二维胶粒计算几何¶

In [ ]:

from deplete.segm import *
from deplete.colloids import *
from deplete.curve import Curve

from deplete.segm import * from deplete.colloids import * from deplete.curve import Curve

Triangular colloids¶

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triangloid(1.4).draw(label="Circle")
triangloid(1.3, 1).draw(label="Arcs")
triangloid(1, 1, 0.1, 0.2).draw(label="Convex")
triangloid(0.8, 1, 0.1, -0.3).draw(label="Concave")
legend();
axis('equal');

triangloid(1.4).draw(label="Circle") triangloid(1.3, 1).draw(label="Arcs") triangloid(1, 1, 0.1, 0.2).draw(label="Convex") triangloid(0.8, 1, 0.1, -0.3).draw(label="Concave") legend(); axis('equal');

Basics¶

• axis('equal'); will give a 1:1 scaling
• .draw() will draw the curve, with matplotlib arguments
• .offset() will offset/etch a colloid by a positive/negative offset argument
• .shift() will move a curve
• .rotate() will rotate curve about the origin
• .area() will compute area of colloid

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c=triangloid(1, 1, 0.2, -0.3)
c.draw(label='Colloid')
c.shift([2,-1]).draw(label='Shifted')
c.rotate(pi/3).draw(label='Rotated')
c.offset(0.1).draw('--', label='Offset')
c.offset(-0.1).draw('--', label='Etched')
legend();
axis('equal');
print("The area of colloid is {}".format(c.area()))

c=triangloid(1, 1, 0.2, -0.3) c.draw(label='Colloid') c.shift([2,-1]).draw(label='Shifted') c.rotate(pi/3).draw(label='Rotated') c.offset(0.1).draw('--', label='Offset') c.offset(-0.1).draw('--', label='Etched') legend(); axis('equal'); print("The area of colloid is {}".format(c.area()))

The area of colloid is 2.483660510623751

Interaction between colloids¶

• The depletion potential is determined by intersection of offset boundaries
• show_colloids() will visualize the interaction between colloids

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c1=triangloid(1,0.5,0.2,0.4).rotate(pi/6)
c2=triangloid(1,0.5,0.2,-0.4).rotate(-pi/6).shift([2.2, 0])
show_colloids(c1, c2, 0.15, inter=True)

c1=triangloid(1,0.5,0.2,0.4).rotate(pi/6) c2=triangloid(1,0.5,0.2,-0.4).rotate(-pi/6).shift([2.2, 0]) show_colloids(c1, c2, 0.15, inter=True)

Dart-shaped colloids¶

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dartoid(0, 0.2).draw(label="Round")
dartoid(1, 0.2).shift([2,-2]).draw(label="Sharp")
dartoid(1, 0.4).shift([0,-2.1]).draw(label="Deep")
#dartoid(1, 1).draw(label="Convex")
#dartoid(0.8, 1).draw(label="Concave")
legend();
axis('equal');

dartoid(0, 0.2).draw(label="Round") dartoid(1, 0.2).shift([2,-2]).draw(label="Sharp") dartoid(1, 0.4).shift([0,-2.1]).draw(label="Deep") #dartoid(1, 1).draw(label="Convex") #dartoid(0.8, 1).draw(label="Concave") legend(); axis('equal');

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c1=dartoid(0, 2-sqrt(3)).rotate(pi/6)
c2=c1.shift([2, 0.07])
show_colloids(c1, c2, 0.15, inter=True)

c1=dartoid(0, 2-sqrt(3)).rotate(pi/6) c2=c1.shift([2, 0.07]) show_colloids(c1, c2, 0.15, inter=True)

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binding_energy(c1, c2, 0.15)

binding_energy(c1, c2, 0.15)

Out[ ]:

0.14404994841823626

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