4. Setting up the system

4.1. Setting global variables

The global system variables are controlled via the Python espressomd.system.System class:

import espressomd
system = espressomd.System(box_l=[10., 10., 10.])
system.time_step = 0.01
system.cell_system.skin = 0.4
system.periodicity = [True, True, True]

This code creates a system with a cubic unit cell of length 10 in simulation units, and sets the skin to 0.4 simulation units and the time step to 0.01 simulation units.

Some variables belong to the System class and will be explained in the list below, while other variables such as the skin belong to objects that are attached to the class, and will be explain in subsequent sections and chapters. Note that for many vectorial properties, e.g. box_l and periodicity, component-wise manipulation like system.box_l[0] = 1 or in-place operators like += or *= are not allowed and result in an error. This behavior is inherited, so the same applies to a after a = system.box_l. If you want to use a vectorial property for further calculations, you should explicitly make a copy e.g. via a = numpy.copy(system.box_l).

  • box_l

    Simulation box lengths of the cuboid box used by ESPResSo. Note that if you change the box length during the simulation, the folded particle coordinates will remain the same, i.e., the particle stay in the same image box, but at the same relative position in their image box. If you want to scale the positions, use the command change_volume_and_rescale_particles().

  • periodicity

    Specifies periodicity for the three directions. ESPResSo can be instructed to treat some dimensions as non-periodic. By default ESPResSo assumes periodicity in all directions which equals setting this variable to [True, True, True]. A dimension is specified as non-periodic via setting the periodicity variable for this dimension to False. E.g. Periodicity only in z-direction is obtained by [False, False, True]. Caveat: Be aware of the fact that making a dimension non-periodic does not hinder particles from leaving the box in this direction; in this case, shape-based constraints can be used to keep particles in the simulation box. For more details, see Boundary conditions.

  • time_step

    Time step for MD integration.

  • time

    The simulation time.

  • min_global_cut

    Minimal total cutoff for real space. Effectively, this plus the skin is the minimally possible cell size. ESPResSo typically determines this value automatically, but some algorithms, virtual sites, require you to specify it manually.

  • max_cut_bonded

    read-only Maximal cutoff of bonded interactions.

  • max_cut_nonbonded

    read-only Maximal cutoff of non-bonded interactions.

4.1.1. Accessing module states

Some variables like or are no longer directly available as attributes. In these cases they can be easily derived from the corresponding Python objects like:

n_part = len(system.part)

or by calling the corresponding get_state() methods like:

temperature = system.thermostat.get_state()[0]['kT']
gamma = system.thermostat.get_state()[0]['gamma']
gamma_rot = system.thermostat.get_state()[0]['gamma_rotation']

4.2. Simulation box

4.2.1. Boundary conditions

4.2.1.1. Periodic boundaries

With periodic boundary conditions, particles interact with periodic images of all particles in the system. This is the default behavior. When particles cross a box boundary, their position are folded and their image box counter are incremented.

From the Python interface, the folded position is accessed with pos_folded and the image box counter with image_box. Note that pos gives the unfolded particle position.

Example:

import espressomd
system = espressomd.System(box_l=[5.0, 5.0, 5.0], periodicity=[True, True, True])
system.time_step = 0.1
system.cell_system.skin = 0.0
p = system.part.add(pos=[4.9, 0.0, 0.0], v=[0.1, 0.0, 0.0])
system.integrator.run(20)
print(f"pos        = {p.pos}")
print(f"pos_folded = {p.pos_folded}")
print(f"image_box  = {p.image_box}")

Output:

pos        = [5.1 0.  0. ]
pos_folded = [0.1 0.  0. ]
image_box  = [1 0 0]

4.2.1.2. Open boundaries

With open boundaries, particles can leave the simulation box. What happens in this case depends on which algorithm is used. Some algorithms may require open boundaries, such as Stokesian Dynamics.

Example:

import espressomd
system = espressomd.System(box_l=[5.0, 5.0, 5.0], periodicity=[False, False, False])
system.time_step = 0.1
system.cell_system.skin = 0.0
p = system.part.add(pos=[4.9, 0.0, 0.0], v=[0.1, 0.0, 0.0])
system.integrator.run(20)
print(f"pos        = {p.pos}")
print(f"pos_folded = {p.pos_folded}")
print(f"image_box  = {p.image_box}")

Output:

pos        = [5.1 0.  0. ]
pos_folded = [5.1 0.  0. ]
image_box  = [0 0 0]

4.2.1.3. Lees–Edwards boundary conditions

Lees–Edwards boundary conditions (LEbc) are special periodic boundary conditions to simulate systems under shear stress [Lees and Edwards, 1972]. Periodic images of particles across the shear boundary appear with a time-dependent position offset. When a particle crosses the shear boundary, it appears to the opposite side of the simulation box with a position offset and a shear velocity [Bindgen et al., 2021].

LEbc require a fully periodic system and are configured with LinearShear and OscillatoryShear. To temporarily disable LEbc, use Off. To completely disable LEbc and reinitialize the box geometry, do system.lees_edwards.protocol = None.

Example:

import espressomd
import espressomd.lees_edwards
system = espressomd.System(box_l=[5.0, 5.0, 5.0])
system.time_step = 0.1
system.cell_system.skin = 0.0
system.cell_system.set_n_square(use_verlet_lists=True)
le_protocol = espressomd.lees_edwards.LinearShear(
    shear_velocity=-0.1, initial_pos_offset=0.0, time_0=-0.1)
system.lees_edwards.set_boundary_conditions(
    shear_direction="y", # shear along y-axis
    shear_plane_normal="x", # shift when crossing the x-boundary
    protocol=le_protocol)
p = system.part.add(pos=[4.9, 0.0, 0.0], v=[0.1, 0.0, 0.0])
system.integrator.run(20)
print(f"pos        = {p.pos}")
print(f"pos_folded = {p.pos_folded}")
print(f"image_box  = {p.image_box}")
print(f"velocity   = {p.v}")

Output:

pos        = [5.1 0.2 0. ]
pos_folded = [0.1 0.2 0. ]
image_box  = [1 0 0]
velocity   = [0.1 0.1 0. ]

Particles inserted outside the box boundaries will be wrapped around using the normal periodic boundary rules, i.e. they will not be sheared, even though their image_box is not zero.

Once a valid tuple (shear_direction, shear_plane_normal, protocol) has been set via set_boundary_conditions(), one can update the protocol via a simple assignment of the form system.lees_edwards.protocol = new_le_protocol, in which case the shear direction and shear normal are left unchanged. The method set_boundary_conditions() is the only way to modify the shear direction and shear normal.

4.2.2. Cell systems

This section deals with the flexible particle data organization of ESPResSo. ESPResSo is able to change the organization of the particles in the computer memory to accommodate for the needs of the algorithms being used. For details on the internal organization, refer to section Internal particle organization.

4.2.2.1. Global properties

The properties of the cell system can be accessed via the system cell_system attribute:

  • node_grid

    3D node grid for real space domain decomposition (optional, if unset an optimal partition is chosen automatically). The domain decomposition can be visualized with samples/visualization_cellsystem.py.

  • skin

    Skin for the Verlet list. This value has to be set, otherwise the simulation will not start.

Details about the cell system can be obtained by get_state():

  • cell_grid Dimension of the inner cell grid (only for regular decomposition).

  • cell_size Box-length of a cell (only for regular decomposition).

  • n_nodes Number of MPI nodes.

  • node_grid MPI domain partition.

  • type The current type of the cell system.

  • skin Verlet list skin.

  • verlet_reuse Average number of integration steps the Verlet list is re-used.

4.2.2.2. Regular decomposition

Invoking set_regular_decomposition() selects the regular decomposition cell scheme, using Verlet lists for the calculation of the interactions. If you specify use_verlet_lists=False, only the regular decomposition is used, but not the Verlet lists.

import espressomd
system = espressomd.System(box_l=[1, 1, 1])
system.cell_system.set_regular_decomposition(use_verlet_lists=True)

The regular decomposition cellsystem is the default system and suits most applications with short ranged interactions. The particles are divided up spatially into small compartments, the cells, such that the cell size is larger than the maximal interaction range. In this case interactions only occur between particles in adjacent cells. Since the interaction range should be much smaller than the total system size, leaving out all interactions between non-adjacent cells can mean a tremendous speed-up. Moreover, since for constant interaction range, the number of particles in a cell depends only on the density. The number of interactions is therefore of the order \(N\) instead of order \(N^2\) if one has to calculate all pair interactions.

With this scheme, there must be at least two cells per direction, and at most 32 cells per direction for a cubic box geometry. The number of cells per direction depends on the interaction range cutoff \(l_{\mathrm{cut}}\), the Verlet list skin \(l_{\mathrm{skin}}\) and the box length \(l_{\mathrm{box}}\), and is determined automatically by solving several equations. It can be useful to know how to estimate the number of cells per direction, because it limits the number of MPI ranks that can be allocated to an MPI-parallel simulation. As a rule of thumb, for a cubic box geometry the number of cells per direction is often:

\[\left\lfloor \frac{l_{\mathrm{box}}}{l_{\mathrm{cut}} + l_{\mathrm{skin}}} \right\rfloor\]

For example, in a system with box length 12, LJ cutoff 2.5 and Verlet skin 0.4, the number of cells cannot be more than 4 in each direction. A runtime error will be triggered during integration when running a simulation with such a system and allocating more than 64 MPI ranks in total, or more than 4 MPI ranks per direction. In this situation, consider increasing the box size or decreasing the interaction cutoff or Verlet list skin.

4.2.2.3. N-squared

Invoking set_n_square() selects the very primitive N-squared cellsystem, which calculates the interactions for all particle pairs. Therefore it loops over all particles, giving an unfavorable computation time scaling of \(N^2\). However, algorithms like MMM1D or the plain Coulomb interaction in the cell model require the calculation of all pair interactions.

import espressomd
system = espressomd.System(box_l=[1, 1, 1])
system.cell_system.set_n_square()

In a multiple processor environment, the N-squared cellsystem uses a simple particle balancing scheme to have a nearly equal number of particles per CPU, \(n\) nodes have \(m\) particles, and \(p-n\) nodes have \(m+1\) particles, such that \(n \cdot m + (p - n) \cdot (m + 1) = N\), the total number of particles. Therefore the computational load should be balanced fairly equal among the nodes, with one exception: This code always uses one CPU for the interaction between two different nodes. For an odd number of nodes, this is fine, because the total number of interactions to calculate is a multiple of the number of nodes, but for an even number of nodes, for each of the \(p-1\) communication rounds, one processor is idle.

E.g. for 2 processors, there are 3 interactions: 0-0, 1-1, 0-1. Naturally, 0-0 and 1-1 are treated by processor 0 and 1, respectively. But the 0-1 interaction is treated by node 1 alone, so the workload for this node is twice as high. For 3 processors, the interactions are 0-0, 1-1, 2-2, 0-1, 1-2, 0-2. Of these interactions, node 0 treats 0-0 and 0-2, node 1 treats 1-1 and 0-1, and node 2 treats 2-2 and 1-2.

Therefore it is highly recommended that you use N-squared only with an odd number of nodes, if with multiple processors at all.

4.2.2.4. Hybrid decomposition

If for a simulation setup the interaction range is much smaller than the system size, use of a Regular decomposition leads to efficient scaling behavior (order \(N\) instead of order \(N^2\)). Consider a system with many small particles, e.g. a polymer solution. There, already the addition of one single large particle increases the maximum interaction range and thus the minimum cell size of the decomposition. Due to this larger cell size, throughout the simulation box a large number of non-interacting pairs of small particles is visited during the short range calculation. This can considerably increase the computational cost of the simulation.

For such simulation setups, i.e. systems with a few large particles and much more small particles, the hybrid decomposition can be used. This hybrid decomposition is backed by two coupled particle decompositions which can be used to efficiently deal with the differently sized particles. Specifically that means putting the small particles into a Regular decomposition. There, the minimum cell size is limited only by the maximum interaction range of all particles within this decomposition. The few large particles are put into a N-squared cellsystem. Particles within this decomposition interact both, amongst each other and with all small particles in the Regular decomposition. The hybrid decomposition can therefore effectively recover the computational efficiency of the regular decomposition, given that only a few large particles have been added.

Invoking set_hybrid_decomposition() selects the hybrid decomposition.

system = espressomd.System(box_l=[10, 10, 10])
system.cell_system.set_hybrid_decomposition(n_square_types={1, 3}, cutoff_regular=1.2)

Here, n_square_types is a python set containing the types of particles to put into the N-squared cellsystem, i.e. the particle types of the large particles. Particles with other types will by default be put into the Regular decomposition. Note that for now it is also necessary to manually set the maximum cutoff to consider for interactions within the Regular decomposition, i.e. the maximum interaction range among all small particle types. Set this via the cutoff_regular parameter.

Note

The hybrid particle decomposition has been added to ESPResSo only recently and for now should be considered an experimental feature. If you notice some unexpected behavior please let us know via github or the mailing list.