Dear Dr. Guyer,
Thanks very much for your reply but I still have several questions in mind.
(1) With respect to my question (2), as far as I understand, you said dbdpsi=d(beta)/d(psi). However, referring to page 65, A=alpha**2*c*(1+c*beta)*[d(Phi)/d(psi)], and the program on page 66, A=alpha**2*c*(1+c*beta)*dbdpsi, I suspect that dbdpsi=[d(Phi)/d(psi)], but I can not see that [d(Phi)/d(psi)]=-N*2*Phi/(1+PhiSq).
(2) With respect to my question (5), I tried to leave the program running for about 16 hours and the program reached 7640 steps, however, I still can not see anything in the two figures on my screen. Could you please have a look and see if there is anything wrong in the program I sent to you previously?
(3) You mentioned Ryo Kobayashi’s Fortran code and I am wondering whether his Fortran code is accessible somewhere to the public? Just for interest, for this particular program, how long it takes for his Fortran code to run?
Thanks and regards,
Zhiheng Huang
----- Original Message ----
From: Jonathan Guyer <[EMAIL PROTECTED]>
To: Multiple recipients of list <[email protected]>
Sent: Friday, 7 April, 2006 7:30:38 PM
Subject: Re: Questions regarding Module exampes.phase.anisotropy.input
On Apr 7, 2006, at 12:46 PM, Zhiheng Huang wrote:
> Could anyone of you answer my questions in the attached
> QFiPy060407.pdf?
> (1) What is \theta in the equation \Phi = \tan(\theta/2 + (N/2)
> arctan\psi)?
\theta is the grain orientation. Taken to be zero in this single-
grain problem. For any questions of mathematical notation, please see
the paper cited at the beginning of the chapter:
James A. Warren, Ryo Kobayashi, Alexander E. Lobkovsky, and W. Craig
Carter, “Extending Phase
Field Models of Solidification to Polycrystalline Materials”. Acta
Materialia, 51(20), (2003) 6035–6058,
URL http://dx.doi.org/10.1016/S1359-6454(03)00388-4 31, 59
> (2) ... dbdpsi=-N*2*Phi/(1+PhiSq), I do not know whether dbdpsi is
> equal to \Phi_\psi?
dbdpsi = d \beta / d \psi = \beta_\psi
> (3) On page 34, it is clearly stated that "ExplicitDiffusionTerm is
> provided only for
> illustrative purposes", but why on page 67, the diffusion term in
> phaseEq is
> constructed using the "ExplicitDiffusionTerm"?
In order to have a reliable benchmark, Daniel wrote this example to
give exact numerical correspondence with Ryo Kobayashi's FORTRAN
code. We don't know why Ryo made this particular term explicit. This
choice on our part isn't ideal for exactly the reason you raise; we
recommend the one, but then use the other. I guess I can only offer
my parents' response to me as a child: "Do as we say, not as we do".
> Would the result be the same if using
> the "ImplictDiffusionTerm" instead?
Not exactly the same, but it should be consistent. In general, we
certainly recommend the ImplicitDiffusionTerm.
> (4) On page 34, when constructing the implicit source term, why is
> it necessary to test
> whether mVar is greater than zero or less than zero? In the case
> of mVar < 0, how the
> ImplicitSourceTerm in the program could match \nabla A \nabla \zeta
> + \phi(1-\phi)m ?
Have you worked through Example 9.1 examples.phase.simple.input ? The
rationale for exactly how to linearize a source is discussed there.
Let us know if we can further clear things up.
> (5) I wish to see the dendritic growth and therefore, I have
> changed the parameters as
> requested on page 65, i.e. numberOfCells=500, steps=10000,
> radius=dx*5.,
> seedCenter=(0.,0,), initialTemperature=-0.5. The program is
> attached. The program
> runs slowly as expected but why I could not see any structure even
> after 155 steps?
I don't recall how many steps it takes, but quite a few. There is no
explicit noise in this problem, only the noise resulting from the
discreteness of the mesh, so it takes a while for branching to be
observable.
--
Jonathan E. Guyer, PhD
Metallurgy Division
National Institute of Standards and Technology
<http://www.metallurgy.nist.gov/>
Thanks very much for your reply but I still have several questions in mind.
