Fractal geometry of collision cascades

1989 ◽  
Vol 4 (1) ◽  
pp. 137-143 ◽  
Author(s):  
François Rossi ◽  
Don M. Parkin ◽  
Michael Nastasi
Keyword(s):  
Monte Carlo ◽  
Fractal Dimension ◽  
Monte Carlo Simulations ◽  
Fractal Geometry ◽  
Critical Energy ◽  
Initial Energy ◽  
Atomic Mass ◽  
Fractal Nature ◽  
Realistic Potential ◽  
Ion Collision

The fractal nature of self-ion collision cascades is first described using an inverse power potential and then by the more realistic potential of Biersack–Ziegler. Based on the model of Cheng et al. and TRIM Monte Carlo simulations, the average cascade fractal dimension is a function of both atomic mass and initial energy. The instantaneous fractal dimension increases as the cascade evolves. A critical energy Ec for producing a dense subcascade is derived and it is shown that Ec agrees well with the onset energy for constant damage efficiency.

scholarly journals CEPA: A LaBr3(Ce)/LaCl3(Ce) PHOSWICH ARRAY FOR SIMULTANEOUS DETECTION OF PROTONS AND GAMMA RADIATION EMITTED IN REACTIONS AT RELATIVISTIC ENERGIES

2014 ◽  
Vol 27 ◽  
pp. 1460143
Author(s):  
J. SÁNCHEZ DEL RÍO ◽  
M. J. G. BORGE ◽  
E. NÁCHER ◽  
A. PEREA ◽  
G. RIBEIRO ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Gamma Radiation ◽  
Monte Carlo Simulations ◽  
Simultaneous Detection ◽  
High Energy ◽  
Initial Energy ◽  
Optical Pulses ◽  
High Energies ◽  
Very High ◽  
Doppler Correction

A sophisticated design of 750 LaBr3(Ce):LaCl3(Ce) phoswich crystals (CEPA10) with a segmentation determined by the Doppler correction and an energy resolution of 5% at 1 MeV is presented. Monte Carlo simulations have been performed for high energy protons (50–500 MeV) and gamma radiation (0.5–30 MeV) to determine the length and shape of the crystals for optimum performance of the detector. In the case of protons, the two-layer detector can be used as a ΔELaBr3 − ETot telescope or, for very high energies, as a double energy loss detector (ΔELaBr3 + ΔELaCl3), in order to determine the initial energy. In addition, an experimental test with high energy protons (70–230 MeV) was performed at the cyclotron center in Krakow, Poland with a first prototype of 2 x 2 phoswich rectangular crystals (CEPA4) packed in an aluminum can (0.5 mm case). To simulate CEPA10 efficiencies and resolutions, optical pulses detected in CEPA4 by photomultiplier tubes with a DAQ system were used as energy input functions in Monte Carlo simulations.

On the fractal nature of crack branching in MgF2

1998 ◽  
Vol 13 (11) ◽  
pp. 3153-3159 ◽  
Author(s):  
J. J. Mecholsky ◽  
Richard Linhart ◽  
Brian D. Kwitkin ◽  
Roy W. Rice
Keyword(s):  
Fractal Dimension ◽  
Fracture Surface ◽  
Fractal Geometry ◽  
Magnesium Fluoride ◽  
Crack Branching ◽  
Far Field ◽  
Fractal Nature ◽  
Branching Patterns ◽  
Basic Studies ◽  
Far Field Stress

Nineteen disks of IR window grade, hot pressed magnesium fluoride (˜0% porosity, grain size ˜1 μm) previously loaded in ring-on-ring flexure tests were used to analyze the crack branching patterns. Fractal geometry was used to determine the crack branching fractal dimension which was named the crack branching coefficient or CBC. The failure stress was proportional to the CBC and the number of pieces generated during the fracture. Thus, the number of pieces was proportional to the crack branching coefficient. The crack branching coefficient is distinct from the fractal dimension obtained from the onset of mist and hackle on the fracture surface. The fractal dimension of the fracture surface is, in most cases for brittle materials, a constant and related to the crack tip stress field. The crack branching fractal dimension is a function of the stress at fracture and the far-field stress distribution, or in other words, related to both the type and magnitude of loading. The findings in this work have strong implications for many commercial processes such as comminution, attrition, grinding, and basic studies in crack branching.

KOZENY–CARMAN CONSTANT FOR GAS FLOW THROUGH FIBROUS POROUS MEDIA BY FRACTAL-MONTE CARLO SIMULATIONS

Fractals ◽  
2019 ◽  
Vol 27 (04) ◽  
pp. 1950062 ◽  
Author(s):  
BOQI XIAO ◽  
XIAN ZHANG ◽  
GUOPING JIANG ◽  
GONGBO LONG ◽  
WEI WANG ◽  
...  
Keyword(s):  
Porous Media ◽  
Monte Carlo ◽  
Fractal Dimension ◽  
Monte Carlo Simulations ◽  
Pore Size ◽  
Fiber Diameter ◽  
Structural Parameters ◽  
Probability Model ◽  
Monte Carlo Technique ◽  
Fibrous Porous Media

