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@ -148,7 +148,7 @@ module function plastic_dislotungsten_init() result(myPlasticity)
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else
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prm%P_nS_pos = prm%P_sl
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prm%P_nS_neg = prm%P_sl
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endif
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end if
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prm%h_sl_sl = lattice_interaction_SlipBySlip(N_sl,pl%get_as1dFloat('h_sl-sl'), &
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phase_lattice(ph))
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@ -209,13 +209,13 @@ module function plastic_dislotungsten_init() result(myPlasticity)
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if (any(prm%f_at <= 0.0_pReal)) extmsg = trim(extmsg)//' f_at or b_sl'
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else slipActive
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rho_mob_0= emptyRealArray; rho_dip_0 = emptyRealArray
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rho_mob_0 = emptyRealArray; rho_dip_0 = emptyRealArray
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allocate(prm%b_sl,prm%d_caron,prm%i_sl,prm%f_at,prm%tau_Peierls, &
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prm%Q_s,prm%v_0,prm%p,prm%q,prm%B,prm%h,prm%w,prm%omega, &
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source = emptyRealArray)
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allocate(prm%forestProjection(0,0))
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allocate(prm%h_sl_sl (0,0))
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endif slipActive
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end if slipActive
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!--------------------------------------------------------------------------------------------------
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! allocate state arrays
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@ -258,7 +258,7 @@ module function plastic_dislotungsten_init() result(myPlasticity)
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! exit if any parameter is out of range
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if (extmsg /= '') call IO_error(211,ext_msg=trim(extmsg)//'(dislotungsten)')
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enddo
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end do
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end function plastic_dislotungsten_init
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@ -267,7 +267,7 @@ end function plastic_dislotungsten_init
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!> @brief Calculate plastic velocity gradient and its tangent.
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!--------------------------------------------------------------------------------------------------
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pure module subroutine dislotungsten_LpAndItsTangent(Lp,dLp_dMp, &
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Mp,T,ph,en)
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Mp,T,ph,en)
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real(pReal), dimension(3,3), intent(out) :: &
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Lp !< plastic velocity gradient
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real(pReal), dimension(3,3,3,3), intent(out) :: &
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@ -287,19 +287,20 @@ pure module subroutine dislotungsten_LpAndItsTangent(Lp,dLp_dMp, &
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dot_gamma_pos,dot_gamma_neg, &
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ddot_gamma_dtau_pos,ddot_gamma_dtau_neg
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Lp = 0.0_pReal
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dLp_dMp = 0.0_pReal
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associate(prm => param(ph))
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call kinetics(Mp,T,ph,en,dot_gamma_pos,dot_gamma_neg,ddot_gamma_dtau_pos,ddot_gamma_dtau_neg)
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do i = 1, prm%sum_N_sl
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Lp = Lp + (dot_gamma_pos(i)+dot_gamma_neg(i))*prm%P_sl(1:3,1:3,i)
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forall (k=1:3,l=1:3,m=1:3,n=1:3) &
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dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
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+ ddot_gamma_dtau_pos(i) * prm%P_sl(k,l,i) * prm%P_nS_pos(m,n,i) &
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+ ddot_gamma_dtau_neg(i) * prm%P_sl(k,l,i) * prm%P_nS_neg(m,n,i)
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enddo
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call kinetics(Mp,T,ph,en,dot_gamma_pos,dot_gamma_neg,ddot_gamma_dtau_pos,ddot_gamma_dtau_neg)
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do i = 1, prm%sum_N_sl
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Lp = Lp + (dot_gamma_pos(i)+dot_gamma_neg(i))*prm%P_sl(1:3,1:3,i)
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forall (k=1:3,l=1:3,m=1:3,n=1:3) &
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dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
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+ ddot_gamma_dtau_pos(i) * prm%P_sl(k,l,i) * prm%P_nS_pos(m,n,i) &
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+ ddot_gamma_dtau_neg(i) * prm%P_sl(k,l,i) * prm%P_nS_neg(m,n,i)
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end do
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end associate
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@ -328,35 +329,36 @@ module subroutine dislotungsten_dotState(Mp,T,ph,en)
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dot_rho_dip_climb, &
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d_hat
