Search results for: Numerical methods

Authors: R. Alipour, F.Najarian

Abstract:

Because of high ductility, aluminum alloys, have been widely used as an important base of metal forming industries. But the main week point of these alloys is their low strength so in forming them with conventional methods like deep drawing, hydro forming, etc have been always faced with problems like fracture during of forming process. Because of this, recently using of explosive forming method for forming of these plates has been recommended. In this paper free explosive forming of A2024 aluminum alloy is numerically simulated and during it, explosion wave propagation process is studied. Consequences of this simulation can be effective in prediction of quality of production. These consequences are compared with an experimental test and show the superiority of this method to similar methods like hydro forming and deep drawing.

Keywords: Free explosive forming, CEL, Johnson cook.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2313

Authors: Avinash Chandra, R. P. Chhabra

Abstract:

Natural convection heat transfer from a heated horizontal semi-circular cylinder (flat surface upward) has been investigated for the following ranges of conditions; Grashof number, and Prandtl number. The governing partial differential equations (continuity, Navier-Stokes and energy equations) have been solved numerically using a finite volume formulation. In addition, the role of the type of the thermal boundary condition imposed at cylinder surface, namely, constant wall temperature (CWT) and constant heat flux (CHF) are explored. Natural convection heat transfer from a heated horizontal semi-circular cylinder (flat surface upward) has been investigated for the following ranges of conditions; Grashof number, and Prandtl number, . The governing partial differential equations (continuity, Navier-Stokes and energy equations) have been solved numerically using a finite volume formulation. In addition, the role of the type of the thermal boundary condition imposed at cylinder surface, namely, constant wall temperature (CWT) and constant heat flux (CHF) are explored. The resulting flow and temperature fields are visualized in terms of the streamline and isotherm patterns in the proximity of the cylinder. The flow remains attached to the cylinder surface over the range of conditions spanned here except that for and ; at these conditions, a separated flow region is observed when the condition of the constant wall temperature is prescribed on the surface of the cylinder. The heat transfer characteristics are analyzed in terms of the local and average Nusselt numbers. The maximum value of the local Nusselt number always occurs at the corner points whereas it is found to be minimum at the rear stagnation point on the flat surface. Overall, the average Nusselt number increases with Grashof number and/ or Prandtl number in accordance with the scaling considerations. The numerical results are used to develop simple correlations as functions of Grashof and Prandtl number thereby enabling the interpolation of the present numerical results for the intermediate values of the Prandtl or Grashof numbers for both thermal boundary conditions.

Keywords: Constant heat flux, Constant surface temperature, Grashof number, natural convection, Prandtl number, Semi-circular cylinder

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3420

Authors: Qingqing Wang, Shouming Zhong

Abstract:

Utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to analyze the global asymptotic stability for delayed neural networks (DNNs),a new sufficient criterion ensuring the global stability of DNNs is obtained.The criteria are formulated in terms of a set of linear matrix inequalities,which can be checked efficiently by use of some standard numercial packages.In order to show the stability condition in this paper gives much less conservative results than those in the literature,numerical examples are considered.

Keywords: Neural networks, Globally asymptotic stability , LMI approach , IIA approach , Time-varying delay.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1947

Authors: A. K. Al-Othman, K. M. EL-Nagger

Abstract:

Direct search methods are evolutionary algorithms used to solve optimization problems. (DS) methods do not require any information about the gradient of the objective function at hand while searching for an optimum solution. One of such methods is Pattern Search (PS) algorithm. This paper presents a new approach based on a constrained pattern search algorithm to solve a security constrained power system economic dispatch problem (SCED). Operation of power systems demands a high degree of security to keep the system satisfactorily operating when subjected to disturbances, while and at the same time it is required to pay attention to the economic aspects. Pattern recognition technique is used first to assess dynamic security. Linear classifiers that determine the stability of electric power system are presented and added to other system stability and operational constraints. The problem is formulated as a constrained optimization problem in a way that insures a secure-economic system operation. Pattern search method is then applied to solve the constrained optimization formulation. In particular, the method is tested using one system. Simulation results of the proposed approach are compared with those reported in literature. The outcome is very encouraging and proves that pattern search (PS) is very applicable for solving security constrained power system economic dispatch problem (SCED).

