Struct Isotropic 

pub struct Isotropic<E> {
    pub interaction: E,
    pub r_cut: f64,
}

Compute isotropic interactions between a pair of sites.

Isotropic provides a single implementation that computes pairwise interactions that are a function only of the distance between sites. It fills the gap between traits like SitePairEnergy / SitePairForceAndVirial which operate on site properties and UnivariateEnergy / UnivariateForce which is a function only of the separation distance.

Isotropic cuts all interactions off when the distance between sites is greater than or equal to r_cut:

U_{ij} =
\begin{cases}
U(r_{ij}) & r_{ij} < r_\mathrm{cut} \\
0 & r_{ij} \ge r_\mathrm{cut}
\end{cases}

\vec{F_{ij}} =
\begin{cases}
-\frac{\mathrm{d} U}{\mathrm{d} r} \biggr\rvert_{r=r_{ji}} \hat{r}_{ji} & r_{ij} < r_\mathrm{cut} \\
\vec{0} & r_{ij} \ge r_\mathrm{cut}
\end{cases}

where $U$ is given by E’s UnivariateEnergy implementation and $-\frac{\mathrm{d} U}{\mathrm{d} r}$ is given by E’s UnivariateForce implementation.

Use Isotropic with PairwiseCutoff in MD and MC simulations.

Example

use approxim::assert_relative_eq;
use hoomd_interaction::{
    SitePairEnergy, SitePairForceAndVirial, pairwise::Isotropic,
    univariate::LennardJones,
};
use hoomd_microstate::property::Point;
use hoomd_vector::Cartesian;

let a = Point {
    position: Cartesian::from([0.0, 0.0]),
};
let b = Point {
    position: Cartesian::from([0.0, 2.0 * 2.0_f64.powf(1.0 / 6.0)]),
};

let lennard_jones: LennardJones = LennardJones {
    epsilon: 1.5,
    sigma: 2.0,
};
let lennard_jones = Isotropic {
    interaction: lennard_jones,
    r_cut: 2.5,
};

let energy = lennard_jones.site_pair_energy(&a, &b);
let (force_ab, virial_ab) =
    lennard_jones.site_pair_force_and_virial(&a, &b);
let (force_ba, virial_ba) =
    lennard_jones.site_pair_force_and_virial(&b, &a);

assert_eq!(energy, -1.5);
assert_eq!(force_ab, -force_ba);
assert_relative_eq!(force_ab, Cartesian::from([0.0, 0.0]), epsilon = 1e-14);

Fields

interaction: E

The site-site interaction.

r_cut: f64

Maximum distance between two interacting sites.

Trait Implementations

impl<E: Clone> Clone for Isotropic<E>

fn clone(&self) -> Isotropic<E>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<E: Debug> Debug for Isotropic<E>

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

Formats the value using the given formatter.

impl<'de, E> Deserialize<'de> for Isotropic<E>

where E: Deserialize<'de>,

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<E> MaximumInteractionRange for Isotropic<E>

fn maximum_interaction_range(&self) -> f64

The maximum interaction range for Isotropic is the given r_cut.

Example

use hoomd_interaction::{
    MaximumInteractionRange, pairwise::Isotropic, univariate::LennardJones,
};

let lennard_jones: LennardJones = LennardJones {
    epsilon: 1.5,
    sigma: 2.0,
};
let lennard_jones = Isotropic {
    interaction: lennard_jones,
    r_cut: 2.5,
};

assert_eq!(lennard_jones.maximum_interaction_range(), 2.5);

impl<E: PartialEq> PartialEq for Isotropic<E>

fn eq(&self, other: &Isotropic<E>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<E> Serialize for Isotropic<E>

where E: Serialize,

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

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl<P, S, E> SitePairEnergy<S> for Isotropic<E>

where S: Position<Position = P>, P: Metric, E: UnivariateEnergy,

fn site_pair_energy(&self, site_properties_i: &S, site_properties_j: &S) -> f64

Compute the energy contribution from a pair of sites.

U_{ij} =
\begin{cases}
U(r_{ij}) & r_{ij} < r_\mathrm{cut} \\
0 & r_{ij} \ge r_\mathrm{cut}
\end{cases}

where $U$ is given by E’s UnivariateEnergy implementation.

Example

use approxim::assert_relative_eq;
use hoomd_interaction::{
    SitePairEnergy, pairwise::Isotropic, univariate::LennardJones,
};
use hoomd_microstate::property::Point;
use hoomd_vector::Cartesian;

let a = Point {
    position: Cartesian::from([0.0, 0.0]),
};
let b = Point {
    position: Cartesian::from([0.0, 2.0 * 2.0_f64.powf(1.0 / 6.0)]),
};

let lennard_jones: LennardJones = LennardJones {
    epsilon: 1.5,
    sigma: 2.0,
};
let lennard_jones = Isotropic {
    interaction: lennard_jones,
    r_cut: 2.5,
};

let energy = lennard_jones.site_pair_energy(&a, &b);

assert_eq!(energy, -1.5);

fn site_pair_energy_initial( &self, site_properties_i: &S, site_properties_j: &S, ) -> f64

Evaluate the energy contribution from a pair of sites in the initial state.

fn is_only_infinite_or_zero() -> bool

Does this potential only ever return infinity or zero?

impl<V, S, E> SitePairForceAndVirial<S> for Isotropic<E>

where V: Default + InnerProduct + Outer, S: Position<Position = V>, E: UnivariateForce, V::Tensor: Default,

fn site_pair_force_and_virial( &self, site_properties_i: &S, site_properties_j: &S, ) -> (Self::Force, <Self::Force as Outer>::Tensor)

Evaluate the force and virial on site i caused by site j.

Isotropic forces always act along the radial direction:

\vec{F_{ij}} =
\begin{cases}
-\frac{\mathrm{d} U}{\mathrm{d} r} \biggr\rvert_{r=r_{ji}} \hat{r}_{ji} & r_{ij} < r_\mathrm{cut} \\
\vec{0} & r_{ij} \ge r_\mathrm{cut}
\end{cases}

where $-\frac{\mathrm{d} U}{\mathrm{d} r}$ is given by E’s UnivariateForce implementation.

Example

use approxim::assert_relative_eq;
use hoomd_interaction::{
    SitePairForceAndVirial, pairwise::Isotropic, univariate::LennardJones,
};
use hoomd_microstate::property::Point;
use hoomd_vector::Cartesian;

let a = Point {
    position: Cartesian::from([0.0, 0.0]),
};
let b = Point {
    position: Cartesian::from([0.0, 2.0 * 2.0_f64.powf(1.0 / 6.0)]),
};

let lennard_jones: LennardJones = LennardJones {
    epsilon: 1.5,
    sigma: 2.0,
};
let lennard_jones = Isotropic {
    interaction: lennard_jones,
    r_cut: 2.5,
};

let (force_ab, virial_ab) =
    lennard_jones.site_pair_force_and_virial(&a, &b);
let (force_ba, virial_ba) =
    lennard_jones.site_pair_force_and_virial(&b, &a);

assert_eq!(force_ab, -force_ba);
assert_relative_eq!(force_ab, Cartesian::from([0.0, 0.0]), epsilon = 1e-14);

type Force = V

The type of the result force.

impl<V, S, E> SitePairForceVirialAndTorque<S> for Isotropic<E>

where V: Default + InnerProduct + Wedge + Outer, V::Bivector: Default, S: Position<Position = V>, E: UnivariateForce, V::Tensor: Default,

fn site_pair_force_virial_and_torque( &self, site_properties_i: &S, site_properties_j: &S, ) -> (V, <Self::Force as Outer>::Tensor, V::Bivector)

Evaluate the force, virial, and torque on site i caused by site j.

Isotropic forces always act along the radial direction:

\vec{F_{ij}} =
\begin{cases}
-\frac{\mathrm{d} U}{\mathrm{d} r} \biggr\rvert_{r=r_{ji}} \hat{r}_{ji} & r_{ij} < r_\mathrm{cut} \\
\vec{0} & r_{ij} \ge r_\mathrm{cut}
\end{cases}

where $-\frac{\mathrm{d} U}{\mathrm{d} r}$ is given by E’s UnivariateForce implementation.

Radial forces produce zero torque.

type Force = V

The type of the result force.

impl<E> StructuralPartialEq for Isotropic<E>