def setup_transition_list():
"""
Creates and returns a list of Transition() objects to represent state
transitions for a biased random walk, in which the rate of downward
motion is greater than the rate in the other three directions.
Parameters
----------
(none)
Returns
-------
xn_list : list of Transition objects
List of objects that encode information about the link-state transitions.
Notes
-----
State 0 represents fluid and state 1 represents a particle (such as a
sediment grain, tea leaf, or dissolved heavy particle).
The states and transitions are as follows:
Pair state Transition to Process Rate (cells/s)
========== ============= ======= ==============
0 (0-0) (none) - -
1 (0-1) 2 (1-0) left motion 10.0
2 (1-0) 1 (0-1) right motion 10.0
3 (1-1) (none) - -
4 (0-0) (none) - -
5 (0-1) 2 (1-0) down motion 10.55
6 (1-0) 1 (0-1) up motion 9.45
7 (1-1) (none) - -
"""
# Create an empty transition list
xn_list = []
# Append four transitions to the list.
# Note that the arguments to the Transition() object constructor are:
# - Tuple representing starting pair state
# (left cell, right cell, orientation [0=horizontal])
# - Tuple representing new pair state
# (bottom cell, top cell, orientation [1=vertical])
# - Transition rate (cells per time step, in this case 1 sec)
# - Name for transition
xn_list.append(Transition((0, 1, 0), (1, 0, 0), 10., "left motion"))
xn_list.append(Transition((1, 0, 0), (0, 1, 0), 10., "right motion"))
xn_list.append(Transition((0, 1, 1), (1, 0, 1), 10.55, "down motion"))
xn_list.append(Transition((1, 0, 1), (0, 1, 1), 9.45, "up motion"))
return xn_list
def setup_transition_list():
"""
Creates and returns a list of Transition() objects to represent state
transitions for a biased random walk, in which the rate of downward
motion is greater than the rate in the other three directions.
Parameters
----------
(none)
Returns
-------
xn_list : list of Transition objects
List of objects that encode information about the link-state transitions.
Notes
-----
State 0 represents fluid and state 1 represents a particle (such as a
sediment grain or dissolved heavy particle).
The states and transitions are as follows:
Pair state Transition to Process Rate
========== ============= ======= ====
0 (0-0) (none) - -
1 (0-1) 2 (1-0) left motion 1.0
2 (1-0) 1 (0-1) right motion 1.0
3 (1-1) (none) - -
4 (0/0) (none) - -
5 (0/1) 6 (1/0) down motion 1.1
6 (1/0) 5 (0/1) up motion 0.9
7 (1/1) (none) - -
"""
xn_list = []
xn_list.append(Transition((0, 1, 0), (1, 0, 0), 1., 'left motion'))
xn_list.append(Transition((1, 0, 0), (0, 1, 0), 1., 'right motion'))
xn_list.append(Transition((0, 1, 1), (1, 0, 1), 1.1, 'down motion'))
xn_list.append(Transition((1, 0, 1), (0, 1, 1), 0.9, 'up motion'))
if _DEBUG:
print()
print('setup_transition_list(): list has', len(xn_list),
'transitions:')
for t in xn_list:
print(' From state', t.from_state, 'to state', t.to_state,
'at rate', t.rate, 'called', t.name)
return xn_list
def setup_transition_list():
"""
Creates and returns a list of Transition() objects to represent the
grain-by-grain transformation of bedrock to saprolite.
Returns
-------
xn_list : list of Transition objects
List of objects that encode information about the link-state transitions.
Notes
-----
Weathering here is treated very simply: a bedrock particle adjacent to a
saprolite particle has a specified probability (rate) of weathering to
saprolite; in other words, a rock-saprolite pair can turn into a
saprolite-saprolite pair.
The states and transitions are as follows:
Pair state Transition to Process Rate (cells/s)
========== ============= ======= ==============
0 (0-0) 1 (0-1) 0.5
2 (1-0) 0.5
1 (0-1) 3 (1-1) 1.0
2 (1-0) 3 (1-1) 1.0
3 (1-1) (none) -
"""
# Create an empty transition list
xn_list = []
# Append two transitions to the list.
# Note that the arguments to the Transition() object constructor are:
# - Tuple representing starting pair state
# (left/bottom cell, right/top cell, orientation)
# - Tuple representing new pair state
# (left/bottom cell, right/top cell, orientation)
# - Transition rate (cells per time step, in this case 1 sec)
# - Name for transition
xn_list.append(Transition((0, 1, 0), (1, 1, 0), 1., 'weathering'))
xn_list.append(Transition((1, 0, 0), (1, 1, 0), 1., 'weathering'))
return xn_list
def setup_transition_list(infection_rate):
"""
Creates and returns a list of Transition() objects to represent state
transitions for the SIR model.
Parameters
----------
(none)
Returns
-------
xn_list : list of Transition objects
List of objects that encode information about the link-state transitions.
Notes
-----
The states and transitions are as follows:
Pair state Transition to Process
========== ============= =======
0 (0-0) (none) -
1 (0-1) 4 (1-1) infection
2 (0-2) recovery
2 (0-2) (none) -
3 (1-0) 4 (1-1) infection
6 (2-0) recovery
4 (1-1) 5 (1-2) recovery
6 (2-1) recovery
5 (1-2) 8 (2-2) recovery
6 (2-0) (none) -
7 (2-1) 8 (2-2) recovery
8 (2-2) (none) -
"""
xn_list = []
xn_list.append( Transition((0,1,0), (1,1,0), infection_rate, 'infection') )
xn_list.append( Transition((0,1,0), (0,2,0), 1., 'recovery') )
xn_list.append( Transition((1,0,0), (1,1,0), infection_rate, 'infection') )
xn_list.append( Transition((1,0,0), (2,0,0), 1., 'recovery') )
xn_list.append( Transition((1,1,0), (1,2,0), 1., 'recovery') )
xn_list.append( Transition((1,1,0), (2,1,0), 1., 'recovery') )
xn_list.append( Transition((1,2,0), (2,2,0), 1., 'recovery') )
xn_list.append( Transition((2,1,0), (2,2,0), 1., 'recovery') )
if _DEBUG:
print()
print('setup_transition_list(): list has',len(xn_list),'transitions:')
for t in xn_list:
print(' From state',t.from_state,'to state',t.to_state,'at rate',t.rate,'called',t.name)
return xn_list
def setup_transition_list(g=1.0, f=0.0):
"""
Creates and returns a list of Transition() objects to represent state
transitions for simple granular mechanics model.
Parameters
----------
(none)
Returns
-------
xn_list : list of Transition objects
List of objects that encode information about the link-state transitions.
