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Two main treatments within classical simulations for modeling a charged surface are using explicit, discrete charges and continuous, uniform charges. The computational cost can be substantially reduced if, instead of discrete surface charges, one uses an electric field to represent continuous surface charges. In addition, many electrolyte theories, including the Poisson--Boltzmann theory, are developed on the assumption of uniform surface charge. However, recent simulations have demonstrated with discrete surface charges, one observes much stronger charge reversal, compared to the surfaces with continuous surface charges, when the lattice constant becomes notably larger than the ion diameter. These examples show that the two treatments for modeling a charged dielectric interface can lead to substantially different results. In this short note, we calculate the electrostatic force for a single point charge above an infinite plane, and compare the differences between discrete and continuous representations of surface charges. Our results show that while the continuous, uniform surface charge model gives a quite simple picture, the discrete surface charge model can offer several different cases even for such a simple problem, depending on the respective values of ion size versus lattice spacing and a self-image interaction parameter.
We present a statistical model which is able to capture some interesting features exhibited in the Brazilian test. The model is based on breakable elements which break when the force experienced by the elements exceed their own load capacity. In this
Granular impact -- the dynamic intrusion of solid objects into granular media -- is widespread across scientific and engineering applications including geotechnics. Existing approaches for simulating granular impact dynamics have relied on either a p
For a collisionless plasma in contact with a dielectric surface, where with unit probability electrons and ions are, respectively, absorbed and neutralized, thereby injecting electrons and holes into the conduction and valence band, we study the kine
We study the Brownian motion of a charged test particle driven by quantum electromagnetic fluctuations in the vacuum region near a non-dispersive and non-absorbing dielectric half-space and calculate the mean squared fluctuations in the velocity of t
Hydrophobic PMMA colloidal particles, when dispersed in oil with a relatively high dielectric constant, can become highly charged. In the presence of an interface with a conducting aqueous phase, image charge effects lead to strong binding of colloid