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We derive a dispersion equation for determining eigenvalues of inhomogeneous quantum wells in terms of spectral parameter power series and apply it for the numerical treatment of eigenvalue problems. The method is algorithmically simple and can be easily implemented using available routines of such environments for scientific computing as MATLAB.
The paper presents the development of a numerical model of the sawing process of AISI 304 thin tubes, which is cut through a circular blade with alternating roughing and finishing teeth. The numerical simulation environment is the three-dimensional FEM software Deform v.10.1. The teeth actual trajectories were determined by a blade kinematics analysis developed in Matlab. Due to the manufacturing rolling steps and subsequent welding stage, the tube material is characterized by a gradient of properties along its thickness. Consequently, a simplified cutting test was set up and carried out in order to identify the values of relevant material parameters to be used in the numerical model. The dedicated test was the Orthogonal Tube Cutting test (OTC), which was performed on an instrumented lathe. The proposed numerical model was validated by comparing numerical results and experimental data obtained from sawing tests carried out on an industrial machine. The following outputs were compared: the cutting force, the chip thickness, and the chip contact area.
In this study, a modified Johnson-Cook (J-C) model and an innovated method to determine (J-C) material parameters are proposed to predict more correctly stress-strain curve for tensile tests in elevated temperatures. A MATLAB tool is used to determine material parameters by fitting a curve to follow Ludwick's hardening law at various elevated temperatures. Those hardening law parameters are then utilized to determine modified (J-C) model material parameters. The modified (J-C) model shows the better prediction compared to the conventional one. As the first verification, an FEM tensile test simulation based on the isotropic hardening model for boron sheet steel at elevated temperatures was carried out via a user-material subroutine, using an explicit finite element code, and compared with the measurements. The temperature decrease of all elements due to the air cooling process was then calculated when considering the modified (J-C) model and coded to VUMAT subroutine for tensile test simulation of cooling process. The modified (J-C) model showed the good agreement between the simulation results and the corresponding experiments. The second investigation was applied for V-bending spring-back prediction of magnesium alloy sheets at elevated temperatures. Here, the combination of proposed J-C model with modified hardening law considering the unusual plastic behaviour for magnesium alloy sheet was adopted for FEM simulation of V-bending spring-back prediction and shown the good comparability with corresponding experiments.
The initial boundary value problem for the neutron transport equation is considered. The first and second orders of accuracy difference schemes for the approximate solution of this problem are presented. In applications, the stability estimates for solutions of difference schemes for the approximate solution of the neutron transport equation are obtained. Numerical techniques are developed and algorithms are tested on an example in MATLAB.
Tsunami is a series of wave trains which travels with high speed on the sea surface. This traveling wave is caused by the displacement of a large volume of water after the occurrence of an underwater earthquake or volcano eruptions. The speed of tsunami decreases when it reaches the sea shore along with the increase of its amplitudes. Two large tsunamis had occurred in the last decades in Indonesia with huge casualties and large damages. Indonesian Tsunami Early Warning System has been installed along the west coast of Sumatra. This early warning system will give about 10-15 minutes to evacuate people from high risk regions to the safe areas. Here in this paper, a mathematical model for Tsunami evacuation is presented with the city of Padang as a study case. In the model, the safe areas are chosen from the existing and selected high rise buildings, low risk region with relatively high altitude and (proposed to be built) a flyover ring road. Each gathering points are located in the radius of approximately 1 km from the ring road. The model is formulated as an optimization problem with the total normalized evacuation time as the objective function. The constraints consist of maximum allowable evacuation time in each route, maximum capacity of each safe area, and the number of people to be evacuated. The optimization problem is solved numerically using linear programming method with Matlab. Numerical results are shown for various evacuation scenarios for the city of Padang.