"""
xn_list = []
# Transitions for particle movement into an empty cell
xn_list.append(Transition((1, 0, 0), (0, 1, 0), 1., 'motion'))
xn_list.append(Transition((2, 0, 1), (0, 2, 1), 1., 'motion'))
xn_list.append(Transition((3, 0, 2), (0, 3, 2), 1., 'motion'))
xn_list.append(Transition((0, 4, 0), (4, 0, 0), 1., 'motion'))
xn_list.append(Transition((0, 5, 1), (5, 0, 1), 1., 'motion'))
xn_list.append(Transition((0, 6, 2), (6, 0, 2), 1., 'motion'))
# Transitions for wall impact
xn_list.append(Transition((1, 8, 0), (4, 8, 0), 1.0, 'wall rebound'))
xn_list.append(Transition((2, 8, 1), (5, 8, 1), 1.0, 'wall rebound'))
xn_list.append(Transition((3, 8, 2), (6, 8, 2), 1.0, 'wall rebound'))
xn_list.append(Transition((8, 4, 0), (8, 1, 0), 1.0, 'wall rebound'))
xn_list.append(Transition((8, 5, 1), (8, 2, 1), 1.0, 'wall rebound'))
xn_list.append(Transition((8, 6, 2), (8, 3, 2), 1.0, 'wall rebound'))
# Transitions for wall impact frictional stop
xn_list.append(Transition((1, 8, 0), (7, 8, 0), f, 'wall stop'))
xn_list.append(Transition((2, 8, 1), (7, 8, 1), f, 'wall stop'))
xn_list.append(Transition((3, 8, 2), (7, 8, 2), f, 'wall stop'))
xn_list.append(Transition((8, 4, 0), (8, 7, 0), f, 'wall stop'))
xn_list.append(Transition((8, 5, 1), (8, 7, 1), f, 'wall stop'))
xn_list.append(Transition((8, 6, 2), (8, 7, 2), f, 'wall stop'))
# Transitions for head-on collision
xn_list.append(Transition((1, 4, 0), (3, 6, 0), 0.5, 'head-on collision'))
xn_list.append(Transition((1, 4, 0), (5, 2, 0), 0.5, 'head-on collision'))
xn_list.append(Transition((2, 5, 1), (4, 1, 1), 0.5, 'head-on collision'))
xn_list.append(Transition((2, 5, 1), (6, 3, 1), 0.5, 'head-on collision'))
xn_list.append(Transition((3, 6, 2), (1, 4, 2), 0.5, 'head-on collision'))
xn_list.append(Transition((3, 6, 2), (5, 2, 2), 0.5, 'head-on collision'))
xn_list.append(Transition((1, 4, 0), (7, 7, 0), f, 'head-on collision'))
xn_list.append(Transition((2, 5, 1), (7, 7, 1), f, 'head-on collision'))
xn_list.append(Transition((3, 6, 2), (7, 7, 2), f, 'head-on collision'))
# Transitions for glancing collision
xn_list.append(Transition((1, 3, 0), (3, 1, 0), 1.0, 'glancing collision'))
xn_list.append(Transition((1, 5, 0), (5, 1, 0), 1.0, 'glancing collision'))
xn_list.append(Transition((2, 4, 0), (4, 2, 0), 1.0, 'glancing collision'))
xn_list.append(Transition((6, 4, 0), (4, 6, 0), 1.0, 'glancing collision'))
xn_list.append(Transition((2, 4, 1), (4, 2, 1), 1.0, 'glancing collision'))
xn_list.append(Transition((2, 6, 1), (6, 2, 1), 1.0, 'glancing collision'))
xn_list.append(Transition((1, 5, 1), (5, 1, 1), 1.0, 'glancing collision'))
xn_list.append(Transition((3, 5, 1), (5, 3, 1), 1.0, 'glancing collision'))
xn_list.append(Transition((3, 1, 2), (1, 3, 2), 1.0, 'glancing collision'))
xn_list.append(Transition((3, 5, 2), (5, 3, 2), 1.0, 'glancing collision'))
xn_list.append(Transition((2, 6, 2), (6, 2, 2), 1.0, 'glancing collision'))
xn_list.append(Transition((4, 6, 2), (6, 4, 2), 1.0, 'glancing collision'))
# Transitions for oblique-from-behind collisions
xn_list.append(Transition((1, 2, 0), (2, 1, 0), 1.0, 'oblique'))
xn_list.append(Transition((1, 6, 0), (6, 1, 0), 1.0, 'oblique'))
xn_list.append(Transition((3, 4, 0), (4, 3, 0), 1.0, 'oblique'))
xn_list.append(Transition((5, 4, 0), (4, 5, 0), 1.0, 'oblique'))
xn_list.append(Transition((2, 1, 1), (1, 2, 1), 1.0, 'oblique'))
xn_list.append(Transition((2, 3, 1), (3, 2, 1), 1.0, 'oblique'))
xn_list.append(Transition((4, 5, 1), (5, 4, 1), 1.0, 'oblique'))
xn_list.append(Transition((6, 5, 1), (5, 6, 1), 1.0, 'oblique'))
xn_list.append(Transition((3, 2, 2), (2, 3, 2), 1.0, 'oblique'))
xn_list.append(Transition((3, 4, 2), (4, 3, 2), 1.0, 'oblique'))
xn_list.append(Transition((1, 6, 2), (6, 1, 2), 1.0, 'oblique'))
xn_list.append(Transition((5, 6, 2), (6, 5, 2), 1.0, 'oblique'))
xn_list.append(Transition((1, 2, 0), (7, 7, 0), f, 'oblique'))
xn_list.append(Transition((1, 6, 0), (7, 7, 0), f, 'oblique'))
xn_list.append(Transition((3, 4, 0), (7, 7, 0), f, 'oblique'))
xn_list.append(Transition((5, 4, 0), (7, 7, 0), f, 'oblique'))
xn_list.append(Transition((2, 1, 1), (7, 7, 1), f, 'oblique'))
xn_list.append(Transition((2, 3, 1), (7, 7, 1), f, 'oblique'))
xn_list.append(Transition((4, 5, 1), (7, 7, 1), f, 'oblique'))
xn_list.append(Transition((6, 5, 1), (7, 7, 1), f, 'oblique'))
xn_list.append(Transition((3, 2, 2), (7, 7, 2), f, 'oblique'))
xn_list.append(Transition((3, 4, 2), (7, 7, 2), f, 'oblique'))
xn_list.append(Transition((1, 6, 2), (7, 7, 2), f, 'oblique'))
xn_list.append(Transition((5, 6, 2), (7, 7, 2), f, 'oblique'))
# Transitions for direct-from-behind collisions
xn_list.append(Transition((1, 1, 0), (2, 6, 0), 0.5, 'behind'))
xn_list.append(Transition((1, 1, 0), (6, 2, 0), 0.5, 'behind'))
xn_list.append(Transition((4, 4, 0), (3, 5, 0), 0.5, 'behind'))
xn_list.append(Transition((4, 4, 0), (5, 3, 0), 0.5, 'behind'))
xn_list.append(Transition((2, 2, 1), (1, 3, 1), 0.5, 'behind'))
xn_list.append(Transition((2, 2, 1), (3, 1, 1), 0.5, 'behind'))
xn_list.append(Transition((5, 5, 1), (4, 6, 1), 0.5, 'behind'))
xn_list.append(Transition((5, 5, 1), (6, 4, 1), 0.5, 'behind'))
xn_list.append(Transition((3, 3, 2), (2, 4, 2), 0.5, 'behind'))
xn_list.append(Transition((3, 3, 2), (4, 2, 2), 0.5, 'behind'))
xn_list.append(Transition((6, 6, 2), (1, 5, 2), 0.5, 'behind'))
xn_list.append(Transition((6, 6, 2), (5, 1, 2), 0.5, 'behind'))
xn_list.append(Transition((1, 1, 0), (7, 1, 0), f, 'behind'))
xn_list.append(Transition((4, 4, 0), (4, 7, 0), f, 'behind'))
xn_list.append(Transition((2, 2, 1), (7, 2, 1), f, 'behind'))
xn_list.append(Transition((5, 5, 1), (5, 7, 1), f, 'behind'))
xn_list.append(Transition((3, 3, 2), (7, 3, 2), f, 'behind'))
xn_list.append(Transition((6, 6, 2), (6, 7, 2), f, 'behind'))
# Transitions for collision with stationary (resting) particle
xn_list.append(Transition((1, 7, 0), (7, 2, 0), 0.5, 'rest'))
xn_list.append(Transition((1, 7, 0), (7, 6, 0), 0.5, 'rest'))
xn_list.append(Transition((7, 4, 0), (3, 7, 0), 0.5, 'rest'))
xn_list.append(Transition((7, 4, 0), (5, 7, 0), 0.5, 'rest'))
xn_list.append(Transition((2, 7, 1), (7, 1, 1), 0.5, 'rest'))
