Monte-Carlo evaluation

Sprik M, Klein M L and Chandler D 1985 Staging—a sampling technique for the Monte-Carlo evaluation of path-integrals Phys. Rev. B 31 4234-44... 

Integrals, Monte Carlo evaluation of, 26 1003-1004, 1005-1007 Integral tripack film structure, 19 241, 243, 244-245... 

As a consequence, the semiclassical propagator is given as a phase-space integral over the initial conditions qo and Po, which is amenable to a Monte Carlo evaluation. For this reason, semiclassical initial-value representations are regarded as the key to the application of semiclassical methods to multidimensional systems. 

The deviation from numerical Monte Carlo evaluations is, as we see later, significant only for light molecules H2 and D2. 

Narita, Y. lida, H. Eberl, S. Nakamura, T. Monte Carlo evaluation of accuracy and noise properties of two scatter correction methods for ° T1 cardiac SPECT. IEEE Trans. Nucl. Sci. 1997, 44 (6), 2465-2472. 

In Monte Carlo evaluations of Eq. (4.21) configurations are generated by a random walk distributed according to the Boltzmann weighting exp[ — K(r)]/ jd "rexp[ — K(r)]. For M such generated configurations we have... 

In Monte Carlo evaluations of Eq. (4.35) the variance can be shown to grow as (km ) The detailed proof of this behavior is given in Doll and Freeman. As a system becomes more quantum, more Fourier coefficients are required for an accurate treatment. The growth of the variance with is a significant... 

For an oscillator potential, the variance obtained in Monte Carlo evaluations of Eq. (4.36) can be shownto be strictly independent of and our experience with other potentials has shown no appreciable dependence of the variance on Although the T-method expression for the kinetic energy is simpler and appears to require less numerical work, our experience with the H-method has been more favorable. The extra work in evaluating the onedimensional u integrations is more than compensated by the smaller number of Monte Carlo points required in the estimation of the averages. 

R. D. Kaminski (1994) Monte-Carlo evaluation of ensemble averages involving particle number variations in dense fluid systems. J. Chem. Phys. 101, pp. 4986-4994... 

The expression for the total energy of a system allows Monte Carlo evaluations of the thermodynamic properties of the sample. The forces (i.e., the energy first derivatives) make molecular dynamics studies possible. 

Figure 9.22 Monte Carlo evaluation of confidence intervals the points indicate the actual number of estimates that fall within each -level ellipse for 500 replicated datasets.

Since the action for each spin path is complex valued, a stochastic Monte Carlo evaluation of the resulting isomorphic Ising chain has to deal with the inevitable dynamical sign problem. Relying on the strategy outlined in Section II, we wish to block configurations together in an optimal way. 

The preceding equations and considerations form the basis for a Monte Carlo evaluation. For this purpose the solutions of Eqs. (10.184) and (10.185) as well as Eqs. (10.191)-(10.197) are evaluated N times. Each time we obtain values for x(t), y(t), x(t), and y(t), from which parameters of interest, e.g. the distance of fragment impact and the corresponding energy are easily derived. The procedure corresponds to that shown in Fig. 4.22. 

R. L. Coldwell, Monte Carlo evaluation of the partition function for a hard disk system, Phys. Rev. A 7 270-281 (1973). 

S. V. Lawande, C. A. Jensen, and H. L. Sahlin, Monte Carlo evaluation of Feynman path integrals in imaginary time and spherical polar coordinates, J. Comp. Phys. 4, 451-464... 

R. D. Richtmyer (this symposium ) and R. D. Richtmyer, R. Van Norton and A. Wolfe, The Monte Carlo evaluation of resonance capture in reactor lattices. Proceedings United Nations Second International Conference on Peaceful Uses of Atomic Energy, United Nations, Geneva, P/2489, 1958. 

We begin with the most rigorous version of self-consistent PRISM based on a Monte Carlo evaluation of the effective single-chain problem. Theoretical predictions of Grayce and co-workers" are compared with many-chain simulation results for the mean-square end-to-end distance of the hard-core chain model as a function of polymer packing fraction in... 

H. Conroy,/. Chem. Phys., 41, 1331 (1964). Molecular Schrodinger Equation. II. Monte Carlo Evaluation of Integrals. See alsoH. Conroy,/. Chem. Phys., 41,1336 (1964). Molecular Schrodinger Equation. III. Calculation of Ground-State Energies by Extrapolation. 

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