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hardsphere.f
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********************************************************************************
** FICHE F.10. HARD SPHERE MOLECULAR DYNAMICS PROGRAM **
** 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. **
********************************************************************************
PROGRAM SPHERE
COMMON / BLOCK1 / RX, RY, RZ, VX, VY, VZ
COMMON / BLOCK2 / COLTIM, PARTNR
C *******************************************************************
C ** MOLECULAR DYNAMICS OF HARD SPHERE ATOMS. **
C ** **
C ** THIS PROGRAM TAKES IN A HARD-SPHERE CONFIGURATION (POSITIONS **
C ** AND VELOCITIES), CHECKS FOR OVERLAPS, AND THEN CONDUCTS A **
C ** MOLECULAR DYNAMICS SIMULATION RUN FOR A SPECIFIED NUMBER OF **
C ** COLLISIONS. THE PROGRAM IS FAIRLY EFFICIENT, BUT USES NO **
C ** SPECIAL NEIGHBOUR LISTS, SO IS RESTRICTED TO A SMALL NUMBER **
C ** OF PARTICLES (<500). IT IS ALWAYS ASSUMED THAT COLLISIONS **
C ** CAN BE PREDICTED BY LOOKING AT NEAREST NEIGHBOUR PARTICLES IN **
C ** THE MINIMUM IMAGE CONVENTION OF PERIODIC BOUNDARIES. **
C ** THE BOX IS TAKEN TO BE OF UNIT LENGTH. **
C ** HOWEVER, RESULTS ARE GIVEN IN UNITS WHERE SIGMA=1, KT=1. **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** INTEGER N NUMBER OF ATOMS **
C ** REAL RX(N),RY(N),RZ(N) ATOM POSITIONS **
C ** REAL VX(N),VY(N),VZ(N) ATOM VELOCITIES **
C ** REAL COLTIM(N) TIME TO NEXT COLLISION **
C ** INTEGER PARTNR(N) COLLISION PARTNER **
C ** REAL SIGMA ATOM DIAMETER **
C ** **
C ** ROUTINES REFERENCED: **
C ** **
C ** SUBROUTINE READCN ( CNFILE ) **
C ** READS IN CONFIGURATION **
C ** SUBROUTINE CHECK ( SIGMA, OVRLAP, E ) **
C ** CHECKS CONFIGURATION AND CALCULATES ENERGY **
C ** SUBROUTINE UPLIST ( SIGMA, I ) **
C ** SEEKS COLLISIONS WITH J>I **
C ** SUBROUTINE DNLIST ( SIGMA, I ) **
C ** SEEKS COLLISIONS WITH J<I **
C ** SUBROUTINE BUMP ( SIGMA, I, J, W ) **
C ** DOES COLLISION DYNAMICS AND CALCULATES COLLISION VIRIAL **
C ** SUBROUTINE WRITCN ( CNFILE ) **
C ** WRITES OUT CONFIGURATION **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
REAL TIMBIG
PARAMETER ( TIMBIG = 1.0E10 )
REAL RX(N), RY(N), RZ(N), VX(N), VY(N), VZ(N)
REAL COLTIM(N)
INTEGER PARTNR(N)
REAL SIGMA
INTEGER I, J, K, NCOLL, COLL
REAL DENSTY, DIJ, TIJ, T, RATE
REAL E, EN, ENKT, W, PVNKT1, ACW, TEMP, TBC
