def calc_variables():
"""Calculates all variables of interest.
They are collected and returned as a list, for use in the main program.
"""
from averages_module import VariableType
import numpy as np
import math
# Preliminary calculations (m_ratio, v_ratio, box are taken from the calling program)
vol = box**3 # Volume
rho = n / vol # Density
# Variables of interest, of class VariableType, containing three attributes:
# .val: the instantaneous value
# .nam: used for headings
# .method: indicating averaging method
# If not set below, .method adopts its default value of avg
# The .nam and some other attributes need only be defined once, at the start of the program,
# but for clarity and readability we assign all the values together below
# Move acceptance ratios
m_r = VariableType(nam='Move ratio', val=m_ratio, instant=False)
v_r = VariableType(nam='Volume ratio', val=v_ratio, instant=False)
# Density
density = VariableType(nam='Density', val=rho)
# Collect together into a list for averaging
return [m_r, v_r, density]
def calc_variables():
"""Calculates all variables of interest.
They are collected and returned as a list, for use in the main program.
"""
from averages_module import VariableType
# Preliminary calculations
kin = 0.5 * p * temperature # Kinetic energy for P-bead system
# Move ratio
m_r = VariableType(nam='Move ratio', val=m_ratio, instant=False)
# Classical potential energy
pe_cl = VariableType(nam='PE classical', val=pot_cl)
# Quantum potential energy
pe_qu = VariableType(nam='PE quantum', val=pot_qu)
# Energy
energy = VariableType(nam='Energy', val=kin + pot_cl - pot_qu)
# Collect together into a list for averaging
return [m_r, pe_cl, pe_qu, energy]
def calc_variables():
"""Calculates all variables of interest.
They are collected and returned as a list, for use in the main program."""
import numpy as np
from averages_module import VariableType
# Preliminary calculations
vol = box**3 # Volume
rho = n / vol # Density
# Variables of interest, of class VariableType, containing three attributes:
# .val: the instantaneous value
# .nam: used for headings
# .method: indicating averaging method
# If not set below, .method adopts its default value of avg
# The .nam and some other attributes need only be defined once, at the start of the program,
# but for clarity and readability we assign all the values together below
# We average over the time step
coll_rate = VariableType(nam='Collision rate',
val=2.0 * col_sum / dt / n,
instant=False)
# ideal + collisional virial / volume averaged over the time step
p_coll = VariableType(nam='P',
val=rho * temp_kinet + vir_sum / dt / vol,
instant=False)
# Collect together into a list for averaging
return [coll_rate, p_coll]
def calc_variables():
"""Calculates all variables of interest.
They are collected and returned as a list, for use in the main program.
"""
from averages_module import VariableType
import numpy as np
import math
from mc_hs_module import n_overlap
# Preliminary calculations (m_ratio, eps_box, box are taken from the calling program)
vir = n_overlap(box / (1.0 + eps_box), r) / (3.0 * eps_box) # Virial
vol = box**3 # Volume
rho = n / vol # Density
# Variables of interest, of class VariableType, containing three attributes:
# .val: the instantaneous value
# .nam: used for headings
# .method: indicating averaging method
# If not set below, .method adopts its default value of avg
# The .nam and some other attributes need only be defined once, at the start of the program,
# but for clarity and readability we assign all the values together below
# Move acceptance ratio
m_r = VariableType(nam='Move ratio', val=m_ratio, instant=False)
# Pressure in units kT/sigma**3
# Ideal gas contribution plus total virial divided by V
p_f = VariableType(nam='P', val=rho + vir / vol)
# Collect together into a list for averaging
return [m_r, p_f]
def calc_variables():
"""Calculates all variables of interest.
They are collected and returned as a list, for use in the main program.
