[CIG-SHORT] PyLith: Stresses not transmitted throughout the domain from Drichlet BCs on CUBIT Mesh

Brad Aagaard baagaard at usgs.gov
Tue Oct 20 15:33:56 PDT 2015 

On 10/20/2015 03:29 PM, Mamun Miah wrote:
> Thanks, Matt and Brad. Actually, I am using a fault similar to what has
> been demonstrated in the PyLith tutorial problems (step**.cfg) for
> hexahedral elements.
> Brad, I have tried with various combination of tolerances by keeping in
> mind that zero_tolerance be greater than the KSP atol and less than the
> SNES atol but did not get convergence.
>
> FYI, we at the LBNL have linked PyLith with a fluid flow simulation code
> TOUGH2 in order to simulate induced earthquakes from fluid injection. The
> coupled simulator is working fine. I am at the final stage of my PhD and in
> need of showing an application using this coupled approach. What would be
> the simplest way of modeling a fault in PyLith considering the convergence
> issue?

A reasonable application is a fault embedded within a domain, but 
extending to the surface. The friction solve will converge much more 
rapidly for this more realistic geometry.

Regards,
Brad


>
> Any suggestion would be appreciated.
>
> Thanks,
> Mamun
>
> On Tue, Oct 20, 2015 at 3:05 PM, Matthew Knepley <knepley at mcs.anl.gov>
> wrote:
>
>> On Tue, Oct 20, 2015 at 4:54 PM, Matthew Knepley <knepley at mcs.anl.gov>
>> wrote:
>>
>>> On Tue, Oct 20, 2015 at 1:35 PM, Mamun Miah <mmiah at go.olemiss.edu> wrote:
>>>
>>>> Please find attached.
>>>>
>>>
>>> Can you rerun without the -snes_view (and -ksp_view if you have it). That
>>> is a lot of noise here.
>>>
>>> It looks like the friction solver is not converging. That is pretty
>>> tricky and we have no theory for
>>> when it should work and fail. I will have to talk to Brad about this one.
>>>
>>
>> Okay, it looks like this is a through-going fault with friction. This can
>> be very very slow to converge
>> with our old formulation. We have an improved formulation with the next
>> release of PyLith. This
>> will have a better solution method.
>>
>>    Thanks,
>>
>>       Matt
>>
>>
>>>    Thanks,
>>>
>>>      Matt
>>>
>>>
>>>> Thanks,
>>>> Mamun
>>>>
>>>> On Tue, Oct 20, 2015 at 11:14 AM, Matthew Knepley <knepley at mcs.anl.gov>
>>>> wrote:
>>>>
>>>>> On Tue, Oct 20, 2015 at 12:29 PM, Mamun Miah <mmiah at go.olemiss.edu>
>>>>> wrote:
>>>>>
>>>>>> Hello Brad et al,
>>>>>>
>>>>>> Following your tips I was able to run my simulation smoothly for 10
>>>>>> years. Now when I increased the same problem for a simulation time of 100
>>>>>> years, I am getting SNESSolve convergence error: 'Nonlinear solve did not
>>>>>> converge due to DIVERGED_MAX_IT iterations 100.' After searching the log
>>>>>> file I have found the following; not sure if that's the root of this issue.
>>>>>>
>>>>>> "Line search: Cubic step no good, shrinking lambda, current gnorm
>>>>>> 9.815191568334e-05 lambda=1.3655042609323631e-01"
>>>>>>
>>>>>
>>>>> For any convergence question I need to see the output from
>>>>>
>>>>>    -snes_view -snes_monitor -ksp_monitor_true_residual
>>>>> -snes_converged_reason -ksp_converged_reason -snes_linesearch_monitor
>>>>>
>>>>>    Thanks,
>>>>>
>>>>>      Matt
>>>>>
>>>>>
>>>>>> I have tried your tips in the following threads:
>>>>>>
>>>>>> http://lists.geodynamics.org/pipermail/cig-short/2012-September/001129.html
>>>>>>
>>>>>> http://lists.geodynamics.org/pipermail/cig-short/2014-October/001881.html
>>>>>> http://lists.geodynamics.org/pipermail/cig-short/2015-July/002174.html
>>>>>>
>>>>>> Also, like Matt suggested in this link:
>>>>>> http://lists.geodynamics.org/pipermail/cig-short/2013-December/001555.html,
>>>>>> that using a
>>>>>>
>>>>>> fs_fieldsplit_0_pc_factor_shift_type nonzero
>>>>>>
>>>>>> for Lagrange multipliers weakens the preconditioner. Could it be an
>>>>>> issue?