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associate(prm => param(ph), stt => state(ph), dot => dotState(ph), dst => dependentState(ph))
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call kinetics(Mp,T,ph,en,&
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dot_gamma_pos,dot_gamma_neg, &
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tau_pos_out = tau_pos,tau_neg_out = tau_neg)
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call kinetics(Mp,T,ph,en,&
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dot_gamma_pos,dot_gamma_neg, &
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tau_pos_out = tau_pos,tau_neg_out = tau_neg)
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dot%gamma_sl(:,en) = abs(dot_gamma_pos+dot_gamma_neg)
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dot%gamma_sl(:,en) = abs(dot_gamma_pos+dot_gamma_neg)
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where(dEq0(tau_pos)) ! ToDo: use avg of +/-
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dot_rho_dip_formation = 0.0_pReal
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dot_rho_dip_climb = 0.0_pReal
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else where
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d_hat = math_clip(3.0_pReal*prm%mu*prm%b_sl/(16.0_pReal*PI*abs(tau_pos)), & ! ToDo: use avg of +/-
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prm%d_caron, & ! lower limit
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dst%Lambda_sl(:,en)) ! upper limit
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dot_rho_dip_formation = merge(2.0_pReal*(d_hat-prm%d_caron)*stt%rho_mob(:,en)*dot%gamma_sl(:,en)/prm%b_sl, &
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0.0_pReal, &
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prm%dipoleformation)
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v_cl = (3.0_pReal*prm%mu*prm%D_0*exp(-prm%Q_cl/(kB*T))*prm%f_at/(2.0_pReal*PI*kB*T)) &
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* (1.0_pReal/(d_hat+prm%d_caron))
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dot_rho_dip_climb = (4.0_pReal*v_cl*stt%rho_dip(:,en))/(d_hat-prm%d_caron) ! ToDo: Discuss with Franz: Stress dependency?
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end where
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where(dEq0(tau_pos)) ! ToDo: use avg of +/-
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dot_rho_dip_formation = 0.0_pReal
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dot_rho_dip_climb = 0.0_pReal
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else where
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d_hat = math_clip(3.0_pReal*prm%mu*prm%b_sl/(16.0_pReal*PI*abs(tau_pos)), & ! ToDo: use avg of +/-
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prm%d_caron, & ! lower limit
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dst%Lambda_sl(:,en)) ! upper limit
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dot_rho_dip_formation = merge(2.0_pReal*(d_hat-prm%d_caron)*stt%rho_mob(:,en)*dot%gamma_sl(:,en)/prm%b_sl, &
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0.0_pReal, &
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prm%dipoleformation)
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v_cl = (3.0_pReal*prm%mu*prm%D_0*exp(-prm%Q_cl/(kB*T))*prm%f_at/(2.0_pReal*PI*kB*T)) &
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* (1.0_pReal/(d_hat+prm%d_caron))
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dot_rho_dip_climb = (4.0_pReal*v_cl*stt%rho_dip(:,en))/(d_hat-prm%d_caron) ! ToDo: Discuss with Franz: Stress dependency?
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end where
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dot%rho_mob(:,en) = dot%gamma_sl(:,en)/(prm%b_sl*dst%Lambda_sl(:,en)) & ! multiplication
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- dot_rho_dip_formation &
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- (2.0_pReal*prm%d_caron)/prm%b_sl*stt%rho_mob(:,en)*dot%gamma_sl(:,en) ! Spontaneous annihilation of 2 edges
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dot%rho_dip(:,en) = dot_rho_dip_formation &
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- (2.0_pReal*prm%d_caron)/prm%b_sl*stt%rho_dip(:,en)*dot%gamma_sl(:,en) & ! Spontaneous annihilation of an edge with a dipole
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- dot_rho_dip_climb
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dot%rho_mob(:,en) = dot%gamma_sl(:,en)/(prm%b_sl*dst%Lambda_sl(:,en)) & ! multiplication
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- dot_rho_dip_formation &
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- (2.0_pReal*prm%d_caron)/prm%b_sl*stt%rho_mob(:,en)*dot%gamma_sl(:,en) ! Spontaneous annihilation of 2 edges
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dot%rho_dip(:,en) = dot_rho_dip_formation &
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- (2.0_pReal*prm%d_caron)/prm%b_sl*stt%rho_dip(:,en)*dot%gamma_sl(:,en) & ! Spontaneous annihilation of an edge with a dipole
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- dot_rho_dip_climb
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end associate
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@ -368,7 +370,7 @@ end subroutine dislotungsten_dotState
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!--------------------------------------------------------------------------------------------------
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module subroutine dislotungsten_dependentState(ph,en)
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integer, intent(in) :: &
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integer, intent(in) :: &
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ph, &
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en
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@ -423,7 +425,7 @@ module subroutine plastic_dislotungsten_results(ph,group)
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'threshold stress for slip','Pa',prm%systems_sl)
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end select
