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Commit 7f50a4d6 authored by muralikrishnan's avatar muralikrishnan
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reference fixed

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......@@ -295,11 +295,13 @@ total force latexmath:[F] into two components
++++
F = F_{sr} + F_{lr}
++++
where latexmath:[F_{sr}] is the short-range component which can be
computed efficiently in the real-space with a small cut-off radius by direct summation,
whereas latexmath:[F_{lr}] is the long-range component and this can be calculated efficiently
in the Fourier space with a few Fourier modes due to its rapid spectral decay. Consequently,
we split the Green's function latexmath:[G] also into two components as
[latexmath#eq-oneterm]
++++
G(r) = \psi(r) + \phi(r) = \frac{1 - f(r)}{r} + \frac{f(r)}{r}
......@@ -310,20 +312,24 @@ latexmath:[\phi(r)] is the long range or the particle-mesh Green's function. Apa
smoothness conditions there is a lot of flexibility in the choice of latexmath:[f(r)] and this
leads to different screening shapes for the particles. The standard choice from the Ewald
summation corresponds to <<bib.p3mulmerthesis>>, <<bib.p3mhuenenberger>>
[latexmath#eq-oneterm]
++++
f(r) = erf(\alpha r)
++++
where latexmath:[\alpha] is the interaction splitting parameter which determines the relative
signifcance of the particle-particle part to the particle-mesh part. It is usually chosen as
latexmath:[\alpha = C/r_c], where latexmath:[r_c] is the cut-off or interaction radius and C is
a postive constant. This choice of Green's function corresponds to Gaussian shaped screening
charges. Another popular choice for latexmath:[f(r)] corresponds to truncated polynomials of different orders
as given in Table I of appendix B in <<bib.huenenberger>>. The lowest order function in the table corresponds to
as given in Table I of appendix B in <<bib.p3mhuenenberger>>. The lowest order function in the table corresponds to
[latexmath#eq-oneterm]
++++
f(r) = \frac{\xi(3 - \xi^2)}{2}
++++
where latexmath:[\xi = r/r_c]. We use the integrated version of this Green's function when we specify the option
for Green's function as `INTEGRATED` in the `P3M` solver in OPAL.
......
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