C ******************************************************************* C ** FICHE F.32 ** C ** ROUTINES TO IMPLEMENT CELL LINKED-LISTS IN SHEARED BOUNDARIES.** C ******************************************************************* 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