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********************************************************************************
** FICHE F.32. CELL LINKED-LISTS IN SHEARED BOUNDARIES. **
** This FORTRAN code is intended to illustrate points made in the text. **
** To our knowledge it works correctly. However it is the responsibility of **
** the user to test it, if it is to be used in a research application. **
********************************************************************************
C *******************************************************************
C ** ROUTINES TO IMPLEMENT CELL LINKED-LISTS IN SHEARED BOUNDARIES.**
C ** **
C ** ROUTINES PROVIDED: **
C ** **
C ** SUBROUTINE MAPS **
C ** SETS UP MAP OF CELL NEIGHBOURS FOR BULK OF SIMULATION BOX **
C ** SUBROUTINE TOPMAP ( STRAIN ) **
C ** SETS UP MAP OF NEIGHBOURS FOR TOP LAYER OF CELLS **
C ** SUBROUTINE LINKS ( RCUT ) **
C ** CONSTRUCTS LINK-LIST GIVEN MAP OF CELL NEIGHBOURS **
C ** SUBROUTINE FORCE ( SIGMA, RCUT, STRAIN, V, W, WXY ) **
C ** CALCULATES FORCES, POTENTIAL, VIRIAL ETC. USING LIST **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** INTEGER N NUMBER OF ATOMS **
C ** REAL RX(N),RY(N),RZ(N) ATOMIC POSITIONS **
C ** REAL VX(N),VY(N),VZ(N) ATOMIC VELOCITIES **
C ** REAL FX(N),FY(N),FZ(N) ATOMIC FORCES **
C ** **
C ** USAGE: **
C ** **
C ** SUBROUTINE MAPS IS CALLED ONCE AT THE START OF THE SIMULATION **
C ** TO DEFINE CELL NEIGHBOURS FOR ALL BUT THE TOP LAYER OF CELLS. **
C ** AT EACH TIME STEP, SUBROUTINE TOPMAP IS CALLED FOR THE TOP **
C ** LAYER, SUBROUTINE LINKS TO ESTABLISH THE ATOM NEIGHBOUR LIST, **
C ** AND THEN THE FORCE SUBROUTINE. **
C ** **
C ** UNITS: **
C ** **
C ** THE PROGRAM ASSUMES A BOX OF UNIT LENGTH AND TAKES THE **
C ** LENNARD-JONES POTENTIAL WITH UNIT WELL-DEPTH. **
C ** SUMMARY FOR BOX LENGTH L, ATOMIC MASS M, AND LENNARD-JONES **
C ** POTENTIAL PARAMETERS SIGMA AND EPSILON: **
C ** **
C ** OUR PROGRAM LENNARD-JONES SYSTEM **
C ** LENGTH L SIGMA **
C ** MASS M M **
C ** ENERGY EPSILON EPSILON **
C ** TIME SQRT(M*L**2/EPSILON) SQRT(M*SIGMA**2/EPSILON)**
C ** VELOCITY SQRT(EPSILON/M) SQRT(EPSILON/M) **
C ** PRESSURE EPSILON/L**3 EPSILON/SIGMA**3 **
C *******************************************************************
SUBROUTINE MAPS
COMMON / BLOCK2 / LIST, HEAD, MAP
C *******************************************************************
C ** CONSTRUCTS MAP OF CELL NEIGHBOURS. **
C ** **
C ** THIS SUBROUTINE SETS UP A LIST OF THE THIRTEEN NEIGHBOURING **
C ** CELLS OF EACH OF THE SMALL CELLS IN THE CENTRAL BOX. THE **
C ** EFFECTS OF THE PERIODIC BOUNDARY CONDITIONS ARE INCLUDED. **
