Search results for: anisotropic diffusion

Authors: Wan Nural Jawahir Wan Yussof, Hans Burkhardt

Abstract:

Liver segmentation is the first significant process for liver diagnosis of the Computed Tomography. It segments the liver structure from other abdominal organs. Sophisticated filtering techniques are indispensable for a proper segmentation. In this paper, we employ a 3D anisotropic diffusion as a preprocessing step. While removing image noise, this technique preserve the significant parts of the image, typically edges, lines or other details that are important for the interpretation of the image. The segmentation task is done by using thresholding with automatic threshold values selection and finally the false liver region is eliminated using 3D connected component. The result shows that by employing the 3D anisotropic filtering, better liver segmentation results could be achieved eventhough simple segmentation technique is used.

Keywords: 3D Anisotropic Diffusion, non-linear filtering, CT Liver.

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Authors: Shujun Fu, Qiuqi Ruan, Wenqia Wang, Yu Li

Abstract:

Utilizing echoic intension and distribution from different organs and local details of human body, ultrasonic image can catch important medical pathological changes, which unfortunately may be affected by ultrasonic speckle noise. A feature preserving ultrasonic image denoising and edge enhancement scheme is put forth, which includes two terms: anisotropic diffusion and edge enhancement, controlled by the optimum smoothing time. In this scheme, the anisotropic diffusion is governed by the local coordinate transformation and the first and the second order normal derivatives of the image, while the edge enhancement is done by the hyperbolic tangent function. Experiments on real ultrasonic images indicate effective preservation of edges, local details and ultrasonic echoic bright strips on denoising by our scheme.

Keywords: anisotropic diffusion, coordinate transformation, directional derivatives, edge enhancement, hyperbolic tangent function, image denoising.

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Authors: Ahmed Badawi, J. Michael Johnson, Mohamed Mahfouz

Abstract:

This paper proposes new enhancement models to the methods of nonlinear anisotropic diffusion to greatly reduce speckle and preserve image features in medical ultrasound images. By incorporating local physical characteristics of the image, in this case scatterer density, in addition to the gradient, into existing tensorbased image diffusion methods, we were able to greatly improve the performance of the existing filtering methods, namely edge enhancing (EE) and coherence enhancing (CE) diffusion. The new enhancement methods were tested using various ultrasound images, including phantom and some clinical images, to determine the amount of speckle reduction, edge, and coherence enhancements. Scatterer density weighted nonlinear anisotropic diffusion (SDWNAD) for ultrasound images consistently outperformed its traditional tensor-based counterparts that use gradient only to weight the diffusivity function. SDWNAD is shown to greatly reduce speckle noise while preserving image features as edges, orientation coherence, and scatterer density. SDWNAD superior performances over nonlinear coherent diffusion (NCD), speckle reducing anisotropic diffusion (SRAD), adaptive weighted median filter (AWMF), wavelet shrinkage (WS), and wavelet shrinkage with contrast enhancement (WSCE), make these methods ideal preprocessing steps for automatic segmentation in ultrasound imaging.

Keywords: Nonlinear anisotropic diffusion, ultrasound imaging, speckle reduction, scatterer density estimation, edge based enhancement, coherence enhancement.

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Authors: Shujun Fu, Qiuqi Ruan, Wenqia Wang, Yu Li

Abstract:

Utilizing echoic intension and distribution from different organs and local details of human body, ultrasonic image can catch important medical pathological changes, which unfortunately may be affected by ultrasonic speckle noise. A feature preserving ultrasonic image denoising and edge enhancement scheme is put forth, which includes two terms: anisotropic diffusion and edge enhancement, controlled by the optimum smoothing time. In this scheme, the anisotropic diffusion is governed by the local coordinate transformation and the first and the second order normal derivatives of the image, while the edge enhancement is done by the hyperbolic tangent function. Experiments on real ultrasonic images indicate effective preservation of edges, local details and ultrasonic echoic bright strips on denoising by our scheme.

Keywords: anisotropic diffusion, coordinate transformationdirectional derivatives, edge enhancement, hyperbolic tangentfunction, image denoising.