The physical modeling of uranium isotopes ({sup 235}U, {sup 238}U) separation process by centrifugation of is a key aspect for predicting the nuclear fuel enrichment plant performances under surveillance by the Nuclear Safeguards Authorities. In this paper are illustrated some aspects of the modeling of fast centrifuges for UF{sub 6} gas enrichment and of a typical cascade enrichment plant with the Theoretical Centrifuge and Cascade Simulator (TCCS). The background theory for reproducing the flow field characteristics of a centrifuge is derived from the work of Cohen where the separation parameters are calculated using the solution of a differential enrichment equation. In our case we chose to solve the hydrodynamic equations for the motion of a compressible fluid in a centrifugal field using the Berman - Olander vertical velocity radial distribution and the solution was obtained using the Matlab software tool. The importance of a correct estimation of the centrifuge separation parameters at different flow regimes, lies in the possibility to estimate in a reliable way the U enrichment plant performances, once the separation external parameters are set (feed flow rate and feed, product and tails assays). Using the separation parameters of a single centrifuge allow to determine the performances of an entire cascade and, for this purpose; the software Simulink was used. The outputs of the calculation are the concentrations (assays) and the flow rates of the enriched (product) and depleted (tails) gas mixture. These models represent a valid additional tool, in order to verify the compliance of the U enrichment plant operator declarations with the 'on site' inspectors' measurements.
The paper presents the measurement of optics parameters in Indus-2 synchrotron radiation source, which include betatron tune, beta function, dispersion function, natural chromaticity, corrected chromaticity, central RF frequency, momentum compaction factor, and linear betatron coupling. Two methods were used for beta function measurement; a conventional quadrupole scan method and a method using the fitting of the orbit response matrix. A robust Levenberg-Marquardt algorithm was used for nonlinear least square fitting of the orbit response matrix. In this paper, detailed methods for the parameter measurements are described. The measured results are discussed and compared with the theoretical values obtained using accelerator simulation code Accelerator Toolbox in MATLAB.
In the framework of the French R and D program for the Generation IV reactors and specifically for the sodium cooled fast reactors (SFR), studies are carried out on innovative instrumentation methods in order to improve safety and to simplify the monitoring of fundamental physical parameters during reactor operation. The aim of the present work is to develop an acoustic thermometry method to follow up the sodium temperature at the outlet of subassemblies. The medium is a turbulent flow of liquid sodium at 550 Degree-Sign C with temperature inhomogeneities. To understand the effect of disturbance created by this medium, numerical simulations are proposed. A ray tracing code has been developed with Matlab Copyright-Sign in order to predict acoustic paths in this medium. This complex medium is accurately described by thermal-hydraulic data which are issued from a simulation of a real experiment in Japan. The analysis of these results allows understanding the effects of medium inhomogeneities on the further thermometric acoustic measurement.
A variable-temperature blackbody (VTBB) is used to calibrate an infrared radiation thermometer (pyrometer). The effective emissivity (ε{sub eff}) of a VTBB is dependent on temperature and wavelength other than the geometry of the VTBB. In the calibration process the effective emissivity is often assumed to be constant within the wavelength and temperature range. There are practical situations where the sensitivity of the effective emissivity needs to be known and correction has to be applied. We present a method using a genetic algorithm to investigate the sensitivity of the effective emissivity to wavelength and temperature variation. Two matlab® programs are generated: the first to model the radiance temperature calculation and the second to connect the model to the genetic algorithm optimization toolbox. The effective emissivity parameter is taken as a chromosome and optimized at each wavelength and temperature point. The difference between the contact temperature (reading from a platinum resistance thermometer or liquid in glass thermometer) and radiance temperature (calculated from the ε{sub eff} values) is used as an objective function where merit values are calculated and best fit ε{sub eff} values selected. The best fit ε{sub eff} values obtained as a solution show how sensitive they are to temperature and wavelength parameter variation. Uncertainty components that arise from wavelength and temperature variation are determined based on the sensitivity analysis. Numerical examples are considered for illustration.
