Initialization¶

---

The basics¶

BubbleBox.mdbox lowers the threshold for initializing systems by assuming lot's of default settings. Actually, you can initialize a system without any parameters, defaulting to an infinite 3D space with a single particle at rest.

In [1]:

import bubblebox as bb

b = bb.mdbox() #initialize a default system

import bubblebox as bb b = bb.mdbox() #initialize a default system

This is of course not that interesting, so you should at least provide a number of bubbles and the system size:

In [ ]:

n_bubbles = 100
size = (10,10)
b = bb.mdbox(n_bubbles, size = size) #initialize closed 10 by 10 box with 100 bubbles distributed in a grid
b.view() #display system to screen

n_bubbles = 100 size = (10,10) b = bb.mdbox(n_bubbles, size = size) #initialize closed 10 by 10 box with 100 bubbles distributed in a grid b.view() #display system to screen

The size parameters¶

You can initialize a system of any dimensionality, and for each dimension you may choose one out of three boundary conditions. The dimensionality is automatically inferred from the number of parameters in size, for instance:

In [ ]:

b = bb.mdbox(n_bubbles, size = (2,2)) # a two dimensional closed system with size 2x2
b = bb.mdbox(n_bubbles, size = (2,3,4)) # a three dimensional closed system with size 2x3x4
b = bb.mdbox(n_bubbles, size = (2,2,2,2)) # a four dimensional closed system with size 2x2x2x2

b = bb.mdbox(n_bubbles, size = (2,2)) # a two dimensional closed system with size 2x2 b = bb.mdbox(n_bubbles, size = (2,3,4)) # a three dimensional closed system with size 2x3x4 b = bb.mdbox(n_bubbles, size = (2,2,2,2)) # a four dimensional closed system with size 2x2x2x2

The boundary conditions are inferred from the sign of the dimension. When negative, the boundary will be periodic (exiting particles will enter on the opposite side), when 0 the dimension will be infinite, and if positive the boundary will yield perfectly inelastic collisions (particles will bounce back). For instance:

In [ ]:

b = bb.mdbox(n_bubbles, size = (2,-2)) # a two dimensional system, closed along x, periodic along y with size 2x2
b = bb.mdbox(n_bubbles, size = (-3,-3,-3)) # a three dimensional periodic system with size 3x3x3
b = bb.mdbox(n_bubbles, size = (0,0,0,0)) # a infinite four dimensional system

b = bb.mdbox(n_bubbles, size = (2,-2)) # a two dimensional system, closed along x, periodic along y with size 2x2 b = bb.mdbox(n_bubbles, size = (-3,-3,-3)) # a three dimensional periodic system with size 3x3x3 b = bb.mdbox(n_bubbles, size = (0,0,0,0)) # a infinite four dimensional system

The showcase module¶

While you can easily build, customize and combine mdbox-systems in various ways, it is in many cases easier to start with a default system. The showcase module contains a range of predefined setups for mdbox. An overview may be found by calling:

In [ ]:

from IPython.display import Markdown
Markdown(help(bb.showcase))

from IPython.display import Markdown Markdown(help(bb.showcase))

These systems are initialized typically as

In [ ]:

b = bb.showcase.fcc_custom() # a face-centered cubic lattice
b.view()

b = bb.showcase.fcc_custom() # a face-centered cubic lattice b.view()

Graph-based (and SMILES) input¶

Finally, you may wish to start from a graph-based definition of connectivity. Two functionalities are included in mdbox for doing this, with one requiring the installation of pysmiles ( ) and the other only requiring lists of nodes and edges.

A typically procedure is as follows:

In [4]:

from bubblebox.mdbox import smiles2graph, graph2bb


atoms, edges = smiles2graph("""CC(=O)NCCC1=CNc2c1cc(OC)cc2""") # read vanillin

b = graph2bb(atoms, edges, relax = False) #convert to mdbox object and relax

#b.evince()
b.view()

from bubblebox.mdbox import smiles2graph, graph2bb atoms, edges = smiles2graph("""CC(=O)NCCC1=CNc2c1cc(OC)cc2""") # read vanillin b = graph2bb(atoms, edges, relax = False) #convert to mdbox object and relax #b.evince() b.view()

MDView(bg_color=[1.0, 1.0, 1.0], box=[50, 50, 50], colors=[[0.8277645921193568, 0.5855073902470505, 0.54152077…

In [5]:

for i in range(10000):
    b.advance()
    b.vel_ *= .999
    b.update_view()

for i in range(10000): b.advance() b.vel_ *= .999 b.update_view()

In [6]:

b.evince()

b.evince()

SpotlightView(aperture=0.0001, bg_color=[1.0, 1.0, 1.0], bonds=[[0, 1], [0, 17], [0, 18], [0, 19], [1, 2], [1,…

In [8]:

B = b*2

B.view()

B = b*2 B.view()

MDView(bg_color=[1.0, 1.0, 1.0], box=[150, 150, 150], colors=[[0.5071324219989345, 0.3372346264213911, 0.92033…

In [10]:

b = bb.mdbox(100, size = (4,4))

b.view()

b = bb.mdbox(100, size = (4,4)) b.view()

MDView(bg_color=[1.0, 1.0, 1.0], box=[4, 4], colors=[[0.16231944653007102, 0.09197764308060097, 0.112859250776…

In [103]:

from bubblebox.mdbox import pos2heatmap, no_force

import numpy as np

def particle_count(b, Nz = 11, col = None):
    """
    Create a 2D density array for a set of various bubbles
    Author: Audun Skau Hansen (a.s.hansen@kjemi.uio.no)
            Hanan Gharayba