>>>>>>
>>>>>> Finally, I have tried various PETSc options from 2015 tutorial but in
>>>>>> vain. I end up with the same SNESSolve error. I would really appreciate any
>>>>>> hints or suggestions in this regard.
>>>>>>
>>>>>> Attached are the relevant files.
>>>>>>
>>>>>> On Thu, Oct 15, 2015 at 5:14 PM, Mamun Miah <mmiah at go.olemiss.edu>
>>>>>> wrote:
>>>>>>
>>>>>>> Thanks, Matt for the clarification of the zero pivots related to
>>>>>>> fault. Yep, setting fieldslpit option along with pc_type = lu results in
>>>>>>> the convergence of the solution. Will make use of the 2015 tutorial like
>>>>>>> you suggested. Really appreciate Charles's, Matt's, and your help.
>>>>>>>
>>>>>>> On Thu, Oct 15, 2015 at 4:48 PM, Brad Aagaard <baagaard at usgs.gov>
>>>>>>> wrote:
>>>>>>>
>>>>>>>> If you tried to use lu with a fault, you will get zero pivots
>>>>>>>> because the Lagrange multiplier constraints have zero entries on the
>>>>>>>> diagonal. Using the fieldsplit settings (see examples/3d/tet4/step04.cfg)
>>>>>>>> will remedy this problem.
>>>>>>>>
>>>>>>>> I strongly recommend that you make use of the PyLith tutorial
>>>>>>>> information posted at
>>>>>>>> https://wiki.geodynamics.org/software:pylith:start. We have a lot
>>>>>>>> of hints on how to check your solution and debug. From the 2015 tutorial,
>>>>>>>> you will likely find the slides from Session I and the presentations for
>>>>>>>> Sessions III and IV most useful.
>>>>>>>>
>>>>>>>> Regards,
>>>>>>>> Brad
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> On 10/15/2015 04:35 PM, Matthew Knepley wrote:
>>>>>>>>
>>>>>>>>> On Thu, Oct 15, 2015 at 6:07 PM, Mamun Miah <mmiah at go.olemiss.edu>
>>>>>>>>> wrote:
>>>>>>>>>
>>>>>>>>> Dear Matt,
>>>>>>>>>>
>>>>>>>>>> I have tried with pc_type = lu, which shows zero pivots in the
>>>>>>>>>> matrices.
>>>>>>>>>> Did not realize that before setting pc_type = lu. Thanks a lot for
>>>>>>>>>> telling
>>>>>>>>>> me that. Then I have tried with pc_type = cholesky, which seems to
>>>>>>>>>> be
>>>>>>>>>> working now resulting in convergence of my problem.
>>>>>>>>>> Thanks to you and Charles again for guiding me in the right
>>>>>>>>>> direction to
>>>>>>>>>> investigate the problem further.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>> If you have zero pivots, that means your problem is
>>>>>>>>> under-constrained, and
>>>>>>>>> you need to fix the model.
>>>>>>>>>
>>>>>>>>>     Thanks,
>>>>>>>>>
>>>>>>>>>        Matt
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> On Thu, Oct 15, 2015 at 3:11 PM, Matthew Knepley <
>>>>>>>>>> knepley at mcs.anl.gov>
>>>>>>>>>> wrote:
>>>>>>>>>>
>>>>>>>>>> On Thu, Oct 15, 2015 at 4:26 PM, Mamun Miah <mmiah at go.olemiss.edu>
>>>>>>>>>>> wrote:
>>>>>>>>>>>
>>>>>>>>>>> Charles,
>>>>>>>>>>>>
>>>>>>>>>>>> Thanks again for your suggestion. I have reproduced the geometry
>>>>>>>>>>>> and
>>>>>>>>>>>> improved the mesh quality by checking with 'Allmetrics' in Cubit
>>>>>>>>>>>> (attached
>>>>>>>>>>>> below). Condition number is below 2 (1.606) and maximum aspect
>>>>>>>>>>>> ratio is 3.
>>>>>>>>>>>> Still I am getting the same convergence errors. I have also
>>>>>>>>>>>> tried the tips
>>>>>>>>>>>> found in the threads that Brad answered in the CIG-SHORT:
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>> Run with LU until you understand the system: --petsc.pc_type=lu
>>>>>>>>>>>
>>>>>>>>>>> There is an entire tutorial on the solvers which tells you to do
>>>>>>>>>>> this
>>>>>>>>>>> first.
