Yuhua,
I think the off-diagonal elements of the stress tensor, not just the diagonal elements ,i.e, emw.dnTx,y,z, is the must to calculate the torque. Maybe we should define the every elements of MST through the variables in COMSOL, then use them in the integration of the shear force. I am not sure. Hope have a further discussion with you.
[QUOTE] Dear Nunoé I am also to caculate the Torque through Maxwell Stress Tensor of the NPs particles. I ask for your help to clear how to solve this problem. I have caculate the Maxwell Stress Tensor. Thanks a lot! Have a good day! Yuhua yuhua.yang.1@ulaval.ca [/QUOTE] Dear Yuhua, I think the off-diagonal elements of the stress tensor, not just the diagonal elements ,i.e, emw.dnTx,y,z, is the must to calculate the torque. Maybe we should define the every elements of MST through the variables in COMSOL, then use them in the integration of the shear force. I am not sure. Hope have a further discussion with you.

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