Keywords: Security Constrained Economic Dispatch, Direct Search method, optimization.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2213

Authors: Anuj K. Sharma, Amit Sharma, Kulbhushan Agnihotri

Abstract:

In this work, we propose and analyze a model of Phytoplankton-Zooplankton interaction with harvesting considering that some species are exploited commercially for food. Criteria for local stability, instability and global stability are derived and some threshold harvesting levels are explored to maintain the population at an appropriate equilibrium level even if the species are exploited continuously.Further,biological and bionomic equilibria of the system are obtained and an optimal harvesting policy is also analysed using the Pantryagin’s Maximum Principle.Finally analytical findings are also supported by some numerical simulations.

Keywords: Phytoplankton-Zooplankton, Global stability, Bionomic Equilibrium, Pontrying-Maximum Principal.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2278

Authors: Ping Liu, Yongkun Li

Abstract:

This paper is concerned with the permanence and extinction problem of enterprises cluster constituted by m satellite enterprises and a dominant enterprise. We present the model involving impulsive effect based on ecology theory, which effectively describe the competition and cooperation of enterprises cluster in real economic environment. Applying comparison theorem of impulsive differential equation, we establish sufficient conditions which ultimately affect the fate of enterprises: permanence, extinction, and co-existence. Finally, we present numerical examples to explain the economical significance of mathematical results.

Keywords: Enterprise cluster, permanence, extinction, impulsive, comparison theorem.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1465

Authors: Bang-Shiuh Chen, Lien-Wen Chen

Abstract:

We have devised a thermal carpet cloak theoretically and implemented in silicon using layered metamaterial. The layered metamaterial is composed of single crystalline silicon and its phononic crystal. The design is based on a coordinate transformation. We demonstrate the result with numerical simulation. Great cloaking performance is achieved as a thermal insulator is well hidden under the thermal carpet cloak. We also show that the thermal carpet cloak can even the temperature on irregular surface. Using thermal carpet cloak to manipulate the heat conduction is effective because of its low complexity.

Keywords: Metamaterial, heat conduction, cloaking, phononic crystal.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2270

Authors: Miloud Frikel , Boubekeur Targui, Francois Hamon, Mohammed M'SAAD

Abstract:

In this paper we propose an enhanced equalization technique for multi-carrier code division multiple access (MC-CDMA). This method is based on the control of Equal Gain Combining (EGC) technique. Indeed, we introduce a new level changer to the EGC equalizer in order to adapt the equalization parameters to the channel coefficients. The optimal equalization level is, first, determined by channel training. The new approach reduces drastically the mutliuser interferences caused by interferes, without increasing the noise power. To compare the performances of the proposed equalizer, the theoretical analysis and numerical performances are given.

Keywords: MC-CDMA, Equalization, EGC, Single User Detection.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1413

Authors: Othman Maklouf, Abdurazag Ghila, Ahmed Abdulla

Abstract:

This paper introduces a low cost INS/GPS algorithm for land vehicle navigation application. The data fusion process is done with an extended Kalman filter in cascade configuration mode. In order to perform numerical simulations, MATLAB software has been developed. Loosely coupled configuration is considered. The results obtained in this work demonstrate that a low-cost INS/GPS navigation system is partially capable of meeting the performance requirements for land vehicle navigation. The relative effectiveness of the kalman filter implementation in integrated GPS/INS navigation algorithm is highlighted. The paper also provides experimental results; field test using a car is carried out.

Keywords: GPS, INS, IMU, Kalman filter.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3856

Authors: Somkid Amornsamankul, Benchawan Wiwatanapataphee, Yong Hong Wu, Yongwimon Lenbury

Abstract:

In this paper, we study the pulsatile flow of blood through stenotic arteries. The inner layer of arterial walls is modeled as a porous medium and human blood is assumed as an incompressible fluid. A numerical algorithm based on the finite element method is developed to simulate the blood flow through both the lumen region and the porous wall. The algorithm is then applied to study the flow behaviour and to investigate the significance of the non-Newtonian effect.

Keywords: Stenotic artery, finite element, porous arterial wall, non-Newtonian model.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2234

Authors: Mohamed A. Khlifi, Badr M. Alshammari

Abstract:

This paper discusses the general methods to saturation in the steady-state, two axis (d & q) frame models of synchronous machines. In particular, the important role of the magnetic coupling between the d-q axes (cross-magnetizing phenomenon), is demonstrated. For that purpose, distinct methods of saturation modeling of dumper synchronous machine with cross-saturation are identified, and detailed models synthesis in d-q axes. A number of models are given in the final developed form. The procedure and the novel models are verified by a critical application to prove the validity of the method and the equivalence between all developed models is reported. Advantages of some of the models over the existing ones and their applicability are discussed.