>>>>>>>>>>>
>>>>>>>>>>>     Thanks,
>>>>>>>>>>>
>>>>>>>>>>>       Matt
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>> http://lists.geodynamics.org/pipermail/cig-short/2014-October/001885.html
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> http://lists.geodynamics.org/pipermail/cig-short/2012-September/001129.html
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Hex quality, 810 elements:
>>>>>>>>>>>>
>>>>>>>>>>>> ------------------------------------
>>>>>>>>>>>>
>>>>>>>>>>>> Function Name  Average  Std Dev   Minimum (id)    Maximum (id)
>>>>>>>>>>>>
>>>>>>>>>>>> -----------------     ---------   ---------      --------------
>>>>>>>>>>>> -------------
>>>>>>>>>>>>
>>>>>>>>>>>> Aspect Ratio 1.222e+00 6.289e-01 1.000e+00 (1) 3.000e+00 (724)
>>>>>>>>>>>>
>>>>>>>>>>>> Skew 8.104e-16 8.536e-16 0.000e+00 (10) 6.821e-15 (733)
>>>>>>>>>>>>
>>>>>>>>>>>> Taper 8.561e-16 8.748e-16 0.000e+00 (3) 6.845e-15 (736)
>>>>>>>>>>>>
>>>>>>>>>>>> Element Volume 2.500e+07 5.660e+06 9.000e+06 (733) 2.700e+07
>>>>>>>>>>>> (505)
>>>>>>>>>>>>
>>>>>>>>>>>> Stretch 9.330e-01 1.895e-01 3.974e-01 (782) 1.000e+00 (10)
>>>>>>>>>>>>
>>>>>>>>>>>> Diagonal Ratio 1.000e+00 4.591e-08 1.000e+00 (372) 1.000e+00 (10)
>>>>>>>>>>>>
>>>>>>>>>>>> Dimension 1.640e+02 2.602e+01 9.045e+01 (809) 1.732e+02 (315)
>>>>>>>>>>>>
>>>>>>>>>>>> Condition No. 1.067e+00 1.907e-01 1.000e+00 (3) 1.606e+00 (737)
>>>>>>>>>>>>
>>>>>>>>>>>> Jacobian 2.500e+07 5.660e+06 9.000e+06 (763) 2.700e+07 (315)
>>>>>>>>>>>>
>>>>>>>>>>>> Scaled Jacobian 1.000e+00 0.000e+00 1.000e+00 (248) 1.000e+00 (1)
>>>>>>>>>>>>
>>>>>>>>>>>> Shear 1.000e+00 0.000e+00 1.000e+00 (248) 1.000e+00 (1)
>>>>>>>>>>>>
>>>>>>>>>>>> Shape 9.648e-01 9.963e-02 6.832e-01 (737) 1.000e+00 (1)
>>>>>>>>>>>>
>>>>>>>>>>>> Relative Size 7.765e-01 2.288e-01 1.296e-01 (733) 8.573e-01 (487)
>>>>>>>>>>>>
>>>>>>>>>>>> Shear And Size 7.765e-01 2.288e-01 1.296e-01 (733) 8.573e-01
>>>>>>>>>>>> (487)
>>>>>>>>>>>>
>>>>>>>>>>>> Shape And Size 7.719e-01 2.418e-01 8.854e-02 (733) 8.573e-01
>>>>>>>>>>>> (487)
>>>>>>>>>>>>
>>>>>>>>>>>> Distortion 1.000e+00 5.167e-08 1.000e+00 (367) 1.000e+00 (11)
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Not sure what else I should try next. Please also see the
>>>>>>>>>>>> attached files.
