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Torque through Maxwell Stress Tensor
Posted 24 feb 2016, 16:12 GMT-5 Low-Frequency Electromagnetics, RF & Microwave Engineering, Structural Mechanics Version 5.2 9 Replies
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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.
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 24 set 2016, 10:38 GMT-4
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Posted:
9 years ago
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
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
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Posted:
9 years ago
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
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
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Posted:
9 years ago
Hi!
Finally I found the solution.
Maxwell stress Tensor must be implemented and all operations become much easier.
Finally I found the solution.
Maxwell stress Tensor must be implemented and all operations become much easier.
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Posted:
9 years ago
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.
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Posted:
8 years ago
Hi, Yao,
I'm calculating the same model.Since that T=-intop(T crossproduct r). Seems you missed a minus sign?
I'm calculating the same model.Since that T=-intop(T crossproduct r). Seems you missed a minus sign?
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Posted:
8 years ago
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!
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!
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Posted:
8 years ago
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
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
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Posted:
8 years ago
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.
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Posted:
8 years ago
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.