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Metropolis Monte Carlo correlation time

By far the most common methods of studying aqueous interfaces by simulations are the Metropolis Monte Carlo (MC) technique and the classical molecular dynamics (MD) techniques. They will not be described here in detail, because several excellent textbooks and proceedings volumes (e.g., [2-8]) on the subject are available. In brief, the stochastic MC technique generates microscopic configurations of the system in the canonical (NYT) ensemble the deterministic MD method solves Newton s equations of motion and generates a time-correlated sequence of configurations in the microcanonical (NVE) ensemble. Structural and thermodynamic properties are accessible by both methods the MD method provides additional information about the microscopic dynamics of the system. [Pg.349]

Figure 7-1. Typical autocorrelation function of the energy. In this example it is calculated for the case of benzophenone in water simulated with Monte Carlo Metropolis method. The calculated auto-correlation function (circles) is fitted to the exponential decay (line) and the correlation time t is obtained using Eq. (7-7) applied in the fitted function shown in Eq. (7-8)... Figure 7-1. Typical autocorrelation function of the energy. In this example it is calculated for the case of benzophenone in water simulated with Monte Carlo Metropolis method. The calculated auto-correlation function (circles) is fitted to the exponential decay (line) and the correlation time t is obtained using Eq. (7-7) applied in the fitted function shown in Eq. (7-8)...
The algorithm updates the entire lattice on each move. In measuring correlation times for this algorithm, one should therefore measure them simply in numbers of Monte Carlo steps, and not steps per site as with the Metropolis algorithm. (In fact, on average, only half the spins get flipped on each move, but the number flipped scales like the size of the system, which is the important point.)... [Pg.499]

In Chapters 3, 6 and 7, the two equivalent descriptions of Brownian motion the Langevin and Smoluchowski equations for an entanglement-free system have been studied in the cases where analytic solutions are obtainable the time-correlation function of the end-to-end vector of a Rouse chain and the constitutive equation of the Rouse model. When the Brownian motion of a more complicated model is to be studied, where an analytical solution cannot be obtained, the Monte Carlo simulation becomes a useful tool. Unlike the Monte Carlo simulation that is employed to calculate static properties using the Metropolis criterion, the simulation based on the Langevin equation can be used to calculate both static and dynamic quantities. [Pg.341]


See other pages where Metropolis Monte Carlo correlation time is mentioned: [Pg.492]    [Pg.48]    [Pg.382]    [Pg.85]    [Pg.275]    [Pg.168]    [Pg.164]    [Pg.88]    [Pg.340]    [Pg.340]    [Pg.127]    [Pg.111]   
See also in sourсe #XX -- [ Pg.492 , Pg.493 ]




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