THE INFLUENCE OF A CRITICAL SIZE ON THE SCALING BEHAVIOR OF CLUSTERS COALESCENCE

1999 ◽  
Vol 13 (18) ◽  
pp. 2397-2404 ◽  
Author(s):  
GUOCE ZHUANG ◽  
XIAOBIN ZHU ◽  
WEI WANG
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Cluster Size ◽  
Critical Size ◽  
Simulation Method ◽  
Monte Carlo Simulation Method ◽  
Critical Cluster ◽  
Cluster Aggregation ◽  
Long Time ◽  
Average Size

By introducing a critical cluster size N c , the irreversible and reversible cluster–cluster aggregation are studied with Monte Carlo simulation method. In a long time limit the average size of cluster <S>∞ reaches its stationary value which depends on the critical size N c and the breakup constant k. Our results indicate that in the presence of critical size the critical exponent y, which is defined as <S(k,∞)>~k-y, increases as the critical size increases and is lower than the value of (α+ξ+2)-1, where the exponents α and ξ associate with the detachment and attachment of clusters.

scholarly journals Uncertainty Cost Functions in Climate-Dependent Controllable Loads in Commercial Environments

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2885
Author(s):  
Daniel Losada ◽  
Ameena Al-Sumaiti ◽  
Sergio Rivera
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Simulation Method ◽  
Electricity Sector ◽  
Cost Functions ◽  
Density Estimator ◽  
Monte Carlo Simulation Method ◽  
Commercial Building ◽  
Complementary Method ◽  
The Cost

This article presents the development, simulation and validation of the uncertainty cost functions for a commercial building with climate-dependent controllable loads, located in Florida, USA. For its development, statistical data on the energy consumption of the building in 2016 were used, along with the deployment of kernel density estimator to characterize its probabilistic behavior. For validation of the uncertainty cost functions, the Monte-Carlo simulation method was used to make comparisons between the analytical results and the results obtained by the method. The cost functions found differential errors of less than 1%, compared to the Monte-Carlo simulation method. With this, there is an analytical approach to the uncertainty costs of the building that can be used in the development of optimal energy dispatches, as well as a complementary method for the probabilistic characterization of the stochastic behavior of agents in the electricity sector.

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