xn_list.append(Transition((2, 7, 1), (7, 3, 1), 0.5, 'rest'))
xn_list.append(Transition((7, 5, 1), (4, 7, 1), 0.5, 'rest'))
xn_list.append(Transition((7, 5, 1), (6, 7, 1), 0.5, 'rest'))
xn_list.append(Transition((3, 7, 2), (7, 2, 2), 0.5, 'rest'))
xn_list.append(Transition((3, 7, 2), (7, 4, 2), 0.5, 'rest'))
xn_list.append(Transition((7, 6, 2), (1, 7, 2), 0.5, 'rest'))
xn_list.append(Transition((7, 6, 2), (5, 7, 2), 0.5, 'rest'))
xn_list.append(Transition((1, 7, 0), (7, 7, 0), f, 'rest'))
xn_list.append(Transition((7, 4, 0), (7, 7, 0), f, 'rest'))
xn_list.append(Transition((2, 7, 1), (7, 7, 1), f, 'rest'))
xn_list.append(Transition((7, 5, 1), (7, 7, 1), f, 'rest'))
xn_list.append(Transition((3, 7, 2), (7, 7, 2), f, 'rest'))
xn_list.append(Transition((7, 6, 2), (7, 7, 2), f, 'rest'))
# Gravity rules
xn_list.append(Transition((1, 0, 0), (7, 0, 0), g, 'up to rest'))
xn_list.append(Transition((1, 1, 0), (7, 1, 0), g, 'up to rest'))
xn_list.append(Transition((1, 2, 0), (7, 2, 0), g, 'up to rest'))
xn_list.append(Transition((1, 3, 0), (7, 3, 0), g, 'up to rest'))
xn_list.append(Transition((1, 4, 0), (7, 4, 0), g, 'up to rest'))
xn_list.append(Transition((1, 5, 0), (7, 5, 0), g, 'up to rest'))
xn_list.append(Transition((1, 6, 0), (7, 6, 0), g, 'up to rest'))
xn_list.append(Transition((1, 7, 0), (7, 7, 0), g, 'up to rest'))
xn_list.append(Transition((0, 1, 0), (0, 7, 0), g, 'up to rest'))
xn_list.append(Transition((1, 1, 0), (1, 7, 0), g, 'up to rest'))
xn_list.append(Transition((2, 1, 0), (2, 7, 0), g, 'up to rest'))
xn_list.append(Transition((3, 1, 0), (3, 7, 0), g, 'up to rest'))
xn_list.append(Transition((4, 1, 0), (4, 7, 0), g, 'up to rest'))
xn_list.append(Transition((5, 1, 0), (5, 7, 0), g, 'up to rest'))
xn_list.append(Transition((6, 1, 0), (6, 7, 0), g, 'up to rest'))
xn_list.append(Transition((7, 1, 0), (7, 7, 0), g, 'up to rest'))
#xn_list.append( Transition((7,0,0), (4,0,0), g, 'rest to down') )
#xn_list.append( Transition((7,1,0), (4,1,0), g, 'rest to down') )
#xn_list.append( Transition((7,2,0), (4,2,0), g, 'rest to down') )
#xn_list.append( Transition((7,3,0), (4,3,0), g, 'rest to down') )
#xn_list.append( Transition((7,4,0), (4,4,0), g, 'rest to down') )
#xn_list.append( Transition((7,5,0), (4,5,0), g, 'rest to down') )
#xn_list.append( Transition((7,6,0), (4,6,0), g, 'rest to down') )
#xn_list.append( Transition((7,7,0), (4,7,0), g, 'rest to down') )
xn_list.append(Transition((0, 7, 0), (0, 4, 0), g, 'rest to down'))
#xn_list.append( Transition((1,7,0), (1,4,0), g, 'rest to down') )
#xn_list.append( Transition((2,7,0), (2,4,0), g, 'rest to down') )
#xn_list.append( Transition((3,7,0), (3,4,0), g, 'rest to down') )
#xn_list.append( Transition((4,7,0), (4,4,0), g, 'rest to down') )
#xn_list.append( Transition((5,7,0), (5,4,0), g, 'rest to down') )
#xn_list.append( Transition((6,7,0), (6,4,0), g, 'rest to down') )
#xn_list.append( Transition((7,7,0), (7,4,0), g, 'rest to down') )
xn_list.append(Transition((7, 0, 2), (3, 0, 2), g, 'rest to right-down'))
xn_list.append(Transition((0, 7, 1), (0, 5, 1), g, 'rest to left-down'))
xn_list.append(
Transition((2, 0, 1), (3, 0, 1), g, 'right up to right down'))
xn_list.append(
Transition((2, 1, 1), (3, 1, 1), g, 'right up to right down'))
xn_list.append(
Transition((2, 2, 1), (3, 2, 1), g, 'right up to right down'))
xn_list.append(
Transition((2, 3, 1), (3, 3, 1), g, 'right up to right down'))
xn_list.append(
Transition((2, 4, 1), (3, 4, 1), g, 'right up to right down'))
xn_list.append(
Transition((2, 5, 1), (3, 5, 1), g, 'right up to right down'))
xn_list.append(
Transition((2, 6, 1), (3, 6, 1), g, 'right up to right down'))
xn_list.append(
Transition((2, 7, 1), (3, 7, 1), g, 'right up to right down'))
xn_list.append(
Transition((0, 2, 1), (0, 3, 1), g, 'right up to right down'))
xn_list.append(
Transition((1, 2, 1), (1, 3, 1), g, 'right up to right down'))
xn_list.append(
Transition((2, 2, 1), (2, 3, 1), g, 'right up to right down'))
xn_list.append(
Transition((3, 2, 1), (3, 3, 1), g, 'right up to right down'))
xn_list.append(
Transition((4, 2, 1), (4, 3, 1), g, 'right up to right down'))
xn_list.append(
Transition((5, 2, 1), (5, 3, 1), g, 'right up to right down'))
xn_list.append(
Transition((6, 2, 1), (6, 3, 1), g, 'right up to right down'))
xn_list.append(
Transition((7, 2, 1), (7, 3, 1), g, 'right up to right down'))
xn_list.append(Transition((6, 0, 2), (5, 0, 2), g, 'left up to left down'))
xn_list.append(Transition((6, 1, 2), (5, 1, 2), g, 'left up to left down'))
xn_list.append(Transition((6, 2, 2), (5, 2, 2), g, 'left up to left down'))
xn_list.append(Transition((6, 3, 2), (5, 3, 2), g, 'left up to left down'))
xn_list.append(Transition((6, 4, 2), (5, 4, 2), g, 'left up to left down'))
xn_list.append(Transition((6, 5, 2), (5, 5, 2), g, 'left up to left down'))
xn_list.append(Transition((6, 6, 2), (5, 6, 2), g, 'left up to left down'))
xn_list.append(Transition((6, 7, 2), (5, 7, 2), g, 'left up to left down'))
xn_list.append(Transition((0, 6, 2), (0, 5, 2), g, 'left up to left down'))
xn_list.append(Transition((1, 6, 2), (1, 5, 2), g, 'left up to left down'))
xn_list.append(Transition((2, 6, 2), (2, 5, 2), g, 'left up to left down'))
xn_list.append(Transition((3, 6, 2), (3, 5, 2), g, 'left up to left down'))
xn_list.append(Transition((4, 6, 2), (4, 5, 2), g, 'left up to left down'))
xn_list.append(Transition((5, 6, 2), (5, 5, 2), g, 'left up to left down'))
xn_list.append(Transition((6, 6, 2), (6, 5, 2), g, 'left up to left down'))
xn_list.append(Transition((7, 6, 2), (7, 5, 2), g, 'left up to left down'))
if _DEBUG:
print()
print('setup_transition_list(): list has', len(xn_list),
'transitions:')
for t in xn_list:
print(' From state', t.from_state, 'to state', t.to_state,
'at rate', t.rate, 'called', t.name)
return xn_list
def setup_transition_list():
"""
Creates and returns a list of Transition() objects to represent state
transitions for simple granular mechanics model.
Parameters
----------
(none)
Returns
-------
xn_list : list of Transition objects
List of objects that encode information about the link-state transitions.
