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********************************************************************************
** FICHE F.33.  BROWNIAN DYNAMICS FOR  A LENNARD-JONES FLUID                  **
** 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 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

Modified: Sat Jul 22 04:41:16 2000 GMT
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