Long-range interactions: P3M, MMMxD, ELC, MEMD ... - ESPResSo

Taking the limit: MMM2D far formulahttp://www.icp.uni-stuttgart.deφ β (r) = ∑k,l∈LZ(= 2 ∑ ∑Lp∈ 2π L Z l∈LZ= 2πL 2⎛= 2π ⎝L 2e −β√ (x+k) 2 +(y+l) 2 +z 2√(x + k)2 + (y + l) 2 + z 2∑p,q∈ 2π L Z∑p 2 +q 2 >0K 0( √β2+ p 2 √(y + l) 2 + z 2 ) ) e ipxe − √β 2 +p 2 +q 2 |z|√β2 + p 2 + q 2 eipx e iqye fpq|z|f pq⎞e ipx e iqy + |z| ⎠ + π L 2 β−1 + O β→0 (β)• singularity cancels due to charge neutrality• bad or no convergence for z ≈ 0A. Arnold Long-range interactions 21/40