"""
xn_list = []
# Rule 1: Transitions for particle movement into an empty cell
xn_list.append( Transition((1,0,0), (0,1,0), 1., 'motion') )
xn_list.append( Transition((2,0,1), (0,2,1), 1., 'motion') )
xn_list.append( Transition((3,0,2), (0,3,2), 1., 'motion') )
xn_list.append( Transition((0,4,0), (4,0,0), 1., 'motion') )
xn_list.append( Transition((0,5,1), (5,0,1), 1., 'motion') )
xn_list.append( Transition((0,6,2), (6,0,2), 1., 'motion') )
# Rule 2: Transitions for head-on collision: elastic
xn_list.append( Transition((1,4,0), (4,1,0), 1./3, 'head-on collision') )
xn_list.append( Transition((1,4,0), (3,6,0), 1./3, 'head-on collision') )
xn_list.append( Transition((1,4,0), (5,2,0), 1./3, 'head-on collision') )
xn_list.append( Transition((2,5,1), (5,2,1), 1./3, 'head-on collision') )
xn_list.append( Transition((2,5,1), (4,1,1), 1./3, 'head-on collision') )
xn_list.append( Transition((2,5,1), (6,3,1), 1./3, 'head-on collision') )
xn_list.append( Transition((3,6,2), (6,3,2), 1./3, 'head-on collision') )
xn_list.append( Transition((3,6,2), (1,4,2), 1./3, 'head-on collision') )
xn_list.append( Transition((3,6,2), (5,2,2), 1./3, 'head-on collision') )
# Rule 3: Transitions for oblique collision: elastic
xn_list.append( Transition((1,3,0), (3,1,0), 1.0, 'glancing collision') )
xn_list.append( Transition((1,5,0), (5,1,0), 1.0, 'glancing collision') )
xn_list.append( Transition((2,4,0), (4,2,0), 1.0, 'glancing collision') )
xn_list.append( Transition((6,4,0), (4,6,0), 1.0, 'glancing collision') )
xn_list.append( Transition((2,4,1), (4,2,1), 1.0, 'glancing collision') )
xn_list.append( Transition((2,6,1), (6,2,1), 1.0, 'glancing collision') )
xn_list.append( Transition((1,5,1), (5,1,1), 1.0, 'glancing collision') )
xn_list.append( Transition((3,5,1), (5,3,1), 1.0, 'glancing collision') )
xn_list.append( Transition((3,1,2), (1,3,2), 1.0, 'glancing collision') )
xn_list.append( Transition((3,5,2), (5,3,2), 1.0, 'glancing collision') )
xn_list.append( Transition((2,6,2), (6,2,2), 1.0, 'glancing collision') )
xn_list.append( Transition((4,6,2), (6,4,2), 1.0, 'glancing collision') )
# Rule 4: Transitions for oblique-from-behind collisions
xn_list.append( Transition((1,2,0), (2,1,0), 1.0, 'oblique') )
xn_list.append( Transition((1,6,0), (6,1,0), 1.0, 'oblique') )
xn_list.append( Transition((3,4,0), (4,3,0), 1.0, 'oblique') )
xn_list.append( Transition((5,4,0), (4,5,0), 1.0, 'oblique') )
xn_list.append( Transition((2,1,1), (1,2,1), 1.0, 'oblique') )
xn_list.append( Transition((2,3,1), (3,2,1), 1.0, 'oblique') )
xn_list.append( Transition((4,5,1), (5,4,1), 1.0, 'oblique') )
xn_list.append( Transition((6,5,1), (5,6,1), 1.0, 'oblique') )
xn_list.append( Transition((3,2,2), (2,3,2), 1.0, 'oblique') )
xn_list.append( Transition((3,4,2), (4,3,2), 1.0, 'oblique') )
xn_list.append( Transition((1,6,2), (6,1,2), 1.0, 'oblique') )
xn_list.append( Transition((5,6,2), (6,5,2), 1.0, 'oblique') )
# Rule 5: Transitions for direct-from-behind collisions
xn_list.append( Transition((1,1,0), (2,6,0), 0.25, 'behind') )
xn_list.append( Transition((1,1,0), (6,2,0), 0.25, 'behind') )
xn_list.append( Transition((4,4,0), (3,5,0), 0.25, 'behind') )
xn_list.append( Transition((4,4,0), (5,3,0), 0.25, 'behind') )
xn_list.append( Transition((2,2,1), (1,3,1), 0.25, 'behind') )
xn_list.append( Transition((2,2,1), (3,1,1), 0.25, 'behind') )
xn_list.append( Transition((5,5,1), (4,6,1), 0.25, 'behind') )
xn_list.append( Transition((5,5,1), (6,4,1), 0.25, 'behind') )
xn_list.append( Transition((3,3,2), (2,4,2), 0.25, 'behind') )
xn_list.append( Transition((3,3,2), (4,2,2), 0.25, 'behind') )
xn_list.append( Transition((6,6,2), (1,5,2), 0.25, 'behind') )
xn_list.append( Transition((6,6,2), (5,1,2), 0.25, 'behind') )
# Rule 6: Transitions for direct collision with stationary (resting) particle
xn_list.append( Transition((1,7,0), (7,1,0), 1./3., 'rest') )
xn_list.append( Transition((1,7,0), (7,2,0), 1./3., 'rest') )
xn_list.append( Transition((1,7,0), (7,6,0), 1./3., 'rest') )
xn_list.append( Transition((7,4,0), (4,7,0), 1./3., 'rest') )
xn_list.append( Transition((7,4,0), (3,7,0), 1./3., 'rest') )
xn_list.append( Transition((7,4,0), (5,7,0), 1./3., 'rest') )
xn_list.append( Transition((2,7,1), (7,2,1), 1./3., 'rest') )
xn_list.append( Transition((2,7,1), (7,1,1), 1./3., 'rest') )
xn_list.append( Transition((2,7,1), (7,3,1), 1./3., 'rest') )
xn_list.append( Transition((7,5,1), (5,7,1), 1./3., 'rest') )
xn_list.append( Transition((7,5,1), (4,7,1), 1./3., 'rest') )
xn_list.append( Transition((7,5,1), (6,7,1), 1./3., 'rest') )
xn_list.append( Transition((3,7,2), (7,3,2), 1./3., 'rest') )
xn_list.append( Transition((3,7,2), (7,2,2), 1./3., 'rest') )
xn_list.append( Transition((3,7,2), (7,4,2), 1./3., 'rest') )
xn_list.append( Transition((7,6,2), (6,7,2), 1./3., 'rest') )
xn_list.append( Transition((7,6,2), (1,7,2), 1./3., 'rest') )
xn_list.append( Transition((7,6,2), (5,7,2), 1./3., 'rest') )
# Rule 7: Transitions for wall impact
xn_list.append( Transition((1,8,0), (4,8,0), 1.0/3, 'wall rebound') )
xn_list.append( Transition((1,8,0), (3,8,0), 1.0/3, 'wall rebound') )
xn_list.append( Transition((1,8,0), (5,8,0), 1.0/3, 'wall rebound') )
xn_list.append( Transition((2,8,1), (5,8,1), 1.0/3, 'wall rebound') )
xn_list.append( Transition((2,8,1), (4,8,1), 1.0/3, 'wall rebound') )
xn_list.append( Transition((2,8,1), (6,8,1), 1.0/3, 'wall rebound') )
xn_list.append( Transition((3,8,2), (6,8,2), 1.0/3, 'wall rebound') )
xn_list.append( Transition((3,8,2), (5,8,2), 1.0/3, 'wall rebound') )
xn_list.append( Transition((3,8,2), (1,8,2), 1.0/3, 'wall rebound') )
xn_list.append( Transition((8,4,0), (8,1,0), 1.0/3, 'wall rebound') )
xn_list.append( Transition((8,4,0), (8,6,0), 1.0/3, 'wall rebound') )
xn_list.append( Transition((8,4,0), (8,2,0), 1.0/3, 'wall rebound') )
xn_list.append( Transition((8,5,1), (8,1,1), 1.0/3, 'wall rebound') )
xn_list.append( Transition((8,5,1), (8,2,1), 1.0/3, 'wall rebound') )
xn_list.append( Transition((8,5,1), (8,3,1), 1.0/3, 'wall rebound') )
xn_list.append( Transition((8,6,2), (8,2,2), 1.0/3, 'wall rebound') )
xn_list.append( Transition((8,6,2), (8,3,2), 1.0/3, 'wall rebound') )
