PhD Memoirs #3 : A Silver Lining

This post is being made with some emotional elements. Readers who wish to understand the below details fully are advised to go through #1, #2 entries.
 

I received a mail today. And it may well turn out to be one of the most blessed ones related to my PhD studies. Certainly I will cherish this moment. Okay I will not keep the reader guessing any longer.

After the discovery mentioned in #2 I decided to write a mail to the 2nd author of 007 (who, very fortunately for me, is still alive and I sincerely hope is in good health!!!), informing him of my discovery and requesting his own comments on it. Here are a few excerpts of that mail:   



Repected Sir,

Greetings!

... This mail is regarding some doubts that I have in Dr. Adnan Niazy's PhD work (1974) on the surface displacement field generated by a moving line-source double-couple model in a homogenous elastic half-space.

I have not been able to understand the particular method of solving the improper integrals adopted by him but I have been able to solve them using Garvin's approach ('Exact Transient Solution of the Buried Line Source Problem', 1956). However, upon obtaining their numerical values (using MATLAB) I am unable to get an exact match between my results and those (given in the form of different plots) of his thesis.

In the paper 'Discrete Wavenumber Representation of Seimic-Source Wave Fields' authored by you and Dr. Aki, it is mentioned that there are some errors in his results in the form of 'unreal high frequency content'. I have been able to get an almost exact match between your results (Figure 9 of the same paper) and mine (please see pages 1 and 2 of attachment). Since I have solved it analytically, assuming it to be correct, my guess is that the slight mismatch is due to absence of contribution from high-frequency terms in your results on account of the summation over finite number of discrete frequencies. Could you kindly let me know what you think of it?

.... Sir, could you also give some of your own comments on this issue or refer someone else who can help in this regard.
In particular, I am interested in knowing whether my plots (pages 3 and 4 of attachment) of the horizontal and vertical displacement field generated due to a buried line-source with step-function time history, are correct. Currently, they do not match with Dr. Niazy's (Figures 6,7; pages 63,64 of his PhD thesis; also shown in the attachment).

This is important for my work since my subsequent computations for a more complex fault geometry are based on those results.

Thanking you!

Sincerely,
Varun Kumar Singla

I sent it on this week's  Saturday (11/1/2014) and got his reply a couple of hours back today (13/1/2014). I wasn't expecting any of the sort below:

Dear Varun Kumar Singla,

         The figures you sent me for the comparison between your calculation and DWN are excellent. Congratulations for solving this problem analytically. I know it is a challenging problem.

      ...I think you should just compare your solution with the discrete wavenumber method which has been thoroughly tested, and unfortunately not rely too much on Dr. Niazy's solution which at the time could not be tested against another method.

With my best wishes for the continuation of your work,
Michel Bouchon

After reading it I experienced a feeling of achievement and some sensation of pride after a long time, I think or least do not recall having felt it to such an extent. After a while I was also filled with gratitude towards Dr. Bouchon for his timely and affectionate reply, which I conveyed him to him properly a moment ago. 

I felt like doing moonwalk like Michael Jackson but sadly didn't know how to. So I simply decided to listen to some of Hans Zimmer's 'Man of Steel' soundtracks and boy, they gave a very different feeling... quite different from those that I have been getting while listening to them almost everyday. I was on my bicycle, heading towards my lab, with a renewed sense of motivation when I was listening to those tracks, and suddenly I had this vision in my mind - I was standing, encircled by Batman, Superman, Henry Barthes (the lead actor in the movie Detachment), Jack Harper (Tom Cruise' character in the movie Oblivion), Arnold Schwarzenegger (with his Terminator looks and outfit), just like the scene in Harry Potter and the Goblet of Fire movie in which Harry gets to talk with his parents after getting his wand connected with Voldemort... and they all shook my hands in a congratulatory manner and had a smile (unique one for every character) on their face. 

I guess I am now almost back to feeling normal again. I still have much more rivers to cross I guess. The difference now being that I know what it feels like to know when a particularly dangerous one has been crossed and I hope it makes all the difference! 

My advice (yup, it does seem very presumptuous of me even to me, but I have a strong feeling about it) to all other struggling, wrestling, stumbling, dreary, restless, withered, etc. PhD students: 

1) Hold on. Don't give up easily without a fight...!

2) Listening to 'Man of Steel', 'The Dark Knight', 'The Dark Knight Rises', 'Oblivion' soundtracks may help.

3) By all means try to get help from outside faculty if facing problems. I hope some of them turn out as nice and kind as Dr. Michel Bouchon!

4) Inspire and help to propagate a culture of collaboration and cooperation in research, both as a student and later on as an academician/researcher. Your help, however small, may be of high value (or even priceless) to the recipient.

One final remark : sense of satisfaction achieved after getting appreciated for one's honest labor and hard-work is seldom possible to get by other means, I think.