>>>>>>>>>>>>
>>>>>>>>>>>> Thanks,
>>>>>>>>>>>> Mamun
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> On Wed, Oct 14, 2015 at 11:11 AM, Charles Williams <
>>>>>>>>>>>> willic3 at gmail.com>
>>>>>>>>>>>> wrote:
>>>>>>>>>>>>
>>>>>>>>>>>> Dear Mamun,
>>>>>>>>>>>>>
>>>>>>>>>>>>> Your linear convergence looks very slow.  You could increase
>>>>>>>>>>>>> the number
>>>>>>>>>>>>> of iterations, but I’m not sure if that would solve your
>>>>>>>>>>>>> problem.  I would
>>>>>>>>>>>>> start with a higher quality mesh.  Ideally, you would like to
>>>>>>>>>>>>> have a mesh
>>>>>>>>>>>>> where the condition number quality measure is less than 2 for
>>>>>>>>>>>>> the entire
>>>>>>>>>>>>> mesh, particularly for problems involving fault friction.  If
>>>>>>>>>>>>> this is too
>>>>>>>>>>>>> difficult to achieve using hexahedral elements, you might need
>>>>>>>>>>>>> to try
>>>>>>>>>>>>> tetrahedral elements.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Cheers,
>>>>>>>>>>>>> Charles
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> On 15/10/2015, at 6:09 am, Mamun Miah <mmiah at go.olemiss.edu>
>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>> Thanks, Charles. Your comments are very helpful. I have been
>>>>>>>>>>>>> going
>>>>>>>>>>>>> through each of your comments and discovered that both KSPSolve
>>>>>>>>>>>>> and
>>>>>>>>>>>>> SNESSolve do not converge when I uncommented corresponding flag
>>>>>>>>>>>>> options. So
>>>>>>>>>>>>> I figured the problem is with the mesh creation. Also set the
>>>>>>>>>>>>> the
>>>>>>>>>>>>> normalizer according to the smallest mesh dimension. Attached
>>>>>>>>>>>>> here is the
>>>>>>>>>>>>> log file in case you want to see.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Thanks again,
>>>>>>>>>>>>> Mamun
>>>>>>>>>>>>>
>>>>>>>>>>>>> On Tue, Oct 13, 2015 at 12:37 PM, Charles Williams <
>>>>>>>>>>>>> willic3 at gmail.com>
>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>> Dear Mamun,
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> It is a bit difficult to diagnose your problem without more
>>>>>>>>>>>>>> information.  However, here are several potential problems:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> 1.  First of all, the mesh you’re using is not of very high
>>>>>>>>>>>>>> quality.
>>>>>>>>>>>>>> The method you’ve used for refinement is pretty crude, and
>>>>>>>>>>>>>> will never
>>>>>>>>>>>>>> result in high quality elements. Trelis/Cubit has a number of
>>>>>>>>>>>>>> more powerful
>>>>>>>>>>>>>> methods for creating a high quality mesh, and I would take
>>>>>>>>>>>>>> advantage of
>>>>>>>>>>>>>> those.
>>>>>>>>>>>>>> 2.  It is unclear why you have set the normalization length
>>>>>>>>>>>>>> scale to 1
>>>>>>>>>>>>>> m, since I believe this is much smaller than your smallest
>>>>>>>>>>>>>> element.
>>>>>>>>>>>>>> 3.  There is no indication of whether the linear and nonlinear
>>>>>>>>>>>>>> solutions are converging, since you have turned off all the
>>>>>>>>>>>>>> solution
>>>>>>>>>>>>>> monitoring options, including the journal options.  You should
>>>>>>>>>>>>>> never do
>>>>>>>>>>>>>> this, as there is then no way to tell what has happened with
>>>>>>>>>>>>>> your solution.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> You should try running your problem again with all the solution
>>>>>>>>>>>>>> monitoring options turned back on, and save the results to a
>>>>>>>>>>>>>> log file.
>>>>>>>>>>>>>> This will help us diagnose your problem further.  I would also
>>>>>>>>>>>>>> try
>>>>>>>>>>>>>> improving your mesh quality and selecting a normalization
>>>>>>>>>>>>>> length scale that
>>>>>>>>>>>>>> is appropriate for your mesh (~equal to the smallest cell
>>>>>>>>>>>>>> dimension).
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Cheers,
>>>>>>>>>>>>>> Charles
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> On 14/10/2015, at 6:26 am, Mamun Miah <mmiah at go.olemiss.edu>
>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Hello Developers,
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> I have created the attached geometry (5kmx5kmx4.1km) in CUBIT.
>>>>>>>>>>>>>> It has
>>>>>>>>>>>>>> three layer of materials (2000m+100m+200m) and a vertical
>>>>>>>>>>>>>> fault (along Z
>>>>>>>>>>>>>> axis) 1000m to the left from the positive X-plane boundary.
