Photon emission as a probe of chaotic processes accompanying fracture

1989 ◽  
Vol 4 (5) ◽  
pp. 1272-1279 ◽  
Author(s):  
S. C. Langford ◽  
Ma Zhenyi ◽  
J. T. Dickinson
Keyword(s):  
Fracture Surface ◽  
Photon Emission ◽  
Deterministic Chaos ◽  
Fractal Dimensions ◽  
Significant Degree ◽  
Box Dimension ◽  
Dynamic Crack ◽  
Emission Data ◽  
Correlation Integral ◽  
The Fourier Transform

Photon emission accompanying the fracture of an epoxy and single crystal MgO is examined for evidence of deterministic chaos by means of the autocorrelation function, the Fourier transform, the correlation integral of Grassberger and Procaccia, and the fractal box dimension. A positive Lyapunov exponent is also obtained from the epoxy phE data. Each of these measures is consistent with a significant degree of deterministic chaos associated with attractors of relatively low dimension. A typical epoxy fracture surface was analyzed for fractal character by means of the slit island technique, yielding a fractal dimension of 1.32 ± 0.03. The fractal dimensions of the fracture surface and the photon emission data (box dimension) of the epoxy are in good agreement. These observations suggest that fluctuations in photon emission intensity during fracture reflect the production of fractal surface features as they are being produced and thus provide important information on the process of dynamic crack growth.

Fractal character of crack propagation in epoxy and epoxy composites as revealed by photon emission during fracture

1991 ◽  
Vol 6 (1) ◽  
pp. 183-195 ◽  
Author(s):  
Ma Zhenyi ◽  
S.C. Langford ◽  
J.T. Dickinson ◽  
M.H. Engelhard ◽  
D.R. Baer
Keyword(s):  
Photoelectron Spectroscopy ◽  
Photon Emission ◽  
Deterministic Chaos ◽  
Fractal Dimensions ◽  
Fractal Nature ◽  
X Ray ◽  
Correlation Exponent ◽  
Alumina Particles ◽  
Fractal Character ◽  
Chaotic Nature

We examine the photon emission accompanying rapid crack growth in an unfilled epoxy resin and in the same resin filled with alumina particles. The alumina particles substantially increase the toughness of the material and increase the photon emission intensities at least tenfold. We attribute the increased photon emission in the filled material to high densities of broken bonds near the alumina particles. The photon emission signals from both filled and unfilled materials show nonintegral (fractal) dimensions which are insensitive to the presence of the particles at the level of precision employed. Fractal dimension measurements of the fracture surfaces are likewise relatively insensitive to the presence of the filler, despite marked variations in apparent surface roughness. The photon emission signals were examined for the presence of chaos. Computations of the correlation exponent of Grassberger and Procaccia indicate that the photon emission fluctuations are not noise-like in character, and suggest deterministic chaos. Lyapunov exponent estimates on photon emission signals confirm the presence of chaotic processes. X-ray photoelectron spectroscopy and electron microscopy of the fracture surface indicate very little interfacial failure; i.e., fracture proceeds predominantly through the epoxy matrix in both filled and unfilled materials. Consequently, the character of the polymer matrix dominates the fracture process and therefore determines the fractal nature of the surface and the chaotic nature of the photon emission intensities in each material.

Collapse models tested in the LNGS underground laboratories

2019 ◽  
Vol 17 (08) ◽  
pp. 1941011
Author(s):  
Catalina Curceanu ◽  
Raffaele Del Grande ◽  
Matthias Laubenstein ◽  
Kristian Piscicchia
Keyword(s):  
Quantum Mechanics ◽  
Measurement Problem ◽  
Photon Emission ◽  
Spontaneous Radiation ◽  
Emission Data ◽  
Standard Quantum ◽  
Wave Function Collapse ◽  
X Ray ◽  
Data Analyses ◽  
Collapse Models

Collapse models consist in dynamical reformulations of the standard quantum mechanics aiming to solve the measurement problem. The standard Schrödinger dynamics is modified with the introduction of nonlinear and stochastic terms, which induce the wave function collapse in space. Collapse models predict slight deviations from the standard quantum mechanics predictions, in particular the emission of a “spontaneous radiation”, which we explored to set the most stringent limits on the collapse models parameters in a broad range. To this end, the X-ray emission data collected by the IGEX collaboration are analyzed and compared with the spectrum of the spontaneous photon emission process predicted by the theories. The results of the data analyses, and the ongoing experimental efforts will be presented.