xn_list.append( Transition((8,6,2), (8,4,2), 1.0/3, 'wall rebound') )
# Rule 8: Transitions for glancing oblique collision
xn_list.append( Transition((2,5,0), (3,6,0), 1.0, 'glancing') )
xn_list.append( Transition((6,3,0), (5,2,0), 1.0, 'glancing') )
xn_list.append( Transition((3,6,1), (4,1,1), 1.0, 'glancing') )
xn_list.append( Transition((1,4,1), (6,3,1), 1.0, 'glancing') )
xn_list.append( Transition((4,1,2), (5,2,2), 1.0, 'glancing') )
xn_list.append( Transition((2,5,2), (1,4,2), 1.0, 'glancing') )
# Rule 9: Transitions for "near-on" collisions
xn_list.append( Transition((6,5,0), (5,6,0), 1.0, 'near-on') )
xn_list.append( Transition((2,3,0), (3,2,0), 1.0, 'near-on') )
xn_list.append( Transition((1,6,1), (6,1,1), 1.0, 'near-on') )
xn_list.append( Transition((3,4,1), (4,3,1), 1.0, 'near-on') )
xn_list.append( Transition((2,1,2), (1,2,2), 1.0, 'near-on') )
xn_list.append( Transition((4,5,2), (5,4,2), 1.0, 'near-on') )
# Rule 10: Transitions for oblique collision with rest particle
xn_list.append( Transition((2,7,0), (7,1,0), 1.0, 'oblique with rest') )
xn_list.append( Transition((6,7,0), (7,1,0), 1.0, 'oblique with rest') )
xn_list.append( Transition((7,3,0), (4,7,0), 1.0, 'oblique with rest') )
xn_list.append( Transition((7,5,0), (4,7,0), 1.0, 'oblique with rest') )
xn_list.append( Transition((3,7,1), (7,2,1), 1.0, 'oblique with rest') )
xn_list.append( Transition((1,7,1), (7,2,1), 1.0, 'oblique with rest') )
xn_list.append( Transition((7,6,1), (5,7,1), 1.0, 'oblique with rest') )
xn_list.append( Transition((7,4,1), (5,7,1), 1.0, 'oblique with rest') )
xn_list.append( Transition((4,7,2), (7,3,2), 1.0, 'oblique with rest') )
xn_list.append( Transition((2,7,2), (7,3,2), 1.0, 'oblique with rest') )
xn_list.append( Transition((7,5,2), (6,7,2), 1.0, 'oblique with rest') )
xn_list.append( Transition((7,1,2), (6,7,2), 1.0, 'oblique with rest') )
# Rule 11: Transitions for oblique collision with wall particle
xn_list.append( Transition((2,8,0), (3,8,0), 1.0, 'oblique with wall') )
xn_list.append( Transition((6,8,0), (5,8,0), 1.0, 'oblique with wall') )
xn_list.append( Transition((8,3,0), (8,2,0), 1.0, 'oblique with wall') )
xn_list.append( Transition((8,5,0), (8,6,0), 1.0, 'oblique with wall') )
xn_list.append( Transition((1,8,1), (6,8,1), 1.0, 'oblique with wall') )
xn_list.append( Transition((3,8,1), (4,8,1), 1.0, 'oblique with wall') )
xn_list.append( Transition((8,4,1), (8,3,1), 1.0, 'oblique with wall') )
xn_list.append( Transition((8,6,1), (8,1,1), 1.0, 'oblique with wall') )
xn_list.append( Transition((4,8,2), (5,8,2), 1.0, 'oblique with wall') )
xn_list.append( Transition((2,8,2), (1,8,2), 1.0, 'oblique with wall') )
xn_list.append( Transition((8,1,2), (8,2,2), 1.0, 'oblique with wall') )
xn_list.append( Transition((8,5,2), (8,4,2), 1.0, 'oblique with wall') )
if _DEBUG:
print()
print('setup_transition_list(): list has',len(xn_list),'transitions:')
for t in xn_list:
print(' From state',t.from_state,'to state',t.to_state,'at rate',t.rate,'called',t.name)
return xn_list
def setup_transition_list(g=0.0, f=0.0, d=0.0, w=0.0):
"""
Creates and returns a list of Transition() objects to represent state
transitions for simple granular mechanics model.
Parameters
----------
(none)
Returns
-------
xn_list : list of Transition objects
List of objects that encode information about the link-state transitions.
Notes
-----
The transitions for this version of lattice gas have 11 pair-transition
rules. The shorthand for the states is as follows:
AR = air/empty
IN = incoming particle (moving toward its neighbor)
OU = outgoing particle (moving away from its neighbor)
IO = incoming at an oblique angle
OO = outgoing at an oblique angle
RE = rest particle
WA = wall particle
op = oblique pair moving in opposite perpendicular direction
sm = oblique pair moving in same perpendicular direction
The 11 pairs with transitions are:
1. AR-IN => IN-AR (move to empty particle)
2. IN-IN => OO-OO-op (1/3 each dir), OU-OU (1/3) (head-on collision)
3. IN-IO => OO-OU (oblique collision)
4. IN-OO => IO-OU (oblique collision from behind)
5. IN-OU => IO-OO (1/4 each of 2 directions) (collision from behind)
6. IN-RE => RE-OU (1/3) RE-OO (1/3 each dir) (collision with rest)
7. IN-WA => OU-WA (1/3) OO-WA (1/3 each dir) (wall collision)
8. IO-IO-op => OO-OO-op (1/2 each dir) (glacing collision)
9. IO-IO-sm => OO-OO-sm (30-degree collision)
10. IO-RE => RE-OU (oblique collision with rest particle)
11. IO-WA => OO-WA (oblique collision with wall)
"""
xn_list = []
p_elast = 1.0 - f # probability of elastic (non-dissipative) collision
# Rule 1: Transitions for particle movement into an empty cell
xn_list.append(Transition((1, 0, 0), (0, 1, 0), 1., 'motion'))
xn_list.append(Transition((2, 0, 1), (0, 2, 1), 1., 'motion'))
xn_list.append(Transition((3, 0, 2), (0, 3, 2), 1., 'motion'))
xn_list.append(Transition((0, 4, 0), (4, 0, 0), 1., 'motion'))
xn_list.append(Transition((0, 5, 1), (5, 0, 1), 1., 'motion'))
xn_list.append(Transition((0, 6, 2), (6, 0, 2), 1., 'motion'))
# Rule 2: Transitions for head-on collision: elastic
xn_list.append(
Transition((1, 4, 0), (4, 1, 0), p_elast / 3, 'head-on collision'))
xn_list.append(
Transition((1, 4, 0), (3, 6, 0), p_elast / 3, 'head-on collision'))
xn_list.append(
Transition((1, 4, 0), (5, 2, 0), p_elast / 3, 'head-on collision'))
xn_list.append(
Transition((2, 5, 1), (5, 2, 1), p_elast / 3, 'head-on collision'))
xn_list.append(
Transition((2, 5, 1), (4, 1, 1), p_elast / 3, 'head-on collision'))
xn_list.append(
Transition((2, 5, 1), (6, 3, 1), p_elast / 3, 'head-on collision'))
xn_list.append(
Transition((3, 6, 2), (6, 3, 2), p_elast / 3, 'head-on collision'))
xn_list.append(
Transition((3, 6, 2), (1, 4, 2), p_elast / 3, 'head-on collision'))
xn_list.append(
Transition((3, 6, 2), (5, 2, 2), p_elast / 3, 'head-on collision'))
# Rule 2: Transitions for head-on collision: frictional dissipation
xn_list.append(Transition((1, 4, 0), (7, 7, 0), f, 'head-on collision'))
xn_list.append(Transition((2, 5, 1), (7, 7, 1), f, 'head-on collision'))
xn_list.append(Transition((3, 6, 2), (7, 7, 2), f, 'head-on collision'))
# Rule 3: Transitions for oblique collision: elastic
xn_list.append(
