Search results for: diffusion equations

Authors: H. D. Ibrahim, H. C. Chinwenyi, T. Danjuma

Abstract:

An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.

Keywords: Option price valuation, Partial Differential Equations, Black-Scholes PDEs, Ito process.

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Authors: M. H. Kargarnovin, K. Momeni

Abstract:

The study of the stress distribution on a hollow cylindrical fiber placed in a composite material is considered in this work and an analytical solution for this stress distribution has been constructed. Finally some parameters such as fiber-s thickness and fiber-s length are considered and their effects on the distribution of stress have been investigated. For finding the governing relations, continuity equations for the axisymmetric problem in cylindrical coordinate (r,o,z) are considered. Then by assuming some conditions and solving the governing equations and applying the boundary conditions, an equation relates the stress applied to the representative volume element with the stress distribution on the fiber has been found.

Keywords: Axial Loading, Composite, Hollow CylindricalFiber, Stress Distribution.

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Authors: Magdy G. Asaad

Abstract:

The objective of this paper is to use the Pfaffian technique to construct different classes of exact Pfaffian solutions and N-soliton solutions to some of the generalized integrable nonlinear partial differential equations in (3+1) dimensions. In this paper, I will show that the Pfaffian solutions to the nonlinear PDEs are nothing but Pfaffian identities. Solitons are among the most beneficial solutions for science and technology, from ocean waves to transmission of information through optical fibers or energy transport along protein molecules. The existence of multi-solitons, especially three-soliton solutions, is essential for information technology: it makes possible undisturbed simultaneous propagation of many pulses in both directions.

Keywords: Bilinear operator, G-BKP equation, Integrable nonlinear PDEs, Jimbo-Miwa equation, Ma-Fan equation, N-soliton solutions, Pfaffian solutions.

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Authors: Arunesh Chandra, Pankaj Chandna, Surinder Deswal, Rajesh Kumar Mishra, Rajender Kumar

Abstract:

The arm length, hand length, hand breadth and middle finger length of 1540 right-handed industrial workers of Haryana state was used to assess the relationship between the upper limb dimensions and stature. Initially, the data were analyzed using basic univariate analysis and independent t-tests; then simple and multiple linear regression models were used to estimate stature using SPSS (version 17). There was a positive correlation between upper limb measurements (hand length, hand breadth, arm length and middle finger length) and stature (p < 0.01), which was highest for hand length. The accuracy of stature prediction ranged from ± 54.897 mm to ± 58.307 mm. The use of multiple regression equations gave better results than simple regression equations. This study provides new forensic standards for stature estimation from the upper limb measurements of male industrial workers of Haryana (India). The results of this research indicate that stature can be determined using hand dimensions with accuracy, when only upper limb is available due to any reasons likewise explosions, train/plane crashes, mutilated bodies, etc. The regression formula derived in this study will be useful for anatomists, archaeologists, anthropologists, design engineers and forensic scientists for fairly prediction of stature using regression equations.

Keywords: Anthropometric dimensions, Forensic identification, Industrial workers, Stature prediction.

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Authors: K. Westmoreland Bowers, Matthew W. Ragas, Jeffrey C. Neely

Abstract:

The purpose of this study was to assess the value of Second Life among post-secondary instructors with experience using Second Life as an educational tool. Using Everett Rogers-s diffusion of innovations theory, survey respondents (N = 162), were divided into three adopter categories: innovators, early adopters and the early majority. Respondents were from 15 countries and 25 academic disciplines, indicating the considerable potential this innovation has to be adopted across many different borders and in many areas of academe. Nearly 94% of respondents said they plan to use Second Life again as an educational tool. However, no significant differences were found in instructors- levels of satisfaction with Second Life as an educational tool or their perceived effect on student learning across adopter categories. On the other hand, instructors who conducted class fully in Second Life were significantly more satisfied than those who used Second Life as only a small supplement to a real-world class. Overall, personal interest factors, rather than interpersonal communication factors, most influenced respondents- decision to adopt Second Life as an educational tool. In light of these findings, theoretical implications are discussed and practical suggestions are provided.

