scholarly journals Theoretical Basis of the Decoupled Cell Monte Carlo Simulation for Quantum System

1988 ◽  
Vol 80 (4) ◽  
pp. 583-587 ◽  
Author(s):  
H. Matsuda ◽  
K. Ishii ◽  
S. Homma ◽  
N. Ogita
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Quantum System ◽  
Theoretical Basis

scholarly journals BiEntropy, TriEntropy and Primality

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 311
Author(s):  
Grenville Croll
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Significant Relationship ◽  
Riemann Hypothesis ◽  
Theoretical Basis ◽  
Natural Numbers ◽  
Tight Bound ◽  
Twin Primes ◽  
Order And Disorder ◽  
Mersenne Primes

The order and disorder of binary representations of the natural numbers < 28 is measured using the BiEntropy function. Significant differences are detected between the primes and the non-primes. The BiEntropic prime density is shown to be quadratic with a very small Gaussian distributed error. The work is repeated in binary using a Monte Carlo simulation of a sample of natural numbers < 232 and in trinary for all natural numbers < 39 with similar but cubic results. We found a significant relationship between BiEntropy and TriEntropy such that we can discriminate between the primes and numbers divisible by six. We discuss the theoretical basis of these results and show how they generalise to give a tight bound on the variance of Pi(x)–Li(x) for all x. This bound is much tighter than the bound given by Von Koch in 1901 as an equivalence for proof of the Riemann Hypothesis. Since the primes are Gaussian due to a simple induction on the binary derivative, this implies that the twin primes conjecture is true. We also provide absolutely convergent asymptotes for the numbers of Fermat and Mersenne primes in the appendices.

The Optimization Analysis of Equipment Maintenance Based on Monte-Carlo Simulation

2011 ◽  
Vol 189-193 ◽  
pp. 424-427 ◽  
Author(s):  
Dai Geng ◽  
Shi Min Zhang ◽  
De Guo Wang ◽  
Jian Gao ◽  
Li Sha Dai
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Distribution Function ◽  
Theoretical Basis ◽  
Economic Benefits ◽  
Maintenance Cost ◽  
Equipment Maintenance ◽  
Maintenance Period ◽  
Optimization Analysis ◽  
Maintenance Decisions

In order to improve the reliability and security in production, effectively checking and maintaining equipment must be put into practice. In this paper, the on-condition maintenance period of the equipment is optimized by Monte-Carlo for the lowest maintenance cost in unit time by expressing the maintenance interval as an exponential function parameterizing Weibull’s distribution function。Finally, the oil centrifugal pump as an example was demonstrated. The results show that our model has the obvious economic benefits. The optimization analysis of equipment maintenance based on Monte-Carlo provides a theoretical basis for optimized detection and maintenance decisions.

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.

Determination of Stoichiometry of GaAs Component in (Gaas)Ge Epitaxially Grown Thin Films by Electron Microprobe X-Ray Analysis

1990 ◽  
Vol 48 (2) ◽  
pp. 264-265
Author(s):  
D. R. Liu ◽  
S. S. Shinozaki ◽  
R. J. Baird
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Compound Semiconductors ◽  
Energy Dispersive Analysis ◽  
X Ray ◽  
Metastable Alloys ◽  
Lower Voltage

The epitaxially grown (GaAs)Ge thin film has been arousing much interest because it is one of metastable alloys of III-V compound semiconductors with germanium and a possible candidate in optoelectronic applications. It is important to be able to accurately determine the composition of the film, particularly whether or not the GaAs component is in stoichiometry, but x-ray energy dispersive analysis (EDS) cannot meet this need. The thickness of the film is usually about 0.5-1.5 μm. If Kα peaks are used for quantification, the accelerating voltage must be more than 10 kV in order for these peaks to be excited. Under this voltage, the generation depth of x-ray photons approaches 1 μm, as evidenced by a Monte Carlo simulation and actual x-ray intensity measurement as discussed below. If a lower voltage is used to reduce the generation depth, their L peaks have to be used. But these L peaks actually are merged as one big hump simply because the atomic numbers of these three elements are relatively small and close together, and the EDS energy resolution is limited.

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