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C *******************************************************************
C ** THIS FORTRAN CODE IS INTENDED TO ILLUSTRATE POINTS MADE IN **
C ** THE TEXT. TO OUR KNOWLEDGE IT WORKS CORRECTLY. HOWEVER IT IS **
C ** THE RESPONSIBILITY OF THE USER TO TEST IT, IF IT IS USED IN A **
C ** RESEARCH APPLICATION. **
C *******************************************************************
C *******************************************************************
C ** FICHE F.33. BROWNIAN DYNAMICS FOR A LENNARD-JONES FLUID **
C *******************************************************************
PROGRAM BROWND
COMMON / BLOCK1 / RX, RY, RZ, FX, FY, FZ
COMMON / BLOCK2 / D, XIC
C *******************************************************************
C ** BROWNIAN DYNAMICS WITH HYDRODYNAMIC INTERACTIONS **
C ** **
C ** REFERENCE: **
C ** **
C ** ERMAK AND MCCAMMON, J CHEM PHYS, 69, 1352, 1982. **
C ** **
C ** THIS PROGRAM TAKES A CONFIGURATION OF LENNARD JONES ATOMS **
C ** AND PERFORMS A BROWNIAN DYNAMICS SIMULATION. **
C ** THE ALGORITHM, DUE TO ERMAK AND MCCAMMON INCLUDES THE **
C ** HYDRODYNAMIC INTERACTION THROUGH EITHER THE OSEEN OR THE **
C ** ROTNE-PRAGER TENSOR. BEWARE! UNDER CERTAIN CONDITIONS THE **
C ** APPROXIMATE DIFFUSION TENSOR MAY NOT BE POSITIVE-DEFINITE **
C ** IN WHICH CASE THE PROGRAM WILL FAIL IN SUBROUTINE COVAR. **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** INTEGER N NUMBER OF ATOMS **
C ** INTEGER N3 NUMBER OF DEGREES OF FREEDOM **
C ** INTEGER MSTEP MAXIMUM NUMBER OF STEPS **
C ** INTEGER ISAVE STEPS BETWEEN DATA SAVE **
C ** INTEGER IPRINT STEPS BETWEEN OUTPUT **
C ** REAL RX(N),RY(N),RZ(N) POSITIONS **
C ** REAL FX(N),FY(N),FZ(N) FORCES **
C ** REAL XIC(I) CORRELATED RANDOM NORMAL DEVIATES **
C ** REAL D(N3,N3) THE DIFFUSION TENSOR **
C ** REAL DENS REDUCED DENSITY **
C ** REAL TEMP REDUCED TEMPERATURE **
C ** REAL DT REDUCED TIMESTEP **
C ** REAL SIGMA REDUCED LJ DIAMETER **
C ** REAL ETA REDUCED VISCOSITY **
C ** REAL CONSII CONSTANT FOR THE DIFFUSION TENSOR **
C ** REAL CONSIJ CONSTANT FOR THE DIFFUSION TENSOR **
C ** REAL RCUT REDUCED CUTOFF DISTANCE **
C ** REAL V THE CONFIGURATIONAL ENERGY **
C ** REAL W THE VIRIAL **
C ** **
C ** USAGE: **
C ** **
C ** THE SIMULATION IS PERFORMED IN A BOX OF UNIT LENGTH CENTRED **
C ** AT THE ORIGIN. **
C ** **
C ** UNITS: **
C ** **
C ** THE PROGRAM USES LENNARD-JONES UNITS FOR USER INPUT AND **
C ** OUTPUT BUT CONDUCTS THE SIMULATION IN A BOX OF UNIT LENGTH. **
C ** FOR EXAMPLE, FOR A BOXLENGTH L, THE UNITS ARE: **
C ** **
C ** PROPERTY LJ UNITS PROGRAM UNITS **
C ** **
C ** TEMP EPSILON/K EPSILON/K **
C ** DENS 1/SIGMA**3 1/L**3 **
C ** ETA SQRT(M*EPSILON/ SQRT(M*EPSILON/ **