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Authors: Tudor Barbu

Abstract:

We present a robust nonlinear parabolic partial differential equation (PDE)-based denoising scheme in this article. Our approach is based on a second-order anisotropic diffusion model that is described first. Then, a consistent and explicit numerical approximation algorithm is constructed for this continuous model by using the finite-difference method. Finally, our restoration experiments and method comparison, which prove the effectiveness of this proposed technique, are discussed in this paper.

Keywords: Image denoising and restoration, nonlinear PDE model, anisotropic diffusion, numerical approximation scheme, finite differences.

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Authors: Benjamin Anderson-Sackaney, Amr Abdel-Dayem

Abstract:

This paper presents a comprehensive survey of recent source camera identification (SCI) systems. Then, the performance of various sensor pattern noise (SPN) estimators was experimentally assessed, under common photo response non-uniformity (PRNU) frameworks. The experiments used 1350 natural and 900 flat-field images, captured by 18 individual cameras. 12 different experiments, grouped into three sets, were conducted. The results were analyzed using the receiver operator characteristic (ROC) curves. The experimental results demonstrated that combining the basic SPN estimator with a wavelet-based filtering scheme provides promising results. However, the phase SPN estimator fits better with both patch-based (BM3D) and anisotropic diffusion (AD) filtering schemes.

Keywords: Sensor pattern noise, source camera identification, photo response non-uniformity, anisotropic diffusion, peak to correlation energy ratio.

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Authors: Shujun Fu, Qiuqi Ruan, Wenqia Wang

Abstract:

Image interpolation is a common problem in imaging applications. However, most interpolation algorithms in existence suffer visually the effects of blurred edges and jagged artifacts in the image to some extent. This paper presents an adaptive feature preserving bidirectional flow process, where an inverse diffusion is performed to sharpen edges along the normal directions to the isophote lines (edges), while a normal diffusion is done to remove artifacts (“jaggies") along the tangent directions. In order to preserve image features such as edges, corners and textures, the nonlinear diffusion coefficients are locally adjusted according to the directional derivatives of the image. Experimental results on synthetic images and nature images demonstrate that our interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional interpolations.

Keywords: anisotropic diffusion, bidirectional flow, directional derivatives, edge enhancement, image interpolation, inverse flow, shock filter.

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Authors: Shujun Fu, Qiuqi Ruan, Wenqia Wang

Abstract:

Image interpolation is a common problem in imaging applications. However, most interpolation algorithms in existence suffer visually to some extent the effects of blurred edges and jagged artifacts in the image. This paper presents an adaptive feature preserving bidirectional flow process, where an inverse diffusion is performed to enhance edges along the normal directions to the isophote lines (edges), while a normal diffusion is done to remove artifacts (''jaggies'') along the tangent directions. In order to preserve image features such as edges, angles and textures, the nonlinear diffusion coefficients are locally adjusted according to the first and second order directional derivatives of the image. Experimental results on synthetic images and nature images demonstrate that our interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional interpolations.

Keywords: anisotropic diffusion, bidirectional flow, directionalderivatives, edge enhancement, image interpolation, inverse flow, shock filter.

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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: K.L. Verma

Abstract:

Analysis for the generalized thermoelastic Lamb waves, which propagates in anisotropic thin plates in generalized thermoelasticity, is presented employing normal mode expansion method. The displacement and temperature fields are expressed by a summation of the symmetric and antisymmetric thermoelastic modes in the surface thermal stresses and thermal gradient free orthotropic plate, therefore the theory is particularly appropriate for waveform analyses of Lamb waves in thin anisotropic plates. The transient waveforms excited by the thermoelastic expansion are analyzed for an orthotropic thin plate. The obtained results show that the theory provides a quantitative analysis to characterize anisotropic thermoelastic stiffness properties of plates by wave detection. Finally numerical calculations have been presented for a NaF crystal, and the dispersion curves for the lowest modes of the symmetric and antisymmetric vibrations are represented graphically at different values of thermal relaxation time. However, the methods can be used for other materials as well

Keywords: Anisotropic, dispersion, frequency, normal, thermoelasticity, wave modes.

