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Presented in the context of classical molecular mechanics and dynamics are multilevel summation methods for the fast calculation of energies/forces for pairwise interactions, which are based on the hierarchical interpolation of interaction potentials on multiple grids. The concepts and details underlying multigrid interpolation are described. For integration of molecular dynamics the use of different time steps for different interactions allows longer time steps for many of the interactions, and this can be combined with multiple grids in space. Comparison is made to the fast multipole method, and evidence is presented suggesting that for molecular simulations multigrid methods may be superior to the fast multipole method and other tree methods. 相似文献
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C.W. Bird H.I. Butler M.P.L. Caton E.C.J. Coffee C.J. Hardy T.W. Hart H.J. Mason 《Tetrahedron letters》1985,26(34):4101-4104
The synthesis is described of (±)-6a-oxo-6,9-methano-15-hydroxyprosta-5,13-dienoic acids as stable analogues of prostacyclin with blood platelet aggregation inhibiting activity. 相似文献
130.
Einar L. Hinrichsen Ammon Aharony Jens Feder Alex Hansen Torstein Jøssang H. H. Hardy 《Transport in Porous Media》1993,12(1):55-72
The problem of estimating large-scale permeabilities of reservoirs based on knowledge of the small-scale permeabilities is addressed. We present an accurate and fast algorithm to calculate the global permeabilities of two- or three-dimensional correlated and anisotropic block samples, thus providing a fast algorithm for obtaining grid block permeabilities for reservoir simulators from small scale data. The algorithm is tested on both two- and three-dimensional tube networks generated from real images and fractal forgeries modeling porous media. In almost all cases, the algorithm estimates the correct global permeability (calculated using exact but slow algorithms) of the network to better than 5%. The new algorithm is comparable in speed to conventional averaging techniques, such as the geometric mean, but the obtained estimates are always much better.List of Symbols
K
permeability of network (global permeability
-
K
e
estimated permeability
-
K
K×(Lx×Ly)/Lz
-
K
permeability perpendicular to layering
-
K
permeability parallel with layering
-
L
x, Ly, Lz
Network size inx, y andz-directions
-
L
Size of quadratic (cubic) network
-
Q
global flux through network
-
U
Q/(Lx×Ly), Darcy velocity (flux per unit area)
-
V
volume of network
- P
pressure drop across network
-
a,b
parameters in Equation (4)
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P
i
pressure at sitei
-
q
ij
flux between nodesi andj
-
parameter of Pareto distribution
-
porosity
-
K(i)
permeability at site (block)i
-
K
ij
permeability of bond between nodesi andj
-
K
min
minimumk(i) for sample
-
K
max
maximumK(i) for sample
-
fluid viscosity 相似文献