>>>>>>>>>>>>>> The exported
>>>>>>>>>>>>>> Exodus mesh is then used to run a PyLith simulation with
>>>>>>>>>>>>>> Dirichlet
>>>>>>>>>>>>>> displacement and displacement rate BCs (e.g. PyLith Tutorial
>>>>>>>>>>>>>> 'step12.cfg')
>>>>>>>>>>>>>> on +x and -x sides. The simulation runs fine but even after
>>>>>>>>>>>>>> running for 100
>>>>>>>>>>>>>> years I don't see any stress being transmitted to the interior
>>>>>>>>>>>>>> domain. All
>>>>>>>>>>>>>> I can see is the stress changes in the boundary elements where
>>>>>>>>>>>>>> the
>>>>>>>>>>>>>> Dirichlet BCs are applied. I am not sure if it is caused by
>>>>>>>>>>>>>> improper
>>>>>>>>>>>>>> meshing or boundary conditions.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Attached also are the .cfg files, geometry journal file, and
>>>>>>>>>>>>>> stress
>>>>>>>>>>>>>> output file from simulation. I would highly appreciate any
>>>>>>>>>>>>>> help.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> --
>>>>>>>>>>>>>> Thanks & Best Regards,
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Mamun Miah
>>>>>>>>>>>>>> Graduate Research Assistant
>>>>>>>>>>>>>> Department of Civil Engineering
>>>>>>>>>>>>>> The University of Mississippi
>>>>>>>>>>>>>> Oxford, MS 38655
>>>>>>>>>>>>>> Phone: (662)-801-1904
>>>>>>>>>>>>>> Website: http://www.linkedin.com/pub/mamun-miah-eit/21/53/339
>>>>>>>>>>>>>> <geometry.jpg><application.cfg><pylithapp.cfg><visit0000.png>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> <application.jou>_______________________________________________
>>>>>>>>>>>>>> CIG-SHORT mailing list
>>>>>>>>>>>>>> CIG-SHORT at geodynamics.org
>>>>>>>>>>>>>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Charles A. Williams
>>>>>>>>>>>>>> Scientist
>>>>>>>>>>>>>> GNS Science
>>>>>>>>>>>>>> 1 Fairway Drive, Avalon
>>>>>>>>>>>>>> PO Box 30368
>>>>>>>>>>>>>> Lower Hutt  5040
>>>>>>>>>>>>>> New Zealand
>>>>>>>>>>>>>> ph (office): 0064-4570-4566
>>>>>>>>>>>>>> fax (office): 0064-4570-4600
>>>>>>>>>>>>>> C.Williams at gns.cri.nz
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> _______________________________________________
>>>>>>>>>>>>>> CIG-SHORT mailing list
>>>>>>>>>>>>>> CIG-SHORT at geodynamics.org
>>>>>>>>>>>>>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> --
>>>>>>>>>>>>> Thanks & Best Regards,
>>>>>>>>>>>>>
>>>>>>>>>>>>> Mamun Miah
>>>>>>>>>>>>> Graduate Research Assistant
>>>>>>>>>>>>> Department of Civil Engineering
>>>>>>>>>>>>> The University of Mississippi
>>>>>>>>>>>>> Oxford, MS 38655
>>>>>>>>>>>>> Phone: (662)-801-1904
>>>>>>>>>>>>> Website: http://www.linkedin.com/pub/mamun-miah-eit/21/53/339
>>>>>>>>>>>>> <log>_______________________________________________
>>>>>>>>>>>>> CIG-SHORT mailing list
>>>>>>>>>>>>> CIG-SHORT at geodynamics.org
>>>>>>>>>>>>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Charles A. Williams
>>>>>>>>>>>>> Scientist
>>>>>>>>>>>>> GNS Science
>>>>>>>>>>>>> 1 Fairway Drive, Avalon
>>>>>>>>>>>>> PO Box 30368
>>>>>>>>>>>>> Lower Hutt  5040
>>>>>>>>>>>>> New Zealand
>>>>>>>>>>>>> ph (office): 0064-4570-4566
>>>>>>>>>>>>> fax (office): 0064-4570-4600
>>>>>>>>>>>>> C.Williams at gns.cri.nz
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> _______________________________________________
>>>>>>>>>>>>> CIG-SHORT mailing list
>>>>>>>>>>>>> CIG-SHORT at geodynamics.org
>>>>>>>>>>>>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> --
>>>>>>>>>>>> Thanks & Best Regards,
>>>>>>>>>>>>
>>>>>>>>>>>> Mamun Miah
>>>>>>>>>>>> Graduate Research Assistant
>>>>>>>>>>>> Department of Civil Engineering
>>>>>>>>>>>> The University of Mississippi
>>>>>>>>>>>> Oxford, MS 38655
>>>>>>>>>>>> Phone: (662)-801-1904
>>>>>>>>>>>> Website: http://www.linkedin.com/pub/mamun-miah-eit/21/53/339
>>>>>>>>>>>>
>>>>>>>>>>>> _______________________________________________
>>>>>>>>>>>> CIG-SHORT mailing list
>>>>>>>>>>>> CIG-SHORT at geodynamics.org
>>>>>>>>>>>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> --
>>>>>>>>>>> What most experimenters take for granted before they begin their
>>>>>>>>>>> experiments is infinitely more interesting than any results to
>>>>>>>>>>> which their
>>>>>>>>>>> experiments lead.
