def InitAccels():
"""Initialize the molecular accelerations
"""
mol = _mdsim_globals['mol']
for m in mol:
m.ra = VecR()
m.ra_zero()
m.ra1 = VecR()
m.ra2 = VecR()
def EvalProps():
"""Evaluate thermodynamic properties
"""
density = _mdsim_globals['density']
deltaT = _mdsim_globals['deltaT']
mol = _mdsim_globals['mol']
nMol = _mdsim_globals['nMol']
uSum = _mdsim_globals['uSum']
virSum = _mdsim_globals['virSum']
vSum = VecR()
vvMax : float = 0.
vvSum : float = 0.
for m in mol:
rv_add(vSum, m)
vv = rv_dot(m, m)
vvSum += vv
vvMax = max([vvMax, vv])
_mdsim_globals['dispHi'] += math.sqrt(vvMax) * deltaT
if _mdsim_globals['dispHi'] > 0.5 * _mdsim_globals['rNebrShell']:
_mdsim_globals['nebrNow'] = True
_mdsim_globals['vSum'] = vSum
_mdsim_globals['kinEnergy'].val = 0.5 * vvSum / nMol
_mdsim_globals['totEnergy'].val = \
_mdsim_globals['kinEnergy'].val + uSum / nMol
_mdsim_globals['pressure'].val = density * (vvSum + virSum) / (nMol * NDIM)
def SetParams():
density = _mdsim_globals['density']
initUcell = _mdsim_globals['initUcell']
nebrTabFac = _mdsim_globals['nebrTabFac']
rNebrShell = _mdsim_globals['rNebrShell']
rCut = math.pow(2., 1./6.)
_mdsim_globals['rCut'] = rCut
region =\
VecR(x=1. / math.pow(density, 1./3.) * initUcell.x, \
y=1. / math.pow(density, 1./3.) * initUcell.y, \
z=1. / math.pow(density, 1./3.) * initUcell.z)
_mdsim_globals['region'] = region
# The total number of molecules
nMol = initUcell.x * initUcell.y * initUcell.z
_mdsim_globals['nMol'] = nMol
_mdsim_globals['velMag'] = \
math.sqrt(NDIM * (1. - 1. / nMol) * _mdsim_globals['temperature'])
_mdsim_globals['cells'] = \
VecI(x=(1. / (rCut + rNebrShell)) * region.x, \
y=(1. / (rCut + rNebrShell)) * region.y, \
z=(1. / (rCut + rNebrShell)) * region.z)
# The neighbor list size
_mdsim_globals['nebrTabMax'] = nebrTabFac * nMol
# Initialize kinEnery, pressure and totEnergy properties
_mdsim_globals['kinEnergy'] = Prop()
_mdsim_globals['pressure'] = Prop()
_mdsim_globals['totEnergy'] = Prop()
def InitVels():
"""Initialize the molecular velocities
"""
mol = _mdsim_globals['mol']
nMol = _mdsim_globals['nMol']
velMag = _mdsim_globals['velMag']
vSum = VecR(x=0., y=0., z=0.)
for m in mol:
m.rv = VecR()
rv_rand(m)
rv_scale(m, velMag)
rv_add(vSum, m)
_mdsim_globals['vSum'] = vSum
# Scale molecular velocities
for m in mol:
rv_sadd(m, -1. / nMol, vSum)
def InitCoords():
"""Initialize the molecular coordinates
"""
mol = _mdsim_globals['mol']
region = _mdsim_globals['region']
initUcell = _mdsim_globals['initUcell']
# gap = vecr_div(region, initUcell)
gap = region / initUcell
n = 0
for nz in range(initUcell.z):
for ny in range(initUcell.y):
for nx in range(initUcell.x):
c = VecR(x=nx + 0.5, y=ny + 0.5, z=nz + 0.5)
c *= gap
c += (-0.5 * region)
mol[n].r = c
mol[n].ro = VecR()
n += 1
def InitCoords():
"""Initialize the molecular coordinates
"""
mol = _mdsim_globals['mol']
region = _mdsim_globals['region']
initUcell = _mdsim_globals['initUcell']
gap = vecr_div(region, initUcell)
n = 0
for ny in range(initUcell.y):
for nx in range(initUcell.x):
c = VecR(x=nx + 0.5, y=ny + 0.5)
c = vecr_mul(c, gap)
c = vecr_sadd(c, -0.5, region)
mol[n].r = c
n += 1
def SetParams():
density = _mdsim_globals['density']
initUcell = _mdsim_globals['initUcell']
_mdsim_globals['rCut'] = math.pow(2., 1. / 6.)