"""
import numpy as np
import math
from averages_module import msd, cke, VariableType
# Preliminary calculations
kin = 0.5 * np.sum(v**2)
rcm = np.sum(r, axis=0) / n # Centre of mass
rsq = np.sum((r - rcm)**2) / n # Mean-squared distance from CM
eng = kin + total.pot # Total energy
# Variables of interest, of class VariableType, containing three attributes:
# .val: the instantaneous value
# .nam: used for headings
# .method: indicating averaging method
# If not set below, .method adopts its default value of avg
# The .nam and some other attributes need only be defined once, at the start of the program,
# but for clarity and readability we assign all the values together below
# Internal energy per atom
# Total KE plus total LJ nonbonded energy divided by N
e_f = VariableType(nam='E/N', val=eng / n)
# Kinetic temperature
# Remove 6 degrees of freedom for conserved linear and angular momentum
# and also (n-1) degrees of freedom for the bond constraints
t_k = VariableType(nam='T kinetic', val=2.0 * kin / (3 * n - (n - 1) - 6))
# Radius of gyration
r_g = VariableType(nam='Rg', val=math.sqrt(rsq))
# MSD of kinetic energy, intensive
# Use special method to convert to Cv/N
c_f = VariableType(nam='Cv/N',
val=kin / math.sqrt(n),
method=cke,
instant=False)
# Mean-squared deviation of conserved energy per atom
conserved_msd = VariableType(nam='Conserved MSD',
val=eng / n,
method=msd,
e_format=True,
instant=False)
# Collect together for averaging
return [e_f, t_k, r_g, c_f, conserved_msd]
def calc_variables():
"""Calculates all variables of interest.
They are collected and returned as a list, for use in the main program.
"""
import numpy as np
import math
from averages_module import msd, VariableType
from mc_chain_lj_module import potential, spring_pot, PotentialType
# Preliminary calculations
total = potential(r) # Nonbonded potential with overlap flag
assert not total.ovr, 'Overlap in configuration'
spr = spring_pot(bond, k_spring, r) # Total spring potential energy
rcm = np.sum(r, axis=0) / n # Centre of mass
rsq = np.sum((r - rcm)**2) / n # Mean-squared distance from CM
# Variables of interest, of class VariableType, containing three attributes:
# .val: the instantaneous value
# .nam: used for headings
# .method: indicating averaging method
# If not set below, .method adopts its default value of avg
# The .nam and some other attributes need only be defined once, at the start of the program,
# but for clarity and readability we assign all the values together below
# Move acceptance ratio
m_r = VariableType(nam='Regrow ratio', val=m_ratio, instant=False)
# Total potential energy per atom (excess, without ideal gas contribution)
# Total PE of bond springs plus total LJ PE (not cut, nor shifted) divided by N
e_x = VariableType(nam='PE/N', val=(spr + total.pot) / n)
# Radius of gyration
r_g = VariableType(nam='Rg', val=np.sqrt(rsq))
# Heat Capacity per atom (excess, without ideal gas contribution)
# MSD of PE / (sqrt(N)*T)
# Total PE of bond springs plus total LJ PE (not cut, nor shifted), divided by T
c_x = VariableType(nam='Cv(ex)/N',
val=(spr + total.pot) / (np.sqrt(n) * temperature),
method=msd,
instant=False)
# Collect together into a list for averaging
return [m_r, e_x, r_g, c_x]
def calc_variables():
"""Calculates all variables of interest.
They are collected and returned as a list, for use in the main program.
"""
# In this example we simulate using the shifted-force potential only
# The values of < p_sf >, < e_sf > and density should be consistent (for this potential)
# There are no long-range or delta corrections
from averages_module import VariableType
# Preliminary calculations
vol = box**3 # Volume
rho = n / vol # Density
# Variables of interest, of class VariableType, containing three attributes:
# .val: the instantaneous value
# .nam: used for headings
# .method: indicating averaging method
# If not set below, .method adopts its default value of avg
# The .nam and some other attributes need only be defined once, at the start of the program,
# but for clarity and readability we assign all the values together below
# Move acceptance ratio
m_r = VariableType(nam='Move ratio', val=m_ratio, instant=False)
# Internal energy per molecule (shifted-force potential)
# Ideal gas contribution (assuming nonlinear molecules) plus total PE divided by N
e_sf = VariableType(nam='E/N shifted force',
val=3.0 * temperature + total.pot / n)
# Pressure (shifted-force potential)
# Ideal gas contribution plus total virial divided by V
p_sf = VariableType(nam='P shifted force',
val=rho * temperature + total.vir / vol)
# Collect together into a list for averaging
return [m_r, e_sf, p_sf]
def calc_variables():
"""Calculates all variables of interest.
They are collected and returned as a list, for use in the main program.
"""
import numpy as np
from averages_module import VariableType
# Variables of interest, of class VariableType, containing three attributes:
# .val: the instantaneous value
# .nam: used for headings
# .method: indicating averaging method
# If not set below, .method adopts its default value of avg
# The .nam and some other attributes need only be defined once, at the start of the program,
# but for clarity and readability we assign all the values together below
# Move acceptance ratios
r_r = VariableType(nam='Regrow ratio', val=r_ratio, instant=False)
c_r = VariableType(nam='Crank ratio', val=c_ratio, instant=False)
p_r = VariableType(nam='Pivot ratio', val=p_ratio, instant=False)
# Collect together into a list for averaging
return [r_r, c_r, p_r]
def calc_variables():
"""Calculates all variables of interest.
