equation equation. . 15 AP AP 3 3 M M algorithm algorithm If If mass mass distribution distribution is is homogeneus homogeneus then then short short range forces range forces F F s s ∼ ∼ O( O(N N) and ) and long long range range forces forces F F l l ∼ ∼ O(...
Summation of coulomb fields in computer-simulated disordered systems, Physica A 176 - Lekner - 1991 () Citation Context ...tochastic molecular dynamics 4, 5 to study the system in equilibrium. The equation of motion for particle i at position r i (t) is the Langevin equation, m d 2 ...
The leading small-N singularity of the anomalous dimension is determined by running coupling corrections which, as already mentioned, determine the small-x asymptotic behaviour of the splitting functions and can be resummed by solving the BFKL evolution equation for \(f_+\) [24–26]. In the AB...
Thus, xi'=aimxm is shorthand for three equations, each having a sum of three terms on its right-hand side. Another simple example of a free index is the following equation defining the components of a vector a in terms of a dot product with each of the base vectors ei, (2.2.4)ai=...
40, No. I, 1999 SUMMATION OF THE WITTING SERIES IN THE SOLITARY-WAVE PROBLEM E. A. Karabut UDC 532.59 Some exact solutions of the Euler equations with a free surface in the presence of gravitation forces are found. They are obtained by summing Witting series applied in the theory of ...
(A.3) One can consider expanding this exponential to any order and observe that correction term, the O(α¯szcautθsa+b) terms on the final line of the above equation, will at most generate N3LL power corrections in both v and zcut once the integral over θs is carried out, which...
In [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 Po... Sperb,René - 《Molecular Simulation》 被引量: 46发表: 1994年 Sums of Fourier coefficients of a Maass form for SL 3 () twiste...
The indices m and r in equation (1) refer to the mirror transistor and reference transistor, respectively. This invention also provides a down current mirror matched in performance with an up current mirror, namely to provide up and down current mirrors that satisfy equation (1) with the ...
long‐range forceselectrostatic potential and energyHere we present a linear order multiscale method for the fast summation of long range forces in a system consisting of a large number of charge and dipolar particles. For a N -body system, our algorithm requires an order of work that is ...
(27,28,30) finally gives the desired pressure equation p V = NkBT \Gamma 1 3 X i!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 ...