C ** HOWEVER THE TOP LAYER (IY = M) IS TACKLED SEPARATELY BECAUSE **
C ** OF THE SHEARED BOUNDARY CONDITIONS, IN SUBROUTINE TOPMAP. **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** INTEGER M NUMBER OF CELLS IN EACH DIRECTION **
C ** INTEGER MAPSIZ SIZE OF CELL-CELL MAP **
C ** INTEGER MAP(MAPSIZ) LIST OF NEIGHBOURING CELLS **
C ** **
C ** USAGE: **
C ** **
C ** THE SUBROUTINE IS CALLED ONCE AT THE BEGINNING OF THE **
C ** SIMULATION AND THE MAP IS USED IN THE FORCE SUBROUTINE **
C *******************************************************************
INTEGER N, M, NCELL, MAPSIZ, M3
PARAMETER ( N = 1372 )
PARAMETER ( M = 5, NCELL = M * M * M, MAPSIZ = 16 * NCELL )
PARAMETER ( M3 = M * 3 )
INTEGER LIST(N), HEAD(NCELL), MAP(MAPSIZ)
INTEGER IX, IY, IZ, IMAP, ICELL
C *******************************************************************
C ** STATEMENT FUNCTION TO GIVE CELL INDEX **
ICELL ( IX, IY, IZ ) = 1 + MOD ( IX - 1 + M3, M )
: + MOD ( IY - 1 + M3, M ) * M
: + MOD ( IZ - 1 + M3, M ) * M * M
C ** FIND HALF THE NEAREST NEIGHBOURS OF EACH CELL **
DO 50 IZ = 1, M
DO 40 IY = 1, M - 1
DO 30 IX = 1, M
IMAP = ( ICELL ( IX, IY, IZ ) - 1 ) * 16
MAP( IMAP + 1 ) = ICELL ( IX + 1, IY , IZ )
MAP( IMAP + 2 ) = ICELL ( IX + 1, IY + 1, IZ )
MAP( IMAP + 3 ) = ICELL ( IX , IY + 1, IZ )
MAP( IMAP + 4 ) = ICELL ( IX - 1, IY + 1, IZ )
MAP( IMAP + 5 ) = ICELL ( IX + 1, IY , IZ - 1 )
MAP( IMAP + 6 ) = ICELL ( IX + 1, IY + 1, IZ - 1 )
MAP( IMAP + 7 ) = ICELL ( IX , IY + 1, IZ - 1 )
MAP( IMAP + 8 ) = ICELL ( IX - 1, IY + 1, IZ - 1 )
MAP( IMAP + 9 ) = ICELL ( IX + 1, IY , IZ + 1 )
MAP( IMAP + 10 ) = ICELL ( IX + 1, IY + 1, IZ + 1 )
MAP( IMAP + 11 ) = ICELL ( IX , IY + 1, IZ + 1 )
MAP( IMAP + 12 ) = ICELL ( IX - 1, IY + 1, IZ + 1 )
MAP( IMAP + 13 ) = ICELL ( IX , IY , IZ + 1 )
MAP( IMAP + 14 ) = 0
MAP( IMAP + 15 ) = 0
MAP( IMAP + 16 ) = 0
30 CONTINUE
40 CONTINUE
50 CONTINUE
RETURN
END
SUBROUTINE TOPMAP ( STRAIN )
COMMON / BLOCK2 / LIST, HEAD, MAP
C *******************************************************************
C ** CALCULATES CELL NEIGHBOUR MAP FOR TOP LAYER. **
C ** **
C ** THIS SUBROUTINE SUPPLEMENTS THE LIST OF NEIGHBOURING CELLS **
C ** FOR THE TOP LAYER (IY = M) WITH SHEARED BOUNDARY CONDITIONS **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** INTEGER M NUMBER OF CELLS IN EACH DIRECTION **
C ** INTEGER MAPSIZ SIZE OF CELL-CELL MAP **
C ** INTEGER MAP(MAPSIZ) LIST OF NEIGHBOURING CELLS **
C ** REAL STRAIN THE X-DISPLACEMENT OF NEXT BOX UP **
C ** **
C ** USAGE: **
C ** **
C ** THE SUBROUTINE IS CALLED AT EVERY TIMESTEP IN THE SIMULATION **