They are collected and returned as a list, for use in the main program.
"""
import numpy as np
from averages_module import msd, VariableType
# Preliminary calculations
rcm = np.sum(r, axis=0) / n # Centre of mass
rsq = np.sum((r - rcm)**2) / n # Mean-squared distance from CM
# Variables of interest, of class VariableType, containing three attributes:
# .val: the instantaneous value
# .nam: used for headings
# .method: indicating averaging method
# If not set below, .method adopts its default value of avg
# The .nam and some other attributes need only be defined once, at the start of the program,
# but for clarity and readability we assign all the values together below
# Move acceptance ratios
r_r = VariableType(nam='Regrow ratio', val=r_ratio, instant=False)
c_r = VariableType(nam='Crank ratio', val=c_ratio, instant=False)
p_r = VariableType(nam='Pivot ratio', val=p_ratio, instant=False)
# Total potential energy per atom
# PE=negative of the number of square-well contacts divided by N
e_x = VariableType(nam='PE/N', val=-q / n)
# Radius of gyration
r_g = VariableType(nam='Rg', val=np.sqrt(rsq))
# Heat Capacity per atom (excess, without ideal gas contribution, extensive)
# MSD of PE / (sqrt(N)*T)
# PE==negative of the number of square-well contacts
c_x = VariableType(nam='Cv(ex)/N',
val=-q / (np.sqrt(n) * temperature),
method=msd,
instant=False)
# Collect together into a list for averaging
return [r_r, c_r, p_r, e_x, r_g, c_x]
def calc_variables ( ):
"""Calculates all variables of interest.
They are collected and returned as a list, for use in the main program.
"""
from averages_module import msd, VariableType
from lrc_module import potential_lrc, pressure_lrc
import numpy as np
import math
# Preliminary calculations (n,r,v,f,total are taken from the calling program)
vol = box**3 # Volume
rho = n / vol # Density
kin = 0.5*np.sum(v**2) # Kinetic energy
fsq = np.sum ( f**2 ) # Total squared force
ext = np.sum(0.5*p_eta**2/q) + np.sum(0.5*p_eta_baro**2/q_baro) + 0.5*p_eps**2/w_eps + temperature * (
g*eta[0] + np.sum(eta[1:])+ np.sum(eta_baro) ) # Extra terms for conserved variable
eng = kin + total.pot # Total energy (cut-and-shifted)
# Variables of interest, of class VariableType, containing three attributes:
# .val: the instantaneous value
# .nam: used for headings
# .method: indicating averaging method
# If not set below, .method adopts its default value of avg
# The .nam and some other attributes need only be defined once, at the start of the program,
# but for clarity and readability we assign all the values together below
# Internal energy (cut-and-shifted) per atom
# Total KE plus total cut-and-shifted PE divided by N
e_s = VariableType ( nam = 'E/N cut&shifted', val = eng/n )
# Internal energy (full, including LRC) per atom
# LRC plus total KE plus total cut (but not shifted) PE divided by N
e_f = VariableType ( nam = 'E/N full', val = potential_lrc(rho,r_cut) + (kin+total.cut)/n )
# Pressure (cut-and-shifted)
# Ideal gas contribution plus total virial divided by V
p_s = VariableType ( nam = 'P cut&shifted', val = rho*temperature + total.vir/vol )
# Pressure (full, including LRC)
# LRC plus ideal gas contribution plus total virial divided by V
p_f = VariableType ( nam = 'P full', val = pressure_lrc(rho,r_cut) + rho*temperature + total.vir/vol )
# Kinetic temperature
t_k = VariableType ( nam = 'T kinetic', val = 2.0*kin/g )
# Configurational temperature
# Total squared force divided by total Laplacian
t_c = VariableType ( nam = 'T config', val = fsq/total.lap )
# Density
density = VariableType ( nam = 'Density', val = rho )
# Conserved energy-like quantity per atom
# Energy plus PV term plus extra terms defined above
enp = eng + pressure*vol
conserved = VariableType ( nam = 'Conserved/N', val = (enp+ext)/n )
# Volume MSD
vol_msd = VariableType ( nam = 'Volume MSD', val = vol, method = msd, instant = False )
# Mean-squared deviation of conserved energy-like quantity
# Energy plus PV term plus extra terms defined above
enp = eng + pressure*vol
conserved_msd = VariableType ( nam = 'Conserved MSD', val = (enp+ext)/n,
method = msd, e_format = True, instant = False )
# Collect together into a list for averaging
return [ e_s, p_s, e_f, p_f, t_k, t_c, density, conserved, vol_msd, conserved_msd ]
def calc_variables():
"""Calculates all variables of interest.
