Representative elementary volume via averaged scalar Minkowski functionals

08/09/2020
by   M. V. Andreeva, et al.
1

Representative Elementary Volume (REV) at which the material properties do not vary with change in volume is an important quantity for making measurements or simulations which represent the whole. We discuss the geometrical method to evaluation of REV based on the quantities coming in the Steiner formula from convex geometry. For bodies in the three-space this formula gives us four scalar functionals known as scalar Minkowski functionals. We demonstrate on certain samples that the values of such averaged functionals almost stabilize for cells for which the length of edges are greater than certain threshold value R. Therefore, from this point of view, it is reasonable to consider cubes of volume R^3 as representative elementary volumes.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/15/2022

An Elementary Proof of the Generalization of the Binet Formula for k-bonacci Numbers

We present an elementary proof of the generalization of the k-bonacci Bi...
research
05/18/2022

Kac-Rice formula: A contemporary overview of the main results and applications

The book develops the fundamental ideas of the famous Kac-Rice formula f...
research
07/12/2019

Elementary proofs of generalized continued fraction formulae for e

In this short note we prove two elegant generalized continued fraction f...
research
12/12/2021

A quick estimate for the volume of a polyhedron

Let P be a bounded polyhedron defined as the intersection of the non-neg...
research
04/11/2021

Compressive Neural Representations of Volumetric Scalar Fields

We present an approach for compressing volumetric scalar fields using im...

Please sign up or login with your details

Forgot password? Click here to reset