THE RELATIONSHIP BETWEEN FRACTAL DIMENSIONS OF BESICOVITCH FUNCTION AND THE ORDER OF HADAMARD FRACTIONAL INTEGRAL

Fractals ◽  
2020 ◽  
Vol 28 (07) ◽  
pp. 2050128
Author(s):  
BIN WANG ◽  
WENLONG JI ◽  
LEGUI ZHANG ◽  
XUAN LI
Keyword(s):  
Fractional Integral ◽  
Fractal Dimensions ◽  
Packing Dimension ◽  
Box Dimension ◽  
Dimension Formula ◽  
The Relationship ◽  
Hadamard Fractional Integral

In this paper, we mainly research on Hadamard fractional integral of Besicovitch function. A series of propositions of Hadamard fractional integral of [Formula: see text] have been proved first. Then, we give some fractal dimensions of Hadamard fractional integral of Besicovitch function including Box dimension, [Formula: see text]-dimension and Packing dimension. Finally, relationship between the order of Hadamard fractional integral and fractal dimensions of Besicovitch function has also been given.

BOX DIMENSION OF COLORED NOISE AND DETERMINISTIC TIME SERIES IN HIGH DIMENSIONAL EUCLIDEAN SPACES

Fractals ◽  
1996 ◽  
Vol 04 (01) ◽  
pp. 91-95 ◽  
Author(s):  
WEN ZHANG ◽  
BRUCE J. WEST
Keyword(s):  
Time Series ◽  
Power Law ◽  
Colored Noise ◽  
Fractal Dimensions ◽  
Inverse Power ◽  
High Dimensional ◽  
Dimensional Euclidean Space ◽  
Box Dimension ◽  
Inverse Power Law ◽  
Lower Graph

We investigate the box dimension of a time series having an inverse power-law spectra in a high dimensional Euclidean space. The time series can be random (colored noise) or deterministic. Both isotropic and anisotropic cases are included in our investigation. We study both the graph dimension and trail dimension of the time series. We show that with the same inverse power-law spectra, the deterministic series has a lower graph dimension than that of the colored noise, though they both can have fractal dimensions. We also derive a sharp upper bound on the trial dimension of the time series.

Shock Spectrum Ratios Applied to the Comparison of Pulse Signatures

1980 ◽  
Vol 102 (1) ◽  
pp. 64-76
Author(s):  
J. R. Houghton
Keyword(s):  
Acoustic Emission ◽  
Transfer Functions ◽  
Time Window ◽  
Relative Size ◽  
Emission Data ◽  
Relative Damage ◽  
New Type ◽  
Ratio Approach ◽  
Spectrum Ratio ◽  
The Fourier Transform

Two extensions of the shock spectrum technique are developed for use in pulse signature analysis. A shock spectrum ratio is proposed and compared to the Fourier transfer function for the detection of small perturbations on a larger pulse shape. The shock spectrum ratio is shown to have good sensitivity to the relative size of the perturbation. The shock spectrum ratio approach is extended to a new type of spectrum named “slot transform.” This specialized transform is shown to have several advantages with respect to the Fourier transform in the development of magnitude transfer functions. The transform was developed for analysis of digitized acoustic emission pulses where a rectangular time window is preferred. These two extensions of shock spectrum methods are tested on experimental data from high g shock tests and acoustic emission measurements from damaged and undamaged ball bearings. Deconvolution of the acoustic emission data was necessary before the shork spectrum, ratio was capable of indicating the relative damage of the bearings.

DIMENSION ANALYSIS OF CONTINUOUS FUNCTIONS WITH UNBOUNDED VARIATION

Fractals ◽  
2017 ◽  
Vol 25 (01) ◽  
pp. 1730001 ◽  
Author(s):  
JUN WANG ◽  
KUI YAO
Keyword(s):  
Hausdorff Dimension ◽  
Fractal Dimensions ◽  
Continuous Functions ◽  
Packing Dimension ◽  
Box Dimension ◽  
Box Counting ◽  
Dimension Analysis ◽  
Box Counting Dimension ◽  
Self Similar

In this paper, we mainly discuss fractal dimensions of continuous functions with unbounded variation. First, we prove that Hausdorff dimension, Packing dimension and Modified Box-counting dimension of continuous functions containing one UV point are [Formula: see text]. The above conclusion still holds for continuous functions containing finite UV points. More generally, we show the result that Hausdorff dimension of continuous functions containing countable UV points is [Formula: see text] also. Finally, Box dimension of continuous functions containing countable UV points has been proved to be [Formula: see text] when [Formula: see text] is self-similar.