CHARACTER TITLE*80, CNFILE*30
LOGICAL OVRLAP
C *******************************************************************
WRITE(*,'(1H1,'' **** PROGRAM SPHERE **** '')')
WRITE(*,'(// '' MOLECULAR DYNAMICS OF HARD SPHERES '')')
WRITE(*,'(// '' RESULTS IN UNITS KT = SIGMA = 1 '')')
C ** READ IN BASIC SIMULATION PARAMETERS **
WRITE(*,'('' ENTER RUN TITLE '')')
READ (*,'(A)') TITLE
WRITE(*,'('' ENTER REDUCED DENSITY (N/V)*SIGMA**3 '')')
READ (*,*) DENSTY
WRITE(*,'('' ENTER NUMBER OF COLLISIONS REQUIRED '')')
READ (*,*) NCOLL
WRITE(*,'('' ENTER CONFIGURATION FILENAME '')')
READ (*,'(A)') CNFILE
WRITE(*,'('' RUN TITLE '',A)' ) TITLE
WRITE(*,'('' REDUCED DENSITY IS '',F15.5)') DENSTY
WRITE(*,'('' COLLISIONS REQUIRED '',I15)' ) NCOLL
WRITE(*,'('' CONFIGURATION FILENAME '',A)' ) CNFILE
SIGMA = ( DENSTY / REAL(N) ) ** ( 1.0 / 3.0 )
C ** READ IN CONFIGURATION **
CALL READCN ( CNFILE )
C ** CHECK FOR PARTICLE OVERLAPS **
C ** CALCULATE ENERGY **
CALL CHECK ( SIGMA, OVRLAP, E )
IF ( OVRLAP ) STOP 'PARTICLE OVERLAP IN INITIAL CONFIGURATION'
EN = E / REAL ( N )
TEMP = 2.0 * EN / 3.0
WRITE(*,'('' TEMPERATURE '',F15.5)') TEMP
ENKT = EN / TEMP
WRITE(*,'('' INITIAL E/NKT '',F15.5)') ENKT
C ** SET UP INITIAL COLLISION LISTS COLTIM AND PARTNR **
DO 10 I = 1, N
COLTIM(I) = TIMBIG
PARTNR(I) = N
10 CONTINUE
DO 20 I = 1, N
CALL UPLIST ( SIGMA, I )
20 CONTINUE
C ** ZERO VIRIAL ACCUMULATOR **
ACW = 0.0
WRITE(*,'(//'' **** START OF DYNAMICS **** '')')
C *******************************************************************
C ** MAIN LOOP BEGINS **
C *******************************************************************
T = 0.0
DO 1000 COLL = 1, NCOLL
C ** LOCATE MINIMUM COLLISION TIME **
TIJ = TIMBIG
DO 200 K = 1, N
IF ( COLTIM(K) .LT. TIJ ) THEN
TIJ = COLTIM(K)
I = K
ENDIF
200 CONTINUE
J = PARTNR(I)
C ** MOVE PARTICLES FORWARD BY TIME TIJ **
C ** AND REDUCE COLLISION TIMES **
C ** APPLY PERIODIC BOUNDARIES **
T = T + TIJ
DO 300 K = 1, N
COLTIM(K) = COLTIM(K) - TIJ
RX(K) = RX(K) + VX(K) * TIJ
RY(K) = RY(K) + VY(K) * TIJ
RZ(K) = RZ(K) + VZ(K) * TIJ
RX(K) = RX(K) - ANINT ( RX(K) )
RY(K) = RY(K) - ANINT ( RY(K) )
RZ(K) = RZ(K) - ANINT ( RZ(K) )
300 CONTINUE
C ** COMPUTE COLLISION DYNAMICS **
CALL BUMP ( SIGMA, I, J, W )
ACW = ACW + W
C ** RESET COLLISION LISTS FOR **
C ** THOSE PARTICLES WHICH NEED IT **
DO 400 K = 1, N
IF ( ( K .EQ. I ) .OR. ( PARTNR(K) .EQ. I ) .OR.