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Authors: K. L. Verma

Abstract:

Analysis for the propagation of elastic waves in arbitrary anisotropic plates is investigated, commencing with a formal analysis of waves in a layered plate of an arbitrary anisotropic media, the dispersion relations of elastic waves are obtained by invoking continuity at the interface and boundary of conditions on the surfaces of layered plate. The obtained solutions can be used for material systems of higher symmetry such as monoclinic, orthotropic, transversely isotropic, cubic, and isotropic as it is contained implicitly in the analysis. The cases of free layered plate and layered half space are considered separately. Some special cases have also been deduced and discussed. Finally numerical solution of the frequency equations for an aluminum epoxy is carried out, and the dispersion curves for the few lower modes are presented. The results obtained theoretically have been verified numerically and illustrated graphically.

Keywords: Anisotropic, layered, dispersion, elastic waves, frequency equations.

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Authors: A. A. Hekmatzadeh, A. Karimi-Jashani, N. Talebbeydokhti

Abstract:

The rate of nitrate adsorption by a nitrate selective ion exchange resin was investigated in a well-stirred batch experiments. The kinetic experimental data were simulated with diffusion models including external mass transfer, particle diffusion and chemical adsorption. Particle pore volume diffusion and particle surface diffusion were taken into consideration separately and simultaneously in the modeling. The model equations were solved numerically using the Crank-Nicholson scheme. An optimization technique was employed to optimize the model parameters. All nitrate concentration decay data were well described with the all diffusion models. The results indicated that the kinetic process is initially controlled by external mass transfer and then by particle diffusion. The external mass transfer coefficient and the coefficients of pore volume diffusion and surface diffusion in all experiments were close to each other with the average value of 8.3×10-3 cm/S for external mass transfer coefficient. In addition, the models are more sensitive to the mass transfer coefficient in comparison with particle diffusion. Moreover, it seems that surface diffusion is the dominant particle diffusion in comparison with pore volume diffusion.

Keywords: External mass transfer, pore volume diffusion, surface diffusion, mass action law isotherm.

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Authors: Paola Lecca, Lorenzo Dematte, Corrado Priami

Abstract:

The present models and simulation algorithms of intracellular stochastic kinetics are usually based on the premise that diffusion is so fast that the concentrations of all the involved species are homogeneous in space. However, recents experimental measurements of intracellular diffusion constants indicate that the assumption of a homogeneous well-stirred cytosol is not necessarily valid even for small prokaryotic cells. In this work a mathematical treatment of diffusion that can be incorporated in a stochastic algorithm simulating the dynamics of a reaction-diffusion system is presented. The movement of a molecule A from a region i to a region j of the space is represented as a first order reaction Ai k- ! Aj , where the rate constant k depends on the diffusion coefficient. The diffusion coefficients are modeled as function of the local concentration of the solutes, their intrinsic viscosities, their frictional coefficients and the temperature of the system. The stochastic time evolution of the system is given by the occurrence of diffusion events and chemical reaction events. At each time step an event (reaction or diffusion) is selected from a probability distribution of waiting times determined by the intrinsic reaction kinetics and diffusion dynamics. To demonstrate the method the simulation results of the reaction-diffusion system of chaperoneassisted protein folding in cytoplasm are shown.

Keywords: Reaction-diffusion systems, diffusion coefficient, stochastic simulation algorithm.

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Authors: Sanghoon Kim, Sun-Tae Chung, Souhwan Jung, Seongwon Cho

Abstract:

Robust face recognition under various illumination environments is very difficult and needs to be accomplished for successful commercialization. In this paper, we propose an improved illumination normalization method for face recognition. Illumination normalization algorithm based on anisotropic smoothing is well known to be effective among illumination normalization methods but deteriorates the intensity contrast of the original image, and incurs less sharp edges. The proposed method in this paper improves the previous anisotropic smoothing-based illumination normalization method so that it increases the intensity contrast and enhances the edges while diminishing the effect of illumination variations. Due to the result of these improvements, face images preprocessed by the proposed illumination normalization method becomes to have more distinctive feature vectors (Gabor feature vectors) for face recognition. Through experiments of face recognition based on Gabor feature vector similarity, the effectiveness of the proposed illumination normalization method is verified.

Keywords: Illumination Normalization, Face Recognition, Anisotropic smoothing, Gabor feature vector.