They are collected and returned as a list, for use in the main program.
"""
# In this example we simulate using the cut (but not shifted) potential
# but we only report results which have had the long-range corrections applied
# The value of the cut-and-shifted potential is not used, in this example
import numpy as np
import math
from averages_module import VariableType
from lrc_module import potential_lrc, pressure_lrc
# Preliminary calculations (n,r,total are taken from the calling program)
vol = box**3 # Volume
rho = n / vol # Density
kin = 1.5 * n * p * temperature # Average kinetic energy for NP-atom system
kin_q = kin - total_spr # Quantum estimator for kinetic energy
rad_g = rad_gyr(r)
# Variables of interest, of class VariableType, containing three attributes:
# .val: the instantaneous value
# .nam: used for headings
# .method: indicating averaging method
# If not set below, .method adopts its default value of avg
# The .nam and some other attributes need only be defined once, at the start of the program,
# but for clarity and readability we assign all the values together below
# Acceptance ratio of atomic moves
r_r = VariableType(nam='Atomic move ratio', val=r_ratio, instant=False)
# Acceptance ratio of centre-of-mass moves
c_r = VariableType(nam='COM move ratio', val=c_ratio, instant=False)
# Internal energy per atom for full potential with LRC
# LRC plus cut (but not shifted) PE already divided by factor P
# plus KE estimator: total classical KE for NP-atom system MINUS total spring potential
# all divided by N
e_f = VariableType(nam='E/N full',
val=potential_lrc(rho, r_cut) + (kin_q + total.pot) / n)
# Kinetic energy per atom, just for interest's sake
k_q = VariableType(nam='KE/N', val=kin_q / n)
# Pressure for full potential with LRC
# LRC plus ideal gas contribution plus total virial divided by V
kin_q = kin_q / 1.5 # Convert KE estimator to kinetic energy part of pressure
p_f = VariableType(nam='P full',
val=pressure_lrc(rho, r_cut) +
(kin_q + total.vir) / vol)
# Quantum spring energy per atom, just for interest's sake
e_q = VariableType(nam='Espring/N', val=total_spr / n)
# Quantum polymer radius of gyration, just for interest's sake
r_g = VariableType(nam='Radius of gyration', val=rad_g)
# Collect together into a list for averaging
return [r_r, c_r, e_f, p_f, e_q, k_q, r_g]
def calc_variables():
"""Calculates all variables of interest.
They are collected and returned as a list, for use in the main program.
"""
# In this example we simulate using the cut (but not shifted) potential
# The values of < p_c >, < e_c > and < density > should be consistent (for this potential)
# For comparison, long-range corrections are also applied to give
# estimates of < e_f > and < p_f > for the full (uncut) potential
# The value of the cut-and-shifted potential is not used, in this example
import numpy as np
import math
from averages_module import msd, VariableType
from lrc_module import potential_lrc, pressure_lrc, pressure_delta
from mc_lj_module import force_sq
# Preliminary calculations (n,r,total are taken from the calling program)
vol = box**3 # Volume
rho = n / vol # Density
fsq = force_sq(box, r_cut, r) # Total squared force
# Variables of interest, of class VariableType, containing three attributes:
# .val: the instantaneous value
# .nam: used for headings
# .method: indicating averaging method
# If not set below, .method adopts its default value of avg
# The .nam and some other attributes need only be defined once, at the start of the program,
# but for clarity and readability we assign all the values together below
# Move, creation, and destruction acceptance ratios
m_r = VariableType(nam='Move ratio', val=m_ratio, instant=False)
c_r = VariableType(nam='Create ratio', val=c_ratio, instant=False)
d_r = VariableType(nam='Destroy ratio', val=d_ratio, instant=False)
# Number
number = VariableType(nam='N', val=float(n))
# Density
density = VariableType(nam='Density', val=rho)
# Internal energy per atom for simulated, cut, potential
# Ideal gas contribution plus cut (but not shifted) PE divided by N
e_c = VariableType(nam='E/N cut', val=1.5 * temperature + total.pot / n)
# Internal energy per atom for full potential with LRC
# LRC plus ideal gas contribution plus cut (but not shifted) PE divided by N
e_f = VariableType(nam='E/N full',
val=potential_lrc(rho, r_cut) + 1.5 * temperature +
total.pot / n)
# Pressure for simulated, cut, potential
# Delta correction plus ideal gas contribution plus total virial divided by V
p_c = VariableType(nam='P cut',
val=pressure_delta(rho, r_cut) + rho * temperature +
total.vir / vol)
# Pressure for full potential with LRC
# LRC plus ideal gas contribution plus total virial divided by V
p_f = VariableType(nam='P full',
val=pressure_lrc(rho, r_cut) + rho * temperature +
total.vir / vol)
# Configurational temperature
# Total squared force divided by total Laplacian
t_c = VariableType(nam='T config', val=fsq / total.lap)
# Number MSD
n_msd = VariableType(nam='N MSD', val=float(n), method=msd, instant=False)
# Collect together into a list for averaging
return [m_r, c_r, d_r, number, density, e_c, p_c, e_f, p_f, t_c, n_msd]
def calc_variables ( ):
"""Calculates all variables of interest.
