翻译:这些数字的总和是100。 原句:In his summation of the case, the lawyer presented the key evidence. 翻译:在案件的总结陈词中,律师呈现了关键证据。 原句:The summation of forces acting on the object is zero. 翻译:作用在物体上的力的总和为零。 原句:The summation ...
Coulomb forcesIn [3] J. Lekner derived an elegant and very useful summation formula for Coulomb forces. In his derivation he used some powerful identities such as the Poisson-Jacobi identity, the application of which was not at all straightforward. In this note it is shown that Lekner's ...
In this case, M cancels out, and then (1.19) (remarkably) becomes more like a law about accelerations than a law about “forces”. That is, once M cancels out, the force law (1.19) is independent of any properties of the object (planet) whose motion it purports to describe. Thus, ...
The conclusion of Theorem 1.1 forces B(q) to have radius of convergence exactly one. We also note that the second condition in (1.2) does not follow from the first using a simple term-by-term estimate, as B e−z ≤ bne−n Re(z) = B e− Re(z) , n≥0 γγ but e Re(...
Price SL, Stone AJ, Alderton M (1984) Explicit formulae for the electrostatic energy, forces and torques between a pair of molecules of arbitrary symmetry. Mol Phys 52:987–1001 Article CAS Google Scholar Mills MJL, Popelier PLA (2012) Polarisable multipolar electrostatics from the machine lea...
Most applications of the Ewald quasi-2D method in computer simulations use precalculated tables of potential energy, forces and second derivatives on a three-dimensional grid and calculations are performed by interpolation of the tables [39, 35, 20]. In ref.[40], Arnold and Holm have shown ...
J. Lekner, Summation of Coulomb Fields in Computer-Simulated Disordered Systems, Physica A 176, 485-498 (1991), R. Sperb, Extension and Simple Proof of Lekner's Summation Formula for Coulomb Forces, Mol. Simulation 13, 189-193 (1994).Lekner, J. Summation of Coulomb Fields in Computer-...
j \Omega r ij \Delta F sr ij ff + 1 3\Omega U C ff ; (31) where F sr ij are the short-range pair forces. In Ref. =-=[44]-=- the virial expression r i \Delta F i for the pressure is compared with Eqn. (31) and it is found that both expressions differ for finite ...
Closed formulae for both real and reciprocal space parts of cutoff errors in the Ewald summation method in cubic periodic boundary conditions are derived. Such estimates are useful in tuning parameters in molecular simulations. Errors in both the electrostatic energy and forces are considered. The ...