[drudox]

Using an in-house Fortran90 code (FVM) I would like to investigate the polymer's chain interaction with homogenous and isotropic turbulence (incompressible fluid).
I've implemented a coupling between the Navier-Stokes equations (for the whole fluid field) and the Langevin equation for the polymer forces, The basic idea behind this coupling is to allow the studying on a Mesoscopic scale, polymer's stretching phenomenon.

I would like to compute the conditional averages (or conditional probability) of the square of the stretching vector () in slots of the alignment between the polymer's end-end vector () and the eigenvector of the Strainrate tensor ().

I've explained the details but my question is how should be computed this conditional statistic in order to evaluate if the amount of stretching vector (Y-axis) is higher or smaller with respect to the value of |cos(p,L_i)| [0;1].

What I've done is: first of all I have chosen to subdivide the range of the possible value of the cosine (0 to 1) in 100 bins and create a 2D array with size bins, dimension = (100,3); then for each time step I'm computed the (value of y) and the cosine of alignment (x) with this cosine value I'm going to find the corresponding bin (example bin=60) then:

1. question:
   1) I've to increase the value of this bin (x=60) to the value of y
   or
   2) I've to increase the value of all the bins lower than the corresponding bins (x <= 60) to the value of y
   
2. question:
   since that, with the previous step, I just create a histogram in order to normalize:
   1) I should have a counter_array(100,3) that increases to the value 1 the corresponding bin (x=60), and at the end of the computation divide the histogram(i,j)/counter_array(i,j) in order to obtain a conditional pdf ?
   
   or
   
   2) I have just to divide the histogram by the number of time steps?

can somebody explain to me the correct procedure?
Thanks a lot !