Characterization of Microstructure of Fibrous Composites Using High-Order Correlation Functions

2015 ◽  
Vol 243 ◽  
pp. 121-129
Author(s):  
Mikhail Tashkinov
Keyword(s):  
Correlation Functions ◽  
Microstructural Characterization ◽  
High Order ◽  
Fibrous Composites ◽  
Representative Volume ◽  
Representative Volume Elements ◽  
High Order Correlation

This paper introduces the methodology of microstructural characterization of fibrous composites using correlation functions of different orders. Its implementation is demonstrated on several examples of modeled representative volume elements. The ways of obtaining values of the functions as well as the procedure of their approximation are presented. The possible applications of such methodology are discussed.

From Brownian Motion to Bending Beams

2021 ◽  
pp. 84-98
Author(s):  
Robert W. Batterman
Keyword(s):  
Brownian Motion ◽  
Correlation Function ◽  
Correlation Functions ◽  
Materials Science ◽  
Prima Facie ◽  
Representative Volume ◽  
Representative Volume Elements ◽  
Hydrodynamic Correlation

This chapter argues that the hydrodynamic, correlation function methodology discussed in “fluid” contexts is really the same methodology employed in materials science to determine effective values for quantities like conductivity, elasticity, stiffness. Thus, Einstein’s arguments discussed in the previous chapter have a bearing on what prima facie appear to be completely different problems. The mesoscale approach using representative volume elements and correlation functions to describe the important features of those representative volume elements is presented in some detail.

HIGH-ORDER PHOTON-NUMBER CORRELATIONS: A RESOURCE FOR CHARACTERIZATION AND APPLICATIONS OF QUANTUM STATES

2012 ◽  
Vol 10 (08) ◽  
pp. 1241003 ◽  
Author(s):  
ALESSIA ALLEVI ◽  
STEFANO OLIVARES ◽  
MARIA BONDANI
Keyword(s):  
Correlation Functions ◽  
Photon Number ◽  
High Order ◽  
Quantum States ◽  
Quantum Behavior ◽  
Twin Beam ◽  
High Order Correlation ◽  
Analytical Expressions ◽  
Good Agreement ◽  
Classical States

We measure high-order correlation functions of detected-photon numbers in the mesoscopic regime by means of hybrid photodetectors. The analytical expressions for correlations are evaluated in terms of quantities that can be experimentally accessed by a selfconsistent analysis of the detectors' outputs. We demonstrate that high-order correlations can be used to characterize the nature of the optical states, for instance by better discriminating between classical and quantum behavior even in critical situations, such as multimode twin-beam state. The results are in very good agreement with the theory, both for classical states and quantum states.

scholarly journals Quantum random walks with multiphoton interference and high-order correlation functions

2013 ◽  
Vol 30 (6) ◽  
pp. 1538 ◽  
Author(s):  
Bryan T. Gard ◽  
Robert M. Cross ◽  
Petr M. Anisimov ◽  
Hwang Lee ◽  
Jonathan P. Dowling
Keyword(s):  
Random Walks ◽  
Correlation Functions ◽  
High Order ◽  
Quantum Random Walks ◽  
High Order Correlation

Role of exterior statistics-based boundary conditions for property-based statistically equivalent representative volume elements of polydispersed elastic composites

2018 ◽  
Vol 52 (21) ◽  
pp. 2919-2928 ◽  
Author(s):  
Dhirendra V Kubair ◽  
Maxwell Pinz ◽  
Kaitlin Kollins ◽  
Craig Przybyla ◽  
Somnath Ghosh
Keyword(s):  
Boundary Conditions ◽  
Matrix Composite ◽  
Representative Volume Element ◽  
Polymer Matrix ◽  
Microstructural Characterization ◽  
Experimental Tests ◽  
Volume Element ◽  
Polymer Matrix Composite ◽  
Representative Volume ◽  
Representative Volume Elements

The property-based statistically equivalent RVE or P-SERVE has been introduced in the literature as the smallest microstructural volume element in non-uniform microstructures that has effective material properties equivalent to those of the entire microstructure. An important consideration is the application of appropriate boundary conditions for optimal property-based statistically equivalent representative volume element domains. The exterior statistics-based boundary conditions have been developed, accounting for the statistics of fiber distributions and interactions in the domain exterior to the property-based statistically equivalent representative volume element. This paper is intended to validate the efficacy of the exterior statistics-based boundary condition-based property-based statistically equivalent representative volume elements for evaluating homogenized stiffnesses of a unidirectional polymer matrix composite with a polydispersed microstructure characterized by nonuniform dispersion of carbon fibers of varying sizes in an epoxy matrix. Experimental tests and microstructural characterization of the polymer matrix composite are conducted for calibration and validation of the model. Statistically equivalent microstructural volume elements are constructed from experimental micrographs for direct numerical simulations. The performance of the property-based statistically equivalent representative volume element with exterior statistics-based boundary conditions is compared with other boundary conditions, as well as with the statistical volume elements. The tests clearly show the significant advantages of the exterior statistics-based boundary conditions in terms of accuracy of the homogenized stiffness and efficiency.

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