They are collected and returned as a list, for use in the main program."""
import numpy as np
import math
from averages_module import msd, cke, VariableType
from lrc_module import potential_lrc, pressure_lrc
from md_lj_module import hessian
# Preliminary calculations (n,r,v,f,total are taken from the calling program)
vol = box**3 # Volume
rho = n / vol # Density
kin = 0.5*np.sum(v**2) # Kinetic energy
tmp = 2.0 * kin / (3*n-3) # Remove three degrees of freedom for momentum conservation
fsq = np.sum ( f**2 ) # Total squared force
hes = hessian(box,r_cut,r,f) # Total Hessian
eng = kin + total.pot # Total energy for simulated system
# Variables of interest, of class VariableType, containing three attributes:
# .val: the instantaneous value
# .nam: used for headings
# .method: indicating averaging method
# If not set below, .method adopts its default value of avg
# The .nam and some other attributes need only be defined once, at the start of the program,
# but for clarity and readability we assign all the values together below
# Internal energy (cut-and-shifted) per atom
# Total KE plus total cut-and-shifted PE divided by N
e_s = VariableType ( nam = 'E/N cut&shifted', val = eng/n )
# Internal energy (full, including LRC) per atom
# LRC plus total KE plus total cut (but not shifted) PE divided by N
e_f = VariableType ( nam = 'E/N full', val = potential_lrc(rho,r_cut) + (kin+total.cut)/n )
# Pressure (cut-and-shifted)
# Ideal gas contribution plus total virial divided by V
p_s = VariableType ( nam = 'P cut&shifted', val = rho*tmp + total.vir/vol )
# Pressure (full, including LRC)
# LRC plus ideal gas contribution plus total virial divided by V
p_f = VariableType ( nam = 'P full', val = pressure_lrc(rho,r_cut) + rho*tmp + total.vir/vol )
# Kinetic temperature
t_k = VariableType ( nam = 'T kinetic', val = tmp )
# Configurational temperature
# Total squared force divided by total Laplacian with small Hessian correction
t_c = VariableType ( nam = 'T config', val = fsq/(total.lap-(2.0*hes/fsq)) )
# MSD of kinetic energy, intensive
# Use special method to convert to Cv/N
c_s = VariableType ( nam = 'Cv/N cut&shifted', val = kin/math.sqrt(n), method = cke, instant = False )
# Mean-squared deviation of conserved energy per atom
conserved_msd = VariableType ( nam = 'Conserved MSD', val = eng/n,
method = msd, e_format = True, instant = False )
# Collect together into a list for averaging
return [ e_s, p_s, e_f, p_f, t_k, t_c, c_s, conserved_msd ]
def calc_variables():
"""Calculates all variables of interest.
They are collected and returned as a list, for use in the main program.
