Monte Carlo test of the T-expansion approach to range and depth calculations at low energies

1979 ◽  
Vol 57 (4) ◽  
pp. 529-538 ◽  
Author(s):  
B. M. Latta
Keyword(s):  
Monte Carlo ◽  
Cross Sections ◽  
Range Data ◽  
Monte Carlo Test ◽  
First Approximation ◽  
Higher Order Terms ◽  
Low Energies ◽  
The Mean ◽  
Light Target ◽  
Equal Spacing

The transport equations for the range and depth are derived in the approximation of equal spacing between collisions. The T-expansion solutions of these equations are compared with results from Monte Carlo simulations in the reduced energy interval from ε = 3.16 × 10−4 to ε = 10−1 for four projectile–target pairs. In the critical region of equal projectile and target masses, the T-expansion solutions for the mean depth were found to converge more rapidly than the mean-range solutions as higher order terms were retained. The greatest errors observed in the first approximation to the mean depth and mean range were, respectively, 21% for Bi on Ge and 59% for Au on Au. In addition, for the case of a heavy projectile on a light target, the standard method of extracting stopping cross sections (S) from experimental range data was investigated. This method, which is based upon the equation for the first approximation to the range, led to an overestimation of S of up to 49% when the method was applied to the Monte Carlo results for Bi on Ge.

Electron Scattering in Solids

1990 ◽  
Vol 48 (2) ◽  
pp. 4-5
Author(s):  
Ryuichi Shimizu ◽  
Ze-Jun Ding
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Angular Distribution ◽  
Elastic Scattering ◽  
Electron Scattering ◽  
Cross Sections ◽  
Expansion Method ◽  
Electron Excitation ◽  
Partial Wave Expansion ◽  
Backscattered Electrons

Monte Carlo simulation has been becoming most powerful tool to describe the electron scattering in solids, leading to more comprehensive understanding of the complicated mechanism of generation of various types of signals for microbeam analysis.The present paper proposes a practical model for the Monte Carlo simulation of scattering processes of a penetrating electron and the generation of the slow secondaries in solids. The model is based on the combined use of Gryzinski’s inner-shell electron excitation function and the dielectric function for taking into account the valence electron contribution in inelastic scattering processes, while the cross-sections derived by partial wave expansion method are used for describing elastic scattering processes. An improvement of the use of this elastic scattering cross-section can be seen in the success to describe the anisotropy of angular distribution of elastically backscattered electrons from Au in low energy region, shown in Fig.l. Fig.l(a) shows the elastic cross-sections of 600 eV electron for single Au-atom, clearly indicating that the angular distribution is no more smooth as expected from Rutherford scattering formula, but has the socalled lobes appearing at the large scattering angle.

scholarly journals Aerodynamics of smooth and rough square-section prisms at incidence in very high Reynolds-number cross-flows

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Nils Paul van Hinsberg
Keyword(s):  
Reynolds Number ◽  
Cross Sections ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Surface Boundary ◽  
Experimental Proof ◽  
Surface Boundary Layer ◽  
Pitch Moment ◽  
The Mean ◽  
High Reynolds

Abstract The aerodynamics of smooth and slightly rough prisms with square cross-sections and sharp edges is investigated through wind tunnel experiments. Mean and fluctuating forces, the mean pitch moment, Strouhal numbers, the mean surface pressures and the mean wake profiles in the mid-span cross-section of the prism are recorded simultaneously for Reynolds numbers between 1$$\times$$ × 10$$^{5}$$ 5 $$\le$$ ≤ Re$$_{D}$$ D $$\le$$ ≤ 1$$\times$$ × 10$$^{7}$$ 7 . For the smooth prism with $$k_s$$ k s /D = 4$$\times$$ × 10$$^{-5}$$ - 5 , tests were performed at three angles of incidence, i.e. $$\alpha$$ α = 0$$^{\circ }$$ ∘ , −22.5$$^{\circ }$$ ∘ and −45$$^{\circ }$$ ∘ , whereas only both “symmetric” angles were studied for its slightly rough counterpart with $$k_s$$ k s /D = 1$$\times$$ × 10$$^{-3}$$ - 3 . First-time experimental proof is given that, within the accuracy of the data, no significant variation with Reynolds number occurs for all mean and fluctuating aerodynamic coefficients of smooth square prisms up to Reynolds numbers as high as $$\mathcal {O}$$ O (10$$^{7}$$ 7 ). This Reynolds-number independent behaviour applies to the Strouhal number and the wake profile as well. In contrast to what is known from square prisms with rounded edges and circular cylinders, an increase in surface roughness height by a factor 25 on the current sharp-edged square prism does not lead to any notable effects on the surface boundary layer and thus on the prism’s aerodynamics. For both prisms, distinct changes in the aerostatics between the various angles of incidence are seen to take place though. Graphic abstract

scholarly journals Statistical Tests of Symbolic Dynamics

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 817
Author(s):  
Fernando López ◽  
Mariano Matilla-García ◽  
Jesús Mur ◽  
Manuel Ruiz Marín
Keyword(s):  
Monte Carlo ◽  
Symbolic Dynamics ◽  
Null Hypothesis ◽  
Statistical Tests ◽  
General Applicability ◽  
Monte Carlo Experiments ◽  
The Mean ◽  
Theoretical Application ◽  
New Statistics ◽  
General Method

A novel general method for constructing nonparametric hypotheses tests based on the field of symbolic analysis is introduced in this paper. Several existing tests based on symbolic entropy that have been used for testing central hypotheses in several branches of science (particularly in economics and statistics) are particular cases of this general approach. This family of symbolic tests uses few assumptions, which increases the general applicability of any symbolic-based test. Additionally, as a theoretical application of this method, we construct and put forward four new statistics to test for the null hypothesis of spatiotemporal independence. There are very few tests in the specialized literature in this regard. The new tests were evaluated with the mean of several Monte Carlo experiments. The results highlight the outstanding performance of the proposed test.

