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TABLE OF CONTENTS

• module response_pd_mod
• procedure init_response_pd
• procedure response_pd_omega
• procedure response_pd_cell
• procedure response_dstress_dcell
• procedure make_correlation

response_pd_mod

MODULE

    response_pd_mod

PURPOSE

    Calculate response of periodic structure to periodic perturbation,
    for use in construction of approximate Jacobian in iterate_mod.
    Calculate approximate functional derivatives of monomer concentration 
    field rho with respect to changes in the periodic potential field 
    omega, i.e.,  derivatives of the coefficients in an expansion of 
    rho with respect to coefficients in the corresponding expansion of 
    omega. Also calculate derivatives of rho with respect to changes 
    in unit cell dimensions. These derivatives can be to construct an 
    approximate Jacobian for use in quasi-Newton iteration schemes. 

SOURCE

module response_pd_mod
   use const_mod
   use io_mod
   implicit none

   PRIVATE
   PUBLIC :: init_response_pd  ! allocate memory to array corrlt
   PUBLIC :: response_pd_omega ! calculate d_rho/d_omega
   PUBLIC :: response_pd_cell  ! calculate d_rho/d_cell_param
   PUBLIC :: make_correlation  ! block-block correlation of ideal chains
   PUBLIC :: corrlt            ! used by spinodal_mod
   PUBLIC :: response_dstress_dcell  ! calculate dstress/dcell only

   real(long), allocatable :: corrlt(:,:,:)   ! correlation function

init_response_pd

SUBROUTINE

     subroutine init_response_pd(N_monomer,N)

PURPOSE

     Allocate memory for module array corrlt. This routine must be 
     called before make_correlation is called

ARGUMENTS

     N_monomer = number monomers
     N         = number of basis functions

SOURCE

   subroutine init_response_pd(N_monomer,N)
   integer :: N_monomer, N

response_pd_omega

SUBROUTINE

     response_pd_omega( N, cut, omega, drho_domega )

PURPOSE

     Calculates matrix representation of response function d rho/d omega 

ARGUMENTS

     N           - total number of symmetry-adapted basis functions
     cut         - number of basis functions treated numerically
     omega       - cofficients of monomer chemical potential field
     drho_domega - response matrix
  
     drho_domega(alpha,i,beta,j) = d rho(alpha,i) / d omega(beta,j)

COMMENT

     Long wavelength entries, with i,j in [1, cut], are calculated 
     numerically, by numerical differentiation. 
 
     Short wavelength entries, i,j in (cut, N], are approximated by the 
     response of a homogeneous ideal gas, which is diagonal in k-space.

SOURCE

   subroutine response_pd_omega( N, cut, omega, drho_domega )
   use chemistry_mod, only : ensemble, N_monomer
   use unit_cell_mod, only : N_cell_param
   use scf_mod,       only : density

   integer, intent(IN)       :: N
   integer, intent(IN)       :: cut
   real(long), intent(IN)    :: omega(:,:)           !(N_monomer, N)
   real(long), intent(OUT)   :: drho_domega(:,:,:,:) !(N_monomer,N,N_monomer,N)

response_pd_cell

SUBROUTINE

     response_pd_cell(N,omega,drho_dcell,dstress_dcell)

PURPOSE

     drho_dcell(alpha,i,j) = d rho(alpha,i) / d cell_param(j)
     dstress_dcell(i,j)    = d stress(i) / d cell_param(j)

SOURCE

   subroutine response_pd_cell(N,omega,drho_dcell,dstress_dcell)
   use chemistry_mod, only : ensemble, N_monomer
   use scf_mod,       only : density, scf_stress
   use grid_mod,      only : make_ksq
   use basis_mod,      only : make_dGsq
   use unit_cell_mod, only : N_cell_param, cell_param, &!
                             G_basis, dGG_basis, make_unit_cell

   integer, intent(IN)       :: N
   real(long), intent(IN)    :: omega(:,:)
   real(long), intent(OUT)   :: drho_dcell(:,:,:)
   real(long), intent(OUT)   :: dstress_dcell(:,:)

response_dstress_dcell

SUBROUTINE

     response_dstress_dcell(N,omega,drho_dcell,dstress_dcell)

PURPOSE

     dstress_dcell(i,j) = d stress(i) / d cell_param(j)

SOURCE

   subroutine response_dstress_dcell(N,omega,dstress_dcell)
   use chemistry_mod, only : ensemble, N_monomer
   use scf_mod,       only : density, scf_stress
   use grid_mod,      only : make_ksq
   use basis_mod,      only : make_dGsq
   use unit_cell_mod, only : N_cell_param, cell_param, &!
                             G_basis, dGG_basis, make_unit_cell

   integer, intent(IN)      :: N
   real(long), intent(IN)   :: omega(:,:)
   real(long), intent(OUT)  :: dstress_dcell(:,:)

make_correlation

SUBROUTINE

     make_correlation(N,[lambda])

PURPOSE

     calculate correlation function of ideal chains melt

SOURCE

   subroutine make_correlation(N, lambda)
   use chemistry_mod
   use group_mod
   use basis_mod, only : wave_of_star
   use scf_mod, only : density
   use unit_cell_mod, only : G_basis
   integer :: N  ! # of stars
   real(long), optional  :: lambda(:)   ! $k^2$