C ** SIGMA**4) L**4) **
C ** DT SQRT(M*SIGMA**2/ SQRT(M*L**2/ **
C ** EPSILON) EPSILON) **
C ** **
C ** ROUTINES SUPPLIED: **
C ** **
C ** SUBROUTINE FORCE ( SIGMA, RCUT, CONSII, CONSIJ, V, W ) **
C ** CALCULATES THE DIFFUSION TENSOR AND THE SYSTEMATIC FORCE **
C ** ON EACH ATOM IN A PARTICULAR CONFIGURATION **
C ** SUBROUTINE MOVE ( DT, TEMP ) **
C ** MOVES THE ATOMS **
C ** SUBROUTINE READCN (CNFILE ) **
C ** READS IN A CONFIGURATION **
C ** SUBROUTINE WRITCN ( CNFILE ) **
C ** WRITES OUT A CONFIGURATION **
C ** SUBROUTINE COVAR ( DT ) **
C ** CALCULATES 3N CORRELATED NORMAL RANDOM DEVIATES **
C ** REAL FUNCTION GAUSS ( DUMMY ) **
C ** CALCULATES A NORMAL RANDOM VARIATE FROM A DISTRIBUTION **
C ** WITH ZERO MEAN AND UNIT VARIANCE **
C ** REAL FUNCTION RANF ( DUMMY ) **
C ** RETURNS A UNIFORM RANDOM NUMBER BETWEEN ZERO AND ONE **
C *******************************************************************
INTEGER N, N3
PARAMETER ( N = 32, N3 = 3 * N )
REAL RX(N), RY(N), RZ(N), FX(N), FY(N), FZ(N)
REAL D(N3,N3), XIC(N3)
REAL DENS, TEMP, DENLJ, ETA, DT
REAL SIGMA, RCUT, CONSII, CONSIJ
REAL PI, ACV, ACP, ACVSQ, ACPSQ
REAL AVV, AVP, FLV, FLP
REAL VLRC, VLRCA, VLRCR, WLRC, WLRCA, WLRCR
REAL V, W, RADIUS, VN, PRES, RANF, GAUSS, DUMMY
INTEGER STEP, I, NSTEP, ISAVE, IPRINT
CHARACTER TITLE*80, CNFILE*30
PARAMETER ( PI = 3.1415927 )
C *******************************************************************
C ** READ INPUT DATA **
WRITE(*,'(1H1,'' **** PROGRAM BROWND **** '')')
WRITE(*,'('' BROWNIAN DYNAMICS SIMULATION '')')
WRITE(*,'('' WITH HYDRODYNAMIC INTERACTIONS '')')
WRITE(*,'('' ENTER THE RUN TITLE '')')
READ (*,'(A)') TITLE
WRITE(*,'('' ENTER NUMBER OF STEPS '')')
READ (*,*) NSTEP
WRITE(*,'('' ENTER NUMBER OF STEPS BETWEEN DATA SAVES '')')
READ (*,*) ISAVE
WRITE(*,'('' ENTER NUMBER OF STEPS BETWEEN OUTPUT '')')
READ (*,*) IPRINT
WRITE(*,'('' ENTER THE CONFIGURATION FILE NAME '')')
READ (*,'(A)') CNFILE
WRITE(*,'(/)')
WRITE(*,'('' ENTER THE FOLLOWING IN LENNARD-JONES UNITS '',/)')
WRITE(*,'('' ENTER THE DENSITY '')')
READ (*,*) DENS
WRITE(*,'('' ENTER THE TEMPERATURE '')')
READ (*,*) TEMP
WRITE(*,'('' ENTER THE VISCOSITY '')')
READ (*,*) ETA
WRITE(*,'('' ENTER THE POTENTIAL CUTOFF DISTANCE '')')
READ (*,*) RCUT
WRITE(*,'('' ENTER THE TIMESTEP '')')
READ (*,*) DT
C ** WRITE INPUT DATA **
WRITE(*,'( //1X ,A )') TITLE
WRITE(*,'('' NUMBER OF ATOMS '',I10 )') N
WRITE(*,'('' NUMBER OF STEPS '',I10 )') NSTEP
WRITE(*,'('' SAVE FREQUENCY '',I10 )') ISAVE
WRITE(*,'('' OUTPUT FREQUENCY '',I10 )') IPRINT
WRITE(*,'('' CONFIGURATION FILE NAME '',A )') CNFILE
WRITE(*,'('' TEMPERATURE '',F10.4 )') TEMP
WRITE(*,'('' DENSITY '',F10.4 )') DENS
WRITE(*,'('' VISCOSITY '',F10.4 )') ETA
