# NB ===> 1/3 * (SIG11+SIG22+SIG33) = Spherique_sig
# NB ===> V = v/v0

#volume initial du pti
v0 = 1/8.

#isohyperbulk ou Favier => K3 = 3*K
K3 = 3000.
K = K3/3.

#potentiel isohyperbulk et ses derivees
w(V) = (K/2.)*log(V)**2
dwdV(V) = K*log(V)/V
d2wdV2(V) = K*(1.-log(V))/V**2

#pression hydro selon equation 18
moins_p(V) = V*dwdV(V) + w(V)
#module secant exact = -d(p)/d(V)
Ks(V) = 2.*dwdV(V) + V*d2wdV2(V)

set xlabel "V - 1"
set ylabel "Spherique sig"
p   "calcul_princ.maple" u ($12/v0 - 1.):5 t 'simulation spherique sig' w lp
rep "calcul_princ.maple" u ($12/v0 - 1.):(moins_p($12/v0)) t 'theorique equation 18' w lp
pause -1


set xlabel "temps"
set ylabel "Ks"
p   "derivee_num_Ks" u 1:2 t 'derivee numerique' w lp
rep "calcul_princ.maple" u 1:(Ks($12/v0)) t 'theorique "exact"' w lp
pause -1