C ** JUST BEFORE THE FORCE SUBROUTINE **
C *******************************************************************
INTEGER N, M, NCELL, MAPSIZ, M3
PARAMETER ( N = 1372 )
PARAMETER ( M = 5, NCELL = M * M * M, MAPSIZ = 16 * NCELL )
PARAMETER ( M3 = M * 3 )
REAL STRAIN
INTEGER LIST(N), HEAD(NCELL), MAP(MAPSIZ)
INTEGER IX, IY, IZ, IMAP, ICELL, IIX
C *******************************************************************
C ** STATEMENT FUNCTION TO GIVE CELL INDEX **
ICELL ( IX, IY, IZ ) = 1 + MOD ( IX - 1 + M3, M )
: + MOD ( IY - 1 + M3, M ) * M
: + MOD ( IZ - 1 + M3, M ) * M * M
C ** CALCULATE X OFFSET IN CELL LENGTHS WHERE STRAIN **
C ** IS BETWEEN -1/2 AND +1/2 AND BOX LENGTH = 1.0 **
C ** ADDING 1.0 SIMPLY GUARANTEES A POSITIVE RESULT **
STRAIN = STRAIN - ANINT ( STRAIN )
IIX = INT ( ( STRAIN + 1.0 ) * REAL ( M ) )
C ** FIND HALF THE NEAREST NEIGHBOURS OF EACH CELL **
IY = M
DO 50 IZ = 1, M
DO 30 IX = 1, M
IMAP = ( ICELL ( IX, IY, IZ ) - 1 ) * 16
MAP( IMAP + 1 ) = ICELL ( IX + 1 , IY , IZ )
MAP( IMAP + 2 ) = ICELL ( IX + 1 - IIX, IY + 1, IZ )
MAP( IMAP + 3 ) = ICELL ( IX - IIX, IY + 1, IZ )
MAP( IMAP + 4 ) = ICELL ( IX - 1 - IIX, IY + 1, IZ )
MAP( IMAP + 5 ) = ICELL ( IX + 1 , IY , IZ - 1 )
MAP( IMAP + 6 ) = ICELL ( IX + 1 - IIX, IY + 1, IZ - 1 )
MAP( IMAP + 7 ) = ICELL ( IX - IIX, IY + 1, IZ - 1 )
MAP( IMAP + 8 ) = ICELL ( IX - 1 - IIX, IY + 1, IZ - 1 )
MAP( IMAP + 9 ) = ICELL ( IX + 1 , IY , IZ + 1 )
MAP( IMAP + 10 ) = ICELL ( IX + 1 - IIX, IY + 1, IZ + 1 )
MAP( IMAP + 11 ) = ICELL ( IX - IIX, IY + 1, IZ + 1 )
MAP( IMAP + 12 ) = ICELL ( IX - 1 - IIX, IY + 1, IZ + 1 )
MAP( IMAP + 13 ) = ICELL ( IX , IY , IZ + 1 )
MAP( IMAP + 14 ) = ICELL ( IX - 2 - IIX, IY + 1, IZ )
MAP( IMAP + 15 ) = ICELL ( IX - 2 - IIX, IY + 1, IZ - 1 )
MAP( IMAP + 16 ) = ICELL ( IX - 2 - IIX, IY + 1, IZ + 1 )
30 CONTINUE
50 CONTINUE
RETURN
END
SUBROUTINE LINKS ( RCUT )
COMMON / BLOCK1 / RX, RY, RZ, VX, VY, VZ, FX, FY, FZ
COMMON / BLOCK2 / LIST, HEAD, MAP
C *******************************************************************
C ** SUBROUTINE TO SET UP LINKED LIST AND THE HEAD OF CHAIN ARRAYS **
C ** **
C ** EACH ATOM IS SORTED INTO ONE OF THE M**3 SMALL CELLS. **
C ** THE FIRST ATOM IN EACH CELL IS PLACED IN THE HEAD ARRAY. **
C ** SUBSEQUENT ATOMS ARE PLACED IN THE LINKED LIST ARRAY. **
C ** ATOM COORDINATES ARE ASSUMED TO BE BETWEEN -0.5 AND +0.5. **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** INTEGER N NUMBER OF ATOMS **
C ** INTEGER M NUMBER OF CELLS IN EACH DIRECTION **
C ** INTEGER NCELL TOTAL NUMBER OF CELLS (M**3) **
C ** INTEGER LIST(N) LINKED LIST OF ATOMS **