_mdsim_globals['region'] = \
VecR(x=1. / math.sqrt(density) * initUcell.x, \
y=1. / math.sqrt(density) * initUcell.y)
# The total number of molecules
nMol = initUcell.x * initUcell.y
_mdsim_globals['nMol'] = nMol
_mdsim_globals['velMag'] = \
math.sqrt(NDIM * (1. - 1. / nMol) * _mdsim_globals['temperature'])
# Initialize kinEnery, pressure and totEnergy properties
_mdsim_globals['kinEnergy'] = Prop()
_mdsim_globals['pressure'] = Prop()
_mdsim_globals['totEnergy'] = Prop()
def EvalProps():
"""Evaluate thermodynamic properties
"""
density= _mdsim_globals['density']
mol = _mdsim_globals['mol']
nMol = _mdsim_globals['nMol']
uSum = _mdsim_globals['uSum']
virSum = _mdsim_globals['virSum']
vSum = VecR()
vvSum : float = 0.
for m in mol:
rv_add(vSum, m)
vvSum += rv_dot(m, m)
_mdsim_globals['vSum'] = vSum
_mdsim_globals['kinEnergy'].val = 0.5 * vvSum / nMol
_mdsim_globals['totEnergy'].val = \
_mdsim_globals['kinEnergy'].val + uSum / nMol
_mdsim_globals['pressure'].val = density * (vvSum + virSum) / (nMol * NDIM)
def BuildNebrList():
cc : VecI = None
m1v: VecI = None
m2v: VecI = None
# Mapping from cell vector to list index (column-major order):
# (c.z * cells.y + c.y) * cells.x + c.x
#
# With cells = VecI(3, 3, 3), list indices are:
vOff = [
VecI(0,0,0), # (0 * 3 + 0) * 3 + 0 -> 0
VecI(1,0,0), # (0 * 3 + 0) * 3 + 1 -> 1
VecI(1,1,0), # (0 * 3 + 1) * 3 + 1 -> 4
VecI(0,1,0), # (0 * 3 + 1) * 3 + 0 -> 3
VecI(-1,1,0), # (0 * 3 + 1) * 3 - 1 -> 2
VecI(0,0,1), # (1 * 3 + 0) * 3 + 0 -> 9
VecI(1,0,1), # (1 * 3 + 0) * 3 + 1 -> 10
VecI(1,1,1), # (1 * 3 + 1) * 3 + 1 -> 13
VecI(0,1,1), # (1 * 3 + 1) * 3 + 0 -> 12
VecI(-1,1,1), # (1 * 3 + 1) * 3 - 1 -> 11
VecI(-1,0,1), # (1 * 3 + 0) * 3 - 1 -> 8
VecI(-1,-1,1), # (1 * 3 - 1) * 3 - 1 -> 5
VecI(0,-1,1), # (1 * 3 - 1) * 3 + 0 -> 6
VecI(1,-1,1), # (1 * 3 - 1) * 3 + 1 -> 7
]
c : int = 0
j1 : int = 0
j2 : int = 0
cells = _mdsim_globals['cells']
cellList = _mdsim_globals['cellList']
nCells = cells.vol()
mol = _mdsim_globals['mol']
nMol = _mdsim_globals['nMol']
rCut = _mdsim_globals['rCut']
region = _mdsim_globals['region']
rNebrShell = _mdsim_globals['rNebrShell']
nebrTab = _mdsim_globals['nebrTab']
nebrTabMax = _mdsim_globals['nebrTabMax']
rrNebr = (rCut + rNebrShell) * (rCut + rNebrShell)
invWid: VecR = cells / region
for n in range(nMol, nMol + nCells):
cellList[n] = -1
for n in range(nMol):
rs = mol[n].r + (0.5 * region)
cc = VecI(rs.x * invWid.x, rs.y * invWid.y, rs.z * invWid.z)
c = cc.vc_to_list_index(cells) + nMol
cellList[n] = cellList[c]
cellList[c] = n
_mdsim_globals['nebrTabLen'] = 0
rshift = VecR()
for m1z in range(cells.z):
for m1y in range(cells.y):
for m1x in range(cells.x):
"""Vector cell index to which this molecule belongs."""
m1v = VecI(m1x,m1y,m1z)
"""Translate vector cell index, m1v, to cell list index."""
m1 = m1v.vc_to_list_index(cells) + nMol
for offset in range(N_OFFSET):
"""Vector cell relative to m1v."""
m2v = m1v + vOff[offset]
""" Periodic boundary-conditions/shift coordinates."""
rshift.zero()
_VCell_wrap_all(m2v, cells, rshift, region)
"""Translate vector cell index, m2v, to cell list index."""
m2 = m2v.vc_to_list_index(cells) + nMol
j1 = cellList[m1]
while j1 >= 0:
j2 = cellList[m2]
while j2 >= 0:
if m1 != m2 or j2 < j1:
a = mol[j1]
b = mol[j2]
dr = a.r_diff(b)
dr -= rshift
rr = vecr_dot(dr, dr)
if rr < rrNebr:
if _mdsim_globals['nebrTabLen'] >= nebrTabMax:
sys.exit(1)
nebrTabLen = _mdsim_globals['nebrTabLen']
nebrTab[2 * nebrTabLen] = j1
nebrTab[2 * nebrTabLen + 1] = j2
_mdsim_globals['nebrTabLen'] += 1
j2 = cellList[j2]
j1 = cellList[j1]
def ComputeForces():
"""Compute the MD forces by evaluating the LJ potential
using cells subdivisions. The simulation area, i.e., region,
is divided into a lattice of small cells and the cell edges all exceed
rcut. For this implementation:
rca = La/Lca, where Lca = FLOOR(La/rcut) (a = x, y, z), and La is
simulation box length in the a direction (region).