: ( K .EQ. J ) .OR. ( PARTNR(K) .EQ. J ) ) THEN
CALL UPLIST ( SIGMA, K )
ENDIF
400 CONTINUE
CALL DNLIST ( SIGMA, I )
CALL DNLIST ( SIGMA, J )
1000 CONTINUE
C *******************************************************************
C ** MAIN LOOP ENDS. **
C *******************************************************************
WRITE(*,'(//'' **** END OF DYNAMICS **** '')')
WRITE(*,'(/'' FINAL COLLIDING PAIR '',2I5)') I, J
C ** CHECK FOR PARTICLE OVERLAPS **
CALL CHECK ( SIGMA, OVRLAP, E )
IF ( OVRLAP ) THEN
WRITE(*,'('' PARTICLE OVERLAP IN FINAL CONFIGURATION '')')
ENDIF
C ** WRITE OUT CONFIGURATION **
CALL WRITCN ( CNFILE )
C ** WRITE OUT INTERESTING INFORMATION **
PVNKT1 = ACW / REAL ( N ) / 3.0 / T / TEMP
EN = E / REAL ( N )
ENKT = EN / TEMP
T = T * SQRT ( TEMP ) / SIGMA
RATE = REAL ( NCOLL ) / T
TBC = REAL ( N ) / RATE / 2.0
WRITE(*,'('' FINAL TIME IS '',F15.8)') T
WRITE(*,'('' COLLISION RATE IS '',F15.8)') RATE
WRITE(*,'('' MEAN COLLISION TIME '',F15.8)') TBC
WRITE(*,'('' FINAL E/NKT IS '',F15.8)') ENKT
WRITE(*,'('' PV/NKT - 1 IS '',F15.8)') PVNKT1
STOP
END
SUBROUTINE CHECK ( SIGMA, OVRLAP, E )
COMMON / BLOCK1 / RX, RY, RZ, VX, VY, VZ
COMMON / BLOCK2 / COLTIM, PARTNR
C *******************************************************************
C ** TESTS FOR PAIR OVERLAPS AND CALCULATES KINETIC ENERGY. **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
REAL RX(N), RY(N), RZ(N), VX(N), VY(N), VZ(N)
REAL COLTIM(N)
INTEGER PARTNR(N)
REAL SIGMA, E
LOGICAL OVRLAP
INTEGER I, J
REAL RXI, RYI, RZI, RXIJ, RYIJ, RZIJ, RIJSQ, SIGSQ, RIJ
REAL TOL
PARAMETER ( TOL = 1.0E-4 )
C *******************************************************************
SIGSQ = SIGMA ** 2
OVRLAP = .FALSE.
E = 0.0
DO 100 I = 1, N - 1
RXI = RX(I)
RYI = RY(I)
RZI = RZ(I)
DO 99 J = I + 1, N
RXIJ = RXI - RX(J)
RYIJ = RYI - RY(J)
RZIJ = RZI - RZ(J)
RXIJ = RXIJ - ANINT ( RXIJ )
RYIJ = RYIJ - ANINT ( RYIJ )
RZIJ = RZIJ - ANINT ( RZIJ )
RIJSQ = RXIJ ** 2 + RYIJ ** 2 + RZIJ ** 2
IF ( RIJSQ .LT. SIGSQ ) THEN
RIJ = SQRT ( RIJSQ / SIGSQ )
WRITE(*,'('' I,J,RIJ/SIGMA = '',2I5,F15.8)')
: I, J, RIJ
IF ( ( 1.0 - RIJ ) .GT. TOL ) OVRLAP = .TRUE.
