Monte Carlo simulation of stiff systems of catalytic reactions by sampling normally distributed rate probabilities

AIChE Journal ◽  
2009 ◽  
Vol 55 (11) ◽  
pp. 3022-3025 ◽  
Author(s):  
S. Guerrero ◽  
E. E. Wolf
2021 ◽  
Vol 14 (2) ◽  
pp. 183-193
Author(s):  
Abdul Hoyyi ◽  
Abdurakhman Abdurakhman ◽  
Dedi Rosadi

The Option is widely applied in the financial sector.  The Black-Scholes-Merton model is often used in calculating option prices on a stock price movement. The model uses geometric Brownian motion which assumes that the data is normally distributed. However, in reality, stock price movements can cause sharp spikes in data, resulting in nonnormal data distribution. So we need a stock price model that is not normally distributed. One of the fastest growing stock price models today is the  process exponential model. The  process has the ability to model data that has excess kurtosis and a longer tail (heavy tail) compared to the normal distribution. One of the members of the  process is the Variance Gamma (VG) process. The VG process has three parameters which each of them, to control volatility, kurtosis and skewness. In this research, the secondary data samples of options and stocks of two companies were used, namely zoom video communications, Inc. (ZM) and Nokia Corporation (NOK).  The price of call options is determined by using closed form equations and Monte Carlo simulation. The Simulation was carried out for various  values until convergent result was obtained.


Author(s):  
Alessio Abrassi ◽  
Alessandra Cuneo ◽  
David Tucker ◽  
Alberto Traverso

The analysis of different energy systems has shown various sources of variability and uncertainty; hence the necessity to quantify and take these into account is becoming more and more important. In this paper, a steady state, off-design model of a solid oxide fuel cell and turbocharger hybrid system with recuperator has been developed. Performances of such stiff systems are affected significantly by uncertainties both in component performance and operating parameters. This work started with the application of Monte Carlo Simulation method, as a reference sampling method, and then compared it with two different approximated methods. The first one is the Response Sensitivity Analysis, based on Taylor series expansion, and the latter is the Polynomial Chaos, based on a linear combination of different polynomials. These are non-intrusive methods, thus the model is treated as a black-box, with the uncertainty propagation method staying at an upper level. The work is focused on the application on highly non-linear complex systems, such as the hybrid systems, without any optimization process included. Hence, only the uncertainty propagation is considered. Uncertainties in the fuel utilization, ohmic resistance of the fuel cell, and efficiency of the recuperator are taken into account. In particular, their effects on fuel cell lifetime and some simple economic parameters are evaluated. The analysis distinguishes the specific features of each approach and identifies the strongest influencing inputs to the monitored output. Both approximated methods allow an important reduction in the number of evaluations while maintaining a good accuracy compared to Monte Carlo Simulation.


Author(s):  
Ryuichi Shimizu ◽  
Ze-Jun Ding

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.


Author(s):  
D. R. Liu ◽  
S. S. Shinozaki ◽  
R. J. Baird

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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