Application of the numerical integration of stochastic equations for the Monte-Carlo computation of Wiener integrals

1995 ◽  
pp. 135-164
Author(s):  
G. N. Milstein
Keyword(s):  
Monte Carlo ◽  
Numerical Integration ◽  
Stochastic Equations ◽  
Monte Carlo Computation

Hermite expansions in Monte-Carlo computation

1971 ◽  
Vol 8 (3) ◽  
pp. 472-482 ◽  
Author(s):  
Alexandre Joel Chorin
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Computation ◽  
Hermite Expansions

The fifth virial coefficient of a fluid of hard spheres

1964 ◽  
Vol 279 (1377) ◽  
pp. 147-160 ◽  
Keyword(s):  
Monte Carlo ◽  
Numerical Integration ◽  
Virial Coefficient ◽  
Monte Carlo Calculation ◽  
Hard Spheres ◽  
Cluster Integrals ◽  
Different Types

The fifth virial coefficient of a fluid of hard spheres is a sum of 238 irreducible cluster integrals of 10 different types. The values of 5 of these types (152 integrals) are obtained analytically, the contributions of a further 4 types (85 integrals) are obtained by a com­bination of analytical and numerical integration, and 1 integral is calculated by an approximation. The result is E = (0·1093 ± 0·0007) b 4 , b = 2/3 πN A σ 3 , where σ is the diameter of a sphere. A combination of the values of 237 of the cluster integrals obtained in this paper with the value of one integral obtained independently by Katsura & Abe from a Monte Carlo calculation yields E = (0·1101 ± 0·0003) b 4 .

SU-FF-T-394: Monte Carlo Computation of the Effective Dose in Scanning Beam Proton Therapy

2009 ◽  
Vol 36 (6Part15) ◽  
pp. 2612-2612
Author(s):  
D Mirkovic ◽  
U Titt ◽  
G Sawakuchi ◽  
X Zhang ◽  
Y Li ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Effective Dose ◽  
Proton Therapy ◽  
Scanning Beam ◽  
Monte Carlo Computation ◽  
Beam Proton
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