In recent years, a variety of film thickness measurement techniques for copper chemical mechanical planarization (CMP) are subsequently proposed. In this paper, the eddy-current technique is used. In the control system of the CMP tool developed in the State Key Laboratory of Tribology, there are in situ module and off-line module for measurement subsystem. The in situ module can get the thickness of copper film on wafer surface in real time, and accurately judge when the CMP process should stop. This is called end-point detection. The off-line module is used for multi-points measurement after CMP process, in order to know the thickness of remained copper film. The whole control system is structured with two levels, and the physical connection between the upper and the lower is achieved by the industrial Ethernet. The process flow includes calibration and measurement, and there are different algorithms for two modules. In the process of software development, C++ is chosen as the programming language, in combination with Qt OpenSource to design two modules’ GUI and OPC technology to implement the communication between the two levels. In addition, the drawing function is developed relying on Matlab, enriching the software functions of the off-line module. The result shows that the control system is running stably after repeated tests and practical operations for a long time.
In this paper we explore a straightforward procedure to price derivatives by using the Monte Carlo approach when the underlying process is a jump-diffusion. We have compared the Black-Scholes model with one of its extensions that is the Merton model. The latter model is better in capturing the market’s phenomena and is comparative to stochastic volatility models in terms of pricing accuracy. We have presented simulations of asset paths and pricing of barrier options for both Geometric Brownian motion and exponential Levy processes as it is the concrete case of the Merton model. A desired level of accuracy is obtained with simple computer operations in MATLAB for efficient computational time.
Grating-based X-ray and neutron interferometry tomography using phase-stepping methods generates large data sets. An improved algorithm is presented for solving for the parameters to calculate transmissions, differential phase contrast, and dark-field images. The method takes advantage of the vectorization inherent in high-level languages such as Mathematica and MATLAB and can solve a 16 × 1k × 1k data set in less than a second. In addition, the algorithm can function with partial data sets. This is demonstrated with processing of a 16-step grating data set with partial use of the original data chosen without any restriction. Also, we have calculated the reduced chi-square for the fit and notice the effect of grating support structural elements upon the differential phase contrast image and have explored expanded basis set representations to mitigate the impact.
A new idea to calculate ultracold neutron (UCN) production by using Monte Carlo simulation method to calculate the cold neutron (CN) flux and an analytical approach to calculate the UCN production from the simulated CN flux was given. A super-thermal source (UCN source) was modeled based on an arrangement of D{sub 2}O and solid D{sub 2} (sD{sub 2}). The D{sub 2}O was investigated as the neutron moderator, and sD{sub 2} as the converter. In order to determine the required parameters, a two-dimensional (2D) neutron balance equation written in Matlab was combined with the MCNPX simulation code. The 2D neutron-transport equation in cylindrical (ρ − z) geometry was considered for 330 neutron energy groups in the sD{sub 2}. The 2D balance equation for UCN and CN was solved using simulated CN flux as boundary value. The UCN source dimensions were calculated for the development of the next UCN source. In the optimal condition, the UCN flux and the UCN production rate (averaged over the sD{sub 2} volume) equal to 6.79 × 10{sup 6} cm{sup −2}s{sup −1} and 2.20 ×10{sup 5} cm{sup −3}s{sup −1}, respectively.
A test of lithium wettability was performed in high vacuum (< 3 × 10{sup −4} Pa). High magnification images of Li droplets on stainless steel substrates were produced and processed using the MATLAB{sup ®} program to obtain clear image edge points. In contrast to the more standard “θ/2” or polynomial fitting methods, ellipse fitting of the complete Li droplet shape resulted in reliable contact angle measurements over a wide range of contact angles. Using the ellipse fitting method, it was observed that the contact angle of a liquid Li droplet on a stainless steel substrate gradually decreased with increasing substrate temperature. The critical wetting temperature of liquid Li on stainless steel was observed to be about 290 °C.
This work evaluates the efficiency calibrating of HpGe detector coupled with Canberra GC3018 with Genie 2000 software and Ortec GEM25-76-XLB-C with Gamma Vision software; available at Neutron activation analysis laboratory in Malaysian Nuclear Agency (NM). The efficiency calibration curve was constructed from measurement of an IAEA, standard gamma–point sources set composed by {sup 214}Am, {sup 57}Co, {sup 133}Ba, {sup 152}Eu, {sup 137}Cs and {sup 60}Co. The efficiency calibrations were performed for three different geometries: 5, 10 and 15 cm distances from the end cap detector. The polynomial parameters functions were simulated through a computer program, MATLAB in order to find an accurate fit to the experimental data points. The efficiency equation was established from the known fitted parameters which allow for the efficiency evaluation at particular energy of interest. The study shows that significant deviations in the efficiency, depending on the source-detector distance and photon energy.
An industrial grade digital radiation survey meter device is currently being developed at Malaysian Nuclear Agency. This device used a cylindrical type Geiger Mueller (GM) which acts as a detector. GM detector operates at relatively high direct current voltages depend on the type of GM tube. This thin/thick walled cylindrical type of GM tube operates at 450-650 volts range. Proper value and stability performance of high voltage are important parameters to ensure that this device give a reliable radiation dose measurement. This paper will present an assessment of the stability and performance of the high voltage supply for radiation detector. The assessment is performed using System Identification tools box in MATLAB and mathematical statistics.
In this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo (KMC). Sensitivity analysis for stochastic systems is typically based on approximating continuous derivatives with respect to model parameters by the mean value of samples from a finite difference scheme. Instead of using independent samples the proposed algorithm reduces the variance of the estimator by developing a strongly correlated-“coupled”- stochastic process for both the perturbed and unperturbed stochastic processes, defined in a common state space. The novelty of our construction is that the new coupled process depends on the targeted observables, e.g., coverage, Hamiltonian, spatial correlations, surface roughness, etc., hence we refer to the proposed method as goal-oriented sensitivity analysis. In particular, the rates of the coupled Continuous Time Markov Chain are obtained as solutions to a goal-oriented optimization problem, depending on the observable of interest, by considering the minimization functional of the corresponding variance. We show that this functional can be used as a diagnostic tool for the design and evaluation of different classes of couplings. Furthermore, the resulting KMC sensitivity algorithm has an easy implementation that is based on the Bortz–Kalos–Lebowitz algorithm's philosophy, where events are divided in classes depending on level sets of the observable of interest. Finally, we demonstrate in several examples including adsorption, desorption, and diffusion Kinetic Monte Carlo that for the same confidence interval and observable, the proposed goal-oriented algorithm can be two orders of magnitude faster than existing coupling algorithms for spatial KMC such as the Common Random Number approach. We also provide a complete implementation of the proposed sensitivity analysis algorithms, including various spatial KMC examples, in a supplementary MATLAB source code.
Phase diagram or phase envelope is a relation between temperature and pressure that shows the condition of equilibria between the different phases of chemical compounds, mixture of compounds, and solutions. Phase diagram is an important issue in chemical thermodynamics and hydrocarbon reservoir. It is very useful for process simulation, hydrocarbon reactor design, and petroleum engineering studies. It is constructed from the bubble line, dew line, and critical point. Bubble line and dew line are composed of bubble points and dew points, respectively. Bubble point is the first point at which the gas is formed when a liquid is heated. Meanwhile, dew point is the first point where the liquid is formed when the gas is cooled. Critical point is the point where all of the properties of gases and liquids are equal, such as temperature, pressure, amount of substance, and others. Critical point is very useful in fuel processing and dissolution of certain chemicals. Here in this paper, we will show the critical point analytically. Then, it will be compared with numerical calculations of Peng-Robinson equation by using Newton-Raphson method. As case studies, several hydrocarbon mixtures are simulated using by Matlab.