Metric Entropy of Some Classes of Sets with Differentiable Boundaries

2010 ◽  
pp. 433-443
Author(s):  
R. M. Dudley
Keyword(s):  
Metric Entropy

scholarly journals Acoustic Emission and K-S Metric Entropy as Methods for Determining Mechanical Properties of Composite Materials

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 145
Author(s):  
Lesław Kyzioł ◽  
Katarzyna Panasiuk ◽  
Grzegorz Hajdukiewicz ◽  
Krzysztof Dudzik
Keyword(s):  
Mechanical Properties ◽  
Acoustic Emission ◽  
Composite Material ◽  
Composite Materials ◽  
Testing Machine ◽  
Measurement Data ◽  
Entropy Method ◽  
Displacement Sensor ◽  
Metric Entropy ◽  
Plastic Phase

Due to the unique properties of polymer composites, these materials are used in many industries, including shipbuilding (hulls of boats, yachts, motorboats, cutters, ship and cooling doors, pontoons and floats, torpedo tubes and missiles, protective shields, antenna masts, radar shields, and antennas, etc.). Modern measurement methods and tools allow to determine the properties of the composite material, already during its design. The article presents the use of the method of acoustic emission and Kolmogorov-Sinai (K-S) metric entropy to determine the mechanical properties of composites. The tested materials were polyester-glass laminate without additives and with a 10% content of polyester-glass waste. The changes taking place in the composite material during loading were visualized using a piezoelectric sensor used in the acoustic emission method. Thanks to the analysis of the RMS parameter (root mean square of the acoustic emission signal), it is possible to determine the range of stresses at which significant changes occur in the material in terms of its use as a construction material. In the K-S entropy method, an important measuring tool is the extensometer, namely the displacement sensor built into it. The results obtained during the static tensile test with the use of an extensometer allow them to be used to calculate the K-S metric entropy. Many materials, including composite materials, do not have a yield point. In principle, there are no methods for determining the transition of a material from elastic to plastic phase. The authors showed that, with the use of a modern testing machine and very high-quality instrumentation to record measurement data using the Kolmogorov-Sinai (K-S) metric entropy method and the acoustic emission (AE) method, it is possible to determine the material transition from elastic to plastic phase. Determining the yield strength of composite materials is extremely important information when designing a structure.

Metric Entropy with Bracketing

2014 ◽  
pp. 269-283
Author(s):  
R. M. Dudley
Keyword(s):  
Metric Entropy

scholarly journals Amount of failure of upper-semicontinuity of entropy in non-compact rank-one situations, and Hausdorff dimension

2015 ◽  
Vol 37 (2) ◽  
pp. 539-563 ◽  
Author(s):  
S. KADYROV ◽  
A. POHL
Keyword(s):  
Hausdorff Dimension ◽  
Homogeneous Spaces ◽  
Upper Semicontinuity ◽  
Metric Entropy ◽  
Real Rank ◽  
Semisimple Lie Group ◽  
Uniform Lattice ◽  
Finite Center ◽  
Rank One ◽  
Set Of Points

Recently, Einsiedler and the authors provided a bound in terms of escape of mass for the amount by which upper-semicontinuity for metric entropy fails for diagonal flows on homogeneous spaces $\unicode[STIX]{x1D6E4}\setminus G$, where $G$ is any connected semisimple Lie group of real rank one with finite center, and $\unicode[STIX]{x1D6E4}$ is any non-uniform lattice in $G$. We show that this bound is sharp, and apply the methods used to establish bounds for the Hausdorff dimension of the set of points that diverge on average.

scholarly journals ON THE METRIC ENTROPY OF THE BANACH–MAZUR COMPACTUM

Mathematika ◽  
2014 ◽  
Vol 61 (1) ◽  
pp. 179-198 ◽  
Author(s):  
Gilles Pisier
Keyword(s):  
Metric Entropy
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