Coulomb Force with Periodic Boundary Conditions#
We consider a 2D torus domain with size \((L_x, L_y)\). The minimum-image displacement between points \(\mathbf{p}_i\) and \(\mathbf{p}_j\) is computed per-axis: \( \Delta x = (x_j - x_i) - L_x \cdot \operatorname{round}\!\left(\frac{x_j - x_i}{L_x}\right),\quad \Delta y = (y_j - y_i) - L_y \cdot \operatorname{round}\!\left(\frac{y_j - y_i}{L_y}\right). \)
Electrostatic force with Plummer-like softening is \( \mathbf{F}_{ij} = k\, q_i q_j \frac{\boldsymbol{\Delta r}}{\left(\|\boldsymbol{\Delta r}\|^2 + \epsilon^2\right)^{3/2}}, \) where \(\epsilon\) is discussed in math/plummer_softening.
Connections:
Implementation:
electrosim.simulation.physics.minimum_image_displacement()andelectrosim.simulation.physics.electric_force_pair().Used by: accelerations, field evaluation, selection, collisions.
References: :cite:griffiths_electrodynamics, :cite:hockney_eastwood.