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I have a bunch of aux functions and constants

S=1; ja=0.98; jb=1; jc=0.0004; j2=0.52; d=0.00143; T=0.001

omega [s_, d_, T_, x_, y_, z_] = Sqrt[(2 s (ja - jb + 2 j2 + jb Cos[y] + 
   d theta))^2 - (2 s (ja Cos[x] + jc Cos[z] + 
   2 j2 Cos[x] Cos[y]))^2] // Simplify

theta = 1 - s/(2 S) (1 + 2 F[s, d, T]) // Simplify

F[s_, d_, T_] := 
 1/(2 π)^3 NIntegrate[(
     2 s (ja - jb + 2*j2 + jb*Cos[y] + d*theta))/
     omega[s, d, T, x, y, z] Coth[omega[s, d, T, x, y, z]/
      T], {x, -π/2, π/2}, {y, -π, π}, {z, -π/
      2, π/2}] - 1/2

That I pass to the function m 

m[s_, d_, T_] = 1/((1 + F[s, d, T])^(2 S + 1) - F[s, d, T]^(
2 S + 1)) ((S - F[s, d, T]) (1 + F[s, d, T])^(
  2 S + 1) + (S + 1 + F[s, d, T]) F[s, d, T]^(2 S + 1)) // Simplify

Later, when I try to use FindRoot on it like so:

FindRoot[m[s, 0.00143, 0.001] == s, {s, 1}]

I get the following error:

Wolfram Kernel for Windows has stopped working

Any suggestions ?

EDIT:

Crash stops if I define all functions with :=. It still takes a very long time to compute and I'm not even sure will it ever give any result.

Djole
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    Should we guess what are the definitions behind those symbols -- omega, theta, etc ? Please, include them and format your code and question properly. Try reading it from the perspective of an unfamiliar-with-the-domain person, but still a user of Mathematica. – Sektor Aug 31 '15 at 07:44
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    Might you have forgotten to include the error by any chance ? – image_doctor Aug 31 '15 at 08:10
  • Well it doesn't really give what the error is, it just gives this Wolfram Kernel for Windows has stopped working – Djole Aug 31 '15 at 08:13
  • You have to read about the differences between Set and SetDelayed, a good start is this very same Mathematica.SE site. Also function definition and passing non-numerical values to NIntegrate. All in all I think that should suffice. – Sektor Aug 31 '15 at 08:41
  • I already have done similar problems with practically same code and function defining and haven't had this kind of error. Btw thanks for editing my question, first time using stackexchange. – Djole Aug 31 '15 at 08:46
  • There are two topics here: 1. Finding a solution for the OP. 2. Understanding the crash. Regardless any mistake of the OP, the kernel should never crash. I think that if a minimal example can reproducibly crash the kernel this should be reported as a bug. – rhermans Aug 31 '15 at 12:00
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    And the usual warning that functions with capital letters, such as, F, are generally a bad idea as they are often used by mathematica. – image_doctor Aug 31 '15 at 12:10
  • by the way, I don't think is FindRoot causing the problem. The evaluation of either theta, F or omega is enough to crash the kernel on my v10.1 – glS Aug 31 '15 at 12:15
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    The definitions are circular. F depends on theta which depends on F – Bob Hanlon Aug 31 '15 at 13:22
  • It's not that. I already solved this kind of equations, so I doubt it's that. – Djole Aug 31 '15 at 14:47
  • @Djole Are you really really sure that the fact that you have a circular definition is not a problem? Can you calculate any values of your auxiliary functions themselves before the FindRoot? I mean, if you try to evaluate e.g. m[s, 0.00143, 0.001] as shown in your code, do you get any result? – MarcoB Aug 31 '15 at 15:35
  • Well of course I can't be 100% sure, but I had similar problem and it was solvable. Indeed it was somewhat easier because it hadn't had so much terms, but nevertheless it had circular definitions in its "body". I can't compute any function that includes this integral, so no, especially because if you keep s as a parameter NIntegrate can't work. – Djole Aug 31 '15 at 17:50
  • (A) Why do you use Set (i.e. the = symbol) in function definitions instead of SetDelayed (i.e. :=)? $$$$ (B) This is probably not the source of your problem, but sometimes it is better to define functions with m[s_?NumericQ...] as discussed here – yohbs Aug 31 '15 at 20:18

1 Answers1

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As Bob Hanlon and MarcoB have already mentioned in the comments, the problem appears to be in the circular definition.

Because of the way these are defined, neither m[s, d, T] nor F[s, d, T] can be evaluated with numerical values of s, d and T, so there isn't much FindRoot could do.

A simplified example might be

 f[s_] := NIntegrate[f[s], {x, 0, 1}, {y, 0, 1}]                         

 f[1]

 (* Segmentation fault (core dumped) *)

NIntegrate should ideally fail in a more graceful way, but I do not see the point of trying to evaluate this input.

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