Has Anybody Been in this Situation Before? (Masters Thesis/Advisor)

[womfalcs3]

I'm working on a project with a professor for my MS. It's computational, and I am currently stuck at a critical point. I can physically justify some assumptions and get the model to work, but I can't do so mathematically. They would be mathematically arbitrary.

I'm working to resolve this problem through more research, but it doesn't seem anybody has solved this specific problem before.

I show him what I've done, and he looks clueless. As if he doesn't know why I'm required to do what I have done, even though my premise is correct.

So I don't know how to mathematically derive the arbitrary values I used, and he doesn't even know what I'm doing, and doesn't have any clue as to how to go about deriving such values.

What am I supposed to do? I'll continue researching and/or hope for a breakthrough, but what if I don't have one? I can't defend my thesis by doing what I've done. Especially given one of the committee members is a math professor, and I just know he's going to grill me for the approximations I've used throughout this project anyway. I can't compound that by using mathematically arbitrary values. He's not going to be thrilled.

The engineering members of the committee I can probably convince if the results are empirically verified, but not a mathematician.

I don't have to defend for another 10 months, but I'm nervous about my status. I don't have much left to do after I can mathematically derive the values in question and get good results, but that's another issue. I need to give myself a lot of time to make sure my results are empirically verified, and make revision accordingly.

 

[Choppy]

Most graduate students reach a point where they know more about their project than their advisor - so this isn't at all uncommon.

Perhaps you may need to put more effort into explaining your problem. Sometimes a supervisor sees only the "bigger picture" and doesn't appreciate the details.

Another option you have is to seek advice from your committee members - including this math professor who you suspect is going to grill you. A committee is there to assist and guide the student, not simply act as judge, jury and executioner.

I have to say that I find the specifics of your problem a little confusing. You have input some parameters to get your computer model to work. At one point you say they are arbitrary, which I take to mean you fiddled around until you got something that works, but then later you say they are empirical, which I take to mean they are parameters that come from a fit to some experimental data. As long as there is not a problem with the data and you understand how uncertainties in the data translate into uncertainties in your parameters (and therefore uncertainties in your results), there is nothing wrong with an empirical result.

It is, however, nice to have a result derived directly from first principles, so I wouldn't give up this pursuit.

 

[millitiz]

Well, I think the OP meant that if his stimulation was empirically verified, then he could convince the engineer prof in the committee, at least that is how I took it. And about the arbitrary thing, I think he meant that he could make this assumption as a physics, but as a mathematician, these assumptions are arbitrary and could not be proved through rigorous proof.

I think that is pretty normal, about the could-not-prove it part.
Maybe these arbitrary assumption could be derived by the fact that your domain is in R^n, real domain? With that assumption, maybe some of your arbitrary assumptions are no longer arbitrary?
Anyway, good luck!

 

[womfalcs3]

My questions to him were questions that anybody in theoretical heat transfer would know. At least the methodology behind my calculations.

I love the guy, but I'm worried now that neither he or I know where to go from here. I have all summer with no courses to dedicate my time to the project, but I don't want to wake up everyday just to do the same thing over and over and over again (i.e. researching published journal articles. I've already spent dozens of hours doing this for this specific issue.).

I'm working on a heat transfer problem, and the only empirical data I have is for the heat flux.

I'm solving a system of PDE's using approximation methods. The parameters in question are values used in solving the system. They're properties of the flow.

What I meant by empirically comparing data is to find the heat flux computationally using these hypothetical values (Yes. I used trial-and-error to find a value that gets the model to yield reasonable results.), then compare it to the experimental results.

My professor has that data, and he says he'll need some time to get them to me. I'm just worried.

 

[junglebeast]

So I don't know how to mathematically derive the arbitrary values I used, and he doesn't even know what I'm doing, and doesn't have any clue as to how to go about deriving such values.

My advisor doesn't have a clue what I'm doing either. But your question is a bit too ambiguous for anyone to even know what you're talking about enough to propose a solution.

Are these arbitrary values you are mentioning just constant parameters of the model representing real world quantities that are then used in theoretically justified experiments? If so, then using any constant should result in a realistic result because different values of the constants just represent different real life situations...and as such, picking them by trial and error is perfectly acceptable. Or alternatively, you should know the units on those constants, and be able to use that to loosely justify some approximate values based on some real world measurements.

Or are these arbitrary values more than just the simple parameters? If you think the math professor is the one who would be likely to grill you on it, then why don't you talk to him for advice first and see what he thinks

 

[atyy]

What I meant by empirically comparing data is to find the heat flux computationally using these hypothetical values (Yes. I used trial-and-error to find a value that gets the model to yield reasonable results.), then compare it to the experimental results.

Nothing wrong with that. Basically you have a model, and you need some way of determining the parameters given the experimental data. For some classes of models, eg. straight lines you have standard ways of finding the best fit parameters eg. linear regression. If you don't have that, I don't see why a computational search of parameter space isn't ok. For example, I think these guys got interesting results: http://www.ncbi.nlm.nih.gov/pubmed/...nel.Pubmed_DefaultReportPanel.Pubmed_RVDocSum