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Authors: Xin Luo, Jin Huang, Chuan-Long Wang

Abstract:

The mechanical quadrature methods for solving the boundary integral equations of the anisotropic Darcy-s equations with Dirichlet conditions in smooth domains are presented. By applying the collectively compact theory, we prove the convergence and stability of approximate solutions. The asymptotic expansions for the error show that the methods converge with the order O (h3), where h is the mesh size. Based on these analysis, extrapolation methods can be introduced to achieve a higher convergence rate O (h5). An a posterior asymptotic error representation is derived in order to construct self-adaptive algorithms. Finally, the numerical experiments show the efficiency of our methods.

Keywords: Darcy's equation, anisotropic, mechanical quadrature methods, extrapolation methods, a posteriori error estimate.

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Authors: Jianwei Ma, Diriba Gemechu

Abstract:

In seismic data processing, attenuation of random noise is the basic step to improve quality of data for further application of seismic data in exploration and development in different gas and oil industries. The signal-to-noise ratio of the data also highly determines quality of seismic data. This factor affects the reliability as well as the accuracy of seismic signal during interpretation for different purposes in different companies. To use seismic data for further application and interpretation, we need to improve the signal-to-noise ration while attenuating random noise effectively. To improve the signal-to-noise ration and attenuating seismic random noise by preserving important features and information about seismic signals, we introduce the concept of anisotropic total fractional order denoising algorithm. The anisotropic total fractional order variation model defined in fractional order bounded variation is proposed as a regularization in seismic denoising. The split Bregman algorithm is employed to solve the minimization problem of the anisotropic total fractional order variation model and the corresponding denoising algorithm for the proposed method is derived. We test the effectiveness of theproposed method for synthetic and real seismic data sets and the denoised result is compared with F-X deconvolution and non-local means denoising algorithm.

Keywords: Anisotropic total fractional order variation, fractional order bounded variation, seismic random noise attenuation, Split Bregman Algorithm.

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Authors: Alonggot Limcharoen Kaeochotchuangkul, Pathomporn Sawatchai

Abstract:

This research aims to design and build a wet etching system, which is suitable for anisotropic wet etching, in order to reduce etching time, to reduce hillocks on the etched surface (to reduce roughness), and to create a 45-degree wall angle (micro-mirror). This study would start by designing a wet etching system. There are four main components in this system: an ultrasonic cleaning, a condenser, a motor and a substrate holder. After that, an ultrasonic machine was modified by applying a condenser to maintain the consistency of the solution concentration during the etching process and installing a motor for improving the roughness. This effect on the etch rate and the roughness showed that the etch rate increased and the roughness was reduced.

Keywords: Anisotropic wet etching, wet etching system, Hillocks, ultrasonic cleaning.

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Authors: Zongqing Lu

Abstract:

It has proved that nonlinear diffusion and bilateral filtering (BF) have a closed connection. Early effort and contribution are to find a generalized representation to link them by using adaptive filtering. In this paper a new further relationship between nonlinear diffusion and bilateral filtering is explored which pays more attention to numerical calculus. We give a fresh idea that bilateral filtering can be accelerated by multigrid (MG) scheme which likes the nonlinear diffusion, and show that a bilateral filtering process with large kernel size can be approximated by a nonlinear diffusion process based on full multigrid (FMG) scheme.

Keywords: Bilateral filter, multigrid

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Authors: Arti Vaish, Harish Parthasarathy

Abstract:

In this paper, a novel wave equation for electromagnetic waves in a medium having anisotropic permittivity has been derived with the help of Maxwell-s curl equations. The x and y components of the Maxwell-s equations are written with the permittivity () being a 3 × 3 symmetric matrix. These equations are solved for Ex , Ey, Hx, Hy in terms of Ez, Hz, and the partial derivatives. The Z components of the Maxwell-s curl are then used to arrive to the generalized Helmholtz equations for Ez and Hz.

Keywords: Electromagnetism, Maxwell's Equations, Anisotropic permittivity, Wave equation, Matrix Equation, Permittivity tensor.

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Authors: Mei-Hsiu Chi, Jyh-Yang Wu, Sheng-Gwo Chen

Abstract:

The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.