WRITE(*,'('' POTENTIAL CUTOFF '',F10.4 )') RCUT
WRITE(*,'('' TIMESTEP '',F10.4 )') DT
C ** READ IN INITIAL CONFIGURATION **
CALL READCN ( CNFILE )
C ** CONVERT INPUT DATA TO PROGRAM UNITS **
SIGMA = ( DENS / REAL(N) ) ** ( 1.0 / 3.0 )
RCUT = RCUT * SIGMA
DENLJ = DENS
DENS = DENS / ( SIGMA ** 3 )
ETA = ETA / ( SIGMA ** 2 )
RADIUS = SIGMA * 0.5
CONSII = TEMP / 6.0 / PI / ETA / RADIUS
CONSIJ = TEMP / 8.0 / PI / ETA
DT = DT * SIGMA
IF ( RCUT .GT. 0.5 ) STOP 'CUT-OFF TOO LARGE'
C ** LONG RANGE CORRECTIONS **
C ** SPECIFIC TO THE LENNARD JONES FLUID **
VLRCR = ( 8.0 * PI * DENLJ * ( SIGMA / RCUT ) ** 9 ) / 9.0
VLRCA = -( 8.0 * PI * DENLJ * ( SIGMA / RCUT ) ** 3 ) / 3.0
VLRC = VLRCR + VLRCA
WLRCR = 4.0 * REAL(N) * VLRCR
WLRCA = 2.0 * REAL(N) * VLRCA
WLRC = WLRCR + WLRCA
C ** ZERO ACCUMULATORS **
ACV = 0.0
ACP = 0.0
ACVSQ = 0.0
ACPSQ = 0.0
FLV = 0.0
FLP = 0.0
C ** WRITE OUT SOME USEFUL INFORMATION **
WRITE(*,'('' SIGMA/BOX = '',F10.4)') SIGMA
WRITE(*,'('' RCUT/BOX = '',F10.4)') RCUT
WRITE(*,'('' DT = '',F10.4)') DT
WRITE(*,'(/'' ** BROWNIAN DYNAMICS BEGINS ** ''/// )')
WRITE(*,'('' STEP V/N P ''/ )')
C *******************************************************************
C ** MAIN LOOP BEGINS **
C *******************************************************************
DO 100 STEP = 1, NSTEP
C ** CALCULATE THE DIFFUSION TENSOR AND SYSTEMATIC **
C ** FORCES AT THE BEGINNING OF THE STEP **
CALL FORCE ( SIGMA, RCUT, CONSII, CONSIJ, V, W )
C ** CALCULATE THE CORRELATED NORMAL VARIATES **
CALL COVAR ( DT )
C ** MOVE THE ATOMS **
CALL MOVE ( DT, TEMP )
C ** CALCULATE INSTANTANEOUS VALUES FOR PREVIOUS STEP **
VN = V / REAL ( N ) + VLRC
PRES = DENS * TEMP + W + WLRC
C ** CONVERT PRESSURE TO LJ UNITS **
PRES = PRES * SIGMA ** 3
C ** UPDATE ACCUMULATORS **
ACV = ACV + VN
ACP = ACP + PRES
ACVSQ = ACVSQ + VN * VN
ACPSQ = ACPSQ + PRES * PRES
C ** WRITE OUT RUNTIME INFORMATION **
IF( MOD( STEP, IPRINT ) .EQ. 0 ) THEN
WRITE( *, '( I8, 3F12.6 )' ) STEP, VN, PRES
ENDIF
C ** WRITE OUT THE CONFIGURATION AT INTERVALS **
IF ( MOD ( STEP, ISAVE ) .EQ. 0 ) THEN
CALL WRITCN ( CNFILE )
ENDIF
100 CONTINUE
C *******************************************************************
C ** MAIN LOOP ENDS **
C *******************************************************************
WRITE(*,'(/'' ** BROWNIAN DYNAMICS ENDS ** ''///)')
C ** CALCULATE AND WRITE OUT RUNNING AVERAGES **
AVV = ACV / REAL ( NSTEP )
AVP = ACP / REAL ( NSTEP )
ACVSQ = ( ACVSQ / REAL ( NSTEP ) ) - AVV ** 2
ACPSQ = ( ACPSQ / REAL ( NSTEP ) ) - AVP ** 2
C ** CALCULATE FLUCTUATIONS **
IF ( ACVSQ .GT. 0.0 ) FLV = SQRT ( ACVSQ )
IF ( ACPSQ .GT. 0.0 ) FLP = SQRT ( ACPSQ )
WRITE(*,'(/'' AVERAGES ''/ )')
WRITE(*,'('' = '',F10.6)') AVV
WRITE(*,'('' = '',F10.6)') AVP