Keywords: Cross-magnetizing, models synthesis, synchronous machine, saturated modeling, state-space vectors.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2254

Authors: M. Caramihai, Irina Severin, H. Balan, A. Blidaru, V. Balanica

Abstract:

Accurate assessment of the primary tumor response to treatment is important in the management of breast cancer. This paper introduces a new set of treatment evaluation indicators for breast cancer cases based on the computational process of three known metrics, the Euclidian, Hamming and Levenshtein distances. The distance principals are applied to pairs of mammograms and/or echograms, recorded before and after treatment, determining a reference point in judging the evolution amount of the studied carcinoma. The obtained numerical results are indeed very transparent and indicate not only the evolution or the involution of the tumor under treatment, but also a quantitative measurement of the benefit in using the selected method of treatment.

Keywords: Breast cancer, Distance metrics, Cancer treatment evaluation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1565

Authors: Giovanni Incerti

Abstract:

The motion planning procedure described in this paper has been developed in order to eliminate or reduce the residual vibrations of electromechanical positioning systems, without augmenting the motion time (usually imposed by production requirements), nor introducing overtime for vibration damping. The proposed technique is based on a suitable choice of the motion law assigned to the servomotor that drives the mechanism. The reference profile is defined by a Bezier curve, whose shape can be easily changed by modifying some numerical parameters. By means of an optimization technique these parameters can be modified without altering the continuity conditions imposed on the displacement and on its time derivatives at the initial and final time instants.

Keywords: Servomechanism, residual vibrations, motion optimization.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1418

Authors: Zarina Bibi Ibrahim, Mohamed Suleiman, Khairil Iskandar Othman

Abstract:

In this paper, a direct method based on variable step size Block Backward Differentiation Formula which is referred as BBDF2 for solving second order Ordinary Differential Equations (ODEs) is developed. The advantages of the BBDF2 method over the corresponding sequential variable step variable order Backward Differentiation Formula (BDFVS) when used to solve the same problem as a first order system are pointed out. Numerical results are given to validate the method.

Keywords: Backward Differentiation Formula, block, secondorder.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2033

Authors: Nafaâ Nacereddine, Latifa Hamami, Djemel Ziou

Abstract:

In non destructive testing by radiography, a perfect knowledge of the weld defect shape is an essential step to appreciate the quality of the weld and make decision on its acceptability or rejection. Because of the complex nature of the considered images, and in order that the detected defect region represents the most accurately possible the real defect, the choice of thresholding methods must be done judiciously. In this paper, performance criteria are used to conduct a comparative study of thresholding methods based on gray level histogram, 2-D histogram and locally adaptive approach for weld defect extraction in radiographic images.

Keywords: 1D and 2D histogram, locally adaptive approach, performance criteria, radiographic image, thresholding, weld defect.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2349

Authors: Mohd Amaluddin Yusoff

Abstract:

In this paper, we consider the design of pulse shaping filter using orthogonal Hermite-Rodriguez basis functions. The pulse shaping filter design problem has been formulated and solved as a quadratic programming problem with linear inequality constraints. Compared with the existing approaches reported in the literature, the use of Hermite-Rodriguez functions offers an effective alternative to solve the constrained filter synthesis problem. This is demonstrated through a numerical example which is concerned with the design of an equalization filter for a digital transmission channel.

Keywords: channel equalization filter, Hermite-Rodriguez, pulseshaping filter, quadratic programming.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1952

Authors: M. Pourahmadi

Abstract:

The performance of time-reversal MUSIC algorithm will be dramatically degrades in presence of strong noise and multiple scattering (i.e. when scatterers are close to each other). This is due to error in determining the number of scatterers. The present paper provides a new approach to alleviate such a problem using an information theoretic criterion referred as minimum description length (MDL). The merits of the novel approach are confirmed by the numerical examples. The results indicate the time-reversal MUSIC yields accurate estimate of the target locations with considerable noise and multiple scattering in the received signals.

Keywords: Microwave imaging, Time reversal, MUSIC algorithm, Minimum Description Length (MDL).

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1730

Authors: Youngpo Lee, Seokho Yoon

Abstract:

In this paper, we propose a novel frequency offset estimation scheme for orthogonal frequency division multiplexing (OFDM) systems. By correlating the OFDM signals within the coherence phase bandwidth and employing a threshold in the frequency offset estimation process, the proposed scheme is not only robust to the timing offset but also has a reduced complexity compared with that of the conventional scheme. Moreover, a timing offset estimation scheme is also proposed as the next stage of the proposed frequency offset estimation. Numerical results show that the proposed scheme can estimate frequency offset with lower computational complexity and does not require additional memory while maintaining the same level of estimation performance.