Keywords: Close surfaces, high-order approach, numerical solutions, reaction-diffusion systems.

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Authors: A. Derardja

Abstract:

The present work is motivated by the idea that the layer deformation in anisotropic elasticity can be estimated from the theory of interfacial dislocations. In effect, this work which is an extension of a previous approach given by one of the authors determines the anisotropic displacement fields and the critical thickness due to a complex biperiodic network of MDs lying just below the free surface in view of the arrangement of dislocations. The elastic fields of such arrangements observed along interfaces play a crucial part in the improvement of the physical properties of epitaxial systems. New results are proposed in anisotropic elasticity for hexagonal networks of MDs which contain intrinsic and extrinsic stacking faults. We developed, using a previous approach based on the relative interfacial displacement and a Fourier series formulation of the displacement fields, the expressions of elastic fields when there is a possible dissociation of MDs. The numerical investigations in the case of the observed system Si/(111)Si with low twist angles show clearly the effect of the anisotropy and thickness when the misfit networks are dissociated.

Keywords: Angular misfit, dislocation networks, plane interfaces, stacking faults.

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Authors: M. M. Rahman

Abstract:

The present contribution deals with the thermophoretic deposition of nanoparticles over a rapidly rotating permeable disk in the presence of partial slip, magnetic field, thermal radiation, thermal-diffusion, and diffusion-thermo effects. The governing nonlinear partial differential equations such as continuity, momentum, energy and concentration are transformed into nonlinear ordinary differential equations using similarity analysis, and the solutions are obtained through the very efficient computer algebra software MATLAB. Graphical results for non-dimensional concentration and temperature profiles including thermophoretic deposition velocity and Stanton number (thermophoretic deposition flux) in tabular forms are presented for a range of values of the parameters characterizing the flow field. It is observed that slip mechanism, thermal-diffusion, diffusion-thermo, magnetic field and radiation significantly control the thermophoretic particles deposition rate. The obtained results may be useful to many industrial and engineering applications.

Keywords: Boundary layer flows, convection, diffusion-thermo, rotating disk, thermal-diffusion, thermophoresis.

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Authors: Y. Obikane, T. Nemoto , K. Ogura, M. Iwata, K. Ono

Abstract:

The objective of this research was to find the diffusion properties of vehicles on the road by using the V-Sphere Code. The diffusion coefficient and the size of the height of the wake were estimated with the LES option and the third order MUSCL scheme. We evaluated the code with the changes in the moments of Reynolds Stress along the mean streamline. The results show that at the leading part of a bluff body the LES has some advantages over the RNS since the changes in the strain rates are larger for the leading part. We estimated that the diffusion coefficient with the computed Reynolds stress (non-dimensional) was about 0.96 times the mean velocity.

Keywords: Wake , bluff body, V-CAD, turbulence diffusion.

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Authors: Alaa H. J. Al-Rkaby, A. Chegenizadeh, H. R. Nikraz

Abstract:

Anisotropy is one of the major aspects that affect soil behavior, and extensive efforts have investigated its effect on the mechanical properties of soil. However, very little attention has been given to the combined effect of anisotropy and fine contents. Therefore, in this paper, the anisotropic strength of sand containing different fine content (F) of 5%, 10%, 15%, and 20%, was investigated using hollow cylinder tests under different principal stress directions of α = 0° and α = 90°. For a given principal stress direction (α), it was found that increasing fine content resulted in decreasing deviator stress (q). Moreover, results revealed that all fine contents showed anisotropic strength where there is a clear difference between the strength under 0° and the strength under 90°. This anisotropy was greatest under F = 5% while it decreased with increasing fine contents, particularly at F = 10%. Mixtures with low fine content show low contractive behavior and tended to show more dilation. Moreover, all sand-clay mixtures exhibited less dilation and more compression at α = 90° compared with that at α = 0°.

Keywords: Anisotropy, principal stress direction, fine content, hollow cylinder sample.

