Brownian#

Definition #

Brownian vertex integrator moves vertices following brownian dynamics.

Brownian dynamics assumes overdamped Langevin dynamics and solves the set of first-order equations for the position of each vertex $\mathbf{r}_i$:

Where $\mathbf{\eta}_{i} \left( t \right) \in \mathbb{R}^{3}$ is a weak random noise obeying:

$langle mathbf{eta}_{i} rangle = 0$
$langle eta_{i}^{m} left( t right) eta_{j}^{n} left( t^{prime} right) rangle = sqrt{2gamma k_{B}T} delta_{ij} delta_{mn} delta left( t - t^{prime} right)$

Where $m, n \in \{x, y, z\}$.

Here, $T$ is the temperature and $\gamma$ is the friction coefficient.

add .. code-block:: python

evolver.add_integrator(“Mesh>brownian”, {“T”: “0.2”})

run .. code-block:: python

evolver.evolveMD()

set .. code-block:: python

evolver.set(“Mesh>brownian”, {“gamma”: “1.0”})

delete .. code-block:: python

evolver.delete_integrator(“Mesh>brownian”)

T Temperature used in simulation.

type: double default: 0.0

gamma Friction coefficient.

type: double default: 1.0

seed Seed used to generate the random number.

type: int default: 123456