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program langevin_motion
use, intrinsic :: iso_fortran_env
use :: omp_lib
implicit none
!> Define some basic parameters
integer(int64), parameter :: n = 1000
real(real64), parameter :: pi = 2.0_real64*asin(1.0_real64)
real(real64), parameter :: L = 1.0_real64
!> Numerical constants and such
real(real64), parameter :: dt = 0.00001_real64
real(real64), parameter :: t_max = 1.0_real64
real(real64), parameter :: kT = 10.0_real64
real(real64), parameter :: g = 1.0_real64
real(real64), parameter :: m = 1.0_real64
real(real64), parameter :: eps = 1.0_real64
real(real64), parameter :: sigma = 1E-03_real64
real(real64), parameter :: rc = sigma*2**(1.0_real64/6.0_real64)
real(real64), parameter :: pref1 = g, pref3 = sqrt(24.0_real64*kT*g/dt)
!> And non-constants
real(real64) :: t = 0.0_real64
real(real64), dimension(n) :: dx, dy, dn
real(real64), dimension(n) :: F
real(real64), dimension(n) :: ran1, ran2
integer(int64) :: i
!> Vectors for positon, velocity, acceleration, and tracking
real(real64), dimension(n) :: px, py, vx, vy, ax, ay, vhx, vhy
logical, dimension(n) :: is_tracked = .TRUE., are_interacting
!> Prepare random numbers
call random_seed()
!> Start by initializing the particles with a random pos. and vel.
call initialize_particles(px, py, vx, vy, ax, ay, kT, L, pi)
!> Now simulate!
do while (t .lt. t_max)
!> Update half-step velocities
vhx = vx + 0.5_real64*ax*dt
vhy = vy + 0.5_real64*ay*dt
!> Update the positions
px = px + vhx*dt
py = py + vhy*dt
!> Impose the boundary conditions
call impose_BC(px, py, vhx, vhy, is_tracked, L)
!> Find the new acceleration
ax = 0.0_real64
ay = 0.0_real64
!> Random numbers
call random_number(ran1)
ran1 = ran1 - 0.5_real64
call random_number(ran2)
ran2 = ran2 - 0.5_real64
!> Random force
!ax = ax - pref1*vhx + pref2*ran1
!ay = ay - pref1*vhy + pref2*ran2
!> Particle-particle interaction force
interactions: do i = 1,n
!> Calculate the distance between the particles:
dx = px(i) - px
dy = py(i) - py
dn = sqrt(dx**2 + dy**2)
!> Check which particles are interacting
are_interacting = (dn .gt. 0.0) .and. (dn .lt. rc) .and. is_tracked
!> Start with no forces
F = 0.0_real64
where (are_interacting)
!> Lennard-Jones force
F = 4.0_real64*eps*(12.0_real64*sigma**12/dn**13 - 6.0_real64*sigma**6/dn**7)
end where
!> Update the accelerations with the new force when a force was calculated
ax(i) = ax(i) + sum(F*dx / (dn*m), mask=are_interacting)
ay(i) = ay(i) + sum(F*dy / (dn*m), mask=are_interacting)
end do interactions
!> Update full velocities
vx = vhx + 0.5_real64*ax*dt
vy = vhy + 0.5_real64*ay*dt
!> Update timestep
t = t + dt
!> Print posiitons to stdout
!print '(e24.12,e24.12)', (px(i), py(i), i=1,n)
print *, sum(0.5_real64*m*vx**2 + 0.5_real64*m*vy**2, mask=is_tracked)
!> This splits timesteps into data blocks for Gnuplot
!print *
!print *
end do
contains
impure elemental subroutine initialize_particles(px, py, vx, vy, ax, ay, kT, L, pi)
real(real64), intent(in out) :: px, py, vx, vy, ax, ay
real(real64), intent(in) :: kT, L, pi
real(real64) :: ran1, ran2
!> Random number seed
!> And 2 random numbers
call random_number(ran1)
call random_number(ran2)
!> Initial position
px = L*(ran1-0.5_real64)
py = L*(ran2-0.5_real64)
!> Initial acceleration is zero
ax = 0.0_real64
ay = 0.0_real64
!> New random numbers
call random_number(ran1)
call random_number(ran2)
!> Initial velocity using Box-Muller transform
vx = sqrt(kT/m)*sqrt(-2.0_real64*log(ran1))*cos(2.0_real64*pi*ran2)
vy = sqrt(kT/m)*sqrt(-2.0_real64*log(ran1))*sin(2.0_real64*pi*ran2)
end subroutine initialize_particles
pure elemental subroutine impose_BC(px, py, vhx, vhy, is_tracked, L)
real(real64), intent(in out) :: px, py, vhx, vhy
real(real64), intent(in) :: L
logical, intent(in out) :: is_tracked
if (is_tracked) then
!> Top boundary
if (py.gt.L/2) then
py = L - py
vhy = -vhy
end if
!> Bottom boundary
if (py.lt.-L/2) then
py = -L - py
vhy = -vhy
end if
!> Left boundary
if (px.gt.L/2) then
px = L - px
vhx = -vhx
end if
!> Right boundary
if (px.lt.-L/2) then
px = -L - px
vhx = -vhx
end if
!> If the particle is still outside, it goes into the garbage
if (abs(px).gt.L/2 .or. abs(py) .gt. L/2) is_tracked = .false.
end if
end subroutine impose_BC
end program langevin_motion
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