Transition((1, 3, 0), (3, 1, 0), p_elast, 'oblique collision'))
xn_list.append(
Transition((1, 5, 0), (5, 1, 0), p_elast, 'oblique collision'))
xn_list.append(
Transition((2, 4, 0), (4, 2, 0), p_elast, 'oblique collision'))
xn_list.append(
Transition((6, 4, 0), (4, 6, 0), p_elast, 'oblique collision'))
xn_list.append(
Transition((2, 4, 1), (4, 2, 1), p_elast, 'oblique collision'))
xn_list.append(
Transition((2, 6, 1), (6, 2, 1), p_elast, 'oblique collision'))
xn_list.append(
Transition((1, 5, 1), (5, 1, 1), p_elast, 'oblique collision'))
xn_list.append(
Transition((3, 5, 1), (5, 3, 1), p_elast, 'oblique collision'))
xn_list.append(
Transition((3, 1, 2), (1, 3, 2), p_elast, 'oblique collision'))
xn_list.append(
Transition((3, 5, 2), (5, 3, 2), p_elast, 'oblique collision'))
xn_list.append(
Transition((2, 6, 2), (6, 2, 2), p_elast, 'oblique collision'))
xn_list.append(
Transition((4, 6, 2), (6, 4, 2), p_elast, 'oblique collision'))
# Rule 3 frictional
xn_list.append(Transition((1, 3, 0), (7, 7, 0), f, 'oblique collision'))
xn_list.append(Transition((1, 5, 0), (7, 7, 0), f, 'oblique collision'))
xn_list.append(Transition((2, 4, 0), (7, 7, 0), f, 'oblique collision'))
xn_list.append(Transition((6, 4, 0), (7, 7, 0), f, 'oblique collision'))
xn_list.append(Transition((2, 4, 1), (7, 7, 1), f, 'oblique collision'))
xn_list.append(Transition((2, 6, 1), (7, 7, 1), f, 'oblique collision'))
xn_list.append(Transition((1, 5, 1), (7, 7, 1), f, 'oblique collision'))
xn_list.append(Transition((3, 5, 1), (7, 7, 1), f, 'oblique collision'))
xn_list.append(Transition((3, 1, 2), (7, 7, 2), f, 'oblique collision'))
xn_list.append(Transition((3, 5, 2), (7, 7, 2), f, 'oblique collision'))
xn_list.append(Transition((2, 6, 2), (7, 7, 2), f, 'oblique collision'))
xn_list.append(Transition((4, 6, 2), (7, 7, 2), f, 'oblique collision'))
# Rule 4: Transitions for oblique-from-behind collisions
xn_list.append(Transition((1, 2, 0), (2, 1, 0), p_elast, 'oblique'))
xn_list.append(Transition((1, 6, 0), (6, 1, 0), p_elast, 'oblique'))
xn_list.append(Transition((3, 4, 0), (4, 3, 0), p_elast, 'oblique'))
xn_list.append(Transition((5, 4, 0), (4, 5, 0), p_elast, 'oblique'))
xn_list.append(Transition((2, 1, 1), (1, 2, 1), p_elast, 'oblique'))
xn_list.append(Transition((2, 3, 1), (3, 2, 1), p_elast, 'oblique'))
xn_list.append(Transition((4, 5, 1), (5, 4, 1), p_elast, 'oblique'))
xn_list.append(Transition((6, 5, 1), (5, 6, 1), p_elast, 'oblique'))
xn_list.append(Transition((3, 2, 2), (2, 3, 2), p_elast, 'oblique'))
xn_list.append(Transition((3, 4, 2), (4, 3, 2), p_elast, 'oblique'))
xn_list.append(Transition((1, 6, 2), (6, 1, 2), p_elast, 'oblique'))
xn_list.append(Transition((5, 6, 2), (6, 5, 2), p_elast, 'oblique'))
# Rule 4 frictional
xn_list.append(Transition((1, 2, 0), (7, 1, 0), f, 'oblique'))
xn_list.append(Transition((1, 6, 0), (7, 1, 0), f, 'oblique'))
xn_list.append(Transition((3, 4, 0), (4, 7, 0), f, 'oblique'))
xn_list.append(Transition((5, 4, 0), (4, 7, 0), f, 'oblique'))
xn_list.append(Transition((2, 1, 1), (7, 2, 1), f, 'oblique'))
xn_list.append(Transition((2, 3, 1), (7, 2, 1), f, 'oblique'))
xn_list.append(Transition((4, 5, 1), (5, 7, 1), f, 'oblique'))
xn_list.append(Transition((6, 5, 1), (5, 7, 1), f, 'oblique'))
xn_list.append(Transition((3, 2, 2), (7, 3, 2), f, 'oblique'))
xn_list.append(Transition((3, 4, 2), (7, 3, 2), f, 'oblique'))
xn_list.append(Transition((1, 6, 2), (6, 7, 2), f, 'oblique'))
xn_list.append(Transition((5, 6, 2), (6, 7, 2), f, 'oblique'))
# Rule 5: Transitions for direct-from-behind collisions
xn_list.append(Transition((1, 1, 0), (2, 6, 0), p_elast / 4, 'behind'))
xn_list.append(Transition((1, 1, 0), (6, 2, 0), p_elast / 4, 'behind'))
xn_list.append(Transition((4, 4, 0), (3, 5, 0), p_elast / 4, 'behind'))
xn_list.append(Transition((4, 4, 0), (5, 3, 0), p_elast / 4, 'behind'))
xn_list.append(Transition((2, 2, 1), (1, 3, 1), p_elast / 4, 'behind'))
xn_list.append(Transition((2, 2, 1), (3, 1, 1), p_elast / 4, 'behind'))
xn_list.append(Transition((5, 5, 1), (4, 6, 1), p_elast / 4, 'behind'))
xn_list.append(Transition((5, 5, 1), (6, 4, 1), p_elast / 4, 'behind'))
xn_list.append(Transition((3, 3, 2), (2, 4, 2), p_elast / 4, 'behind'))
xn_list.append(Transition((3, 3, 2), (4, 2, 2), p_elast / 4, 'behind'))
xn_list.append(Transition((6, 6, 2), (1, 5, 2), p_elast / 4, 'behind'))
xn_list.append(Transition((6, 6, 2), (5, 1, 2), p_elast / 4, 'behind'))
# Rule 5 frictional
xn_list.append(Transition((1, 1, 0), (7, 1, 0), f / 4, 'behind'))
xn_list.append(Transition((4, 4, 0), (4, 7, 0), f / 4, 'behind'))
xn_list.append(Transition((2, 2, 1), (7, 2, 1), f / 4, 'behind'))
xn_list.append(Transition((5, 5, 1), (5, 7, 1), f / 4, 'behind'))
xn_list.append(Transition((3, 3, 2), (7, 3, 2), f / 4, 'behind'))
xn_list.append(Transition((6, 6, 2), (6, 7, 2), f / 4, 'behind'))
# Rule 6: Transitions for direct collision with stationary (resting) particle
xn_list.append(Transition((1, 7, 0), (7, 1, 0), p_elast / 3., 'rest'))
xn_list.append(Transition((1, 7, 0), (7, 2, 0), p_elast / 3., 'rest'))
xn_list.append(Transition((1, 7, 0), (7, 6, 0), p_elast / 3., 'rest'))
xn_list.append(Transition((7, 4, 0), (4, 7, 0), p_elast / 3., 'rest'))
xn_list.append(Transition((7, 4, 0), (3, 7, 0), p_elast / 3., 'rest'))
xn_list.append(Transition((7, 4, 0), (5, 7, 0), p_elast / 3., 'rest'))
xn_list.append(Transition((2, 7, 1), (7, 2, 1), p_elast / 3., 'rest'))
xn_list.append(Transition((2, 7, 1), (7, 1, 1), p_elast / 3., 'rest'))
xn_list.append(Transition((2, 7, 1), (7, 3, 1), p_elast / 3., 'rest'))
xn_list.append(Transition((7, 5, 1), (5, 7, 1), p_elast / 3., 'rest'))
xn_list.append(Transition((7, 5, 1), (4, 7, 1), p_elast / 3., 'rest'))
xn_list.append(Transition((7, 5, 1), (6, 7, 1), p_elast / 3., 'rest'))
xn_list.append(Transition((3, 7, 2), (7, 3, 2), p_elast / 3., 'rest'))
xn_list.append(Transition((3, 7, 2), (7, 2, 2), p_elast / 3., 'rest'))
xn_list.append(Transition((3, 7, 2), (7, 4, 2), p_elast / 3., 'rest'))
xn_list.append(Transition((7, 6, 2), (6, 7, 2), p_elast / 3., 'rest'))
xn_list.append(Transition((7, 6, 2), (1, 7, 2), p_elast / 3., 'rest'))
xn_list.append(Transition((7, 6, 2), (5, 7, 2), p_elast / 3., 'rest'))
