Questions on 'density considered significant' in the nonlocal plastic model

[ruanqc]

Dear all,
I'm trying to learn and modified the nonlocal model, here for the 'density considered significantin src/phase_mechanical_plastic_nonlocal.f90_ . I am not sure with the following where condition in the getRho0 function （line 1635） :

where (abs(rho_0) < max(prm%rho_min/geom(ph)%v_0(en)**(2.0_pREAL/3.0_pREAL),prm%rho_significant)) &  
rho_0 = 0.0_pREAL

and similarly, for getRho0 function (Line 1661)

 where (abs(rho_0) < max(prm%rho_min/geom(ph)%v_0(en)**(2.0_pREAL/3.0_pREAL),prm%rho_significant)) &
  rho_0 = 0.0_pREAL

From my understanding, these two lines are used to zero out dislocation density values ($\rho$, or $\rho_0$) that are considered smaller than threshold by the maximum of two quantities:
$\frac{ \rho_{min} }{ v_0(en) ^{2/3} }$, and $\rho_{significant}$.

I am still not sure that,
(1) here, prm%rho_min / geom(ph)%v_0(en)**(2/3) seems to scale a minimum density by the cell volume or grid cell. I could found the referece equations for this implemenation code line in reference (eg.C. Kords (2013) PhD thesis, C. Reuber et al., (2014) Acta Materialia), please remind me if i have missed them.

(2) How coule we set a typically rho_significant in our simulations? Should it be related to the initial density values, or is it more about numerical stability/noise filtering? (it use rho_significant=1.e6 while $\rho_0^{\alpha}=1.25e9$ in the referece input file.)

for example, when i set initial density $\rho_0=$ 8.0e9, once I set rho_significant =1.0e7 or =1.e5, the simulation can simulate a much longer time, while a smaller value like 0.0 or 1.0e-12 easier give rise to fluctautation in the region of haveing significant dislocation density gradient, and simulation aborted. So I think the above two parameters, rho_significant plays a critical role in the cutoff.

      rho_u_ed_pos_0: [8.0e+9] #[1.25e9]
      rho_u_ed_neg_0: [8.0e+9]  
      rho_u_sc_pos_0: [0]      #[1.25e9] # 1.6e10 / (12*4)
      rho_u_sc_neg_0: [0]      #[1.25e9] # 1.6e10 / (12*4)
      rho_d_ed_0: [0]
      rho_d_sc_0: [0]
      N_sl: [1]  
      rho_significant: 1.0e8 # 0.0, 1.0e-12, 1.0e7, 1.0e8,  ref: kords 1.e6       

I'd very appriciated if anyone can give me some advises and suggestions on these questions, and thank you in advance.
ruanqc