scholarly journals Extension of Pin-Based Point-Wise Energy Slowing-Down Method for VHTR Fuel with Double Heterogeneity

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2179
Author(s):  
Tae-Young Han ◽  
Jin-Young Cho ◽  
Chang-Keun Jo ◽  
Hyun-Chul Lee
Keyword(s):  
Cross Sections ◽  
Cell Model ◽  
Unit Cell ◽  
Moderation Effect ◽  
Slowing Down ◽  
Matrix Layer ◽  
The Mean ◽  
Dancoff Factor ◽  
Double Heterogeneity ◽  
Very High

For the resonance treatment of a very high temperature reactors (VHTR) fuel with the double heterogeneity, an extension of the pin-based pointwise energy slowing-down method (PSM) was developed and implemented into DeCART. The proposed method, PSM-double heterogeneity (DH), has an improved spherical unit cell model with an explicit tri-structural isotropic (TRISO) model, a matrix layer, and a moderator for reflecting the moderation effect. The moderator volume was analytically derived using the relation of the Dancoff factor and the mean chord length. In the first step, the pointwise homogenized cross-sections for the compact was obtained after solving the slowing down equation for the spherical unit cell. Then, the shielded cross-section for the homogenized fuel compact was generated using the original PSM. The verification calculations were performed for the fuel pins with various packing fractions, compact sizes, TRISO sizes, and fuel temperatures. Additionally, two fuel block problems with very different sizes were examined and the depletion calculation was carried out for investigating the accuracy of the proposed method. They revealed that the PSM-DH has a good performance in the VHTR problems.

Rigorous time-domain analysis of statistically oriented graphene sheet fluctuations

2017 ◽  
Vol 36 (5) ◽  
pp. 1351-1363 ◽  
Author(s):  
Athanasios N. Papadimopoulos ◽  
Stamatios A. Amanatiadis ◽  
Nikolaos V. Kantartzis ◽  
Theodoros T. Zygiridis ◽  
Theodoros D. Tsiboukis
Keyword(s):  
Monte Carlo ◽  
Standard Deviation ◽  
Finite Difference ◽  
Surface Waves ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Mean Value ◽  
Content Type ◽  
The Mean ◽  
Difference Time

Purpose Important statistical variations are likely to appear in the propagation of surface plasmon polariton waves atop the surface of graphene sheets, degrading the expected performance of real-life THz applications. This paper aims to introduce an efficient numerical algorithm that is able to accurately and rapidly predict the influence of material-based uncertainties for diverse graphene configurations. Design/methodology/approach Initially, the surface conductivity of graphene is described at the far infrared spectrum and the uncertainties of its main parameters, namely, the chemical potential and the relaxation time, on the propagation properties of the surface waves are investigated, unveiling a considerable impact. Furthermore, the demanding two-dimensional material is numerically modeled as a surface boundary through a frequency-dependent finite-difference time-domain scheme, while a robust stochastic realization is accordingly developed. Findings The mean value and standard deviation of the propagating surface waves are extracted through a single-pass simulation in contrast to the laborious Monte Carlo technique, proving the accomplished high efficiency. Moreover, numerical results, including graphene’s surface current density and electric field distribution, indicate the notable precision, stability and convergence of the new graphene-based stochastic time-domain method in terms of the mean value and the order of magnitude of the standard deviation. Originality/value The combined uncertainties of the main parameters in graphene layers are modeled through a high-performance stochastic numerical algorithm, based on the finite-difference time-domain method. The significant accuracy of the numerical results, compared to the cumbersome Monte Carlo analysis, renders the featured technique a flexible computational tool that is able to enhance the design of graphene THz devices due to the uncertainty prediction.

Development of SiO2 based doped with LiF, Cr2O3, CoO4 and B2O3 glasses for gamma and fast neutron shielding

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Bünyamin Aygün ◽  
Erdem Şakar ◽  
Abdulhalik Karabulut ◽  
Bünyamin Alım ◽  
Mohammed I. Sayyed ◽  
...  
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Fast Neutron ◽  
Cross Sections ◽  
Gamma Ray ◽  
Absorbed Dose ◽  
Neutron Shielding ◽  
Shielding Properties ◽  
Effective Neutron ◽  
Simulation Codes

AbstractIn this study, the fast neutron and gamma-ray absorption capacities of the new glasses have been investigated, which are obtained by doping CoO,CdWO4,Bi2O3, Cr2O3, ZnO, LiF,B2O3 and PbO compounds to SiO2 based glasses. GEANT4 and FLUKA Monte Carlo simulation codes have been used in the planning of the samples. The glasses were produced using a well-known melt-quenching technique. The effective neutron removal cross-sections, mean free paths, half-value layer, and transmission numbers of the fabricated glasses have been calculated through both GEANT4 and FLUKA Monte Carlo simulation codes. Experimental neutron absorbed dose measurements have been carried out. It was found that GS4 glass has the best neutron protection capacity among the produced glasses. In addition to neutron shielding properties, the gamma-ray attenuation capacities, were calculated using newly developed Phy-X/PSD software. The gamma-ray shielding properties of GS1 and GS2 are found to be equivalent to Pb-based glass.

Crossover scaling in semidilute polymer solutions: a Monte Carlo test

1991 ◽  
Vol 1 (1) ◽  
pp. 37-60 ◽  
Author(s):  
Wolfgang Paul ◽  
Kurt Binder ◽  
Dieter W. Heermann ◽  
Kurt Kremer
Keyword(s):  
Monte Carlo ◽  
Polymer Solutions ◽  
Monte Carlo Test
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