(1) With respect to my question (2), as far as I understand, you said dbdpsi=d(beta)/d(psi). However, referring to page 65, A=alpha**2*c*(1+c*beta)*[d(Phi)/d(psi)], and the program on page 66, A=alpha**2*c*(1+c*beta)*dbdpsi, I suspect that dbdpsi=[d(Phi)/d(psi)], but I can not see that [d(Phi)/d(psi)]=-N*2*Phi/(1+PhiSq).
(2) With respect to my question (5), I tried to leave the program running for about 16 hours and the program reached 7640 steps, however, I still can not see anything in the two figures on my screen. Could you please have a look and see if there is anything wrong in the program I sent to you previously?
(3) You mentioned Ryo Kobayashi’s Fortran code and I am wondering whether his Fortran code is accessible somewhere to the public? Just for interest, for this particular program, how long it takes for his Fortran code to run?
Thanks and regards,
Zhiheng Huang
----- Original Message ----
From: Jonathan Guyer <[EMAIL PROTECTED]>
To: Multiple recipients of list <[email protected]>
Sent: Friday, 7 April, 2006 7:30:38 PM
Subject: Re: Questions regarding Module exampes.phase.anisotropy.input
On Apr 7, 2006, at 12:46 PM, Zhiheng Huang wrote:
> Could anyone of you answer my questions in the attached
> QFiPy060407.pdf?
> (1) What is \theta in the equation \Phi = \tan(\theta/2 + (N/2)
> arctan\psi)?
\theta is the grain orientation. Taken to be zero in this single-
grain problem. For any questions of mathematical notation, please see
the paper cited at the beginning of the chapter:
James A. Warren, Ryo Kobayashi, Alexander E. Lobkovsky, and W. Craig
Carter, “Extending Phase
Field Models of Solidification to Polycrystalline Materials”. Acta
Materialia, 51(20), (2003) 6035–6058,
URL http://dx.doi.org/10.1016/S1359-6454(03)00388-4 31, 59
> (2) ... dbdpsi=-N*2*Phi/(1+PhiSq), I do not know whether dbdpsi is
> equal to \Phi_\psi?
dbdpsi = d \beta / d \psi = \beta_\psi
> (3) On page 34, it is clearly stated that "ExplicitDiffusionTerm is
> provided only for
> illustrative purposes", but why on page 67, the diffusion term in
> phaseEq is
> constructed using the "ExplicitDiffusionTerm"?
In order to have a reliable benchmark, Daniel wrote this example to
give exact numerical correspondence with Ryo Kobayashi's FORTRAN
code. We don't know why Ryo made this particular term explicit. This
choice on our part isn't ideal for exactly the reason you raise; we
recommend the one, but then use the other. I guess I can only offer
my parents' response to me as a child: "Do as we say, not as we do".
> Would the result be the same if using
> the "ImplictDiffusionTerm" instead?
Not exactly the same, but it should be consistent. In general, we
certainly recommend the ImplicitDiffusionTerm.
> (4) On page 34, when constructing the implicit source term, why is
> it necessary to test
> whether mVar is greater than zero or less than zero? In the case
> of mVar < 0, how the
> ImplicitSourceTerm in the program could match \nabla A \nabla \zeta
> + \phi(1-\phi)m ?
Have you worked through Example 9.1 examples.phase.simple.input ? The
rationale for exactly how to linearize a source is discussed there.
Let us know if we can further clear things up.
> (5) I wish to see the dendritic growth and therefore, I have
> changed the parameters as
> requested on page 65, i.e. numberOfCells=500, steps=10000,
> radius=dx*5.,
> seedCenter=(0.,0,), initialTemperature=-0.5. The program is
> attached. The program
> runs slowly as expected but why I could not see any structure even
> after 155 steps?
I don't recall how many steps it takes, but quite a few. There is no
explicit noise in this problem, only the noise resulting from the
discreteness of the mesh, so it takes a while for branching to be
observable.
--
Jonathan E. Guyer, PhD
Metallurgy Division
National Institute of Standards and Technology
<http://www.metallurgy.nist.gov/>