"""
# In this example we simulate using the cut (but not shifted) potential
# Accordingly, < p_c > should match the input pressure and the values
# of < p_c >, < e_c > and density should be consistent (for this potential)
# For comparison, long-range corrections are also applied to give
# estimates of < e_f > and < p_f > for the full (uncut) potential
# The value of the cut-and-shifted potential is not used, in this example
import numpy as np
import math
from averages_module import msd, VariableType
from lrc_module import potential_lrc, pressure_lrc, pressure_delta
from mc_lj_module import force_sq
# Preliminary calculations (n,r,total are taken from the calling program)
vol = box**3 # Volume
rho = n / vol # Density
fsq = force_sq(box, r_cut, r) # Total squared force
# Variables of interest, of class VariableType, containing three attributes:
# .val: the instantaneous value
# .nam: used for headings
# .method: indicating averaging method
# If not set below, .method adopts its default value of avg
# The .nam and some other attributes need only be defined once, at the start of the program,
# but for clarity and readability we assign all the values together below
# Move and volume acceptance ratios
m_r = VariableType(nam='Move ratio', val=m_ratio, instant=False)
v_r = VariableType(nam='Volume ratio', val=v_ratio, instant=False)
# Density
density = VariableType(nam='Density', val=rho)
# Internal energy per atom for simulated, cut, potential
# Ideal gas contribution plus cut (but not shifted) PE divided by N
e_c = VariableType(nam='E/N cut', val=1.5 * temperature + total.pot / n)
# Internal energy per atom for full potential with LRC
# LRC plus ideal gas contribution plus cut (but not shifted) PE divided by N
e_f = VariableType(nam='E/N full',
val=potential_lrc(rho, r_cut) + 1.5 * temperature +
total.pot / n)
# Pressure for simulated, cut, potential
# Delta correction plus ideal gas contribution plus total virial divided by V
p_c = VariableType(nam='P cut',
val=pressure_delta(rho, r_cut) + rho * temperature +
total.vir / vol)
# Pressure for full potential with LRC
# LRC plus ideal gas contribution plus total virial divided by V
p_f = VariableType(nam='P full',
val=pressure_lrc(rho, r_cut) + rho * temperature +
total.vir / vol)
# Configurational temperature
# Total squared force divided by total Laplacian
t_c = VariableType(nam='T config', val=fsq / total.lap)
# Heat capacity (cut but not shifted)
# MSD of excess "enthalpy" divided by temperature and sqrt(N) to make result intensive
# NB this is not really the excess Cp/NkB, it simply omits the kinetic energy fluctuations
# i.e. we add the ideal gas part of Cv/NkB, 1.5, to get total Cp/NkB
enp = total.pot + pressure * vol
c_c = VariableType(nam='Cp/N cut',
val=enp / (temperature * math.sqrt(n)),
method=msd,
add=1.5,
instant=False)
# Heat capacity (full)
# MSD of excess "enthalpy" divided by temperature and sqrt(N) to make result intensive
# NB this is not really the excess Cp/NkB, it simply omits the kinetic energy fluctuations
# i.e. we add the ideal gas part of Cv/NkB, 1.5, to get total Cp/NkB
enp = n * potential_lrc(rho, r_cut) + total.pot + pressure * vol
c_f = VariableType(nam='Cp/N full',
val=enp / (temperature * math.sqrt(n)),
method=msd,
add=1.5,
instant=False)
# Volume MSD
vol_msd = VariableType(nam='Volume MSD',
val=vol,
method=msd,
instant=False)
# Collect together into a list for averaging
return [m_r, v_r, density, e_c, p_c, e_f, p_f, t_c, c_c, c_f, vol_msd]
def calc_variables():
"""Calculates all variables of interest.
They are collected and returned as a list, for use in the main program.
"""
import numpy as np
import math
from averages_module import msd, VariableType
from lrc_module import potential_lrc, pressure_lrc
# Preliminary calculations (n,r,total are taken from the calling program)
vol = box**3 # Volume
rho = n / vol # Density
fsq = np.sum(f**2) # Total squared force
# Variables of interest, of class VariableType, containing three attributes:
# .val: the instantaneous value
# .nam: used for headings
# .method: indicating averaging method
# If not set below, .method adopts its default value of avg
# The .nam and some other attributes need only be defined once, at the start of the program,
# but for clarity and readability we assign all the values together below
# Move acceptance ratio
m_r = VariableType(nam='Move ratio', val=m_ratio, instant=False)
# Internal energy per atom for simulated, cut-and-shifted, potential
# Ideal gas contribution plus total cut-and-shifted PE divided by N
e_s = VariableType(nam='E/N cut&shifted',
val=1.5 * temperature + total.pot / n)
# Internal energy per atom for full potential with LRC
# LRC plus ideal gas contribution plus total cut (but not shifted) PE divided by N
e_f = VariableType(nam='E/N full',
val=potential_lrc(rho, r_cut) + 1.5 * temperature +
total.cut / n)
# Pressure for simulated, cut-and-shifted, potential
# Ideal gas contribution plus total virial divided by V
p_s = VariableType(nam='P cut&shifted',
val=rho * temperature + total.vir / vol)
# Pressure for full potential with LRC
# LRC plus ideal gas contribution plus total virial divided by V
p_f = VariableType(nam='P full',
val=pressure_lrc(rho, r_cut) + rho * temperature +
total.vir / vol)
# Configurational temperature
# Total squared force divided by total Laplacian
t_c = VariableType(nam='T config', val=fsq / total.lap)
# Heat capacity (excess, cut-and-shifted)
# Total PE divided by temperature and sqrt(N) to make result intensive
# We add ideal gas contribution, 1.5, afterwards
c_s = VariableType(nam='Cv/N cut&shifted',
val=total.pot / (temperature * math.sqrt(n)),
method=msd,
add=1.5,
instant=False)
# Heat capacity (excess, full)
# Total PE divided by temperature and sqrt(N) to make result intensive; LRC does not contribute
# We add ideal gas contribution, 1.5, afterwards
c_f = VariableType(nam='Cv/N full',
val=total.cut / (temperature * math.sqrt(n)),
method=msd,
add=1.5,
instant=False)
# Collect together into a list for averaging
return [m_r, e_s, p_s, e_f, p_f, t_c, c_s, c_f]
def calc_variables():
"""Calculates all variables of interest.