scholarly journals COMBINING METHODS OF FREQUENCY FILTERING AND NONLINEAR ANALYSIS FOR SOMNOLOGICAL STUDY OF EEG SIGNALS

2016 ◽  
Vol 1 (3) ◽  
pp. 45-50
Author(s):  
O I Antipov ◽  
A V Zakharov
Keyword(s):  
Nonlinear Analysis ◽  
Classical Method ◽  
Deterministic Chaos ◽  
Entropy Method ◽  
Preliminary Treatment ◽  
Frequency Filtering ◽  
Eeg Signals ◽  
Recovery Method ◽  
Correlation Integral ◽  
Non Linear

Aim - combined use of frequency and nonlinear analysis methods for obtaining hypnograms by analyzing electroencephalographic (EEG) signals during somnological studies. Methods. Frequency filtering methods were used for preliminary treatment of EEG signals before the following nonlinear analysis. As non-linear methods of analysis we used fractal methods of deterministic chaos, such as Hurst’s method of the normalized amplitude, approximate entropy method, calculation of the correlation integral by Grassberger and Procaccia’s method. For the possibility of applying the last two methods we used quasi phase space recovery method according to the Taken’s theorem. As a result of non-linear analysis we obtained hypnograms reflecting the transition between the stages of sleep in patients undergoing somnological examination. To assess the reliability of the results, they were compared to the hypnograms obtained by the classical method based on the rules of Rehchaffen and Keyls. Also the problems associated with the occurrence of various types of interference were considered and methods for reducing their influence on the final results were suggested. Results. We can conclude that using these methods with appropriate selection of the parameters, employing the necessary normalization of raw data, and averaging the results allow us to obtain hypnogram having a full match of defined phases of sleep for about half of the periods recorded by EEG. To obtain these results it is sufficient to use only one channel of EEG recording.

FRACTAL DIMENSIONS OF WEYL–MARCHAUD FRACTIONAL DERIVATIVE OF CERTAIN ONE-DIMENSIONAL FUNCTIONS

Fractals ◽  
2019 ◽  
Vol 27 (07) ◽  
pp. 1950114
Author(s):  
Y. S. LIANG ◽  
N. LIU
Keyword(s):  
Fractional Derivative ◽  
Fractal Dimensions ◽  
Continuous Functions ◽  
Box Dimension ◽  
One Dimensional ◽  
Dimension One

Fractal dimensions of Weyl–Marchaud fractional derivative of certain continuous functions are investigated in this paper. Upper Box dimension of Weyl–Marchaud fractional derivative of certain continuous functions with Box dimension one has been proved to be no more than the sum of one and its order.

scholarly journals Temperature dependent crack initiation of 42CrMo4 steel at high loading rates

2018 ◽  
Vol 183 ◽  
pp. 02001
Author(s):  
Sebastian Henschel ◽  
Lutz KrÜger
Keyword(s):  
Fracture Surface ◽  
Crack Initiation ◽  
Split Hopkinson Pressure Bar ◽  
Crack Tip ◽  
Shear Zones ◽  
Initiation Toughness ◽  
High Speed Photography ◽  
Dynamic Crack ◽  
Loading Rates ◽  
42Crmo4 Steel

Dynamic crack initiation with crack tip loading rates K˙ of approximately 2 ‧ 106 MPa√ms− in high-strength 42CrMo4 steel was investigated. To this end, a recently developed split Hopkinson pressure bar with four-point bending was utilized. V-notched and precracked Charpy specimens were tested. The tests were performed at temperatures of –40 °C and 20 °C. The loading of the specimen was determined by analyzing the strain in the incident and transmission bars. Furthermore, strain gauges at the specimen’s surface were applied to measure the crack tip loading. High-speed photography complemented the analysis of the specimens loading and the detection of the crack initiation. Fracture surface analysis by means of scanning electron microscopy enabled the measurement of the fracture surface topography and, consequently, stretch zone height and width. Hence, the macroscopically measured dynamic crack initiation toughness was correlated with the toughness at microscopic scale. It was observed that the resistance against dynamic crack initiation decreased with decreasing temperature. Microscopically, a decrease in toughness was analogously observed. Non-metallic inclusions resulted in crack path deflection with localized shear zones. After a small stable crack extension, cleavage fracture was observed.

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