In this paper, the Kozeny–Carman constant of fibrous porous media is simulated by the Fractal-Monte Carlo technique. The proposed probability model of the Kozeny–Carman constant is obtained based on the fractal distribution of pore size in fibrous porous media, and thus can be expressed as a function of structural parameters of fibrous porous media, including porosity, micro-pore size, fiber diameter, tortuosity fractal dimension and area fractal dimension of pores. Our results demonstrate that the Kozeny–Carman constant of fibrous porous media increases with increases in tortuosity fractal dimension and fiber diameter. Our results also illustrate a satisfying agreement of the Fractal Monte-Carlo simulations obtained by the proposed model and the existing experimental data. Therefore, the proposed Fractal-Monte Carlo technique can be used to characterize other transport properties of fluid in fibrous porous media.

scholarly journals Spectral albedo of photons of initial energies below 100 keV

2007 ◽  
Vol 22 (1) ◽  
pp. 40-47 ◽  
Author(s):  
Srpko Markovic ◽  
Rodoljub Simovic ◽  
Vladan Ljubenov ◽  
Radovan Ilic
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Numerical Experiments ◽  
Polar Angle ◽  
Initial Energy ◽  
Photon Beam ◽  
Initial Photon ◽  
The Usa ◽  
Perpendicular Incidence

This paper shows the results of Monte Carlo simulations of the photon reflection from homogenous plates of the shield materials made of water, aluminum, and iron. Perpendicular incidence of a monoenergetic photon beam of the initial energy of 20 keV up to 100 keV is considered. The numerical experiments were performed using the verified Monte Carlo programs MCNP-4C, FOTELP-2K3, and PENELOPE-2005. As the result, the values of difference number albedo distributed in ten even intervals according to the energy and nine even intervals according to the polar angle of reflected photons were obtained. Out of these data, the spectral albedo coefficients for all three materials and three initial photon energies of 40 keV, 60 keV, and 100 keV were calculated, graphically presented, and analyzed. The values of the spectral albedo determined on the basis of MCNP-4C code were compared to the results of the early simulations of the photon reflection performed in Russia and in the USA. Also, with the help of MCNP-4C program, the yield of fluorescent photons to the spectrum of the reflected radiation was registered, which can be seen in the graphs in the form of the peak at the energy of 7.112 keV only at the shielding plates made of iron.

scholarly journals OPTIMIZATION OF THE HIGUCHI METHOD

2021 ◽  
Vol 9 (11) ◽  
pp. 202-213
Author(s):  
J. Wanliss ◽  
R. Hernandez Arriaza ◽  
G. Wanliss ◽  
S. Gordon
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Fractal Dimension ◽  
Monte Carlo Simulations ◽  
Ad Hoc ◽  
A Priori ◽  
Fractal Dimensions ◽  
Correct Choice ◽  
Tuning Parameter ◽  
Data Set

Background and Objective: Higuchi’s method of determining fractal dimension (HFD) occupies a valuable place in the study of a wide variety of physical signals. In comparison to other methods, it provides more rapid, accurate estimations for the entire range of possible fractal dimensions. However, a major difficulty in using the method is the correct choice of tuning parameter (kmax) to compute the most accurate results. In the past researchers have used various ad hoc methods to determine the appropriate kmax choice for their particular data. We provide a more objective method of determining, a priori, the best value for the tuning parameter, given a particular length data set. Methods: We create numerous simulations of fractional Brownian motion to perform Monte Carlo simulations of the distribution of the calculated HFD. Results: Experimental results show that HFD depends not only on kmax but also on the length of the time series, which enable derivation of an expression to find the appropriate kmax for an input time series of unknown fractal dimension. Conclusion: The Higuchi method should not be used indiscriminately without reference to the type of data whose fractal dimension is examined. Monte Carlo simulations with different fractional Brownian motions increases the confidence of evaluation results.

Low-voltage EDS of magnesium ferrite Dendrites in a FEG-SEM

1996 ◽  
Vol 54 ◽  
pp. 478-479
Author(s):  
Matthew T. Johnson ◽  
Ian M. Anderson ◽  
Jim Bentley ◽  
C. Barry Carter
Keyword(s):  
Monte Carlo ◽  
Quantitative Analysis ◽  
Monte Carlo Simulations ◽  
Cross Section ◽  
Spatial Resolution ◽  
Low Voltage ◽  
Magnesium Ferrite ◽  
X Ray ◽  
Interaction Volume ◽  
Ferrite Spinel

Energy-dispersive X-ray spectrometry (EDS) performed at low (≤ 5 kV) accelerating voltages in the SEM has the potential for providing quantitative microanalytical information with a spatial resolution of ∼100 nm. In the present work, EDS analyses were performed on magnesium ferrite spinel [(MgxFe1−x)Fe2O4] dendrites embedded in a MgO matrix, as shown in Fig. 1. spatial resolution of X-ray microanalysis at conventional accelerating voltages is insufficient for the quantitative analysis of these dendrites, which have widths of the order of a few hundred nanometers, without deconvolution of contributions from the MgO matrix. However, Monte Carlo simulations indicate that the interaction volume for MgFe2O4 is ∼150 nm at 3 kV accelerating voltage and therefore sufficient to analyze the dendrites without matrix contributions.Single-crystal {001}-oriented MgO was reacted with hematite (Fe2O3) powder for 6 h at 1450°C in air and furnace cooled. The specimen was then cleaved to expose a clean cross-section suitable for microanalysis.

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