C ** INTEGER HEAD(NCELL) HEAD OF CHAIN FOR EACH CELL **
C ** REAL RX(N),RY(N),RZ(N) POSITIONS **
C ** REAL RCUT THE CUTOFF DISTANCE FOR THE FORCE **
C ** **
C ** USAGE: **
C ** **
C ** THE ROUTINE IS CALLED EVERY TIMESTEP BEFORE THE FORCE ROUTINE.**
C *******************************************************************
INTEGER N, M, NCELL, MAPSIZ
PARAMETER ( N = 1372 )
PARAMETER ( M = 5, NCELL = M * M * M, MAPSIZ = 16 * NCELL )
REAL RX(N), RY(N), RZ(N)
REAL VX(N), VY(N), VZ(N)
REAL FX(N), FY(N), FZ(N)
INTEGER HEAD(NCELL), LIST(N), MAP(MAPSIZ)
REAL CELLI, RCUT, CELL
INTEGER ICELL, I
C *******************************************************************
C ** ZERO HEAD OF CHAIN ARRAY **
DO 10 ICELL = 1, NCELL
HEAD(ICELL) = 0
10 CONTINUE
CELLI = REAL ( M )
CELL = 1.0 / CELLI
IF ( CELL. LT. RCUT ) THEN
WRITE(*,'('' CELL SIZE TOO SMALL FOR CUTOFF '')')
STOP
ENDIF
C ** SORT ALL ATOMS **
DO 20 I = 1, N
ICELL = 1 + INT ( ( RX(I) + 0.5 ) * CELLI )
: + INT ( ( RY(I) + 0.5 ) * CELLI ) * M
: + INT ( ( RZ(I) + 0.5 ) * CELLI ) * M * M
LIST(I) = HEAD(ICELL)
HEAD(ICELL) = I
20 CONTINUE
RETURN
END
SUBROUTINE FORCE ( SIGMA, RCUT, STRAIN, V, W, WXY )
COMMON / BLOCK1 / RX, RY, RZ, VX, VY, VZ, FX, FY, FZ
COMMON / BLOCK2 / LIST, HEAD, MAP
C *******************************************************************
C ** COMPUTES FORCES, ETC. USING A LINK LIST IN SHEARED BOUNDARIES.**
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** INTEGER N NUMBER OF ATOMS **
C ** INTEGER M NUMBER OF CELLS IN EACH DIRECTION **
C ** INTEGER NCELL NUMBER OF SMALL CELLS (M**3) **
C ** INTEGER MAPSIZ SIZE OF CELL-CELL MAP **
C ** INTEGER LIST(N) THE LINKED LIST **
C ** INTEGER HEAD(NCELL) THE HEAD OF CHAIN ARRAY **
C ** INTEGER MAP(MAPSIZ) LIST OF NEIGHBOURING CELLS **
C ** REAL RX(N),RY(N),RZ(N) POSITIONS **
C ** REAL FX(N),FY(N),FZ(N) FORCES **
C ** REAL SIGMA THE LJ LENGTH PARAMETER **
C ** REAL RCUT THE CUT-OFF DISTANCE **
C ** REAL STRAIN X OFFSET OF SUCCESSIVE BOXES **
C ** REAL V THE POTENTIAL ENERGY **
C ** **
C ** USAGE: **
C ** **
C ** FORCE IS CALLED IN AN MD PROGRAM TO CALCULATE THE FORCE ON **
C ** EACH ATOM. THE ROUTINE IS WRITTEN FOR A LIQUID OF LENNARD **
C ** JONES ATOMS. SUBROUTINE FORCE REQUIRES A LINKED LIST SET UP **
C ** USING SUBROUTINE LINKS AND THE MAP OF THE SMALL CELLS SET UP **
C ** USING SUBROUTINES MAPS AND TOPMAP. **
C *******************************************************************
INTEGER N, M, NCELL, MAPSIZ
PARAMETER ( N = 1372 )
PARAMETER ( M = 5, NCELL = M * M * M, MAPSIZ = 16 * NCELL )
REAL RX(N), RY(N), RZ(N)
REAL VX(N), VY(N), VZ(N)
REAL FX(N), FY(N), FZ(N)