Keywords: Second Life, Virtual Worlds, Educational Technology, Diffusion of Innovations

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Authors: Arun Goel

Abstract:

The present paper attempts to investigate the prediction of air entrainment rate and aeration efficiency of a free overfall jets issuing from a triangular sharp crested weir by using regression based modelling. The empirical equations, Support vector machine (polynomial and radial basis function) models and the linear regression techniques were applied on the triangular sharp crested weirs relating the air entrainment rate and the aeration efficiency to the input parameters namely drop height, discharge, and vertex angle. It was observed that there exists a good agreement between the measured values and the values obtained using empirical equations, Support vector machine (Polynomial and rbf) models and the linear regression techniques. The test results demonstrated that the SVM based (Poly & rbf) model also provided acceptable prediction of the measured values with reasonable accuracy along with empirical equations and linear regression techniques in modelling the air entrainment rate and the aeration efficiency of a free overfall jets issuing from triangular sharp crested weir. Further sensitivity analysis has also been performed to study the impact of input parameter on the output in terms of air entrainment rate and aeration efficiency.

Keywords: Air entrainment rate, dissolved oxygen, regression, SVM, weir.

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Authors: Jamal A. Gledan, Othman A. Azzeidani

Abstract:

During the last decade, Libya established a new Geodetic Datum called Libyan Geodetic Datum 2006 (LGD 2006) by using GPS, whereas the ground traversing method was used to establish the last Libyan datum which was called the Europe Libyan Datum 79 (ELD79). The current research paper introduces ELD79 to LGD2006 coordinate transformation technique, the accurate comparison of transformation between multiple regression equations and the three – parameters model (Bursa-Wolf). The results had been obtained show that the overall accuracy of stepwise multi regression equations is better than that can be determined by using Bursa-Wolf transformation model.

Keywords: Geodetic datum, horizontal control points, traditional similarity transformation model, unconventional transformation techniques.

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Authors: N. Outili, A-H. Meniai

Abstract:

Modeling transfer phenomena in several chemical engineering operations leads to the resolution of partial differential equations systems. According to the complexity of the operations mechanisms, the equations present a nonlinear form and analytical solution became difficult, we have then to use numerical methods which are based on approximations in order to transform a differential system to an algebraic one.Finite element method is one of numerical methods which can be used to obtain an accurate solution in many complex cases of chemical engineering.The packed columns find a large application like contactor for liquid-liquid systems such solvent extraction. In the literature, the modeling of this type of equipment received less attention in comparison with the plate columns.A mathematical bidimensionnal model with radial and axial dispersion, simulating packed tower extraction behavior was developed and a partial differential equation was solved using the finite element method by adopting the Galerkine model. We developed a Mathcad program, which can be used for a similar equations and concentration profiles are obtained along the column. The influence of radial dispersion was prooved and it can-t be neglected, the results were compared with experimental concentration at the top of the column in the extraction system: acetone/toluene/water.

Keywords: finite element method, Galerkine method, liquidliquid extraction modelling, packed column simulation, two dimensional model

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Authors: Edward J. Kansa, Pavel Holoborodko

Abstract:

Continuously differentiable radial basis functions (RBFs) are meshfree, converge faster as the dimensionality increases, and is theoretically spectrally convergent. When implemented on current single and double precision computers, such RBFs can suffer from ill-conditioning because the systems of equations needed to be solved to find the expansion coefficients are full. However, the Advanpix extended precision software package allows computer mathematics to resemble asymptotically ideal Platonic mathematics. Additionally, full systems with extended precision execute faster graphical processors units and field-programmable gate arrays because no branching is needed. Sparse equation systems are fast for iterative solvers in a very limited number of cases.

Keywords: Meshless spectrally convergent, partial differential equations, extended arithmetic precision, no branching.

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Authors: S. Grishin

Abstract:

This article is dedicated to development of mathematical models for determining the dynamics of concentration of hazardous substances in urban turbulent atmosphere. Development of the mathematical models implied taking into account the time-space variability of the fields of meteorological items and such turbulent atmosphere data as vortex nature, nonlinear nature, dissipativity and diffusivity. Knowing the turbulent airflow velocity is not assumed when developing the model. However, a simplified model implies that the turbulent and molecular diffusion ratio is a piecewise constant function that changes depending on vertical distance from the earth surface. Thereby an important assumption of vertical stratification of urban air due to atmospheric accumulation of hazardous substances emitted by motor vehicles is introduced into the mathematical model. The suggested simplified non-linear mathematical model of determining the sought exhaust concentration at a priori unknown turbulent flow velocity through non-degenerate transformation is reduced to the model which is subsequently solved analytically.

Keywords: Urban ecology, time-dependent mathematical model, exhaust concentration, turbulent and molecular diffusion, airflow velocity.

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Authors: Yiqin Lin, Liang Bao, Yimin Wei

Abstract:

In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.

Keywords: Arnoldi process, Krylov subspace, Iterative method, Sylvester equation, Dissipative matrix.

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Authors: Ramandeep Behl, S. S. Motsa

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The main focus of this manuscript is to provide a highly efficient two-point sixth-order family of super-Halley type methods that do not require any second-order derivative evaluation for obtaining simple roots of nonlinear equations, numerically. Each member of the proposed family requires two evaluations of the given function and two evaluations of the first-order derivative per iteration. By using Mathematica-9 with its high precision compatibility, a variety of concrete numerical experiments and relevant results are extensively treated to confirm t he t heoretical d evelopment. From their basins of attraction, it has been observed that the proposed methods have better stability and robustness as compared to the other sixth-order methods available in the literature.

Keywords: Basins of attraction, nonlinear equations, simple roots, Super-Halley.

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Authors: Ioan Popa, Cristiana Tudor, Radu Lupu

Abstract:

The interdependences among stock market indices were studied for a long while by academics in the entire world. The current financial crisis opened the door to a wide range of opinions concerning the understanding and measurement of the connections considered to provide the controversial phenomenon of market integration. Using data on the log-returns of 17 stock market indices that include most of the CEE markets, from 2005 until 2009, our paper studies the problem of these dependences using a new methodological tool that takes into account both the volatility clustering effect and the stochastic properties of these linkages through a Dynamic Conditional System of Simultaneous Equations. We find that the crisis is well captured by our model as it provides evidence for the high volatility – high dependence effect.

Keywords: Stock market interdependences, Dynamic System ofSimultaneous Equations, financial crisis

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Authors: Chyi Jaw

Abstract:

Prior literature on innovation diffusion or acceptance has almost exclusively concentrated on consumers’ positive attitudes and behaviors for new products/services. Consumers’ negative attitudes or behaviors to innovations have received relatively little marketing attention, but it happens frequently in practice. This study discusses consumer psychological factors when they try to learn or use new technologies. According to recent research, technological innovation acceptance has been considered as a dynamic or mediated process. This research argues that consumers can experience inertia and emotions in the initial use of new technologies. However, given such consumer psychology, the argument can be made as to whether the inclusion of consumer inertia (routine seeking and cognitive rigidity) and emotions increases the predictive power of new technology acceptance model. As data from the empirical study find, the process is potentially consumer emotion changing (independent of performance benefits) because of technology complexity and consumer inertia, and impact innovative technology use significantly. Finally, the study presents the superior predictability of the hypothesized model, which let managers can better predict and influence the successful diffusion of complex technological innovations.

Keywords: Cognitive rigidity, consumer emotions, new technology acceptance, routine seeking, technology complexity.

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Authors: Djemai Bara, Mohamed Faouzi Mahboub, Djamila Bennaceur-Doumaz

Abstract:

In this work, the role of the preformed plasma created on the front face of a target, irradiated by a high intensity short pulse laser, in the framework of ion acceleration process, modeled by Target Normal Sheath Acceleration (TNSA) mechanism, is studied. This plasma is composed of cold ions governed by fluid equations and non-thermal & trapped with densities represented by a "Cairns-Gurevich" equation. The self-similar solution of the equations shows that electronic trapping and the presence of non-thermal electrons in the pre-plasma are both responsible in ion acceleration as long as the proportion of energetic electrons is not too high. In the case where the majority of electrons are energetic, the electrons are accelerated directly by the ponderomotive force of the laser without the intermediate of an accelerating plasma wave.

Keywords: Cairns-Gurevich Equation, ion acceleration, plasma expansion, pre-plasma.

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Authors: Motahar Reza, Rajni Chahal, Neha Sharma

Abstract:

This article addresses the boundary layer flow and heat transfer of Casson fluid over a nonlinearly permeable stretching surface with chemical reaction in the presence of variable magnetic field. The effect of thermal radiation is considered to control the rate of heat transfer at the surface. Using similarity transformations, the governing partial differential equations of this problem are reduced into a set of non-linear ordinary differential equations which are solved by finite difference method. It is observed that the velocity at fixed point decreases with increasing the nonlinear stretching parameter but the temperature increases with nonlinear stretching parameter.

