# 5. Running the simulation¶

## 5.1. Integrator¶

To run the integrator call the method espressomd.integrate.Integrator.run():

system.integrator.run(steps=number_of_steps, recalc_forces=False, reuse_forces=False)


where number_of_steps is the number of time steps the integrator should perform.

ESPResSo uses the Velocity Verlet algorithm for the integration of the equations of motion.

Note that this implementation of the Velocity Verlet algorithm reuses forces. That is, they are computed once in the middle of the time step, but used twice, at the beginning and end. In the first time step after setting up, there are no forces present yet. Therefore, ESPResSo has to compute them before the first time step. That has two consequences: first, random forces are redrawn, resulting in a narrower distribution of the random forces, which we compensate by stretching. Second, coupling forces of e.g. the lattice Boltzmann fluid cannot be computed and are therefore lacking in the first half time step. In order to minimize these effects, ESPResSo has a quite conservative heuristics to decide whether a change makes it necessary to recompute forces before the first time step. Therefore, calling 100 times espressomd.integrate.Integrator.run() with steps=1 does the same as with steps=100, apart from some small calling overhead.

However, for checkpointing, there is no way for ESPResSo to tell that the forces that you read back in actually match the parameters that are set. Therefore, ESPResSo would recompute the forces before the first time step, which makes it essentially impossible to checkpoint LB simulations, where it is vital to keep the coupling forces. To work around this, there is an additional parameter reuse_forces, which tells integrate to not recalculate the forces for the first time step, but use that the values still stored with the particles. Use this only if you are absolutely sure that the forces stored match your current setup!

The opposite problem occurs when timing interactions: In this case, one would like to recompute the forces, despite the fact that they are already correctly calculated. To this aim, the option recalc_forces can be used to enforce force recalculation.

## 5.2. Run steepest descent minimization¶

espressomd.espresso.thermostat.Thermostat.set_steepest_descent()

This feature is used to propagate each particle by a small distance parallel to the force acting on it. When only conservative forces for which a potential exists are in use, this is equivalent to a steepest descent energy minimization. A common application is removing overlap between randomly placed particles.

Please note that the behavior is undefined if either a thermostat, Maggs electrostatics or lattice Boltzmann is activated. It runs a simple steepest descent algorithm:

Iterate

$p_i = p_i + \min(\texttt{gamma} \times F_i, \texttt{max_displacement}),$

while the maximal force is bigger than f_max or for at most max_steps times. The energy is relaxed by gamma, while the change per coordinate per step is limited to max_displacement. The combination of gamma and max_displacement can be used to get a poor man’s adaptive update. Rotational degrees of freedom are treated similarly: each particle is rotated around an axis parallel to the torque acting on the particle. Please be aware of the fact that this needs not to converge to a local minimum in periodic boundary conditions. Translational and rotational coordinates that are fixed using the fix and rotation attribute of particles are not altered.

Usage example:

system.integrator.set_steepest_descent(
f_max=0, gamma=0.1, max_displacement=0.1)
system.integrator.run(20)
system.integrator.set_vv()  # to switch back to velocity verlet


## 5.3. Multi-timestepping¶

Required feature: MULTI_TIMESTEP

The multi-timestepping integrator allows to run two concurrent integration time steps within a simulation, associating beads with either the large espressomd.system.System.time_step or the other espressomd.system.System.smaller_time_step. Setting espressomd.system.System.smaller_time_step to a positive value turns on the multi-timestepping algorithm. Beads are by default associated with espressomd.system.System.time_step, corresponding to the particle property espressomd.particle_data.ParticleHandle.smaller_timestep set to 0. Setting to espressomd.particle_data.ParticleHandle.smaller_timestep to 1 associates the particle to the espressomd.system.System.smaller_time_step integration. The integrator can be used in the NVE ensemble, as well as with the Langevin thermostat and the modified Andersen barostat for NVT and NPT simulations, respectively. See [Ber15] for more details.

## 5.4. Integrating rotational degrees of freedom¶

When the feature ROTATION is compiled in, Particles not only have a position, but also an orientation. Just as a force on a particle leads to an increase in linear velocity, a torque on a particle leads to an increase in angular velocity. The rotational degrees of freedom are also integrated using a velocity Verlet scheme. When the Langevin thermostat is enabled, the rotational degrees of freedom are also thermalized.

Whether or not rotational degrees of freedom are propagated, is controlled on a per-particle and per-axis level, where the axes are the Cartesian axes of the particle in its body-fixed frame. It is important to note that starting from version 4.0 and unlike in earlier versions of ESPResSo, the particles’ rotation is disabled by default. In this way, just compiling in the ROTATION feature no longer changes the physics of the system.

The rotation of a particle is controlled via the espressomd.particle_data.ParticleHandle.rotation property. E.g., the following code adds a particle with rotation on the x axis enabled:

import espressomd
s = espressomd.System()
s.part.add(pos=(0, 0, 0), rotation=(1, 0, 0))


Notes:

• The orientation of a particle is stored as a quaternion in the espressomd.particle_data.ParticleHandle.quat property. For a value of (1,0,0,0), the body and space frames coincide.
• The space-frame direction of the particle’s z-axis in its body frame is accessible through the espressomd.particle_data.ParticleHandle.director property.
• Any other vector can be converted from body to space fixed frame using the espressomd.particle_data.ParticleHandle.convert_vector_body_to_space method.
• When DIPOLES are compiled in, the particles dipole moment is always co-aligned with the z-axis in the body-fixed frame.
• Changing the particles dipole moment and director will re-orient the particle such that its z-axis in space frame is aligned parallel to the given vector. No guarantees are made for the other two axes after setting the director or the dipole moment.

The following particle properties are related to rotation: