Periodic boundary conditions are essential in MD simulations, allowing the extension of a system to an infinite degree, by replicating the images of the main simulation box in all simulated directions. Primary and image cells ( replicated boxes), all have the same -Number, position, momentum of atoms, -Size -Shape

There are many different boundary conditions, the simplest form of boundary conditions are the periodic boundary conditions, that replicate a small system called unit cell.

Boundary conditions are an essential part of the simulation. Their presentation must be clear and concise during practice talks, research talks, literature talks or during exams, as many questions arise from incompetent explanation of bc. They are critical as they ensure that trajectories of particles remain continuous. In case this condition is not satisfied, many errors can arise in calculation of specific properties, thermostatting of the system etc.

Under the effect of flow, and considering a specific type of flow, there are different types of boundary conditions, i.e. under shear Lees-Edwards boundary conditions are a common choice. Another common choice is SLLOD boundary conditions for simulating shear flow. With SLLOD boundary conditions, atoms exiting through the left/right faces of the box are reintroduced at the right/left faces. Atoms moving through the top/bottom faces,are reintroduced at bottom/top faces, displaces by an ammount of ∓𝐿_2𝑦 𝛾 ̇Δ𝑡. L_2y in this case is the simulation box vector, which evolves over time when box is sheared, according to the relationship : 𝐋 ̇_𝑘 (t)=𝐋_𝑘 (𝑡)∙∇𝐯Θ(t) To avoid numerical instabilities and difficult calculations during the integration of the simulated system, the box is always specified to deform up to a specified angle of θ=45o.

You can find different types of Boundary conditions for different types of flows in the book “Nonequilibrium Molecular Dynamics:Theory, Algorithms and Applications” by Todd and Daivis, available in the library of our group.