Keywords: Boundary layer flow, nonlinear stretching, Casson fluid, heat transfer, radiation.

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Authors: Jason Chien-Hsun Tseng, Nguyen Dong-Thai Dao, Chong-Ching Chang

Abstract:

A novel PDE solver using the multidimensional wave digital filtering (MDWDF) technique to achieve the solution of a 2D seismic wave system is presented. In essence, the continuous physical system served by a linear Kirchhoff circuit is transformed to an equivalent discrete dynamic system implemented by a MD wave digital filtering (MDWDF) circuit. This amounts to numerically approximating the differential equations used to describe elements of a MD passive electronic circuit by a grid-based difference equations implemented by the so-called state quantities within the passive MDWDF circuit. So the digital model can track the wave field on a dense 3D grid of points. Details about how to transform the continuous system into a desired discrete passive system are addressed. In addition, initial and boundary conditions are properly embedded into the MDWDF circuit in terms of state quantities. Graphic results have clearly demonstrated some physical effects of seismic wave (P-wave and S–wave) propagation including radiation, reflection, and refraction from and across the hard boundaries. Comparison between the MDWDF technique and the finite difference time domain (FDTD) approach is also made in terms of the computational efficiency.

Keywords: Seismic Wave Propagation, Multi-dimension WaveDigital Filters, Partial Differential Equations.

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Authors: Sacide Güzin Mazman, Yasemin Koçak Usluel

Abstract:

Possible advantages of technology in educational context required the defining boundaries of formal and informal learning. Increasing opportunity to ubiquitous learning by technological support has revealed a question of how to discover the potential of individuals in the spontaneous environments such as social networks. This seems to be related with the question of what purposes in social networks have been being used? Social networks provide various advantages in educational context as collaboration, knowledge sharing, common interests, active participation and reflective thinking. As a consequence of these, the purpose of this study is composed of proposing a new model that could determine factors which effect adoption of social network applications for usage in educational context. While developing a model proposal, the existing adoption and diffusion models have been reviewed and they are thought to be suitable on handling an original perspective instead of using completely other diffusion or acceptance models because of different natures of education from other organizations. In the proposed model; social factors, perceived ease of use, perceived usefulness and innovativeness are determined four direct constructs that effect adoption process. Facilitating conditions, image, subjective norms and community identity are incorporated to model as antecedents of these direct four constructs.

Keywords: Adoption of innovation, educational context, social networks.

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Authors: Isaac Kofi Mensah, Jianing Mi, Feng Cheng

Abstract:

This research paper seeks to investigate the factors determining the continuance usage of online mobile payment applications among WECHAT users in China. Technology Acceptance Model (TAM) and the Diffusion of Innovation (DOI) theory would both be applied as the theoretical foundation for this study. A developed instrument would be administered to the targeted sample of 1000 WECHAT Users in the City of Harbin, China, through an online questionnaire administration platform. Factors such as perceived usefulness, perceived ease of use, perceived service quality, social influence, trust in the internet, internet self-efficacy, relative advantage, compatibility, and complexity would be explored to determine its significant impact on the continuance intention to use mobile payment apps. This study is at the development and implementation stage. The successful completion of this research article would not only provide an insightful understanding of the factors influencing the decision of WECHAT users in China to use mobile payment applications but also enrich the e-commerce adoption literature.

Keywords: Diffusion of innovation (DOI), e-commerce, mobile payment, technology acceptance model (TAM), WECHAT.

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Authors: Hesham A. Elkaranshawy, Amr M. Abdelrazek, Hosam M. Ezzat

Abstract:

The system of ordinary nonlinear differential equations describing sliding velocity during impact with friction for a three-dimensional rigid-multibody system is developed. No analytical solutions have been obtained before for this highly nonlinear system. Hence, a power series solution is proposed. Since the validity of this solution is limited to its convergence zone, a suitable time step is chosen and at the end of it a new series solution is constructed. For a case study, the trajectory of the sliding velocity using the proposed method is built using 6 time steps, which coincides with a Runge- Kutta solution using 38 time steps.

