Long-range interactions, computation forces

An exact determination of the relative values of P for the BPTI and villin simulations is not possible, because some algorithmic developments reduce computational costs (particularly methods that allow one to increase the size of the time step and to efficiently treat long-range interactions), while others increase the costs (e.g., more detailed force fields and appropriate boundary conditions). But we can place reasonable bounds on the historical growth rate of P by using r=l and r=2 as lower and upper limits on the costs of calculating interatomic interactions. 

As an example of application of the generalized Cahn-Hilliard equation, we consider the case when a droplet is set into slow motion due to either external forces or long-range interactions. We assume that the deviation from equihb-rium shape remains weak and can be treated as a small perturbation everywhere. The droplet mobility can be deduced then from integral conditions based on an equihbrium solution. This allows us to avoid solving dynantic equations exphcitiy and computing a perturbed shape. 

For the long-range interactions such as gravitational and electrostatic the forces acting on each particle i can be computed by using Particle-Mesh (PM) approximation of the Gauss equation... 

Fully atomistic molecular dynamics simulations quickly require excessive computer time as systems become large. This is despite the fact that the computational effort for large n, governed by the calculation of the nonbonded forces or interactions, scales as 0(n) for short-range interactions and as 0(n in n) for long-range interactions. This improvement over the naively expected 0(n ) behavior (assuming simple pairwise additive interactions) is achieved by the use of various cell techniques, which are discussed in this book. Actually, a more severe restriction than the limited... 

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