scholarly journals The Use of the Maximum Entropy Principle to Approximate Turbulent Probability Density Functions

2020 ◽  
Author(s):  
Robert Derksen
Keyword(s):  
Probability Density ◽  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Probability Density Functions ◽  
Density Functions ◽  
Entropy Principle

Maximum Entropy Methods in the Mechanics of Quasi-Static Deformation of Granular Materials

2002 ◽  
Author(s):  
N. P. Kruyt ◽  
L. Rothenburg
Keyword(s):  
Probability Density ◽  
Maximum Entropy ◽  
Granular Materials ◽  
Probability Density Functions ◽  
Contact Forces ◽  
Static Deformation ◽  
Density Functions ◽  
Two Dimensional ◽  
Entropy Methods ◽  
Theoretical Predictions

In statistical physics of dilute gases maximum entropy methods are widely used for theoretical predictions of macroscopic quantities in terms of microscopic quantities. In this study an analogous approach to the mechanics of quasi-static deformation of granular materials is proposed. The reasoning is presented that leads to the definition of an entropy that is appropriate to quasi-static deformation of granular materials. This entropy is formulated in terms of contact quantities, since contacts constitute the relevant microscopic level for granular materials that consist of semirigid particles. The proposed maximum entropy approach is then applied to two cases. The first case deals with the probability density functions of contact forces in a two-dimensional assembly with frictional contacts under prescribed hydrostatic stress. The second case deals with the elastic behaviour of two-dimensional assemblies of non-rotating particles with bonded contacts. For both cases the probability density functions of contact forces are determined from the proposed maximum entropy method, under the constraints appropriate to the case. These constraints form the macroscopic information available about the system. With the probability density functions for contact forces thus determined, theoretical predictions of macroscopic quantities can be made. These theoretical predictions are then compared with results obtained from two-dimensional Discrete Element simulations and from experiments.

A new stochastic analysis method for mechanical components

2012 ◽  
Vol 227 (8) ◽  
pp. 1818-1829 ◽  
Author(s):  
YL Zhang ◽  
YM Zhang
Keyword(s):  
Finite Element ◽  
Dimension Reduction ◽  
Probability Density ◽  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Entropy Principle ◽  
Input Variables ◽  
First Four Moments

Univariate dimension-reduction integration, maximum entropy principle, and finite element method are employed to present a computational procedure for estimating probability densities and distributions of stochastic responses of structures. The proposed procedure can be described as follows: 1. Choose input variables and corresponding distributions. 2. Calculate the integration points and perform finite element analysis. 3. Calculate the first four moments of structural responses by univariate dimension-reduction integration. 4. Estimate probability density function and cumulative distribution function of responses by maximum entropy principle. Numerical integration formulas are obtained for non-normal distributions. The non-normal input variables need not to be transformed into equivalent normal ones. Three numerical examples involving explicit performance functions and solid mechanic problems without explicit performance functions are used to illustrate the proposed procedure. Accuracy and efficiency of the proposed procedure are demonstrated by comparisons of the estimated probability density functions and cumulative distribution functions obtained by maximum entropy principle and Monte Carlo simulation.

Notes on Bell-Sejnowski PDF-Matching Neuron

2002 ◽  
Vol 14 (12) ◽  
pp. 2847-2855 ◽  
Author(s):  
Simone Fiori
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Maximum Entropy ◽  
Density Function ◽  
Single Unit ◽  
Neuron Model ◽  
Maximum Entropy Principle ◽  
Entropy Principle ◽  
Single Input ◽  
Pdf Matching

This article investigates the behavior of a single-input, single-unit neuron model of the Bell-Sejnowski class, which learn through the maximum-entropy principle, in order to understand its probability density function matching ability.

Sign in / Sign up

Export Citation Format

Share Document