ENDIF
99 CONTINUE
100 CONTINUE
DO 200 I = 1, N
E = E + VX(I) ** 2 + VY(I) ** 2 + VZ(I) ** 2
200 CONTINUE
E = 0.5 * E
RETURN
END
SUBROUTINE UPLIST ( SIGMA, I )
COMMON / BLOCK1 / RX, RY, RZ, VX, VY, VZ
COMMON / BLOCK2 / COLTIM, PARTNR
C *******************************************************************
C ** LOOKS FOR COLLISIONS WITH ATOMS J > I **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
REAL TIMBIG
PARAMETER ( TIMBIG = 1.0E10 )
INTEGER I
REAL SIGMA
REAL RX(N), RY(N), RZ(N), VX(N), VY(N), VZ(N)
REAL COLTIM(N)
INTEGER PARTNR(N)
INTEGER J
REAL RXI, RYI, RZI, RXIJ, RYIJ, RZIJ
REAL VXI, VYI, VZI, VXIJ, VYIJ, VZIJ
REAL RIJSQ, VIJSQ, BIJ, TIJ, DISCR, SIGSQ
C *******************************************************************
IF ( I .EQ. N ) RETURN
SIGSQ = SIGMA ** 2
COLTIM(I) = TIMBIG
RXI = RX(I)
RYI = RY(I)
RZI = RZ(I)
VXI = VX(I)
VYI = VY(I)
VZI = VZ(I)
DO 100 J = I + 1, N
RXIJ = RXI - RX(J)
RYIJ = RYI - RY(J)
RZIJ = RZI - RZ(J)
RXIJ = RXIJ - ANINT ( RXIJ )
RYIJ = RYIJ - ANINT ( RYIJ )
RZIJ = RZIJ - ANINT ( RZIJ )
VXIJ = VXI - VX(J)
VYIJ = VYI - VY(J)
VZIJ = VZI - VZ(J)
BIJ = RXIJ * VXIJ + RYIJ * VYIJ + RZIJ * VZIJ
IF ( BIJ .LT. 0.0 ) THEN
RIJSQ = RXIJ ** 2 + RYIJ ** 2 + RZIJ ** 2
VIJSQ = VXIJ ** 2 + VYIJ ** 2 + VZIJ ** 2
DISCR = BIJ ** 2 - VIJSQ * ( RIJSQ - SIGSQ )
IF ( DISCR .GT. 0.0 ) THEN
TIJ = ( -BIJ - SQRT ( DISCR ) ) / VIJSQ
IF ( TIJ .LT. COLTIM(I) ) THEN
COLTIM(I) = TIJ
PARTNR(I) = J
ENDIF
ENDIF
ENDIF
100 CONTINUE
RETURN
END
SUBROUTINE DNLIST ( SIGMA, J )
COMMON / BLOCK1 / RX, RY, RZ, VX, VY, VZ
COMMON / BLOCK2 / COLTIM, PARTNR
C *******************************************************************
C ** LOOKS FOR COLLISIONS WITH ATOMS I < J **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
REAL TIMBIG
PARAMETER ( TIMBIG = 1.E10 )
INTEGER J
REAL SIGMA
REAL RX(N), RY(N), RZ(N), VX(N), VY(N), VZ(N)
REAL COLTIM(N)
INTEGER PARTNR(N)
INTEGER I
REAL RXJ, RYJ, RZJ, RXIJ, RYIJ, RZIJ
REAL VXJ, VYJ, VZJ, VXIJ, VYIJ, VZIJ
REAL RIJSQ, VIJSQ, BIJ, TIJ, DISCR, SIGSQ
C *******************************************************************
IF ( J .EQ. 1 ) RETURN
SIGSQ = SIGMA ** 2
RXJ = RX(J)
RYJ = RY(J)
RZJ = RZ(J)
VXJ = VX(J)
VYJ = VY(J)
VZJ = VZ(J)
DO 100 I = 1, J - 1
RXIJ = RX(I) - RXJ
RYIJ = RY(I) - RYJ
RZIJ = RZ(I) - RZJ
RXIJ = RXIJ - ANINT ( RXIJ )
RYIJ = RYIJ - ANINT ( RYIJ )
RZIJ = RZIJ - ANINT ( RZIJ )
VXIJ = VX(I) - VXJ
VYIJ = VY(I) - VYJ
VZIJ = VZ(I) - VZJ
BIJ = RXIJ * VXIJ + RYIJ * VYIJ + RZIJ * VZIJ
IF ( BIJ .LT. 0.0 ) THEN
RIJSQ = RXIJ ** 2 + RYIJ ** 2 + RZIJ ** 2
VIJSQ = VXIJ ** 2 + VYIJ ** 2 + VZIJ ** 2
