Notes on statistical ensembles in the Cell Model

2020 ◽  
Vol 29 (08) ◽  
pp. 2050060
Author(s):  
M. Gazdzicki ◽  
M. I. Gorenstein ◽  
O. Savchuk ◽  
L. Tinti
Keyword(s):  
Statistical Physics ◽  
Cell Model ◽  
Probability Distributions ◽  
Joint Probability ◽  
Second Moments ◽  
Statistical Ensembles ◽  
Volume Limit ◽  
Joint Probability Distributions ◽  
Infinite Volume Limit ◽  
Number Of Particles

Properties of basic statistical ensembles in the Cell Model are discussed. The simplest version of the model with a fixed total number of particles is considered. The microcanonical ensembles of distinguishable and indistinguishable particles, with and without a limit on the maximum number of particles in a single cell, are discussed. The joint probability distributions of particle multiplicities in cells for different ensembles are derived, and their second moments are calculated. The results for infinite volume limit are calculated. The obtained results resemble those in the statistical physics of bosons, fermions and boltzmanions.

scholarly journals A Consistent Track-to-Track Fusion Method Based on Copula Theory

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Kelin Lu ◽  
K. C. Chang ◽  
Rui Zhou
Keyword(s):  
Probability Distributions ◽  
A Priori ◽  
Joint Probability ◽  
Network Connectivity ◽  
Consistent Estimate ◽  
Fusion Algorithm ◽  
Copula Theory ◽  
Wide Range ◽  
Primary Advantage ◽  
Joint Probability Distributions

This paper addresses the problem of distributed fusion when the conditional independence assumptions on sensor measurements or local estimates are not met. A new data fusion algorithm called Copula fusion is presented. The proposed method is grounded on Copula statistical modeling and Bayesian analysis. The primary advantage of the Copula-based methodology is that it could reveal the unknown correlation that allows one to build joint probability distributions with potentially arbitrary underlying marginals and a desired intermodal dependence. The proposed fusion algorithm requires no a priori knowledge of communications patterns or network connectivity. The simulation results show that the Copula fusion brings a consistent estimate for a wide range of process noises.

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