WRITE(*,'(/'' FLUCTUATIONS ''/)')
WRITE(*,'('' FLUCTUATION IN = '',F10.6)') FLV
WRITE(*,'('' FLUCTUATION IN = '',F10.6)') FLP
WRITE(*,'(/'' END OF SIMULATION '')')
C ** WRITE OUT THE FINAL CONFIGURATION FROM THE RUN **
CALL WRITCN ( CNFILE )
STOP
END
SUBROUTINE READCN ( CNFILE )
COMMON / BLOCK1 / RX, RY, RZ
C *******************************************************************
C ** SUBROUTINE TO READ IN THE CONFIGURATION FROM UNIT 10 **
C *******************************************************************
INTEGER N
PARAMETER ( N = 32 )
CHARACTER CNFILE * ( * )
REAL RX(N), RY(N), RZ(N)
INTEGER CNUNIT, NN
PARAMETER ( CNUNIT = 10 )
C ********************************************************************
OPEN ( UNIT = CNUNIT, FILE = CNFILE, STATUS = 'UNKNOWN',
: FORM = 'UNFORMATTED' )
READ ( CNUNIT ) NN
IF ( NN .NE. N ) STOP 'PROBLEM WITH N IN READCN'
READ ( CNUNIT ) RX, RY, RZ
CLOSE ( UNIT = CNUNIT )
RETURN
END
SUBROUTINE WRITCN ( CNFILE )
COMMON / BLOCK1 / RX, RY, RZ
C *******************************************************************
C ** SUBROUTINE TO WRITE OUT THE CONFIGURATION TO UNIT 10 **
C *******************************************************************
INTEGER N
PARAMETER ( N = 32 )
CHARACTER CNFILE * ( * )
REAL RX(N), RY(N), RZ(N)
INTEGER CNUNIT
PARAMETER ( CNUNIT = 10 )
C ********************************************************************
OPEN ( UNIT = CNUNIT, FILE = CNFILE, STATUS = 'OLD',
: FORM = 'UNFORMATTED' )
WRITE ( CNUNIT ) N
WRITE ( CNUNIT ) RX, RY, RZ
CLOSE ( UNIT = CNUNIT )
RETURN
END
SUBROUTINE FORCE ( SIGMA, RCUT, CONSII, CONSIJ, V, W )
COMMON / BLOCK1 / RX, RY, RZ, FX, FY, FZ
COMMON / BLOCK2 / D, XIC
C *******************************************************************
C ** ROUTINE TO COMPUTE SYSTEMATIC FORCES AND THE DIFFUSION TENSOR **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** INTEGER N NUMBER OF ATOMS **
C ** INTEGER N3 NUMBER OF DEGREES OF FREEDOM **
C ** REAL RX(N),RY(N),RZ(N) POSITIONS **
C ** REAL FX(N),FY(N),FZ(N) FORCES **
C ** REAL D(N3,N3) THE DIFFUSION TENSOR **
C ** REAL XIC(N3) CORRELATED RANDOM NORMAL DEVIATES **
C ** REAL SIGMA THE LJ LENGTH PARAMETER **
C ** REAL RCUT THE CUT-OFF DISTANCE **
C ** REAL CONSII CONSTANT IN THE DIFFUSION TENSOR **
C ** REAL CONSIJ CONSTANT IN THE DIFFUSION TENSOR **
C ** REAL V THE POTENTIAL ENERGY **
C ** REAL W THE VIRIAL **
C ** **
C ** USAGE: **
C ** **
C ** FORCE IS CALLED IN A BROWNIAN DYNAMICS PROGRAM TO CALCULATE **
C ** THE SYSTEMATIC FORCE ON EACH ATOM AND THE ELEMENTS OF THE **
C ** DIFFUSION TENSOR. A CUTOFF IS APPLIED TO THE SYSTEMATIC FORCE **
C ** IT IS ASSUMED THAT THE LENNARD-JONES SIGMA IS ALSO THE ATOMIC **
C ** DIAMETER. **
C *******************************************************************