# Rule 6 frictionl
xn_list.append(Transition((1, 7, 0), (7, 7, 0), f, 'rest'))
xn_list.append(Transition((7, 4, 0), (7, 7, 0), f, 'rest'))
xn_list.append(Transition((2, 7, 1), (7, 7, 1), f, 'rest'))
xn_list.append(Transition((7, 5, 1), (7, 7, 1), f, 'rest'))
xn_list.append(Transition((3, 7, 2), (7, 7, 2), f, 'rest'))
xn_list.append(Transition((7, 6, 2), (7, 7, 2), f, 'rest'))
# Rule 7: Transitions for wall impact
xn_list.append(
Transition((1, 8, 0), (4, 8, 0), p_elast / 3, 'wall rebound'))
xn_list.append(
Transition((1, 8, 0), (3, 8, 0), p_elast / 3, 'wall rebound'))
xn_list.append(
Transition((1, 8, 0), (5, 8, 0), p_elast / 3, 'wall rebound'))
xn_list.append(
Transition((2, 8, 1), (5, 8, 1), p_elast / 3, 'wall rebound'))
xn_list.append(
Transition((2, 8, 1), (4, 8, 1), p_elast / 3, 'wall rebound'))
xn_list.append(
Transition((2, 8, 1), (6, 8, 1), p_elast / 3, 'wall rebound'))
xn_list.append(
Transition((3, 8, 2), (6, 8, 2), p_elast / 3, 'wall rebound'))
xn_list.append(
Transition((3, 8, 2), (5, 8, 2), p_elast / 3, 'wall rebound'))
xn_list.append(
Transition((3, 8, 2), (1, 8, 2), p_elast / 3, 'wall rebound'))
xn_list.append(
Transition((8, 4, 0), (8, 1, 0), p_elast / 3, 'wall rebound'))
xn_list.append(
Transition((8, 4, 0), (8, 6, 0), p_elast / 3, 'wall rebound'))
xn_list.append(
Transition((8, 4, 0), (8, 2, 0), p_elast / 3, 'wall rebound'))
xn_list.append(
Transition((8, 5, 1), (8, 1, 1), p_elast / 3, 'wall rebound'))
xn_list.append(
Transition((8, 5, 1), (8, 2, 1), p_elast / 3, 'wall rebound'))
xn_list.append(
Transition((8, 5, 1), (8, 3, 1), p_elast / 3, 'wall rebound'))
xn_list.append(
Transition((8, 6, 2), (8, 2, 2), p_elast / 3, 'wall rebound'))
xn_list.append(
Transition((8, 6, 2), (8, 3, 2), p_elast / 3, 'wall rebound'))
xn_list.append(
Transition((8, 6, 2), (8, 4, 2), p_elast / 3, 'wall rebound'))
# Rule 7 frictional
xn_list.append(Transition((1, 8, 0), (7, 8, 0), f, 'wall rebound'))
xn_list.append(Transition((2, 8, 1), (7, 8, 1), f, 'wall rebound'))
xn_list.append(Transition((3, 8, 2), (7, 8, 2), f, 'wall rebound'))
xn_list.append(Transition((8, 4, 0), (8, 7, 0), f, 'wall rebound'))
xn_list.append(Transition((8, 5, 1), (8, 7, 1), f, 'wall rebound'))
xn_list.append(Transition((8, 6, 2), (8, 7, 2), f, 'wall rebound'))
# Rule 8: Transitions for glancing oblique collision
xn_list.append(Transition((2, 5, 0), (3, 6, 0), p_elast, 'glancing'))
xn_list.append(Transition((6, 3, 0), (5, 2, 0), p_elast, 'glancing'))
xn_list.append(Transition((3, 6, 1), (4, 1, 1), p_elast, 'glancing'))
xn_list.append(Transition((1, 4, 1), (6, 3, 1), p_elast, 'glancing'))
xn_list.append(Transition((4, 1, 2), (5, 2, 2), p_elast, 'glancing'))
xn_list.append(Transition((2, 5, 2), (1, 4, 2), p_elast, 'glancing'))
# Rule 8 frictional
xn_list.append(Transition((2, 5, 0), (7, 7, 0), f, 'glancing'))
xn_list.append(Transition((6, 3, 0), (7, 7, 0), f, 'glancing'))
xn_list.append(Transition((3, 6, 1), (7, 7, 1), f, 'glancing'))
xn_list.append(Transition((1, 4, 1), (7, 7, 1), f, 'glancing'))
xn_list.append(Transition((4, 1, 2), (7, 7, 2), f, 'glancing'))
xn_list.append(Transition((2, 5, 2), (7, 7, 2), f, 'glancing'))
# Rule 9: Transitions for "near-on" collisions
xn_list.append(Transition((6, 5, 0), (5, 6, 0), p_elast, 'near-on'))
xn_list.append(Transition((2, 3, 0), (3, 2, 0), p_elast, 'near-on'))
xn_list.append(Transition((1, 6, 1), (6, 1, 1), p_elast, 'near-on'))
xn_list.append(Transition((3, 4, 1), (4, 3, 1), p_elast, 'near-on'))
xn_list.append(Transition((2, 1, 2), (1, 2, 2), p_elast, 'near-on'))
xn_list.append(Transition((4, 5, 2), (5, 4, 2), p_elast, 'near-on'))
# Rule 9 frictional
xn_list.append(Transition((6, 5, 0), (7, 6, 0), f / 2, 'near-on'))
xn_list.append(Transition((6, 5, 0), (5, 7, 0), f / 2, 'near-on'))
xn_list.append(Transition((2, 3, 0), (7, 2, 0), f / 2, 'near-on'))
xn_list.append(Transition((2, 3, 0), (3, 7, 0), f / 2, 'near-on'))
xn_list.append(Transition((1, 6, 1), (7, 1, 1), f / 2, 'near-on'))
xn_list.append(Transition((1, 6, 1), (6, 7, 1), f / 2, 'near-on'))
xn_list.append(Transition((3, 4, 1), (7, 3, 1), f / 2, 'near-on'))
xn_list.append(Transition((3, 4, 1), (4, 7, 1), f / 2, 'near-on'))
xn_list.append(Transition((2, 1, 2), (7, 2, 2), f / 2, 'near-on'))
xn_list.append(Transition((2, 1, 2), (1, 7, 2), f / 2, 'near-on'))
xn_list.append(Transition((4, 5, 2), (7, 4, 2), f / 2, 'near-on'))
xn_list.append(Transition((4, 5, 2), (5, 7, 2), f / 2, 'near-on'))
# Rule 10: Transitions for oblique collision with rest particle
xn_list.append(
Transition((2, 7, 0), (7, 1, 0), p_elast, 'oblique with rest'))
xn_list.append(
Transition((6, 7, 0), (7, 1, 0), p_elast, 'oblique with rest'))
xn_list.append(
Transition((7, 3, 0), (4, 7, 0), p_elast, 'oblique with rest'))
xn_list.append(
Transition((7, 5, 0), (4, 7, 0), p_elast, 'oblique with rest'))
xn_list.append(
Transition((3, 7, 1), (7, 2, 1), p_elast, 'oblique with rest'))
xn_list.append(
Transition((1, 7, 1), (7, 2, 1), p_elast, 'oblique with rest'))
xn_list.append(
Transition((7, 6, 1), (5, 7, 1), p_elast, 'oblique with rest'))
xn_list.append(
Transition((7, 4, 1), (5, 7, 1), p_elast, 'oblique with rest'))
xn_list.append(
Transition((4, 7, 2), (7, 3, 2), p_elast, 'oblique with rest'))
xn_list.append(
Transition((2, 7, 2), (7, 3, 2), p_elast, 'oblique with rest'))
xn_list.append(
Transition((7, 5, 2), (6, 7, 2), p_elast, 'oblique with rest'))
xn_list.append(
Transition((7, 1, 2), (6, 7, 2), p_elast, 'oblique with rest'))
# Rule 10 frictional
xn_list.append(Transition((2, 7, 0), (7, 7, 0), f, 'oblique with rest'))
xn_list.append(Transition((6, 7, 0), (7, 7, 0), f, 'oblique with rest'))
xn_list.append(Transition((7, 3, 0), (7, 7, 0), f, 'oblique with rest'))
xn_list.append(Transition((7, 5, 0), (7, 7, 0), f, 'oblique with rest'))
xn_list.append(Transition((3, 7, 1), (7, 7, 1), f, 'oblique with rest'))
xn_list.append(Transition((1, 7, 1), (7, 7, 1), f, 'oblique with rest'))
xn_list.append(Transition((7, 6, 1), (7, 7, 1), f, 'oblique with rest'))
xn_list.append(Transition((7, 4, 1), (7, 7, 1), f, 'oblique with rest'))
xn_list.append(Transition((4, 7, 2), (7, 7, 2), f, 'oblique with rest'))