    Keyword arguments:
    
    pos              -- array (2,n_particles) containing positions
    masses           -- array (n_particles) containing masses
    Lx, Ly           -- box dimensions
    Nz               -- number of bins in each dimension

    Returns an Nz by Nz by 3 array containing colors according to 
    bubble density
    """

    if type(Nz) in [int, float]:
        Nz_ = [Nz for i in range(len(b.size))]
        Nz = np.array(Nz_)
        
    print(Nz)

    Z = np.zeros(Nz, dtype = int)


    for i in range(b.pos.shape[1]):
        indx = []
        for j in range(len(b.size)):
            indx.append( int( Nz[j]*(b.pos[j,i] + b.size[j])/(2*b.size[j]) ) )
        
        #ix, iy = int( Nz*(b.pos[0,i] + b.size[0])/(2*b.size[0]) ), int( Nz*(b.pos[1,i] + b.size[1])/(2*b.size[1]) )
        
        Z[tuple(indx)] += 1

    return Z

b = bb.mdbox(100, size =(4,4), vel = 2)
b.pos *= 0.0
b.set_forces(no_force)
for i in range(10):
    b.advance()
    #b.vel_ *= 0.998
    
Z = particle_count(b, Nz = np.array([6,4])) #pos2heatmap(b.pos, b.masses, b.size[0], b.size[1], Nz = 5)
#Z[:,:, 3]
print(np.sum(Z))

from bubblebox.mdbox import pos2heatmap, no_force import numpy as np def particle_count(b, Nz = 11, col = None): """ Create a 2D density array for a set of various bubbles Author: Audun Skau Hansen (a.s.hansen@kjemi.uio.no) Hanan Gharayba Keyword arguments: pos -- array (2,n_particles) containing positions masses -- array (n_particles) containing masses Lx, Ly -- box dimensions Nz -- number of bins in each dimension Returns an Nz by Nz by 3 array containing colors according to bubble density """ if type(Nz) in [int, float]: Nz_ = [Nz for i in range(len(b.size))] Nz = np.array(Nz_) print(Nz) Z = np.zeros(Nz, dtype = int) for i in range(b.pos.shape[1]): indx = [] for j in range(len(b.size)): indx.append( int( Nz[j]*(b.pos[j,i] + b.size[j])/(2*b.size[j]) ) ) #ix, iy = int( Nz*(b.pos[0,i] + b.size[0])/(2*b.size[0]) ), int( Nz*(b.pos[1,i] + b.size[1])/(2*b.size[1]) ) Z[tuple(indx)] += 1 return Z b = bb.mdbox(100, size =(4,4), vel = 2) b.pos *= 0.0 b.set_forces(no_force) for i in range(10): b.advance() #b.vel_ *= 0.998 Z = particle_count(b, Nz = np.array([6,4])) #pos2heatmap(b.pos, b.masses, b.size[0], b.size[1], Nz = 5) #Z[:,:, 3] print(np.sum(Z))

[6 4]
100

In [106]:

import matplotlib.pyplot as plt



for i in range(1000):
    b.advance()


Nz = 4
Z = particle_count(b, Nz = np.array([4,4]))
plt.figure(figsize = (8,8))
#for i in range(Nz):
#    plt.axhline(b.size[0]/)



for i in range(Nz):
    plt.axhline(i-.5, linewidth = 1, color = (0,0,0))
    plt.axvline(i-.5, linewidth = 1, color = (0,0,0))
    for j in range(Nz):
        t = np.linspace(0,2*np.pi, Z[i,j]+1)[:-1]
        plt.plot(i+.2*np.cos(t), j+.2*np.sin(t), ".", markersize = 10, color = (.7,0,0))
        plt.text(i, j, "%i" %Z[i,j], ha = "center", va = "center")

plt.axhline(Nz-.5, linewidth = 1, color = (0,0,0))
plt.axvline(Nz-.5, linewidth = 1, color = (0,0,0))
        
plt.axis("off")
plt.xlim(-1, Nz)
plt.ylim(-1, Nz)
plt.show()

print(np.sum(Z))

import matplotlib.pyplot as plt for i in range(1000): b.advance() Nz = 4 Z = particle_count(b, Nz = np.array([4,4])) plt.figure(figsize = (8,8)) #for i in range(Nz): # plt.axhline(b.size[0]/) for i in range(Nz): plt.axhline(i-.5, linewidth = 1, color = (0,0,0)) plt.axvline(i-.5, linewidth = 1, color = (0,0,0)) for j in range(Nz): t = np.linspace(0,2*np.pi, Z[i,j]+1)[:-1] plt.plot(i+.2*np.cos(t), j+.2*np.sin(t), ".", markersize = 10, color = (.7,0,0)) plt.text(i, j, "%i" %Z[i,j], ha = "center", va = "center") plt.axhline(Nz-.5, linewidth = 1, color = (0,0,0)) plt.axvline(Nz-.5, linewidth = 1, color = (0,0,0)) plt.axis("off") plt.xlim(-1, Nz) plt.ylim(-1, Nz) plt.show() print(np.sum(Z))

[4 4]

100

In [45]:

b.view()

b.view()

MDView(bg_color=[1.0, 1.0, 1.0], box=[4, 4], colors=[[0.029335247596076308, 0.9416819404860864, 0.524573650447…

In [84]:

a = np.random.uniform(-1,1,(5,5,5))
a[tuple([1,2,3])]

a = np.random.uniform(-1,1,(5,5,5)) a[tuple([1,2,3])]

Out[84]:

-0.7412144383030279

In [ ]: