Struct MartynaTuckermanTobiasKlein 

pub struct MartynaTuckermanTobiasKlein { /* private fields */ }

Nosé-Hoover thermostat.

MartynaTuckermanTobiasKlein adds a new degree of freedom ($\eta$) to a molecular dynamics simulation in such a way that the existing degrees of freedom sample a constant temperature ensemble. Each MartynaTuckermanTobiasKlein instance stores $\eta$ and its momentum, $\xi$, internally.

The extended Hamiltonian $H$ is:

   H = K + U
        + N kT \eta
        +  \frac{1}{2} N kT \tau^2\xi^2

Where $K$ is the kinetic energy of the system, $U$ is the potential energy of the system, $N$ is the number of degrees of freedom, and $kT$ is the temperature.

Following the Trotter decomposition of Liouvillian, MartynaTuckermanTobiasKlein integrates $\eta$ and $\xi$ forward by half time step $\frac{\delta t}{2}$ via the following procedure:

\begin{align*}

G_\mathrm{old} &= \frac{1}{\tau^2} \left( \frac{2 K}{N kT} - 1 \right) \\

\xi \left\{ t+\frac{\delta t} {4} \right\} &= \xi \{ t \} + G_\mathrm{old}\frac{\delta t}{4} \\

\alpha &= \exp\left[ -\xi \left\{ t+\frac{\delta t} {4} \right\} \frac{dt}{2} \right]  \\

K_{new} &= K \alpha^2 \\

\eta \left\{ t+\frac{\delta t} {2} \right\} &= \eta \{ t \} + \xi \left\{ t+\frac{\delta t} {4} \right\} \frac{\delta t}{2} \\

G_\mathrm{new} &= \frac{1}{\tau^2} \left( \frac{2 K_\mathrm{new} }{kT} - 1 \right) \\

\xi \left\{ t+\frac{\delta t} {2} \right\} &= \xi \left\{ t+\frac{\delta t} {4} \right\} + G_\mathrm{new} \frac{\delta t}{4}

\end{align*}

Warning

MartynaTuckermanTobiasKlein fails to sample the correct distribution when there are strong harmonic interactions in the system. In such situations, use Bussi or NoséHooverChain instead.

References

• Tuckerman et al. 2006
• Martyna et al. 1994

Example

use hoomd_md::thermostat::MartynaTuckermanTobiasKlein;

let thermostat = MartynaTuckermanTobiasKlein::zero(0.5.try_into()?);

Implementations

impl MartynaTuckermanTobiasKlein

pub fn zero(tau: PositiveReal) -> Self

Construct a new MartynaTuckermanTobiasKlein thermostat with the given time constant, $\xi = 0$, and $\eta = 0$ .

This initial condition is likely to be very far from equilibrium which will result in wild kinetic energy oscillations for the first hundred to thousand time steps. Use thermalized to choose the initial position and momentum from a thermal distribution.

Example

use hoomd_md::thermostat::MartynaTuckermanTobiasKlein;

let thermostat = MartynaTuckermanTobiasKlein::zero(0.5.try_into()?);

pub fn thermalized<M, R: Rng + ?Sized>( rng: &mut R, tau: PositiveReal, macrostate: &M, degrees_of_freedom: usize, ) -> Self

where M: Temperature,

Construct a new MartynaTuckermanTobiasKlein thermostat with a random $\xi$ drawn from a thermal distribution.

Panics

This method will panic when degrees_of_freedom is 0.

Example

use hoomd_md::{
    TranslationalKineticEnergy, thermostat::MartynaTuckermanTobiasKlein,
};
use hoomd_microstate::{
    Body, Microstate,
    property::{DynamicPoint, Point},
};
use hoomd_simulation::macrostate::Isothermal;
use hoomd_vector::Cartesian;

let mut microstate = Microstate::builder()
    .bodies([
        Body::single_site(
            DynamicPoint {
                position: Cartesian::from([1.0, 2.0]),
                ..Default::default()
            },
            Point::default(),
        ),
        Body::single_site(
            DynamicPoint {
                position: Cartesian::from([-2.0, 3.0]),
                ..Default::default()
            },
            Point::default(),
        ),
    ])
    .try_build()?;

let macrostate = Isothermal { temperature: 1.5 };
let mut rng = microstate.counter().make_rng();
let translational_thermostat = MartynaTuckermanTobiasKlein::thermalized(
    &mut rng,
    0.5.try_into()?,
    &macrostate,
    microstate.translational_kinetic_energy().1,
);
microstate.increment_substep();

pub fn energy(&self) -> f64

The total energy of the thermostat.

Example

use hoomd_md::thermostat::MartynaTuckermanTobiasKlein;

let thermostat = MartynaTuckermanTobiasKlein::zero(0.5.try_into()?);

let energy = thermostat.energy();

pub fn eta(&self) -> f64

The thermostat’s position.

Example

use hoomd_md::thermostat::MartynaTuckermanTobiasKlein;

let thermostat = MartynaTuckermanTobiasKlein::zero(0.5.try_into()?);

let eta = thermostat.eta();

pub fn xi(&self) -> f64

The thermostat’s momentum.

Example

use hoomd_md::thermostat::MartynaTuckermanTobiasKlein;

let thermostat = MartynaTuckermanTobiasKlein::zero(0.5.try_into()?);

let xi = thermostat.xi();

Trait Implementations

impl Clone for MartynaTuckermanTobiasKlein

fn clone(&self) -> MartynaTuckermanTobiasKlein

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for MartynaTuckermanTobiasKlein

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for MartynaTuckermanTobiasKlein

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

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl PartialEq for MartynaTuckermanTobiasKlein

fn eq(&self, other: &MartynaTuckermanTobiasKlein) -> 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 Serialize for MartynaTuckermanTobiasKlein

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

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl<M> Thermostat<M> for MartynaTuckermanTobiasKlein

where M: Temperature,

fn integrate_half_step_one<R: Rng + ?Sized>( &mut self, _rng: &mut R, macrostate: &M, delta_t: f64, kinetic_energy: f64, degrees_of_freedom: usize, ) -> f64

Integrate the thermostat one half step forward in time.

fn integrate_half_step_two<R: Rng + ?Sized>( &mut self, rng: &mut R, macrostate: &M, delta_t: f64, kinetic_energy: f64, degrees_of_freedom: usize, ) -> f64

Integrate the thermostat one half step forward in time.

impl StructuralPartialEq for MartynaTuckermanTobiasKlein