Kinetics

Kinetics shared by the chemistry packages: reactors and reactions that a reactor and the sites of a field run.

BrusselatorReactionElement(label, visual=None, *, u=1.0, v=1.0, a=1.0, b=3.0)

Bases: Element

Reactor of the Brusselator, the concentrations u and v of its two intermediates.

The reactions A -> U, B + U -> V + D, 2U + V -> 3U, and U -> E change the concentrations, with the buffered reactants A and B held at the supplies a and b, which the reactions read as modifiers. The well-mixed brusselator_ode runs them in one reactor and the reaction-diffusion brusselator at every site of a field.

Parameters:

Name	Type	Description	Default
label	str	The label of the reactor.	required
visual	VisualSpec | None	How the element is drawn, or None for default_visual_.	None
u	Annotated[float, StateSpec(domain=closed_open(0, oo))]	The initial concentration of the autocatalytic intermediate.	1.0
v	Annotated[float, StateSpec(domain=closed_open(0, oo))]	The initial concentration of the second intermediate.	1.0
a	Annotated[float, ParameterSpec(domain=closed_open(0, oo))]	The constant supply of the first reactant.	1.0
b	Annotated[float, ParameterSpec(domain=closed_open(0, oo))]	The constant supply of the second reactant.	3.0

Examples:

>>> from skcomplex.models.chemistry.common.kinetics import BrusselatorReactionElement
>>> BrusselatorReactionElement('reactor').b
3.0

Source code in src/skcomplex/models/chemistry/common/kinetics/_brusselator.py

def __init__(
    self,
    label: str,
    visual: VisualSpec | None = None,
    *,
    u: Annotated[float, StateSpec(domain=RealSet.closed_open(0, oo))] = 1.0,
    v: Annotated[float, StateSpec(domain=RealSet.closed_open(0, oo))] = 1.0,
    a: Annotated[float, ParameterSpec(domain=RealSet.closed_open(0, oo))] = 1.0,
    b: Annotated[float, ParameterSpec(domain=RealSet.closed_open(0, oo))] = 3.0,
) -> None:
    super().__init__(label, visual=visual)
    self.u = u
    self.v = v
    self.a = a
    self.b = b

CubicAutocatalysisInteraction(label, *, target, substrate='u', autocatalyst='v', k=1.0, mode='rate')

Bases: ReactionInteraction

Cubic autocatalysis A + 2B -> 3B at the mass-action rate k a b^2, between two states of the target.

The autocatalyst B converts the substrate A into itself. The reaction is the autocatalytic step of the Gray-Scott model, with the substrate u and the autocatalyst v, and of the Brusselator and the Schnakenberg model, 2U + V -> 3U, with the substrate v and the autocatalyst u. A target that is a field reacts at every site.

Parameters:

Name	Type	Description	Default
label	str	The label of the reaction.	required
target	Annotated[str, RoleSpec()]	The path of the reactor, or of the field whose every site reacts.	required
substrate	str	The name of the state of the substrate.	'u'
autocatalyst	str	The name of the state of the autocatalyst.	'v'
k	Annotated[float, ParameterSpec(domain=closed_open(0, oo))]	The rate constant.	1.0
mode	str	The form of the laws, 'rate', 'jump', or 'langevin'.	'rate'

Raises:

Type	Description
ValidationError	The mode is unknown, or a state name is not an identifier.

Examples:

>>> from skcomplex.core.system import System
>>> from skcomplex.engine.runtime import Simulation
>>> from skcomplex.models.chemistry.common.kinetics import CubicAutocatalysisInteraction
>>> from skcomplex.models.chemistry.kinetics import CubicAutocatalysisElement
>>> reaction = CubicAutocatalysisInteraction('autocatalysis', target='reactor', substrate='a', autocatalyst='b')
>>> reactor = CubicAutocatalysisElement('reactor', a=1.0, b=0.5)
>>> trajectory = Simulation(System(elements=[reactor], interactions=[reaction]), dt=1.0).check().prepare()
>>> states = trajectory.run(until=10).trajectory_.states
>>> round(float(states[-1].sum()), 6)
1.5

Source code in src/skcomplex/models/chemistry/common/kinetics/_cubic_autocatalysis.py

def __init__(
    self,
    label: str,
    *,
    target: Annotated[str, RoleSpec()],
    substrate: str = 'u',
    autocatalyst: str = 'v',
    k: Annotated[float, ParameterSpec(domain=RealSet.closed_open(0, oo))] = 1.0,
    mode: str = 'rate',
) -> None:
    super().__init__(label, target=target, k=k, mode=mode)
    self.substrate = substrate
    self.autocatalyst = autocatalyst