scholarly journals Monte Carlo Algorithms for the Extracting of Electrical Capacitance

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2922
Author(s):  
Andrei Kuznetsov ◽  
Alexander Sipin
Keyword(s):  
Monte Carlo ◽  
Random Walk ◽  
Harmonic Functions ◽  
Statistical Error ◽  
Mean Value ◽  
Difference Problem ◽  
Monte Carlo Algorithms ◽  
Calculation Results ◽  
Biased Estimators ◽  
New Algorithms

We present new Monte Carlo algorithms for extracting mutual capacitances for a system of conductors embedded in inhomogeneous isotropic dielectrics. We represent capacitances as functionals of the solution of the external Dirichlet problem for the Laplace equation. Unbiased and low-biased estimators for the capacitances are constructed on the trajectories of the Random Walk on Spheres or the Random Walk on Hemispheres. The calculation results show that the accuracy of these new algorithms does not exceed the statistical error of estimators, which is easily determined in the course of calculations. The algorithms are based on mean value formulas for harmonic functions in different domains and do not involve a transition to a difference problem. Hence, they do not need a lot of storage space.

Uncertainty Quantification of NEPTUN Analysis Using Wilks’ Formula With an Extended Number of Calculations

2006 ◽  
Author(s):  
Moonkyu Hwang ◽  
Young-Jin Lee ◽  
Bub-Dong Chung
Keyword(s):  
Monte Carlo ◽  
Uncertainty Quantification ◽  
System Analysis ◽  
Sensitivity Study ◽  
Mean Value ◽  
Model Parameters ◽  
Phase System ◽  
Two Phase ◽  
Mars Model ◽  
Calculation Results

The two-phase system analysis code MARS [1] has been used for the uncertainty quantification of NEPTUN reflood test [2] analysis. By performing 10,000 calculations based on a random variation of the MARS model parameters and measured data, a mean value, and the 95% upper bounds are traced along the number of calculations. The CPU-intensive calculations were performed using the 11 node PC-cluster under Linux platform. The Monte-Carlo calculation results suggest a total number of 2,000 calculations would be sufficient to determine the stable mean and 95% upper bound values. The peak temperatures predictions are also used to find the 95% bounding values by using the Wilks’ method. For the 1st order one-sided formula, every 59 peak temperatures are examined to locate the bounding temperature, with a 95% confidence. The 2nd and 3rd order values were found in a similar way. The uncertainty band by the Wilks’ formula, when compared with the true 95% bounding value, is observed to be quite broad, especially in the case of the 1st order. The 2nd or 3rd orders or a full Monte-Carlo method would be necessary to demonstrate that the safety of the plant is ensured with a sufficient margin. A supplementary sensitivity study, for the nine uncertain parameters selected for the NEPTUN analysis, is also performed to find the degree of influence of each parameter on the peak rod temperature.

scholarly journals Monte Carlo Algorithms for Finding the Maximum of a Random Walk with Negative Drift

2006 ◽  
Vol 43 (01) ◽  
pp. 74-86
Author(s):  
Ludwig Baringhaus ◽  
Rudolf Grübel
Keyword(s):  
Monte Carlo ◽  
Random Walk ◽  
Simple Random Walk ◽  
Mathematical Statistics ◽  
Global Maximum ◽  
Random Input ◽  
Monte Carlo Algorithms ◽  
Negative Drift

We discuss two Monte Carlo algorithms for finding the global maximum of a simple random walk with negative drift. This problem can be used to connect the analysis of random input Monte Carlo algorithms with ideas and principles from mathematical statistics.

LATTICE SPIN MODELS AND NEW ALGORITHMS — A REVIEW OF MONTE CARLO COMPUTER SIMULATIONS

1990 ◽  
Vol 01 (01) ◽  
pp. 91-117 ◽  
Author(s):  
CLIVE F. BAILLIE
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Critical Exponent ◽  
Computer Simulations ◽  
Critical Slowing Down ◽  
Spin Models ◽  
Slowing Down ◽  
Monte Carlo Algorithms ◽  
Lattice Spin Models ◽  
New Algorithms

We review Monte Carlo computer simulations of spin models — both discrete and continuous. We explain the phenomenon of critical slowing which seriously degrades the efficiency of standard local Monte Carlo algorithms such as the Metropolis algorithm near phase transitions. We then go onto describe in detail the new algorithms which ameliorate the problem of critical slowing down, and give their dynamical critical exponent values.

scholarly journals Monte Carlo Algorithms for Finding the Maximum of a Random Walk with Negative Drift

2006 ◽  
Vol 43 (1) ◽  
pp. 74-86
Author(s):  
Ludwig Baringhaus ◽  
Rudolf Grübel
Keyword(s):  
Monte Carlo ◽  
Random Walk ◽  
Simple Random Walk ◽  
Mathematical Statistics ◽  
Global Maximum ◽  
Random Input ◽  
Monte Carlo Algorithms ◽  
Negative Drift

We discuss two Monte Carlo algorithms for finding the global maximum of a simple random walk with negative drift. This problem can be used to connect the analysis of random input Monte Carlo algorithms with ideas and principles from mathematical statistics.

Monte Carlo Algorithms for Moments of Transition Arrays

1988 ◽  
Vol 102 ◽  
pp. 79-81
Author(s):  
A. Goldberg ◽  
S.D. Bloom
Keyword(s):  
Monte Carlo ◽  
State Vector ◽  
Basis Vector ◽  
Collective State ◽  
Dispersion Characteristics ◽  
Dipole Strength ◽  
The Third ◽  
Monte Carlo Algorithms ◽  
Third Moment ◽  
Very High

AbstractClosed expressions for the first, second, and (in some cases) the third moment of atomic transition arrays now exist. Recently a method has been developed for getting to very high moments (up to the 12th and beyond) in cases where a “collective” state-vector (i.e. a state-vector containing the entire electric dipole strength) can be created from each eigenstate in the parent configuration. Both of these approaches give exact results. Herein we describe astatistical(or Monte Carlo) approach which requires onlyonerepresentative state-vector |RV> for the entire parent manifold to get estimates of transition moments of high order. The representation is achieved through the random amplitudes associated with each basis vector making up |RV>. This also gives rise to the dispersion characterizing the method, which has been applied to a system (in the M shell) with≈250,000 lines where we have calculated up to the 5th moment. It turns out that the dispersion in the moments decreases with the size of the manifold, making its application to very big systems statistically advantageous. A discussion of the method and these dispersion characteristics will be presented.

Evaluation of Distribution Network Customer Outage Costs

2009 ◽  
Vol 25 (25) ◽  
pp. 7-12 ◽  
Author(s):  
Laila Zemīte ◽  
Jānis Gerhards
Keyword(s):  
Distribution Network ◽  
Mean Value ◽  
Estimation Model ◽  
Energy Assessment ◽  
Calculation Results ◽  
Rate Calculation

Evaluation of Distribution Network Customer Outage CostsCustomer outage cost criteria are considered, collected and analyzed outage costs in Latvia distribution network, as well as distribution network outage elimination structure, the most common outage causes, are proposed outage costs estimation model. Finally the discussion of results of expected customer outage costs and interrupted energy assessment rate calculation results in Latvia distribution network in 2007 are presented, based on customers' mean value of incomes, outcomes and profitability.

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