xn_list.append(Transition((2, 7, 2), (7, 7, 2), f, 'oblique with rest'))
xn_list.append(Transition((7, 5, 2), (7, 7, 2), f, 'oblique with rest'))
xn_list.append(Transition((7, 1, 2), (7, 7, 2), f, 'oblique with rest'))
# Rule 11: Transitions for oblique collision with wall particle
xn_list.append(
Transition((2, 8, 0), (3, 8, 0), p_elast, 'oblique with wall'))
xn_list.append(
Transition((6, 8, 0), (5, 8, 0), p_elast, 'oblique with wall'))
xn_list.append(
Transition((8, 3, 0), (8, 2, 0), p_elast, 'oblique with wall'))
xn_list.append(
Transition((8, 5, 0), (8, 6, 0), p_elast, 'oblique with wall'))
xn_list.append(
Transition((1, 8, 1), (6, 8, 1), p_elast, 'oblique with wall'))
xn_list.append(
Transition((3, 8, 1), (4, 8, 1), p_elast, 'oblique with wall'))
xn_list.append(
Transition((8, 4, 1), (8, 3, 1), p_elast, 'oblique with wall'))
xn_list.append(
Transition((8, 6, 1), (8, 1, 1), p_elast, 'oblique with wall'))
xn_list.append(
Transition((4, 8, 2), (5, 8, 2), p_elast, 'oblique with wall'))
xn_list.append(
Transition((2, 8, 2), (1, 8, 2), p_elast, 'oblique with wall'))
xn_list.append(
Transition((8, 1, 2), (8, 2, 2), p_elast, 'oblique with wall'))
xn_list.append(
Transition((8, 5, 2), (8, 4, 2), p_elast, 'oblique with wall'))
# Rule 11 frictional
xn_list.append(Transition((2, 8, 0), (7, 8, 0), f, 'oblique with wall'))
xn_list.append(Transition((6, 8, 0), (7, 8, 0), f, 'oblique with wall'))
xn_list.append(Transition((8, 3, 0), (8, 7, 0), f, 'oblique with wall'))
xn_list.append(Transition((8, 5, 0), (8, 7, 0), f, 'oblique with wall'))
xn_list.append(Transition((1, 8, 1), (7, 8, 1), f, 'oblique with wall'))
xn_list.append(Transition((3, 8, 1), (7, 8, 1), f, 'oblique with wall'))
xn_list.append(Transition((8, 4, 1), (8, 7, 1), f, 'oblique with wall'))
xn_list.append(Transition((8, 6, 1), (8, 7, 1), f, 'oblique with wall'))
xn_list.append(Transition((4, 8, 2), (7, 8, 2), f, 'oblique with wall'))
xn_list.append(Transition((2, 8, 2), (7, 8, 2), f, 'oblique with wall'))
xn_list.append(Transition((8, 1, 2), (8, 7, 2), f, 'oblique with wall'))
xn_list.append(Transition((8, 5, 2), (8, 7, 2), f, 'oblique with wall'))
# Gravity rule 1: rising particles become rest particles
xn_list.append(Transition((0, 1, 0), (0, 7, 0), g, 'gravity 1'))
xn_list.append(Transition((1, 1, 0), (1, 7, 0), g, 'gravity 1'))
xn_list.append(Transition((2, 1, 0), (2, 7, 0), g, 'gravity 1'))
xn_list.append(Transition((3, 1, 0), (3, 7, 0), g, 'gravity 1'))
xn_list.append(Transition((4, 1, 0), (4, 7, 0), g, 'gravity 1'))
xn_list.append(Transition((5, 1, 0), (5, 7, 0), g, 'gravity 1'))
xn_list.append(Transition((6, 1, 0), (6, 7, 0), g, 'gravity 1'))
xn_list.append(Transition((7, 1, 0), (7, 7, 0), g, 'gravity 1'))
xn_list.append(Transition((8, 1, 0), (8, 7, 0), g, 'gravity 1'))
# Gravity rule 2: resting particles become falling particles (if not above
# rest or wall?)
xn_list.append(Transition((0, 7, 0), (0, 4, 0), g, 'gravity 2'))
xn_list.append(Transition((1, 7, 0), (1, 4, 0), g, 'gravity 2'))
xn_list.append(Transition((2, 7, 0), (2, 4, 0), g, 'gravity 2'))
xn_list.append(Transition((3, 7, 0), (3, 4, 0), g, 'gravity 2'))
xn_list.append(Transition((4, 7, 0), (4, 4, 0), g, 'gravity 2'))
xn_list.append(Transition((5, 7, 0), (5, 4, 0), g, 'gravity 2'))
xn_list.append(Transition((6, 7, 0), (6, 4, 0), g, 'gravity 2'))
# Gravity rule 3: up/sideways particles become down/sideways particles
xn_list.append(Transition((0, 2, 0), (0, 3, 0), g, 'gravity 3'))
xn_list.append(Transition((1, 2, 0), (1, 3, 0), g, 'gravity 3'))
xn_list.append(Transition((2, 2, 0), (2, 3, 0), g, 'gravity 3'))
xn_list.append(Transition((3, 2, 0), (3, 3, 0), g, 'gravity 3'))
xn_list.append(Transition((4, 2, 0), (4, 3, 0), g, 'gravity 3'))
xn_list.append(Transition((5, 2, 0), (5, 3, 0), g, 'gravity 3'))
xn_list.append(Transition((6, 2, 0), (6, 3, 0), g, 'gravity 3'))
xn_list.append(Transition((7, 2, 0), (7, 3, 0), g, 'gravity 3'))
xn_list.append(Transition((8, 2, 0), (8, 3, 0), g, 'gravity 3'))
xn_list.append(Transition((0, 6, 0), (0, 5, 0), g, 'gravity 3'))
xn_list.append(Transition((1, 6, 0), (1, 5, 0), g, 'gravity 3'))
xn_list.append(Transition((2, 6, 0), (2, 5, 0), g, 'gravity 3'))
xn_list.append(Transition((3, 6, 0), (3, 5, 0), g, 'gravity 3'))
xn_list.append(Transition((4, 6, 0), (4, 5, 0), g, 'gravity 3'))
xn_list.append(Transition((5, 6, 0), (5, 5, 0), g, 'gravity 3'))
xn_list.append(Transition((6, 6, 0), (6, 5, 0), g, 'gravity 3'))
xn_list.append(Transition((7, 6, 0), (7, 5, 0), g, 'gravity 3'))
xn_list.append(Transition((8, 6, 0), (8, 5, 0), g, 'gravity 3'))
# Gravity rule 4: down/side to straight down
xn_list.append(Transition((0, 3, 0), (0, 4, 0), g, 'gravity 4'))
xn_list.append(Transition((1, 3, 0), (1, 4, 0), g, 'gravity 4'))
xn_list.append(Transition((2, 3, 0), (2, 4, 0), g, 'gravity 4'))
xn_list.append(Transition((3, 3, 0), (3, 4, 0), g, 'gravity 4'))
xn_list.append(Transition((4, 3, 0), (4, 4, 0), g, 'gravity 4'))
xn_list.append(Transition((5, 3, 0), (5, 4, 0), g, 'gravity 4'))
xn_list.append(Transition((6, 3, 0), (6, 4, 0), g, 'gravity 4'))
xn_list.append(Transition((7, 3, 0), (7, 4, 0), g, 'gravity 4'))
xn_list.append(Transition((8, 3, 0), (8, 4, 0), g, 'gravity 4'))
xn_list.append(Transition((0, 5, 0), (0, 4, 0), g, 'gravity 4'))
xn_list.append(Transition((1, 5, 0), (1, 4, 0), g, 'gravity 4'))
xn_list.append(Transition((2, 5, 0), (2, 4, 0), g, 'gravity 4'))
xn_list.append(Transition((3, 5, 0), (3, 4, 0), g, 'gravity 4'))
xn_list.append(Transition((4, 5, 0), (4, 4, 0), g, 'gravity 4'))
xn_list.append(Transition((5, 5, 0), (5, 4, 0), g, 'gravity 4'))
xn_list.append(Transition((6, 5, 0), (6, 4, 0), g, 'gravity 4'))
xn_list.append(Transition((7, 5, 0), (7, 4, 0), g, 'gravity 4'))
xn_list.append(Transition((8, 5, 0), (8, 4, 0), g, 'gravity 4'))
# Uncertain gravity rule!
xn_list.append(Transition((7, 0, 2), (3, 0, 2), g / 2.0, 'gravity??'))
xn_list.append(Transition((0, 7, 1), (0, 5, 1), g / 2.0, 'gravity??'))
if _DEBUG:
print
print 'setup_transition_list(): list has', len(xn_list), 'transitions:'
for t in xn_list:
print ' From state', t.from_state, 'to state', t.to_state, 'at rate', t.rate, 'called', t.name
return xn_list