Keywords: OFDM, frequency offset estimation, threshold.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2221

Authors: L. Zehtaban, D. Roller

Abstract:

Apart from geometry, functionality is one of the most significant hallmarks of a product. The functionality of a product can be considered as the fundamental justification for a product existence. Therefore a functional analysis including a complete and reliable descriptor has a high potential to improve product development process in various fields especially in knowledge-based design. One of the important applications of the functional analysis and indexing is in retrieval and design reuse concept. More than 75% of design activity for a new product development contains reusing earlier and existing design know-how. Thus, analysis and categorization of product functions concluded by functional indexing, influences directly in design optimization. This paper elucidates and evaluates major classes for functional analysis by discussing their major methods. Moreover it is finalized by presenting a noble hybrid approach for functional analysis.

Keywords: Functional analysis, design reuse, functionalindexing and representation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5185

Authors: John P. O’Sullivan, Thomas M. P. Ratouis, Michael J. O’Sullivan

Abstract:

As the use of geothermal energy grows internationally more effort is required to monitor and protect areas with rare and important geothermal surface features. A number of approaches are presented for developing and calibrating numerical geothermal reservoir models that are capable of accurately representing geothermal surface features. The approaches are discussed in the context of cases studies of the Rotorua geothermal system and the Orakei-korako geothermal system, both of which contain important surface features. The results show that models are able to match the available field data accurately and hence can be used as valuable tools for predicting the future response of the systems to changes in use.

Keywords: Geothermal reservoir models, surface features, monitoring, TOUGH2.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2077

Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

Abstract:

Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, Step method, delay differential equation, simulation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 750

Authors: M. Sinecen, M. Makinacı

Abstract:

The purpose of this paper is to assess the value of neural networks for classification of cancer and noncancer prostate cells. Gauss Markov Random Fields, Fourier entropy and wavelet average deviation features are calculated from 80 noncancer and 80 cancer prostate cell nuclei. For classification, artificial neural network techniques which are multilayer perceptron, radial basis function and learning vector quantization are used. Two methods are utilized for multilayer perceptron. First method has single hidden layer and between 3-15 nodes, second method has two hidden layer and each layer has between 3-15 nodes. Overall classification rate of 86.88% is achieved.

Keywords: Artificial neural networks, texture classification, cancer diagnosis.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1600

Authors: Arash Mir Abdolah Lavasani, Hamidreza Bayat

Abstract:

In this paper flow around two cam shaped cylinders had been studied numerically. The equivalent diameter of cylinders is 27.6 mm. The space between center to center of two cam shaped cylinders is define as longitudinal pitch ratio and it varies in range of 2 varies in range of 50 both cylinders depends on pitch ratio. However drag coefficient of downstream cylinder is more dependent on the pitch ratio.

Keywords: Cam shaped, tandem cylinders, numerical, drag coefficient.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1647

Authors: Junghan Kim, Wonkyu Chung, Sunyoung Bu, Philsu Kim

Abstract:

In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower degree polynomial. The constructed algorithm controls both the error and the time step size simultaneously and further the errors at each integration step are embedded in the algorithm itself, which provides the efficiency of the computational cost. For the assessment of the effectiveness, numerical results obtained by the proposed method and the Radau IIA are presented and compared.

Keywords: Generalized Chebyshev Collocation method, Generalized Chebyshev Polynomial, Initial value problem.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2646

Authors: Klio Monokrousou, Maria Giannopoulou

Abstract:

Urban areas, as they have been developed and operate today, are areas of accumulation of a significant amount of people and a large number of activities that generate desires and reasons for traveling. The territorial expansion of the cities as well as the need to preserve the importance of the central city areas lead to the continuous increase of transportation needs which in the limited urban space results in creating serious traffic and operational problems. The modern perception of urban planning is directed towards more holistic approaches and integrated policies that make it economically competitive, socially just and more environmentally friendly. Over the last 25 years, the goal of sustainable transport development has been central to the agenda of any plan or policy for the city. The modern planning of urban space takes into account the economic and social aspects of the city and the importance of the environment to sustainable urban development. In this context, the European Union promotes direct or indirect related interventions according to the cohesion and environmental policies; many countries even had the chance to actually test them. This paper explores the methods and processes that have been developed towards this direction and presents a review and systematic presentation of this work. The ultimate purpose of this research is to effectively use this review to create a decision making methodological framework which can be the basis of a useful operational tool for sustainable urban planning.

