QUANTIFYING MORPHOLOGY OF SCALE-INVARIANT STRUCTURES BEYOND THE FRACTAL DIMENSION

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 985-991
Author(s):  
RAPHAEL BLUMENFELD ◽  
ROBIN C. BALL
Keyword(s):  
Correlation Function ◽  
Fractal Dimension ◽  
Pair Correlation Function ◽  
Pair Correlation ◽  
Scale Invariant ◽  
Diffusion Limited Aggregation ◽  
Suitable Candidate ◽  
Diffusion Limited ◽  
Invariant Structures ◽  
Admissible Solutions

We present a correlation scheme to quantify the morphology beyond the standard fractal dimension which corresponds to information from the pair correlation function. The method consists of analyzing hierarchical correlations in log-space thus summing contributions from higher order correlations in the usual space coordinates. The scheme gives information on the characteristics of structure which can be used as a fingerprint to distinguish between structures with the same fractal dimension. The method is also sensitive to oscillations in logarithmic scales, which are admissible solutions for renormalisation equations. Such oscillations appear as resonances, thus making this scheme suitable to analyze such phenomena experimentally. Illustrative examples are given for all those applications by analyzing numerically grown structures. The case of the unrestricted Brownian walk is exactly calculated. We discuss an application of this scheme to check recent analytic results obtained for scale-invariant branching mechanisms in slow cracking patterns and in noise-reduced diffusion-limited-aggregation. We propose that this method is a suitable candidate to quantify the presently qualitative concept of morphology.

Characterizing Fractal and Hierarchical Morphologies Beyond the Fractal Dimension

1994 ◽  
Vol 367 ◽  
Author(s):  
Raphael Blumenfeld ◽  
Robin C. Ball
Keyword(s):  
Asymptotic Behavior ◽  
Fractal Dimension ◽  
Finite Size ◽  
Size Analysis ◽  
Corrections To Scaling ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Markovian Processes ◽  
Branching Patterns ◽  
Admissible Solutions

AbstractWe present a novel correlation scheme to characterize the morphology of fractal and hierarchical patterns beyond traditional scaling. The method consists of analysing correlations between more than two-points in logarithmic coordinates. This technique has several advantages: i) It can be used to quantify the currently vague concept of morphology; ii) It allows to distinguish between different signatures of structures with similar fractal dimension but different morphologies already for relatively small systems; iii) The method is sensitive to oscillations in logarithmic coordinates, which are both admissible solutions for renormalization equations and which appear in many branching patterns (e.g., noise-reduced diffusion-limited-aggregation and bronchial structures); iv) The methods yields information on corrections to scaling from the asymptotic behavior, which is very useful in finite size analysis. Markovian processes are calculated exactly and several structures are analyzed by this method to demonstrate its advantages.

scholarly journals Molecular Dynamics Simulations for Effects of Fluoropolymer Binder Content in CL-20/TNT Based Polymer-Bonded Explosives

Molecules ◽  
2021 ◽  
Vol 26 (16) ◽  
pp. 4876
Author(s):  
Shenshen Li ◽  
Jijun Xiao
Keyword(s):  
Mechanical Properties ◽  
Molecular Dynamics ◽  
Correlation Function ◽  
Binding Energy ◽  
Hydrogen Bonds ◽  
Bond Length ◽  
Pair Correlation Function ◽  
Pair Correlation ◽  
Binder Content ◽  
Polymer Bonded Explosives

In order to better understand the role of binder content, molecular dynamics (MD) simulations were performed to study the interfacial interactions, sensitivity and mechanical properties of 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane/2,4,6-trinitrotoluene (CL-20/TNT) based polymer-bonded explosives (PBXs) with fluorine rubber F2311. The binding energy between CL-20/TNT co-crystal (1 0 0) surface and F2311, pair correlation function, the maximum bond length of the N–NO2 trigger bond, and the mechanical properties of the PBXs were reported. From the calculated binding energy, it was found that binding energy increases with increasing F2311 content. Additionally, according to the results of pair correlation function, it turns out that H–O hydrogen bonds and H–F hydrogen bonds exist between F2311 molecules and the molecules in CL-20/TNT. The length of trigger bond in CL-20/TNT were adopted as theoretical criterion of sensitivity. The maximum bond length of the N–NO2 trigger bond decreased very significantly when the F2311 content increased from 0 to 9.2%. This indicated increasing F2311 content can reduce sensitivity and improve thermal stability. However, the maximum bond length of the N–NO2 trigger bond remained essentially unchanged when the F2311 content was further increased. Additionally, the calculated mechanical data indicated that with the increase in F2311 content, the rigidity of CL-20/TNT based PBXs was decrease, the toughness was improved.

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