They are collected and returned as a list, for use in the main program.
"""
from averages_module import msd, VariableType
from lrc_module import potential_lrc, pressure_lrc
import numpy as np
import math
# Preliminary calculations (n,v,f,total are taken from the calling program)
vol = box**3 # Volume
rho = n / vol # Density
kin = 0.5 * np.sum(v**2) # Kinetic energy
fsq = np.sum(f**2) # Total squared force
# Variables of interest, of class VariableType, containing three attributes:
# .val: the instantaneous value
# .nam: used for headings
# .method: indicating averaging method
# If not set below, .method adopts its default value of avg
# The .nam and some other attributes need only be defined once, at the start of the program,
# but for clarity and readability we assign all the values together below
# Internal energy (cut-and-shifted) per atom
# Total KE plus total cut-and-shifted PE divided by N
e_s = VariableType(nam='E/N cut&shifted', val=(kin + total.pot) / n)
# Internal energy (full, including LRC) per atom
# LRC plus total KE plus total cut (but not shifted) PE divided by N
e_f = VariableType(nam='E/N full',
val=potential_lrc(rho, r_cut) + (kin + total.cut) / n)
# Pressure (cut-and-shifted)
# Ideal gas contribution plus total virial divided by V
p_s = VariableType(nam='P cut&shifted',
val=rho * temperature + total.vir / vol)
# Pressure (full, including LRC)
# LRC plus ideal gas contribution plus total virial divided by V
p_f = VariableType(nam='P full',
val=pressure_lrc(rho, r_cut) + rho * temperature +
total.vir / vol)
# Kinetic temperature
# Momentum is not conserved, hence 3N degrees of freedom
t_k = VariableType(nam='T kinetic', val=2.0 * kin / (3 * n))
# Configurational temperature
# Total squared force divided by total Laplacian
t_c = VariableType(nam='T config', val=fsq / total.lap)
# Heat capacity (cut-and-shifted)
# Total energy divided by temperature and sqrt(N) to make result intensive
c_s = VariableType(nam='Cv/N cut&shifted',
val=(kin + total.pot) / (temperature * math.sqrt(n)),
method=msd,
instant=False)
# Heat capacity (full)
# Total energy divided by temperature and sqrt(N) to make result intensive; LRC does not contribute
c_f = VariableType(nam='Cv/N full',
val=(kin + total.cut) / (temperature * math.sqrt(n)),
method=msd,
instant=False)
# Collect together into a list for averaging
return [e_s, p_s, e_f, p_f, t_k, t_c, c_s, c_f]
def calc_variables():
"""Calculates all variables of interest.
They are collected and returned as a list, for use in the main program.
"""