INTEGER N, N3
PARAMETER ( N = 32, N3 = N * 3 )
REAL SIGMA, RCUT, CONSII, CONSIJ, V, W
REAL RX(N), RY(N), RZ(N), FX(N), FY(N), FZ(N)
REAL D(N3,N3), XIC(N3)
INTEGER IC, JC, I, J
REAL RXI, RYI, RZI, FXIJ, FYIJ, FZIJ, FIJ, RCUTSQ
REAL SIGSQ, FXI, FYI, FZI, SR2, SR6, RIJ, RRIJSQ, SIGSQ6
REAL RIJSQ ,RXIJ, RYIJ, RZIJ, VIJ, WIJ, OIJ, RPIJ
C *******************************************************************
SIGSQ = SIGMA ** 2
RCUTSQ = RCUT ** 2
SIGSQ6 = SIGSQ / 6.0
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
C ** LOOP OVER ALL PAIRS OF ATOMS **
DO 100 I = 1, N - 1
RXI = RX(I)
RYI = RY(I)
RZI = RZ(I)
FXI = FX(I)
FYI = FY(I)
FZI = FZ(I)
IC = 3 * ( I - 1) + 1
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 * RXIJ + RYIJ * RYIJ + RZIJ * RZIJ
C ** CALCULATE OFF-DIAGONAL BLOCKS OF DIFFUSION TENSOR **
C ** HERE WE ASSUME THE ROTNE-PRAGER TENSOR FORM **
C ** TAKE RPIJ = 0 INSTEAD BELOW FOR OSEEN TENSOR **
JC = ( J - 1 ) * 3 + 1
RIJ = SQRT ( RIJSQ )
RRIJSQ = 1.0 / RIJSQ
OIJ = CONSIJ / RIJ
RPIJ = OIJ * SIGSQ6 * RRIJSQ
D( IC , JC ) = OIJ + RPIJ
: + ( OIJ - 3.0 * RPIJ ) * RXIJ * RXIJ * RRIJSQ
D( IC+1, JC+1 ) = OIJ + RPIJ
: + ( OIJ - 3.0 * RPIJ ) * RYIJ * RYIJ * RRIJSQ
D( IC+2, JC+2 ) = OIJ + RPIJ
: + ( OIJ - 3.0 * RPIJ ) * RZIJ * RZIJ * RRIJSQ
D( IC , JC+1 ) =
: ( OIJ - 3.0 * RPIJ ) * RXIJ * RYIJ * RRIJSQ
D( IC , JC+2 ) =
: ( OIJ - 3.0 * RPIJ ) * RXIJ * RZIJ * RRIJSQ
D( IC+1, JC+2 ) =
: ( OIJ - 3.0 * RPIJ ) * RYIJ * RZIJ * RRIJSQ
D( IC+1, JC ) = D( IC , JC+1 )
D( IC+2, JC ) = D( IC , JC+2 )
D( IC+2, JC+1 ) = D( IC+1, JC+2 )
C ** CALCULATE SYSTEMATIC FORCES **
IF( RIJSQ .LT. RCUTSQ ) THEN
SR2 = SIGSQ * RRIJSQ
SR6 = SR2 * SR2 * SR2
VIJ = SR6 * ( SR6 - 1.0 )
WIJ = SR6 * ( SR6 - 0.5 )
FIJ = WIJ * RRIJSQ
FXIJ = FIJ * RXIJ
FYIJ = FIJ * RYIJ
FZIJ = FIJ * RZIJ
V = V + VIJ
W = W + WIJ
FXI = FXI + FXIJ
FYI = FYI + FYIJ
FZI = FZI + FZIJ
FX(J) = FX(J) - FXIJ
FY(J) = FY(J) - FYIJ
FZ(J) = FZ(J) - FZIJ
ENDIF
99 CONTINUE
FX(I) = FXI
FY(I) = FYI
FZ(I) = FZI
100 CONTINUE
C ** INCORPORATE FACTORS **
V = V * 4.0
W = W * 48.0 / 3.0
DO 50 I = 1, N
FX(I) = FX(I) * 48.0
FY(I) = FY(I) * 48.0
FZ(I) = FZ(I) * 48.0
C ** CALCULATE ON-DIAGONAL BLOCKS OF DIFFUSION TENSOR **
IC = 3 * ( I - 1 ) + 1
D( IC , IC ) = CONSII
D( IC+1, IC+1 ) = CONSII
D( IC+2, IC+2 ) = CONSII
D( IC , IC+1 ) = 0.0
D( IC , IC+2 ) = 0.0
D( IC+1, IC+2 ) = 0.0
50 CONTINUE
C ** FILL THE LOWER TRIANGLE OF THE DIFFUSION TENSOR **
DO 70 IC = 1, N3 - 1
DO 60 JC = IC + 1, N3
D( JC, IC ) = D( IC, JC )
60 CONTINUE
70 CONTINUE
RETURN
END
SUBROUTINE COVAR ( DT )
COMMON / BLOCK2 / D, XIC
C *******************************************************************
C ** ROUTINE TO COMPUTE 3N CORRELATED RANDOM NORMAL DEVIATES. **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** INTEGER N NUMBER OF ATOMS **