Keywords: Sustainable urban development, urban mobility, urban regeneration methods.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3509

Authors: Xueting Liu, Daojin Song, Chuandai Dong, Hongkui Li

Abstract:

From a set of shifted, blurred, and decimated image , super-resolution image reconstruction can get a high-resolution image. So it has become an active research branch in the field of image restoration. In general, super-resolution image restoration is an ill-posed problem. Prior knowledge about the image can be combined to make the problem well-posed, which contributes to some regularization methods. In the regularization methods at present, however, regularization parameter was selected by experience in some cases and other techniques have too heavy computation cost for computing the parameter. In this paper, we construct a new super-resolution algorithm by transforming the solving of the System stem Є=An into the solving of the equations X+A*X-1A=I , and propose an inverse iterative method.

Keywords: High-resolution MAP image, Reconstruction, Image interpolation, Motion Estimation, Hermitian positive definite solutions.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2161

Authors: Leon Pan

Abstract:

The first programming course within post-secondary education has long been recognized as a challenging endeavor for both educators and students alike. Historically, these courses have exhibited high failure rates and a notable number of dropouts. Instructors often lament students' lack of effort on their coursework, and students often express frustration that the teaching methods employed are not effective. Drawing inspiration from the successful principles of Extreme Programming, this study introduces an approach—the Extremes-based teaching model—aimed at enhancing the teaching of introductory programming courses. To empirically determine the effectiveness of the model, a comparison was made between a section taught using the extreme-based model and another utilizing traditional teaching methods. Notably, the extreme-based teaching class required students to work collaboratively on projects, while also demanding continuous assessment and performance enhancement within groups. This paper details the application of the extreme-based model within the post-secondary online classroom context and presents the compelling results that emphasize its effectiveness in advancing the teaching and learning experiences. The extreme-based model led to a significant increase of 13.46 points in the weighted total average and a commendable 10% reduction in the failure rate.

Keywords: Extreme-based teaching model, innovative pedagogical methods, project-based learning, team-based learning.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 147

Authors: E. Khorram, S.M. Mirzababaei

Abstract:

Everyday the usages of the Internet increase and simply a world of the data become accessible. Network providers do not want to let the provided services to be used in harmful or terrorist affairs, so they used a variety of methods to protect the special regions from the harmful data. One of the most important methods is supposed to be the firewall. Firewall stops the transfer of such packets through several ways, but in some cases they do not use firewall because of its blind packet stopping, high process power needed and expensive prices. Here we have proposed a method to find a discriminate function to distinguish between usual packets and harmful ones by the statistical processing on the network router logs. So an administrator can alarm to the user. This method is very fast and can be used simply in adjacent with the Internet routers.

Keywords: Data Mining, Firewall, Optimization, Packetclassification, Statistical Pattern Recognition.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1416

Authors: Seul-Kee Kim, Chi-Seung Lee, Myung-Hyun Kim, Jae-Myung Lee

Abstract:

In this study, the hydrogen transport phenomenon was numerically evaluated by using hydrogen-enhanced localized plasticity (HELP) mechanisms. Two dominant governing equations, namely, the hydrogen transport model and the elasto-plastic model, were introduced. In addition, the implicitly formulated equations of the governing equations were implemented into ABAQUS UMAT user-defined subroutines. The simulation results were compared to published results to validate the proposed method.

Keywords: Hydrogen-enhanced localized plasticity (HELP), Hydrogen embrittlement, Hydrogen transport analysis, ABAQUS UMAT, Finite element method (FEM).

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2432

Authors: Edward Aris D. Fajardo, Hamdi Muhyuddin D. Barra

Abstract:

This study employs the use of the fourth order Numerov scheme to determine the eigenstates and eigenvalues of particles, electrons in particular, in single and double delta function potentials. For the single delta potential, it is found that the eigenstates could only be attained by using specific potential depths. The depth of the delta potential well has a value that varies depending on the delta strength. These depths are used for each well on the double delta function potential and the eigenvalues are determined. There are two bound states found in the computation, one with a symmetric eigenstate and another one which is antisymmetric.

Keywords: Double Delta Potential, Eigenstates, Eigenvalue, Numerov Method, Single Delta Potential

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3067