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enddo
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end do
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end associate
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@ -456,6 +458,7 @@ pure subroutine kinetics(Mp,T,ph,en, &
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ddot_gamma_dtau_neg, &
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tau_pos_out, &
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tau_neg_out
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real(pReal), dimension(param(ph)%sum_N_sl) :: &
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StressRatio, &
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StressRatio_p,StressRatio_pminus1, &
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@ -464,80 +467,80 @@ pure subroutine kinetics(Mp,T,ph,en, &
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t_n, t_k, dtk,dtn
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integer :: j
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associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
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do j = 1, prm%sum_N_sl
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tau_pos(j) = math_tensordot(Mp,prm%P_nS_pos(1:3,1:3,j))
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tau_neg(j) = math_tensordot(Mp,prm%P_nS_neg(1:3,1:3,j))
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enddo
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do j = 1, prm%sum_N_sl
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tau_pos(j) = math_tensordot(Mp,prm%P_nS_pos(1:3,1:3,j))
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tau_neg(j) = math_tensordot(Mp,prm%P_nS_neg(1:3,1:3,j))
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end do
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if (present(tau_pos_out)) tau_pos_out = tau_pos
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if (present(tau_neg_out)) tau_neg_out = tau_neg
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if (present(tau_pos_out)) tau_pos_out = tau_pos
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if (present(tau_neg_out)) tau_neg_out = tau_neg
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associate(BoltzmannRatio => prm%Q_s/(kB*T), &
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dot_gamma_0 => stt%rho_mob(:,en)*prm%b_sl*prm%v_0, &
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effectiveLength => dst%Lambda_sl(:,en) - prm%w)
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associate(BoltzmannRatio => prm%Q_s/(kB*T), &
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dot_gamma_0 => stt%rho_mob(:,en)*prm%b_sl*prm%v_0, &
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effectiveLength => dst%Lambda_sl(:,en) - prm%w)
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significantPositiveTau: where(abs(tau_pos)-dst%tau_pass(:,en) > tol_math_check)
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StressRatio = (abs(tau_pos)-dst%tau_pass(:,en))/prm%tau_Peierls
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StressRatio_p = StressRatio** prm%p
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StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal)
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significantPositiveTau: where(abs(tau_pos)-dst%tau_pass(:,en) > tol_math_check)
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StressRatio = (abs(tau_pos)-dst%tau_pass(:,en))/prm%tau_Peierls
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StressRatio_p = StressRatio** prm%p
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StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal)
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t_n = prm%b_sl/(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q)*prm%omega*effectiveLength)
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t_k = effectiveLength * prm%B /(2.0_pReal*prm%b_sl*tau_pos)
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t_n = prm%b_sl/(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q)*prm%omega*effectiveLength)
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t_k = effectiveLength * prm%B /(2.0_pReal*prm%b_sl*tau_pos)
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vel = prm%h/(t_n + t_k)
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vel = prm%h/(t_n + t_k)
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dot_gamma_pos = dot_gamma_0 * sign(vel,tau_pos) * 0.5_pReal
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else where significantPositiveTau
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dot_gamma_pos = 0.0_pReal
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end where significantPositiveTau
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dot_gamma_pos = dot_gamma_0 * sign(vel,tau_pos) * 0.5_pReal
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else where significantPositiveTau
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dot_gamma_pos = 0.0_pReal
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end where significantPositiveTau
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if (present(ddot_gamma_dtau_pos)) then
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significantPositiveTau2: where(abs(tau_pos)-dst%tau_pass(:,en) > tol_math_check)
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dtn = -1.0_pReal * t_n * BoltzmannRatio * prm%p * prm%q * (1.0_pReal-StressRatio_p)**(prm%q - 1.0_pReal) &
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* (StressRatio)**(prm%p - 1.0_pReal) / prm%tau_Peierls
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dtk = -1.0_pReal * t_k / tau_pos
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if (present(ddot_gamma_dtau_pos)) then
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significantPositiveTau2: where(abs(tau_pos)-dst%tau_pass(:,en) > tol_math_check)
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dtn = -1.0_pReal * t_n * BoltzmannRatio * prm%p * prm%q * (1.0_pReal-StressRatio_p)**(prm%q - 1.0_pReal) &