C ** INTEGER N3 NUMBER OF DEGREES OF FREEDOM **
C ** REAL D(N3,N3) THE DIFFUSION TENSOR **
C ** REAL XIC(N3) CORRELATED RANDOM NORMAL DEVIATES **
C ** REAL XI(N3) UNCORRELATED RANDOM NORMAL DEVIATES **
C ** REAL L(N3,N3) A LOWER TRIANGULAR MATRIX **
C ** REAL DT REDUCED TIMESTEP **
C ** **
C ** USAGE: **
C ** **
C ** COVAR IS CALLED IN A BROWNIAN DYNAMICS SIMULATION AFTER THE **
C ** THE DIFFUSION TENSOR HAS BEEN CONSTRUCTED IN FORCE. ON EXIT **
C ** THE ARRAY XIC CONTAINS THE CORRELATED GAUSSIAN DISPLACEMENTS. **
C ** **
C ** ***************************************************** **
C ** ** WARNING ** **
C ** ** ** **
C ** ** THIS ROUTINE PERFORMS A STANDARD DECOMPOSITION ** **
C ** ** OF A POSITIVE DEFINITE MATRIX D INTO A PRODUCT ** **
C ** ** L * L(TRANSPOSE), WHERE L IS A LOWER TRIANGULAR ** **
C ** ** MATRIX. THIS IS EXPENSIVE FOR A LARGE MATRIX ** **
C ** ** AND YOU MAY FIND A MORE EFFICIENT OR ACCURATE ** **
C ** ** MACHINE CODE ROUTINE IN THE COMMON SCIENTIFIC ** **
C ** ** LIBRARIES SUCH AS NAG OR IMSL. IF THE MATRIX ** **
C ** ** IS NOT POSITIVE DEFINITE THE METHOD WILL FAIL. ** **
C ** ***************************************************** **
C ** **
C *******************************************************************
INTEGER N, N3
PARAMETER ( N = 32, N3 = N * 3 )
REAL D(N3,N3), XIC(N3)
REAL DT
INTEGER I, J, K, IC
REAL GAUSS, DUMMY, L(N3,N3), SUM, XI(N3)
C *******************************************************************
C ** CALCULATE THE LOWER TRIANGULAR MATRIX L **
L(1, 1) = SQRT ( D(1, 1) )
L(2, 1) = D(2, 1) / L(1, 1)
L(2, 2) = SQRT ( D(2, 2) - L(2, 1) * L(2, 1) )
DO 60 I = 3, N3
L(I, 1) = D(I, 1) / L(1, 1)
DO 40 J = 2, I - 1
SUM = 0.0
DO 30 K = 1, J - 1
SUM = SUM + L(I, K) * L(J, K)
30 CONTINUE
L(I, J) = ( D(I, J) - SUM ) / L(J, J)
40 CONTINUE
SUM = 0.0
DO 50 K = 1, I - 1
SUM = SUM + L(I, K) * L(I, K)
50 CONTINUE
L(I, I) = SQRT ( D(I, I) - SUM )
60 CONTINUE
C ** CALCULATE CORRELATED RANDOM DISPLACEMENTS **
DO 80 I = 1, N3
C ** CALCULATE UNCORRELATED RANDOM NORMAL DEVIATES **
C ** WITH ZERO MEAN AND VARIANCE 2.0 * DT **
XI(I) = GAUSS ( DUMMY ) * SQRT ( 2.0 * DT )
SUM = 0.0
DO 70 J = 1, I
SUM = SUM + L(I, J) * XI(J)
70 CONTINUE
XIC(I) = SUM
80 CONTINUE
RETURN
END
SUBROUTINE MOVE ( DT, TEMP )
COMMON / BLOCK1 / RX, RY, RZ, FX, FY, FZ
COMMON / BLOCK2 / D, XIC
C *******************************************************************
C ** ROUTINE TO MOVE THE ATOMS IN A BROWNIAN DYNAMICS SIMULATION **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** INTEGER N NUMBER OF ATOMS **
C ** INTEGER N3 NUMBER OF DEGREES OF FREEDOM **
C ** REAL RX(N),RY(N),RZ(N) POSITIONS **
C ** REAL FX(N),FY(N),FZ(N) FORCES **