Keywords: Impact with friction, nonlinear ordinary differential equations, power series solutions, rough collision.

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Authors: Hnin Hnin Kyi, Khaing Khaing Aye

Abstract:

Acoustic function plays an important role in aerodynamic mechanical engineering. It can classify the kind of air-vehicle such as subsonic or supersonic. Acoustic velocity relates with velocity and Mach number. Mach number relates again acoustic stability or instability condition. Mach number plays an important role in growth or decay in energy system. Acoustic is a function of temperature and temperature is directly proportional to pressure. If we control the pressure, we can control acoustic function. To get pressure stability condition, we apply Navier-Stokes equations.

Keywords: Acoustic velocity, Irrotational, Mach number, Rotational.

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Authors: Tusharkanta Das, Tumbanath Samantara, Sukanta Kumar Sahoo

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Unsteady effects of MHD free convection flow past in an infinite vertical plate with heat source in presence of radiation with reference to all critical parameters that appear in field equations are studied in this paper. The governing equations are developed by usual Boussinesq’s approximation. The problem is solved by using perturbation technique. The results are obtained for velocity, temperature, Nusselt number and skin-friction. The effects of magnetic parameter, prandtl number, Grashof number, permeability parameter, heat source/sink parameter and radiation parameter are discussed on flow characteristics and shown by means of graphs and tables.

Keywords: Heat transfer, radiation, MHD, free convection, porous medium, suction.

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Authors: E. Keramaris, V. Kanakoudis

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In this study the water flow in an open channel over a sharp-crested weir is investigated experimentally. For this reason a series of laboratory experiments were performed in an open channel with a sharp-crested weir. The maximum head expected over the weir, the total upstream water height and the downstream water height of the impact in the constant bed of the open channel were measured. The discharge was measured using a tank put right after the open channel. In addition, the discharge and the upstream velocity were also calculated using already known equations. The main finding is that the relative error percentage for the majority of the experimental measurements is ± 4%, meaning that the calculation of the discharge with a sharp-crested weir gives very good results compared to the numerical results from known equations.

Keywords: Sharp-crested weir, weir height, flow measurement, open channel flow.

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Authors: Safaa Al-Ali, Ahmad Shahin, Fadi Chakik

Abstract:

Image coding based on clustering provides immediate access to targeted features of interest in a high quality decoded image. This approach is useful for intelligent devices, as well as for multimedia content-based description standards. The result of image clustering cannot be precise in some positions especially on pixels with edge information which produce ambiguity among the clusters. Even with a good enhancement operator based on PDE, the quality of the decoded image will highly depend on the clustering process. In this paper, we introduce an ambiguity cluster in image coding to represent pixels with vagueness properties. The presence of such cluster allows preserving some details inherent to edges as well for uncertain pixels. It will also be very useful during the decoding phase in which an anisotropic diffusion operator, such as Perona-Malik, enhances the quality of the restored image. This work also offers a comparative study to demonstrate the effectiveness of a fuzzy clustering technique in detecting the ambiguity cluster without losing lot of the essential image information. Several experiments have been carried out to demonstrate the usefulness of ambiguity concept in image compression. The coding results and the performance of the proposed algorithms are discussed in terms of the peak signal-tonoise ratio and the quantity of ambiguous pixels.

Keywords: Ambiguity Cluster, Anisotropic Diffusion, Fuzzy Clustering, Image Compression.

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Authors: Balgaisha Mukanova, Tolkyn Mirgalikyzy

Abstract:

Theory of interpretation of electromagnetic fields studied in the electrical prospecting with direct current is mainly developed for the case of a horizontal surface observation. However in practice we often have to work in difficult terrain surface. Conducting interpretation without the influence of topography can cause non-existent anomalies on sections. This raises the problem of studying the impact of different shapes of ground surface relief on the results of electrical prospecting's research. This research examines the numerical solutions of the direct problem of electrical prospecting for two-dimensional and three-dimensional media, taking into account the terrain. The problem is solved using the method of integral equations. The density of secondary currents on the relief surface is obtained.

Keywords: Ground surface relief, method of integral equations, numerical method.