DISCR = BIJ ** 2 - VIJSQ * ( RIJSQ - SIGSQ )
IF ( DISCR .GT. 0.0 ) THEN
TIJ = ( - BIJ - SQRT ( DISCR ) ) / VIJSQ
IF ( TIJ .LT. COLTIM(I) ) THEN
COLTIM(I) = TIJ
PARTNR(I) = J
ENDIF
ENDIF
ENDIF
100 CONTINUE
RETURN
END
SUBROUTINE BUMP ( SIGMA, I, J, W )
COMMON / BLOCK1 / RX, RY, RZ, VX, VY, VZ
C *******************************************************************
C ** COMPUTES COLLISION DYNAMICS FOR PARTICLES I AND J. **
C ** **
C ** IT IS ASSUMED THAT I AND J ARE IN CONTACT. **
C ** THE ROUTINE ALSO COMPUTES COLLISIONAL VIRIAL W. **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
INTEGER I, J
REAL SIGMA, W
REAL RX(N), RY(N), RZ(N), VX(N), VY(N), VZ(N)
REAL RXIJ, RYIJ, RZIJ, FACTOR
REAL DELVX, DELVY, DELVZ, SIGSQ
C *******************************************************************
SIGSQ = SIGMA ** 2
RXIJ = RX(I) - RX(J)
RYIJ = RY(I) - RY(J)
RZIJ = RZ(I) - RZ(J)
RXIJ = RXIJ - ANINT ( RXIJ )
RYIJ = RYIJ - ANINT ( RYIJ )
RZIJ = RZIJ - ANINT ( RZIJ )
FACTOR = ( RXIJ * ( VX(I) - VX(J) ) +
: RYIJ * ( VY(I) - VY(J) ) +
: RZIJ * ( VZ(I) - VZ(J) ) ) / SIGSQ
DELVX = - FACTOR * RXIJ
DELVY = - FACTOR * RYIJ
DELVZ = - FACTOR * RZIJ
VX(I) = VX(I) + DELVX
VX(J) = VX(J) - DELVX
VY(I) = VY(I) + DELVY
VY(J) = VY(J) - DELVY
VZ(I) = VZ(I) + DELVZ
VZ(J) = VZ(J) - DELVZ
W = DELVX * RXIJ + DELVY * RYIJ + DELVZ * RZIJ
RETURN
END
SUBROUTINE READCN ( CNFILE )
COMMON / BLOCK1 / RX, RY, RZ, VX, VY, VZ
C *******************************************************************
C ** READS CONFIGURATION FROM CHANNEL 10 **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
INTEGER CNUNIT
PARAMETER ( CNUNIT = 10 )
INTEGER NN
CHARACTER CNFILE*(*)
REAL RX(N), RY(N), RZ(N), VX(N), VY(N), VZ(N)
C *******************************************************************
OPEN ( UNIT = CNUNIT, FILE = CNFILE,
: STATUS = 'OLD', FORM = 'UNFORMATTED' )
READ ( CNUNIT ) NN
IF ( NN .NE. N ) STOP 'N ERROR IN READCN'
READ ( CNUNIT ) RX, RY, RZ
READ ( CNUNIT ) VX, VY, VZ
CLOSE ( UNIT = CNUNIT )
RETURN
END
SUBROUTINE WRITCN ( CNFILE )
COMMON / BLOCK1 / RX, RY, RZ, VX, VY, VZ
C *******************************************************************
C ** WRITES CONFIGURATION TO CHANNEL 10 **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
INTEGER CNUNIT
PARAMETER ( CNUNIT = 10 )
CHARACTER CNFILE*(*)
REAL RX(N), RY(N), RZ(N), VX(N), VY(N), VZ(N)
C *******************************************************************
OPEN ( UNIT = CNUNIT, FILE = CNFILE,
: STATUS = 'UNKNOWN', FORM = 'UNFORMATTED' )
WRITE ( CNUNIT ) N
WRITE ( CNUNIT ) RX, RY, RZ
WRITE ( CNUNIT ) VX, VY, VZ
CLOSE ( UNIT = CNUNIT )
RETURN
END