C ** REAL D(N3,N3) THE DIFFUSION TENSOR **
C ** REAL XIC(N3) CORRELATED RANDOM NORMAL DEVIATES **
C ** REAL DT REDUCED TIMESTEP **
C ** REAL TEMP REDUCED TEMPERATURE **
C ** **
C ** USAGE: **
C ** **
C ** MOVE IS CALLED AFTER FORCE AND COVAR TO MOVE THE ATOMS. **
C *******************************************************************
INTEGER N, N3
PARAMETER ( N = 32, N3 = N * 3 )
REAL RX(N), RY(N), RZ(N), FX(N), FY(N), FZ(N)
REAL D(N3,N3), XIC(N3)
REAL DT, TEMP
REAL F(N3), SUMX, SUMY, SUMZ
INTEGER I, J, IC, JC
C *******************************************************************
C ** PLACE FORCES IN A TEMPORARY ARRAY OF SIZE 3N **
DO 10 I = 1, N
IC = ( I - 1 ) * 3 + 1
F(IC) = FX(I)
F(IC+1) = FY(I)
F(IC+2) = FZ(I)
10 CONTINUE
C ** MOVE THE ATOMS **
DO 30 I = 1, N
IC = ( I - 1 ) * 3 + 1
SUMX = 0.0
SUMY = 0.0
SUMZ = 0.0
DO 20 JC = 1, N3
SUMX = SUMX + D( IC , JC ) * F(JC)
SUMY = SUMY + D( IC+1, JC ) * F(JC)
SUMZ = SUMZ + D( IC+2, JC ) * F(JC)
20 CONTINUE
RX(I) = RX(I) + SUMX * DT / TEMP + XIC( IC )
RY(I) = RY(I) + SUMY * DT / TEMP + XIC( IC + 1 )
RZ(I) = RZ(I) + SUMZ * DT / TEMP + XIC( IC + 2 )
30 CONTINUE
RETURN
END
REAL FUNCTION RANF ( DUMMY )
C *******************************************************************
C ** FUNCTION RANF RETURNS A UNIFORM RANDOM VARIATE BETWEEN 0 AND 1**
C ** **
C ** *************** **
C ** ** WARNING ** **
C ** *************** **
C ** **
C ** GOOD RANDOM NUMBER GENERATORS ARE MACHINE SPECIFIC. **
C ** PLEASE USE THE ONE RECOMMENDED FOR YOUR MACHINE. **
C *******************************************************************
INTEGER L, C, M
PARAMETER ( L = 1029, C = 221591, M = 1048576 )
INTEGER SEED
REAL DUMMY
SAVE SEED
DATA SEED / 0 /
C *******************************************************************
SEED = MOD ( SEED * L + C, M )
RANF = REAL ( SEED ) / M
END
REAL FUNCTION GAUSS ( DUMMY )
C *******************************************************************
C ** FUNCTION GAUSS RETURNS A UNIFORM RANDOM NORMAL VARIATE FROM **
C ** A DISTRIBUTION WITH ZERO MEAN AND UNIT VARIANCE. **
C ** **
C ** REFERENCE: **
C ** KNUTH D, THE ART OF COMPUTER PROGRAMMING, (2ND EDITION **
C ** ADDISON-WESLEY), 1978. **
C *******************************************************************
REAL A1, A3, A5, A7, A9
PARAMETER ( A1 = 3.949846138, A3 = 0.252408784 )
PARAMETER ( A5 = 0.076542912, A7 = 0.008355968 )
PARAMETER ( A9 = 0.029899776 )
REAL SUM, R, R2
INTEGER I
C *******************************************************************
SUM = 0.0
DO 10 I = 1, 12
SUM = SUM + RANF ( DUMMY )
10 CONTINUE
R = ( SUM - 6.0 ) / 4.0
R2 = R * R
GAUSS = (((( A9 * R2 + A7 ) * R2 + A5 ) * R2 + A3 ) * R2 + A1 )
: * R
END
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