Unit_Conversion
The main purpose of this program is to facilitate the conversion between the International System of Units (SI) and the Natural Units (NU).
I will briefly explain the methods for converting between unit systems and the definition of initial values, and provide a conversion table from SI to NU units.
Conversion Methods and Initial Values
- Some initial values defined in the International System of Units (SI) ：
Based on these initial values, we can start the conversion between different units ；
-
Let’s take the conversion of meters (m) as an example；
First, we identify the variables related to meters in the initial values and eliminate other variables except for energy：
Next, we adjust and simplify the equations to extract the desired units of length ：
The final value of 1m in the natural unit system is obtained; using the above method to convert common units, the results are as follows :
- Conversion tables between the natural system of units and the International System of Units ：
Methods for calling specific functions：
The function is divided into three parts: conversion from NU to SI, conversion from SI to NU, and the search for conversion parameters.
- The conversion from SI to NU.
where coef_J_to_E = λ； epsilon0 = ε ； k = kb; hbar = h
x = coef_J_to_E
conversion_dictionary = \
{'Joules':1/x,'meter': 3.16304*10**(25)*hbar*c*x,'second':9.48253*10**(33)*hbar*x,\
'kilogram':8.98752*10**(16)/(x*c**2),'Kelvin':1.38065*10**(-23)/(x*k),\
'Ampere':1.99347*10**(-16)*math.sqrt(c*epsilon0)/(x*math.sqrt(hbar)),\
'Coulomb':1.89032*10**(18)*math.sqrt(hbar*c*epsilon0),\
'Tesla':5.01397*10**(-36)/(x**2*hbar**(3/2)*c**(5/2)*math.sqrt(epsilon0)),\
'Volt/m':1.67248*10**(-44)/(x**2*hbar**(3/2)*c**(3/2)*math.sqrt(epsilon0)), \
'momentum':2.99792*10**8/(x*c),'force':3.16152*10**-26/(x**2*hbar*c),\
'unit charge': 0.302862*math.sqrt(hbar*c*epsilon0)}
- The conversion from NU to SI.
if conversion_direction == 'LHQCD_to_SI':
conversion_dictionaryy = \
{'TO_Joules':1/conversion_dictionary['Joules'],'TO_meter': 1/conversion_dictionary['meter'],\
'TO_second':1/conversion_dictionary['second'],'TO_kilogram':1/conversion_dictionary['kilogram'],\
'TO_Kelvin':1/conversion_dictionary['Kelvin'],'TO_Ampere':1/conversion_dictionary['Ampere'],\
'TO_Coulomb':1/conversion_dictionary['Coulomb'],'TO_Tesla':1/conversion_dictionary['Tesla'],\
'TO_Volt/m':1/conversion_dictionary['Volt/m'], 'TO_momentum':1/conversion_dictionary['momentum'],\
'TO_force':1/conversion_dictionary['force'],'TO_unit charge':1/conversion_dictionary['unit charge']}
return conversion_dictionaryy
- The selection of conversion parameters.
def determine_coefficient_for_unit_conversion(dt, dx, dx_volume, dp, dp_volume,\
n_max, n_average, v_max, E, B):
print('Searching for proper scaling parameters...')
print('This may take several minutes.')
for i in range(-35,35,1):
hbar = 10**i
for j in range(9,-9,-1):
c = 10**j
for k in range(-30,30,1):
lambdax = 10**k
for h in range(-13,13,1):
epsilon0 = 10**h
try:
conversion_table = \
unit_conversion('SI_to_LHQCD', coef_J_to_E=lambdax, hbar=hbar, c=c, k=1., epsilon0=epsilon0)
dt_converted = dt*conversion_table['second']
dx_converted = dx*conversion_table['meter']
dp_converted = dp*conversion_table['momentum']
dx_volum_converted = dx_volume*conversion_table['meter']**3
dp_volume_converted = dp_volume*conversion_table['momentum']**3
f_max_converted = n_max/(dx_volum_converted*dp_volume_converted)
unit_charge_converted = 1.6*10**(-19)*conversion_table['Coulomb']
v_max_converted = v_max*conversion_table['meter']/conversion_table['second']
rho_max_converted = unit_charge_converted*\
n_average/dx_volum_converted
J_max_converted = rho_max_converted*v_max_converted
E_coef_converted = 1/(4*math.pi*epsilon0)*rho_max_converted*dx +\
E*conversion_table['Volt/m']
B_coef_converted = 1/(4*math.pi*epsilon0*c**2)*J_max_converted*dx+\
B*conversion_table['Tesla']
F_converted = unit_charge_converted*(E_coef_converted+v_max_converted*B_coef_converted)
if 10**(-10)<abs(E_coef_converted)<10**10 and\
10**(-10)<abs(B_coef_converted)<10**10 and\
10**(-10)<(1/dt_converted)<10**10 and \
10**(-10)<abs((F_converted/dp_converted)<10**10 and \
10**(-10)<(v_max_converted/dx_converted))<10**10 and \
10**(-5)<rho_max_converted<10**5 and \
10**(-5)<J_max_converted<10**5 and\
10**(-10)<f_max_converted<10**10:
return hbar, c, lambdax, epsilon0
except: pass