Struct BoundLennardJones

pub struct BoundLennardJones {
    pub epsilon: f64,
    pub sigma: f64,
    pub bound: f64,
    pub cutoff: f64,
}

Lennard-Jones interaction potential with numerical upper and lower limit.

Parameters & Variables

Symbol	Struct Field	Description
$\sigma$	sigma	Measure for the size of the particle.
$\epsilon$	epsilon	Interaction Strength
$\beta$	bound	Upper bound on the interaction strength.
$\xi$	cutoff	Cutoff after which the interaction strength is identically 0
$r$		Distance between interacting particles

Equations

The pure Lennard-Jones potential has many numerical downsides as it is very unstable to use and thus typically only recommended with extremely small integration steps. Here, we artificially limit the repelling part of the potential thus increasing numerical usability. However, it also has in principle infinite range. This is directly contrary to one of the fundamental assumptions of cellular_raza. We resolve the latter problem by simply assigning the value 0 if $r>=\zeta$ although this behavior is not continuous anymore. The potential of the interaction is given by \begin{align} U(r) &= 4\epsilon\left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6\right]\\ V(r) &= \min(U(r), \beta)\theta(r-\zeta) \end{align} where $\epsilon$ determines the overall interaction strength of the potential and $\sigma$ the shape and interaction range. The function $\theta(r-\zeta)$ is the heaviside function which sets the interaction to zero when reaching the cutoff point. The minimum of this potential is at $r_\text{min}=2^{1/6}\sigma$. For two identically-sized spherical interacting particles $r_\text{min}$ has to align with the diameter of their size. The interaction is artificially bound from above by a value $\beta$ in order to obtain better numerical stability.

References

[1] “On the determination of molecular fields.—I. From the variation of the viscosity of a gas with temperature,” Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, vol. 106, no. 738. The Royal Society, pp. 441–462, Oct. 1924. doi: 10.1098/rspa.1924.0081.

Fields

epsilon: f64

Interaction strength $\epsilon$ of the potential.

sigma: f64

Overall size $\sigma$ of the object of the potential.

bound: f64

Numerical bound $\beta$ of the interaction strength.

cutoff: f64

Defines a cutoff $\zeta$ after which the potential will be fixed to exactly zero.

Trait Implementations

impl Clone for BoundLennardJones

fn clone(&self) -> BoundLennardJones

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for BoundLennardJones

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for BoundLennardJones

fn deserialize<__D>( __deserializer: __D, ) -> Result<BoundLennardJones, <__D as Deserializer<'de>>::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<const D: usize> Interaction<Matrix<f64, Const<D>, Const<1>, ArrayStorage<f64, D, 1>>, Matrix<f64, Const<D>, Const<1>, ArrayStorage<f64, D, 1>>, Matrix<f64, Const<D>, Const<1>, ArrayStorage<f64, D, 1>>> for BoundLennardJones

fn calculate_force_between( &self, own_pos: &Matrix<f64, Const<D>, Const<1>, ArrayStorage<f64, D, 1>>, _own_vel: &Matrix<f64, Const<D>, Const<1>, ArrayStorage<f64, D, 1>>, ext_pos: &Matrix<f64, Const<D>, Const<1>, ArrayStorage<f64, D, 1>>, _ext_vel: &Matrix<f64, Const<D>, Const<1>, ArrayStorage<f64, D, 1>>, _ext_information: &(), ) -> Result<(Matrix<f64, Const<D>, Const<1>, ArrayStorage<f64, D, 1>>, Matrix<f64, Const<D>, Const<1>, ArrayStorage<f64, D, 1>>), CalcError>

Calculates the forces (velocity-derivative) on the corresponding external position given external velocity. By providing velocities, we can calculate terms that are related to friction. The function returns two forces, one acting on the current agent and the other on the external agent.

fn get_interaction_information(&self)

Get additional information of cellular properties (ie. for cell-specific interactions). For now, this can also be used to get the mass of the other cell-agent. In the future, we will probably provide a custom function for this.

fn is_neighbor( &self, own_pos: &Pos, ext_pos: &Pos, ext_inf: &Inf, ) -> Result<bool, CalcError>

Checks if the other cell represented by position and information is a neighbor to the current one or not.

fn react_to_neighbors(&mut self, neighbors: usize) -> Result<(), CalcError>

Reacts to the results gathered by the Interaction::is_neighbor method and changes the state of the cell.

impl IntoPy<Py<PyAny>> for BoundLennardJones

fn into_py(self, py: Python<'_>) -> Py<PyAny>

Performs the conversion.

impl PyClass for BoundLennardJones

type Frozen = False

Whether the pyclass is frozen.

impl PyTypeInfo for BoundLennardJones

const NAME: &'static str = "BoundLennardJones"

Class name.

const MODULE: Option<&'static str> = ::core::option::Option::None

Module name, if any.

fn type_object_raw(py: Python<'_>) -> *mut PyTypeObject

Returns the PyTypeObject instance for this type.

fn type_object_bound(py: Python<'_>) -> Bound<'_, PyType>

Returns the safe abstraction over the type object.

fn is_type_of_bound(object: &Bound<'_, PyAny>) -> bool

Checks if object is an instance of this type or a subclass of this type.

fn is_exact_type_of_bound(object: &Bound<'_, PyAny>) -> bool

Checks if object is an instance of this type.

impl Serialize for BoundLennardJones

fn serialize<__S>( &self, __serializer: __S, ) -> Result<<__S as Serializer>::Ok, <__S as Serializer>::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl DerefToPyAny for BoundLennardJones