INTEGER HEAD(NCELL), LIST(N), MAP(MAPSIZ)
REAL RCUT, SIGMA, STRAIN, V, W, WXY
REAL RXI, RYI, RZI, FXIJ, FYIJ, FZIJ, RCUTSQ
REAL VIJ, WIJ, FIJ
REAL SIGSQ, FXI, FYI, FZI, SR2, SR6, SR12
REAL RIJSQ, RXIJ, RYIJ, RZIJ, CORY
INTEGER ICELL, JCELL0, JCELL, I, J, NABOR
C *******************************************************************
SIGSQ = SIGMA ** 2
RCUTSQ = RCUT ** 2
C ** ZERO FORCES AND POTENTIAL **
DO 10 I = 1, N
FX(I) = 0.0
FY(I) = 0.0
FZ(I) = 0.0
10 CONTINUE
V = 0.0
W = 0.0
WXY = 0.0
C ** LOOP OVER ALL CELLS **
DO 5000 ICELL = 1, NCELL
I = HEAD(ICELL)
C ** LOOP OVER ALL MOLECULES IN THE CELL **
1000 IF ( I .GT. 0 ) THEN
RXI = RX(I)
RYI = RY(I)
RZI = RZ(I)
FXI = FX(I)
FYI = FY(I)
FZI = FZ(I)
C ** LOOP OVER ALL MOLECULES BELOW I IN THE CURRENT CELL **
J = LIST(I)
2000 IF ( J .GT. 0 ) THEN
RXIJ = RXI - RX(J)
RYIJ = RYI - RY(J)
RZIJ = RZI - RZ(J)
CORY = ANINT ( RYIJ )
RXIJ = RXIJ - CORY * STRAIN
RXIJ = RXIJ - ANINT ( RXIJ )
RYIJ = RYIJ - CORY
RZIJ = RZIJ - ANINT ( RZIJ )
RIJSQ = RXIJ * RXIJ + RYIJ * RYIJ + RZIJ * RZIJ
IF ( RIJSQ .LT. RCUTSQ ) THEN
SR2 = SIGSQ / RIJSQ
SR6 = SR2 * SR2 * SR2
SR12 = SR6 ** 2
VIJ = SR12 - SR6
V = V + VIJ
WIJ = VIJ + SR12
W = W + WIJ
FIJ = WIJ / RIJSQ
FXIJ = FIJ * RXIJ
FYIJ = FIJ * RYIJ
FZIJ = FIJ * RZIJ
FXI = FXI + FXIJ
FYI = FYI + FYIJ
FZI = FZI + FZIJ
FX(J) = FX(J) - FXIJ
FY(J) = FY(J) - FYIJ
FZ(J) = FZ(J) - FZIJ
WXY = WXY + RXIJ * FYIJ
ENDIF
J = LIST(J)
GOTO 2000
ENDIF
C ** LOOP OVER NEIGHBOURING CELLS **
JCELL0 = 16 * ( ICELL - 1 )
DO 4000 NABOR = 1, 16
JCELL = MAP( JCELL0 + NABOR )
IF ( JCELL .GT. 0 ) THEN
C ** LOOP OVER ALL MOLECULES IN NEIGHBOURING CELLS **
J = HEAD(JCELL)
3000 IF ( J .NE. 0 ) THEN
RXIJ = RXI - RX(J)
RYIJ = RYI - RY(J)
RZIJ = RZI - RZ(J)
CORY = ANINT ( RYIJ )
RXIJ = RXIJ - CORY * STRAIN
RXIJ = RXIJ - ANINT ( RXIJ )
RYIJ = RYIJ - CORY
RZIJ = RZIJ - ANINT ( RZIJ )
RIJSQ = RXIJ * RXIJ + RYIJ * RYIJ + RZIJ * RZIJ
IF ( RIJSQ. LT. RCUTSQ ) THEN
SR2 = SIGSQ / RIJSQ
SR6 = SR2 * SR2 * SR2
SR12 = SR6 ** 2
VIJ = SR12 - SR6
V = V + VIJ
WIJ = VIJ + SR12
W = W + WIJ
FIJ = WIJ / RIJSQ
FXIJ = FIJ * RXIJ
FYIJ = FIJ * RYIJ
FZIJ = FIJ * RZIJ
FXI = FXI + FXIJ
FYI = FYI + FYIJ
FZI = FZI + FZIJ
FX(J) = FX(J) - FXIJ
FY(J) = FY(J) - FYIJ
FZ(J) = FZ(J) - FZIJ
WXY = WXY + RXIJ * FYIJ
ENDIF
J = LIST(J)
GOTO 3000
ENDIF
ENDIF
4000 CONTINUE
FX(I) = FXI
FY(I) = FYI
FZ(I) = FZI
I = LIST(I)
GOTO 1000
ENDIF
5000 CONTINUE
C ** INCORPORATE ENERGY FACTORS **
DO 6000 I = 1, N
FX(I) = FX(I) * 24.0
FY(I) = FY(I) * 24.0
FZ(I) = FZ(I) * 24.0
6000 CONTINUE
V = V * 4.0
W = W * 24.0 / 3.0
WXY = WXY * 24.0
RETURN
END
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