+---------------------------------------------+
| | | |
| -1 | 0 Lcx-1|Lcx |
| +---+---+---+---+---+---+---+---+ |
| | | | | |
+------+---+---+---+---+---+---+---+---+------+
"""
cc: VecI = None
m1v: VecI = None
m2v: VecI = None
# Mapping from cell vector to list index (column-major order):
# (c.z * cells.y + c.y) * cells.x + c.x
#
# With cells = VecI(3, 3, 3), list indices are:
vOff = [
VecI(0, 0, 0), # (0 * 3 + 0) * 3 + 0 -> 0
VecI(1, 0, 0), # (0 * 3 + 0) * 3 + 1 -> 1
VecI(1, 1, 0), # (0 * 3 + 1) * 3 + 1 -> 4
VecI(0, 1, 0), # (0 * 3 + 1) * 3 + 0 -> 3
VecI(-1, 1, 0), # (0 * 3 + 1) * 3 - 1 -> 2
VecI(0, 0, 1), # (1 * 3 + 0) * 3 + 0 -> 9
VecI(1, 0, 1), # (1 * 3 + 0) * 3 + 1 -> 10
VecI(1, 1, 1), # (1 * 3 + 1) * 3 + 1 -> 13
VecI(0, 1, 1), # (1 * 3 + 1) * 3 + 0 -> 12
VecI(-1, 1, 1), # (1 * 3 + 1) * 3 - 1 -> 11
VecI(-1, 0, 1), # (1 * 3 + 0) * 3 - 1 -> 8
VecI(-1, -1, 1), # (1 * 3 - 1) * 3 - 1 -> 5
VecI(0, -1, 1), # (1 * 3 - 1) * 3 + 0 -> 6
VecI(1, -1, 1), # (1 * 3 - 1) * 3 + 1 -> 7
]
c: int = 0
j1: int = 0
j2: int = 0
fcVal: float = 0.
uVal: float = 0.
rr: float = 0.
rrCut: float = 0.
rri: float = 0.
rri3: float = 0.
cells = _mdsim_globals['cells']
cellList = _mdsim_globals['cellList']
nCells = cells.vol()
mol = _mdsim_globals['mol']
nMol = _mdsim_globals['nMol']
region = _mdsim_globals['region']
rrCut = _mdsim_globals['rCut'] * _mdsim_globals['rCut']
invWid: VecR = cells / region
for n in range(nMol, nMol + nCells):
cellList[n] = -1
for n in range(nMol):
rs = mol[n].r + (0.5 * region)
cc = VecI(rs.x * invWid.x, rs.y * invWid.y, rs.z * invWid.z)
c = cc.vc_to_list_index(cells) + nMol
cellList[n] = cellList[c]
cellList[c] = n
for m in mol:
m.ra_zero()
_mdsim_globals['uSum'] = 0.
_mdsim_globals['virSum'] = 0.
# Compute cells interactions
shift = VecR()
for m1z in range(cells.z):
for m1y in range(cells.y):
for m1x in range(cells.x):
"""Vector cell index to which this molecule belongs."""
m1v = VecI(m1x, m1y, m1z)
"""Translate vector cell index, m1v, to cell list index."""
m1 = m1v.vc_to_list_index(cells) + nMol
for offset in range(N_OFFSET):
"""Vector cell relative to m1v."""
m2v = m1v + vOff[offset]
""" Periodic boundary-conditions/shift coordinates."""
shift.zero()
_VCell_wrap_all(m2v, cells, shift, region)
"""Translate vector cell index, m2v, to cell list index."""
m2 = m2v.vc_to_list_index(cells) + nMol
j1 = cellList[m1]
while j1 >= 0:
j2 = cellList[m2]
while j2 >= 0:
if m1 != m2 or j2 < j1:
a = mol[j1]
b = mol[j2]
dr = a.r_diff(b)
dr -= shift
rr = vecr_dot(dr, dr)
if rr < rrCut:
rri = 1. / rr
rri3 = rri**3
fcVal = 48.0 * rri3 * (rri3 - 0.5) * rri
uVal = 4. * rri3 * (rri3 - 1.) + 1.
# Molecule at: j1
a.ra_sadd(fcVal, dr)
# Molecule at: j2
b.ra_sadd(-fcVal, dr)
_mdsim_globals['uSum'] += uVal
_mdsim_globals['virSum'] += fcVal * rr
j2 = cellList[j2]
j1 = cellList[j1]
def ra_diff(a, b):
"""Return molecular acceleration difference.
"""
return VecR(a.ra.x - b.ra.x, a.ra.y - b.ra.y, a.ra.z - b.ra.z)
def rv_diff(a, b):
"""Return molecular velocity difference.
"""
return VecR(a.rv.x - b.rv.x, a.rv.y - b.rv.y, a.rv.z - b.rv.z)