# In this example we simulate using the cut (but not shifted) potential
# The values of < p_c >, < e_c > and < density > should be consistent (for this potential)
# For simplicity, long-range corrections are not applied here to give estimates of
# < e_f > and < p_f > for the full (uncut) potential, but this is straightforward to do.
# The value of the cut-and-shifted potential is not used, in this example
import numpy as np
import math
from averages_module import VariableType
from lrc_module import potential_lrc, pressure_lrc, pressure_delta
# Preliminary calculations (n1,n2,r1,r2,etc are taken from the calling program)
vol1 = box1**3 # Volume
vol2 = box2**3 # Volume
rho1 = n1 / vol1 # Density
rho2 = n2 / vol2 # Density
# Variables of interest, of class VariableType, containing three attributes:
# .val: the instantaneous value
# .nam: used for headings
# .method: indicating averaging method
# If not set below, .method adopts its default value of avg
# The .nam and some other attributes need only be defined once, at the start of the program,
# but for clarity and readability we assign all the values together below
# Move, swap, volume exchange acceptance ratios
m1_r = VariableType(nam='Move ratio (1)', val=m1_ratio, instant=False)
m2_r = VariableType(nam='Move ratio (2)', val=m2_ratio, instant=False)
x12_r = VariableType(nam='Swap ratio (1->2)', val=x12_ratio, instant=False)
x21_r = VariableType(nam='Swap ratio (2->1)', val=x21_ratio, instant=False)
v_r = VariableType(nam='Volume ratio', val=v_ratio, instant=False)
# Number of particles
n_1 = VariableType(nam='Number (1)', val=float(n1))
n_2 = VariableType(nam='Number (2)', val=float(n2))
# Density
density_1 = VariableType(nam='Density (1)', val=rho1)
density_2 = VariableType(nam='Density (2)', val=rho2)
# Internal energy per atom for simulated, cut, potential
# Ideal gas contribution plus cut (but not shifted) PE divided by N
e1_c = VariableType(nam='E/N cut (1)',
val=1.5 * temperature + total1.pot / n1)
e2_c = VariableType(nam='E/N cut (2)',
val=1.5 * temperature + total2.pot / n2)
# Pressure for simulated, cut, potential
# Delta correction plus ideal gas contribution plus total virial divided by V
p1_c = VariableType(nam='P cut (1)',
val=pressure_delta(rho1, r_cut) + rho1 * temperature +
total1.vir / vol1)
p2_c = VariableType(nam='P cut (2)',
val=pressure_delta(rho2, r_cut) + rho2 * temperature +
total2.vir / vol2)
# Collect together into a list for averaging
return [
m1_r, m2_r, x12_r, x21_r, v_r, n_1, n_2, density_1, density_2, e1_c,
e2_c, p1_c, p2_c
]
def calc_variables():
"""Calculates all variables of interest.
They are collected and returned as a list, for use in the main program."""
import numpy as np
import math
from averages_module import msd, VariableType
from maths_module import q_to_a
# Preliminary calculations (n,r,v,total are taken from the calling program)
vol = box**3 # Volume
rho = n / vol # Density
kin_t = 0.5 * np.sum(v**2) # Translational kinetic energy
kin_r = 0.0
for i, ei in enumerate(e):
ai = q_to_a(ei) # Rotation matrix for i
ell_i = np.dot(ai, ell[i, :]) # Get body-fixed angular momentum
kin_r = kin_r + np.sum(
(ell_i**2) / inertia) # Increment kinetic energy
kin_r = kin_r / 2 # Rotational kinetic energy
tmp_t = 2.0 * kin_t / (
3 * n - 3) # Remove three degrees of freedom for momentum conservation
tmp_r = 2.0 * kin_r / (3 * n) # 3N degrees of rotational freedom
eng = kin_t + kin_r + total.pot # Total energy for simulated system
# Variables of interest, of class VariableType, containing three attributes:
# .val: the instantaneous value
# .nam: used for headings
# .method: indicating averaging method
# If not set below, .method adopts its default value of avg
# The .nam and some other attributes need only be defined once, at the start of the program,
# but for clarity and readability we assign all the values together below
# Internal energy (shifted-force potential) per atom
# Total translational and rotational KE plus total PE divided by N
if nvt:
e_sf = VariableType(nam='E/N shifted force',
val=3.0 * temperature + total.pot / n)
else:
e_sf = VariableType(nam='E/N shifted force', val=eng / n)
# Pressure (shifted-force potential)
# Ideal gas contribution plus total virial divided by V
if nvt:
p_sf = VariableType(nam='P shifted force',
val=rho * temperature + total.vir / vol)
else:
p_sf = VariableType(nam='P shifted force',
val=rho * tmp_t + total.vir / vol)
# Kinetic translational temperature
t_t = VariableType(nam='T translational', val=tmp_t)
# Kinetic rotational temperature
t_r = VariableType(nam='T rotational', val=tmp_r)
# Mean-squared deviation of conserved energy per atom
conserved_msd = VariableType(nam='Conserved MSD',
val=eng / n,
method=msd,
e_format=True,
instant=False)
# Collect together into a list for averaging
return [e_sf, p_sf, t_t, t_r, conserved_msd]