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Authors: MA. Ansari

Abstract:

In cancer progress, the optical properties of tissues like absorption and scattering coefficient change, so by these changes, we can trace the progress of cancer, even it can be applied for pre-detection of cancer. In this paper, we investigate the effects of changes of optical properties on light penetrated into tissues. The diffusion equation is widely used to simulate light propagation into biological tissues. In this study, the boundary integral method (BIM) is used to solve the diffusion equation. We illustrate that the changes of optical properties can modified the reflectance or penetrating light.

Keywords: Diffusion equation, boundary element method, refractive index

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Authors: F. Isada, Y. Isada

Abstract:

In this research, the diffusion of innovation regarding smartphone usage is analysed through a consumer behaviour theory. This research aims to determine whether a pattern surrounding the diffusion of innovation exists. As a methodology, an empirical study of the switch from a conventional cell phone to a smartphone was performed. Specifically, a questionnaire survey was completed by general consumers, and the situational and behavioural characteristics of switching from a cell phone to a smartphone were analysed. In conclusion, we found that the speed of the diffusion of innovation, the consumer behaviour characteristics, and the utilities of the product vary according to the stage of the product life cycle.

Keywords: Diffusion of innovation, consumer behaviour, product life cycle, smartphone, empirical study, questionnaire survey.

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Authors: Ramakrishnan Ramanathan, Yanqing Duan, Guangming Cao, Elaine Philpott

Abstract:

We discuss a theoretical conceptual framework to help understand how the new business analytics technologies have diffused in firms. We draw on three theoretical perspectives for this purpose. They are innovation diffusion theory, IT Business Value and the technology-organization-environment theory. We develop a conceptual framework that helps understand the interlinkages among factors affecting diffusion of business analytics and its impact on performance.

Keywords: Innovation diffusion, IT-Business Value, Technology-Organization-Environment, Business Analytics, Business performance

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Authors: Gkolfo I. Smani, Vasileios Megalooikonomou

Abstract:

Influence and influence diffusion have been studied extensively in social networks. However, most existing literature on this task are limited on static networks, ignoring the fact that the interactions between users change over time. In this paper, the problem of maximizing influence diffusion in dynamic social networks, i.e., the case of networks that change over time is studied. The DM algorithm is an extension of Matrix Influence (MATI) algorithm and solves the Influence Maximization (IM) problem in dynamic networks and is proposed under the Linear Threshold (LT) and Independent Cascade (IC) models. Experimental results show that our proposed algorithm achieves a diffusion performance better by 1.5 times than several state-of-the-art algorithms and comparable results in diffusion scale with the Greedy algorithm. Also, the proposed algorithm is 2.4 times faster than previous methods.

Keywords: Influence maximization, dynamic social networks, diffusion, social influence.

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Authors: Ren Jian, Yang Shulin

Abstract:

In this paper, the difference between the Alternating Direction Method (ADM) and the Non-Splitting Method (NSM) is investigated, while both methods applied to the simulations for 2-D multimaterial radiation diffusion issues. Although the ADM have the same accuracy orders with the NSM on the uniform meshes, the accuracy of ADM will decrease on the distorted meshes or the boundary of domain. Numerical experiments are carried out to confirm the theoretical predication.

Keywords: Alternating Direction Method, Non-SplittingMethod, Radiation Diffusion.

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Authors: Pavlo Selyshchev, Samuel Akintunde

Abstract:

A theoretical approach to consider formation of chemical compound layer at the interface between initial substances A and B due to the interfacial interaction and diffusion is developed. It is considered situation when speed of interfacial interaction is large enough and diffusion of A-atoms through AB-layer is much more then diffusion of B-atoms. Atoms from A-layer diffuse toward B-atoms and form AB-atoms on the surface of B-layer. B-atoms are assumed to be immobile. The growth kinetics of the AB-layer is described by two differential equations with non-linear coupling, producing a good fit to the experimental data. It is shown that growth of the thickness of the AB-layer determines by dependence of chemical reaction rate on reactants concentration. In special case the thickness of the AB-layer can grow linearly or parabolically depending on that which of processes (interaction or the diffusion) controls the growth. The thickness of AB-layer as function of time is obtained. The moment of time (transition point) at which the linear growth are changed by parabolic is found.

Keywords: Phase formation, Binary systems, Interfacial Reaction, Diffusion, Compound layers, Growth kinetics.

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