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* (StressRatio)**(prm%p - 1.0_pReal) / prm%tau_Peierls
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dtk = -1.0_pReal * t_k / tau_pos
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dvel = -1.0_pReal * prm%h * (dtk + dtn) / (t_n + t_k)**2.0_pReal
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dvel = -1.0_pReal * prm%h * (dtk + dtn) / (t_n + t_k)**2.0_pReal
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ddot_gamma_dtau_pos = dot_gamma_0 * dvel* 0.5_pReal
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else where significantPositiveTau2
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ddot_gamma_dtau_pos = 0.0_pReal
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end where significantPositiveTau2
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end if
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ddot_gamma_dtau_pos = dot_gamma_0 * dvel* 0.5_pReal
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else where significantPositiveTau2
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ddot_gamma_dtau_pos = 0.0_pReal
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end where significantPositiveTau2
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endif
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significantNegativeTau: where(abs(tau_neg)-dst%tau_pass(:,en) > tol_math_check)
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StressRatio = (abs(tau_neg)-dst%tau_pass(:,en))/prm%tau_Peierls
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StressRatio_p = StressRatio** prm%p
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StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal)
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significantNegativeTau: where(abs(tau_neg)-dst%tau_pass(:,en) > tol_math_check)
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StressRatio = (abs(tau_neg)-dst%tau_pass(:,en))/prm%tau_Peierls
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StressRatio_p = StressRatio** prm%p
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StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal)
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t_n = prm%b_sl/(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q)*prm%omega*effectiveLength)
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t_k = effectiveLength * prm%B /(2.0_pReal*prm%b_sl*tau_pos)
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t_n = prm%b_sl/(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q)*prm%omega*effectiveLength)
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t_k = effectiveLength * prm%B /(2.0_pReal*prm%b_sl*tau_pos)
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vel = prm%h/(t_n + t_k)
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vel = prm%h/(t_n + t_k)
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dot_gamma_neg = dot_gamma_0 * sign(vel,tau_neg) * 0.5_pReal
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else where significantNegativeTau
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dot_gamma_neg = 0.0_pReal
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end where significantNegativeTau
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dot_gamma_neg = dot_gamma_0 * sign(vel,tau_neg) * 0.5_pReal
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else where significantNegativeTau
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dot_gamma_neg = 0.0_pReal
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end where significantNegativeTau
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if (present(ddot_gamma_dtau_neg)) then
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significantNegativeTau2: where(abs(tau_neg)-dst%tau_pass(:,en) > tol_math_check)
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dtn = -1.0_pReal * t_n * BoltzmannRatio * prm%p * prm%q * (1.0_pReal-StressRatio_p)**(prm%q - 1.0_pReal) &
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* (StressRatio)**(prm%p - 1.0_pReal) / prm%tau_Peierls
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dtk = -1.0_pReal * t_k / tau_neg
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if (present(ddot_gamma_dtau_neg)) then
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significantNegativeTau2: where(abs(tau_neg)-dst%tau_pass(:,en) > tol_math_check)
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dtn = -1.0_pReal * t_n * BoltzmannRatio * prm%p * prm%q * (1.0_pReal-StressRatio_p)**(prm%q - 1.0_pReal) &
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* (StressRatio)**(prm%p - 1.0_pReal) / prm%tau_Peierls
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dtk = -1.0_pReal * t_k / tau_neg
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dvel = -1.0_pReal * prm%h * (dtk + dtn) / (t_n + t_k)**2.0_pReal
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dvel = -1.0_pReal * prm%h * (dtk + dtn) / (t_n + t_k)**2.0_pReal
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ddot_gamma_dtau_neg = dot_gamma_0 * dvel * 0.5_pReal
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else where significantNegativeTau2
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ddot_gamma_dtau_neg = 0.0_pReal
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end where significantNegativeTau2
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end if
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ddot_gamma_dtau_neg = dot_gamma_0 * dvel * 0.5_pReal
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else where significantNegativeTau2
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ddot_gamma_dtau_neg = 0.0_pReal
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end where significantNegativeTau2
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end if
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end associate
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end associate
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end associate
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end subroutine kinetics
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