Talk:World3 nonrenewable resource sector
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[edit] Python program used to simulate the nonrenewable resource sector:
#!/usr/bin/env python
import math
from dynamo import *
#levels
nr = "nr" #Nonrenewable resources
ic = "ic" #Industrial Captial
nrtd = "nrtd" #Nonrenewable resource technology initiated
#nruf2_l1 = "nruf2_l1" #Nonrenewable resource usage rate delay level
#nruf2_l2 = "nruf2_l2" #Nonrenewable resource usage rate delay level
#nruf2_l3 = "nruf2_l3" #Nonrenewable resource usage rate delay level
#rates
nrur = "nrur" #Nonrenewabel resource usage rate
icir = "icir" #Industrial capital investment rate
icdr = "icdr" #Industrial capital depreciation rate
#nruf2_r1 = "nruf2_r1" #Nonrenewable resource usage rate delay rate
#nruf2_r2 = "nruf2_r2" #Nonrenewable resource usage rate delay rate
#nruf2_r3 = "nruf2_r3" #Nonrenewable resource usage rate delay rate
nrate = "nrate" #Nonrenewable resource technology improvement rate
#axillaries
nruf = "nruf" #Nonrenewable resource usage factor
pcrum = "pcrum" #Per capita resource use multiplier
nrfr = "nrfr" #Nonrenewable resource fraction remaining
fcaor ="fcaor" #Fraction of capital allocated to obtaining resources
fcaor1 = "fcaor1" #Normal fcaor
fcaor2 = "fcaor2" #Alternative fcaor
pop = "pop" #Population
pop1 = "pop1" #Exponentially growing pop
io = "io" #Industrial output
iopc = "iopc" #Industrial output percapita
nruf2 = "nruf2" #Nonrenewable resource usage factor after recycle year
nrcm = "nrcm" #Resource technological change multiplier
icor = "icor" #Industrial capital output ratio
#constants
nri = 1e12 #Nonrenewable resources initial
nruf1 = 1 #Nonrenewable resource usage factor 1
popi = 1.65e9 #Initial population in 1900
gc = 0.012 #Population growth constant
zpgt = 2500 #Zero population growth time
pop2 = popi*math.exp(gc*(zpgt-1900)) #population at zpgt
ici = 2.1e11 #Industrial capital initial
fioaa = 0.12 #Fraction of industrial output allocated to agriculture
fioas = 0.12 #Fraction of industrial output allocated to services
fioac = 0.43 #Fraction of industrial output allocated to consumption
alic = 14.0 #Average life of industrial capital
pyear = 1995 #Year to switch nruf
tdd=10 #Technological development and implementation delay
dnrur=2e9 #Desired nonrenewable resource usage rate
#parameters
dt = 1.0
initial_time = 1900.0
#initial data
i = {}
#Initial levels
i[nr] = nri
i[ic] = ici
i[nrtd]=1.0
smooth3_init(i,nruf2,i[nrtd])
def calc_auxiliaries_and_rates(n,time):
#first the auxiliaries
n[nruf2] = smooth3_cur_value(n,nruf2)
n[nruf] = clip(n[nruf2],nruf1,time,pyear)
n[nrfr] = n[nr]/nri
n[fcaor1] = table_lookup(n[nrfr],0.0,1.0,0.1,[1.0, 0.9, 0.7, 0.5, 0.2, 0.1, 0.05, 0.05, 0.05, 0.05, 0.05])
n[fcaor2] = table_lookup(n[nrfr],0.0,1.0,0.1,[1.0, 0.9, 0.7, 0.5, 0.2, 0.1, 0.05, 0.05, 0.05, 0.05, 0.05])
n[fcaor] = clip(n[fcaor2],n[fcaor1],time,pyear)
n[pop1] = popi*math.exp(gc*(time-1900.0))
n[pop] = clip(pop2,n[pop1],time,zpgt)
n[icor] = table_lookup(n[nrtd],0.0,1.0,0.2,[6.0,3.3,3.1,3.06,3.02,3.0])
n[io] = n[ic]*(1.0 - n[fcaor])/n[icor]
n[iopc] = n[io]/n[pop]
n[pcrum] = table_lookup(n[iopc],0.0,1600.0,200.0,[0.0, 0.85, 2.6, 4.4, 5.4, 6.2, 6.8, 7.0, 7.0])
#then the rates
n[nrur] = n[pop]*n[pcrum]*n[nruf]
n[icir] = n[io]*(1.0-fioaa-fioas-fioac)
n[icdr] = n[ic]/alic
n[nrcm] = table_lookup(1.0-n[nrur]/dnrur,-1.0,0.0,1.0,[-0.05,0.0])
n[nrate] = clip(n[nrtd]*n[nrcm],0.0,time,pyear)
smooth3_next_rates(n, nruf2, n[nrtd], tdd)
calc_auxiliaries_and_rates(i,initial_time)
def get_next_time_step(j,time):
n = {}
#nextize levels
n[nr] = j[nr]+dt*(-j[nrur])
n[ic] = j[ic]+dt*(j[icir]-j[icdr])
n[nrtd] = j[nrtd]+dt*(j[nrate])
smooth3_next_levels(n,j,nruf2,dt)
calc_auxiliaries_and_rates(n,time)
return n
run_times(initial_time,dt,200,i,get_next_time_step)
Dynamo include:
import math
def print_sorted_keys(dict,width):
keys = dict.keys()
keys.sort()
f = "%"+str(width)+"s"
for key in keys[:-1]:
print (f+",") % key,
print f % keys[-1]
def print_sorted_values(dict,width):
keys = dict.keys()
keys.sort()
f = "%"+str(width)+"s"
for key in keys[:-1]:
print (f+",") % dict[key],
print f % dict[keys[-1]]
def run_times(initial_time,dt,times,initial,get_next_time_step):
prev = initial
width = 20
f = "%"+str(width)+"s,"
print f % "time",
print_sorted_keys(initial,width)
print f % initial_time,
print_sorted_values(initial,width)
for i in range(1,times+1):
time = i*dt + initial_time
next = get_next_time_step(prev,time)
print f % time,
print_sorted_values(next,width)
prev = next
print f % "time",
print_sorted_keys(initial,width)
def step(value,time,currentTime):
if currentTime >= time:
return value
else:
return 0.0
def clip(after_cutoff,before,value,cutoff_value):
if value < cutoff_value:
return before
else:
return after_cutoff
def table_lookup(value,low,high,increment,list):
if value <= low:
return list[0]
elif high <= value:
return list[-1]
else:
trans = (value - low)/increment
low_index = int(math.floor(trans))
delta = trans - low_index
return list[low_index]*(1.0-delta)+list[low_index+1]*delta
def smooth3_init(init_dictionary,name,value):
init_dictionary[name+"_l1"] = value
init_dictionary[name+"_l2"] = value
init_dictionary[name+"_l3"] = value
def smooth3_next_levels(cur_dict, prev_dict, name, dt):
cur_dict[name+"_l1"] = prev_dict[name+"_l1"]+dt*prev_dict[name+"_r1"]
cur_dict[name+"_l2"] = prev_dict[name+"_l2"]+dt*prev_dict[name+"_r2"]
cur_dict[name+"_l3"] = prev_dict[name+"_l3"]+dt*prev_dict[name+"_r3"]
def smooth3_next_rates(cur_dict, name, value, delay):
cur_dict[name+"_r1"] = (value - cur_dict[name+"_l1"])/(delay/3.0)
cur_dict[name+"_r2"] = (cur_dict[name+"_l1"] - cur_dict[name+"_l2"])/(delay/3.0)
cur_dict[name+"_r3"] = (cur_dict[name+"_l2"] - cur_dict[name+"_l3"])/(delay/3.0)
def smooth3_cur_value(cur_dict, name):
return cur_dict[name+"_l3"]