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Authors: Li Zong-Cheng

Abstract:

The deviation between the target state variable and the practical state variable should be used to form the state tending factor of complex systems, which can reflect the process for the complex system to tend rationalization. Relating to the system of basic equations of complete factor synergetics consisting of twenty nonlinear stochastic differential equations, the two new models are considered to set, which should be called respectively the rationalizing tendency model and the non- rationalizing tendency model. Therefore we can extend the theory of programming with the objective function & constraint condition suitable only for the realm of man-s activities into the new analysis with the tendency function & constraint condition suitable for all the field of complex system.

Keywords: complex system, complete factor synergetics, basicequation, rationalizing tendency model, non-rationalizing tendencymodel.

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Authors: Mostafa Raki, Mahdi Hamzehei

Abstract:

Equilibrium and stability equations of a thin rectangular plate with length a, width b, and thickness h(x)=C1x+C2, made of functionally graded materials under thermal loads are derived based on the first order shear deformation theory. It is assumed that the material properties vary as a power form of thickness coordinate variable z. The derived equilibrium and buckling equations are then solved analytically for a plate with simply supported boundary conditions. One type of thermal loading, uniform temperature rise and gradient through the thickness are considered, and the buckling temperatures are derived. The influences of the plate aspect ratio, the relative thickness, the gradient index and the transverse shear on buckling temperature difference are all discussed.

Keywords: Stability of plate, thermal buckling, rectangularplate, functionally graded material, first order shear deformationtheory.

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Authors: Dmitry V. Fomichev, Vladimir I. Solonin

Abstract:

This paper presents the findings from a numerical simulation of the flow in 37-rod fuel assembly models spaced by a double-wire trapezoidal wrapping as applied to the BREST-OD-300 experimental nuclear reactor. Data on a high static pressure distribution within the models, and equations for determining the fuel bundle flow friction factors have been obtained. Recommendations are provided on using the closing turbulence models available in the ANSYS Fluent. A comparative analysis has been performed against the existing empirical equations for determining the flow friction factors. The calculated and experimental data fit has been shown.

An analysis into the experimental data and results of the numerical simulation of the BREST-OD-300 fuel rod assembly hydrodynamic performance are presented.

Keywords: BREST-OD-300, ware-spaces, fuel assembly, computation fluid dynamics.

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Authors: Kaltima Phichai, Pornchanoke Pragrobpondee, Thaweesak Khumpart, Samorn Hirunpraditkoon

Abstract:

The paper provides biomasses characteristics by proximate analysis (volatile matter, fixed carbon and ash) and ultimate analysis (carbon, hydrogen, nitrogen and oxygen) for the prediction of the heating value equations. The heating value estimation of various biomasses can be used as an energy evaluation. Thirteen types of biomass were studied. Proximate analysis was investigated by mass loss method and infrared moisture analyzer. Ultimate analysis was analyzed by CHNO analyzer. The heating values varied from 15 to 22.4MJ kg-1. Correlations of the calculated heating value with proximate and ultimate analyses were undertaken using multiple regression analysis and summarized into three and two equations, respectively. Correlations based on proximate analysis illustrated that deviation of calculated heating values from experimental heating values was higher than the correlations based on ultimate analysis.

Keywords: Heating value equation, Proximate analysis, Ultimate analysis.

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Authors: A. R. Shahani, E. Mahdavi, M. Amidpour

Abstract:

Environment-assisted cracking (EAC) is one of the most serious causes of structural failure over a broad range of industrial applications including offshore structures. In EAC condition there is not a definite relation such as Paris equation in Linear Elastic Fracture Mechanics (LEFM). According to studying and searching a lot what the researchers said either a material has contact with hydrogen or any other corrosive environment, phenomenon of electrical and chemical reactions of material with its environment will be happened. In the literature, there are many different works to consider fatigue crack growing and solve it but they are experimental works. Thus, in this paper, authors have an aim to evaluate mathematically the pervious works in LEFM. Obviously, if an environment is more sour and corrosive, the changes of stress intensity factor is more and the calculation of stress intensity factor is difficult. A mathematical relation to deal with the stress intensity factor during the diffusion of sour environment especially hydrogen in a marine pipeline is presented. By using this relation having and some experimental relation an analytical formulation will be presented which enables the fatigue crack growth and critical crack length under cyclic loading to be predicted. In addition, we can calculate KSCC and stress intensity factor in the pipeline caused by EAC.

Keywords: Embrittlement, Fracture mechanics, Hydrogen diffusion, Stress intensity factor.

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