Comparison of three distributions¶
Code: #131-000
File: apps/fermi_gas/distribution_comparison.ipynb
Run it online: 
The aim of this notebook is to compare the distribution funciton for the Fermi-Dirac, Bose-Einstein and Maxwell-Boltzmann statistics.
Interface¶
The main interface (main_block_131_000) is divided in two VBox: left_block_131_000 and center_block_124_000.
left_block_124_000 contains three widgets to control scale and center of the figure: x_center_slider, x_width_slider and y_width_slider.
center_block_124_000 contains only the bqplot figure fig_131_001.
[1]:
from IPython.display import Image
Image(filename='../../static/images/apps/fermi_gas/131-000.png')
[1]:
The history saving thread hit an unexpected error (DatabaseError('database disk image is malformed')).History will not be written to the database.
Packages¶
[ ]:
import numpy as np
from bqplot import *
import bqplot as bq
import bqplot.marks as bqm
import bqplot.scales as bqs
import bqplot.axes as bqa
import ipywidgets as widgets
Main interface¶
[ ]:
#######################
### PARAMETERS ###
#######################
# Plot parameters
pts = 5000 # Number of points to calculate
# Initial values
x_center = 0.0 # Center of x-axis
x_width = 4.0 # Max. displacement from the center to either side
# Define x-axis values
x_values = np.linspace(-105.0,105.0,pts)
# Calculate distributions
BoseEinstein_values = np.empty(pts)
MaxwellBoltzmann_values = np.empty(pts)
FermiDirac_values = np.empty(pts)
for i in range(pts):
x = x_values[i]
if x > 0.01:
BoseEinstein_values[i] = 1.0/(np.exp(x)-1.0)
else:
BoseEinstein_values[i] = None #Cut off negative values and infinite at x=0.
if x > -5.0:
MaxwellBoltzmann_values[i] = 1.0/np.exp(x)
else:
MaxwellBoltzmann_values[i] = None #Cut off too high values
#MaxwellBoltzmann_values[i] = 1.0/np.exp(x)
FermiDirac_values[i] = 1.0/(np.exp(x)+1.0)
########################
###CREATE THE FIGURES###
########################
fig_131_001 = bq.Figure(title='Hiru banaketen konparazioa',
marks=[],
axes=[],
padding_x=0.0,
animation_duration=0,
legend_location='top-right',
legend_style= {'fill': 'white', 'stroke': 'grey'},
background_style= {'fill': 'white', 'stroke': 'black'},
fig_margin=dict(top=70, bottom=60, left=80, right=30),
layout = widgets.Layout(width='95%'),
toolbar = True,
)
scale_x_131_001 = bqs.LinearScale(min = x_center - x_width, max = x_center + x_width, allow_padding = False)
scale_y_131_001 = bqs.LinearScale(min = 0.0, max = 3.0)
axis_x_131_001 = bqa.Axis(
scale=scale_x_131_001,
tick_format='.1f',#'0.2f',
tick_style={'font-size': '15px'},
#tick_values = np.linspace(p_min, p_max, 7),
num_ticks=9,
grid_lines = 'none',
grid_color = '#8e8e8e',
label='e-mu/kbT',
label_location='middle',
label_style={'stroke': 'black', 'default-size': 35},
label_offset='50px')
axis_y_131_001 = bqa.Axis(
scale=scale_y_131_001,
tick_format='.1f',#'0.2f',
tick_style={'font-size': '15px'},
tick_values = np.linspace(0.0,5.0,6),
grid_lines = 'none',
grid_color = '#8e8e8e',
orientation='vertical',
label='n',
label_location='middle',
label_style={'stroke': 'red', 'default_size': 35},
label_offset='50px')
fig_131_001.axes = [axis_x_131_001, axis_y_131_001]
########################
####CREATE THE MARKS####
########################
lines_BoseEinstein_131_001 = bqm.Lines(
x = x_values,
y = BoseEinstein_values,
scales = {'x': scale_x_131_001, 'y': scale_y_131_001},
opacities = [1.0],
visible = True, #True, #t == '1.00',
colors = ["Blue"],
labels = ["Bose-Einstein"],
display_legend = True
)
lines_MaxwellBoltzmann_131_001 = bqm.Lines(
x = x_values,
y = MaxwellBoltzmann_values,
scales = {'x': scale_x_131_001, 'y': scale_y_131_001},
opacities = [1.0],
visible = True, #True, #t == '1.00',
colors = ["Green"],
labels = ["Maxwell-Boltzmann"],
display_legend = True
)
lines_FermiDirac_131_001 = bqm.Lines(
x = x_values,
y = FermiDirac_values,
scales = {'x': scale_x_131_001, 'y': scale_y_131_001},
opacities = [1.0],
visible = True, #True, #t == '1.00',
colors = ["Red"],
labels = ["Fermi-Dirac"],
display_legend = True
)
fig_131_001.marks = [lines_BoseEinstein_131_001, lines_MaxwellBoltzmann_131_001, lines_FermiDirac_131_001]
########################
###### WIDGETS #######
########################
x_center_slider = widgets.IntSlider(
value=0,
min=-4,
max=4,
step=1,
description='Zentroa:',
disabled=False,
continuous_update=True,
orientation='horizontal',
readout=True,
readout_format='d'
)
x_center_slider.observe(update_scales, 'value')
x_width_slider = widgets.IntSlider(
value=4,
min=1,
max=100,
step=1,
description='Zabalera:',
disabled=False,
continuous_update=True,
orientation='horizontal',
readout=True,
readout_format='d'
)
x_width_slider.observe(update_scales, 'value')
y_width_slider = widgets.IntSlider(
value=3,
min=1,
max=5,
step=1,
description='Zabalera:',
disabled=False,
continuous_update=True,
orientation='horizontal',
readout=True,
readout_format='d'
)
y_width_slider.observe(update_scales, 'value')
########################
###### INIT ########
########################
update_scales(None)
########################
###### LAYOUT ########
########################
## Left Block ##
left_block_131_000 = widgets.VBox([], layout=widgets.Layout(width='30%', align_items='center'))
left_block_131_000.children = [widgets.Label(value='$x$ ardatza zehaztu:'),
widgets.HBox([x_center_slider, widgets.Label(value='$(\epsilon-\mu )/ k_B T$')]),
widgets.HBox([x_width_slider, widgets.Label(value='$(\epsilon-\mu )/ k_B T$')]),
widgets.Label(value='$y$ ardatza zehaztu:'),
y_width_slider,
]
## Center Block ##
center_block_131_000 = widgets.VBox([], layout=widgets.Layout(width='70%', align_items='center'))
center_block_131_000.children = [fig_131_001]
## Main Block ##
main_block_131_000 = widgets.HBox([],layout=widgets.Layout(width='100%', align_items='center'))
main_block_131_000.children = [left_block_131_000, center_block_131_000]
main_block_131_000