>>>>>>>>>>> -- Norbert Wiener
>>>>>>>>>>>
>>>>>>>>>>> _______________________________________________
>>>>>>>>>>> CIG-SHORT mailing list
>>>>>>>>>>> CIG-SHORT at geodynamics.org
>>>>>>>>>>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> --
>>>>>>>>>> Thanks & Best Regards,
>>>>>>>>>>
>>>>>>>>>> Mamun Miah
>>>>>>>>>> Graduate Research Assistant
>>>>>>>>>> Department of Civil Engineering
>>>>>>>>>> The University of Mississippi
>>>>>>>>>> Oxford, MS 38655
>>>>>>>>>> Phone: (662)-801-1904
>>>>>>>>>> Website: http://www.linkedin.com/pub/mamun-miah-eit/21/53/339
>>>>>>>>>>
>>>>>>>>>> _______________________________________________
>>>>>>>>>> CIG-SHORT mailing list
>>>>>>>>>> CIG-SHORT at geodynamics.org
>>>>>>>>>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> _______________________________________________
>>>>>>>>> CIG-SHORT mailing list
>>>>>>>>> CIG-SHORT at geodynamics.org
>>>>>>>>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>>>>>>>>>
>>>>>>>>>
>>>>>>>> _______________________________________________
>>>>>>>> CIG-SHORT mailing list
>>>>>>>> CIG-SHORT at geodynamics.org
>>>>>>>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> --
>>>>>>> Thanks & Best Regards,
>>>>>>>
>>>>>>> Mamun Miah
>>>>>>> Graduate Research Assistant
>>>>>>> Department of Civil Engineering
>>>>>>> The University of Mississippi
>>>>>>> Oxford, MS 38655
>>>>>>> Phone: (662)-801-1904
>>>>>>> Website: http://www.linkedin.com/pub/mamun-miah-eit/21/53/339
>>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>> --
>>>>>> Thanks & Best Regards,
>>>>>>
>>>>>> Mamun Miah
>>>>>> Graduate Research Assistant
>>>>>> Department of Civil Engineering
>>>>>> The University of Mississippi
>>>>>> Oxford, MS 38655
>>>>>> Phone: (662)-801-1904
>>>>>> Website: http://www.linkedin.com/pub/mamun-miah-eit/21/53/339
>>>>>>
>>>>>> _______________________________________________
>>>>>> CIG-SHORT mailing list
>>>>>> CIG-SHORT at geodynamics.org
>>>>>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>>>>>>
>>>>>
>>>>>
>>>>>
>>>>> --
>>>>> What most experimenters take for granted before they begin their
>>>>> experiments is infinitely more interesting than any results to which their
>>>>> experiments lead.
>>>>> -- Norbert Wiener
>>>>>
>>>>> _______________________________________________
>>>>> CIG-SHORT mailing list
>>>>> CIG-SHORT at geodynamics.org
>>>>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>>>>>
>>>>
>>>>
>>>>
>>>> --
>>>> Thanks & Best Regards,
>>>>
>>>> Mamun Miah
>>>> Graduate Research Assistant
>>>> Department of Civil Engineering
>>>> The University of Mississippi
>>>> Oxford, MS 38655
>>>> Phone: (662)-801-1904
>>>> Website: http://www.linkedin.com/pub/mamun-miah-eit/21/53/339
>>>>
>>>> _______________________________________________
>>>> CIG-SHORT mailing list
>>>> CIG-SHORT at geodynamics.org
>>>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>>>>
>>>
>>>
>>>
>>> --
>>> What most experimenters take for granted before they begin their
>>> experiments is infinitely more interesting than any results to which their
>>> experiments lead.
>>> -- Norbert Wiener
>>>
>>
>>
>>
>> --
>> What most experimenters take for granted before they begin their
>> experiments is infinitely more interesting than any results to which their
>> experiments lead.
>> -- Norbert Wiener
>>
>> _______________________________________________
>> CIG-SHORT mailing list
>> CIG-SHORT at geodynamics.org
>> http://lists.geodynamics.org/cgi-bin/mailman/listinfo/cig-short
>>
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