Additional documentation for the RE-squared ellipsoidal ... - Lammps

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η = det[S1]/σ 2 1 + det[S2]/σ 2 2 [det[H]/(σ1 + σ2)] 1/2 , σi = (ˆr T A T i S −2 i Aiˆr) −1/2 , H = 1 A σ1 T 1 S 2 1A1 + 1 A σ2 T 2 S 2 2A2 Here, we use the distance of closest approach approximation given by the Perram reference, namely and h = |r| − σ12, σ12 = [ 1 2 ˆrT G −1 ˆr] −1/2 , G = A T 1 S 2 1A1 + A T 2 S 2 2A2 The RE-squared anisotropic interaction between a ellipsoidal particle and a Lennard-Jones sphere is defined as the lima2−>0 U under the constraints that a2 = b2 = c2 and 4 3 πa3 2ρ = 1: Uαelj = (3σ3 c 3 α 4πh 3 elj ) A12elj ( mα σ helj Uelj = UAelj + URelj , ) nα (1+oαχelj σ helj A12elj = 4π2 ɛLJ(ρσ 3 ), a1b1c1 )× (a1 + helj/pα)(b1 + helj/pα)(c1 + helj/pα) , with helj and χelj calculated as above by replacing B with Belj and G with Gelj: Belj = A T 1 E1A1 + I, 2
Gelj = A T 1 S 2 1A1. The interaction between two LJ spheres is calculated as: ⎡ σ Ulj = 4ɛ ⎣ |r| 12 − ⎤ 6 σ ⎦ |r| The analytic derivatives are used for all force and torque calculation. 3
Page 1: Additional documentation for the RE

Additional documentation for the RE-squared ellipsoidal ... - Lammps

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