Lower and upper bounds for the absolute free energy by the hypothetical scanning Monte Carlo method: Application to liquid argon and water

2004 ◽  
Vol 121 (22) ◽  
pp. 10889 ◽  
Author(s):  
Ronald P. White ◽  
Hagai Meirovitch
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Monte Carlo Method ◽  
Liquid Argon ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
The Absolute

THE MEAN WAITING TIME FOR A PATTERN

1999 ◽  
Vol 13 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Sheldon M. Ross
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Waiting Time ◽  
Random Variables ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Mean Waiting Time ◽  
The Mean ◽  
Mean Time

Consider a sequence of independent and identically distributed random variables along with a specified set of k-vectors. We present an expression for E [T], the mean time until the last k observed random variables fall within this set. Not only can this expression often be used to obtain bounds on E[T], it also gives rise to an efficient way of approximating E[T] by a simulation. Specific lower and upper bounds for E[T] are also derived. These latter bounds are given in terms of a parameter, and a Markov chain Monte Carlo approach to approximate this parameter by a simulation is indicated. The results of this paper are illustrated by considering the problem of determining the mean time until a sequence of k-valued random variables has a run of size k that encompasses each value.

scholarly journals Monte Carlo Calculation: Thermodynamic Functions in Zeolites. I. Theoretical Fundamentals

1986 ◽  
Vol 3 (3) ◽  
pp. 181-187 ◽  
Author(s):  
K. Fiedler ◽  
B. Grauert
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Monte Carlo Method ◽  
Thermodynamic Functions ◽  
Monte Carlo Calculation ◽  
Sampling Strategy ◽  
Canonical Measure

A Monte Carlo method for calculating thermodynamic functions of zeolitic adsoption systems is presented, which is different from the method of Metropolis et al. (1949; 1953). The method is based on emphasizing sampling strategy for representing the canonical measure by means of a trajectory averaging. The method allows the calculation of free energy, energy and other derived thermodynamic functions directly from the histogram as well as the calculation of the empirical dispersion and the bias.

Triplet Correlation in Liquid Argon by Monte Carlo Method: Low Densities

1972 ◽  
Vol 56 (5) ◽  
pp. 2034-2041 ◽  
Author(s):  
J. A. Krumhansl ◽  
Shein‐shion Wang
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Liquid Argon ◽  
Triplet Correlation
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