Search results for: Solution Diffusion

Authors: Paola Lecca, Lorenzo Dematte

Abstract:

Reactiondiffusion systems are mathematical models that describe how the concentration of one or more substances distributed in space changes under the influence of local chemical reactions in which the substances are converted into each other, and diffusion which causes the substances to spread out in space. The classical representation of a reaction-diffusion system is given by semi-linear parabolic partial differential equations, whose general form is ÔêétX(x, t) = DΔX(x, t), where X(x, t) is the state vector, D is the matrix of the diffusion coefficients and Δ is the Laplace operator. If the solute move in an homogeneous system in thermal equilibrium, the diffusion coefficients are constants that do not depend on the local concentration of solvent and of solutes and on local temperature of the medium. In this paper a new stochastic reaction-diffusion model in which the diffusion coefficients are function of the local concentration, viscosity and frictional forces of solvent and solute is presented. Such a model provides a more realistic description of the molecular kinetics in non-homogenoeus and highly structured media as the intra- and inter-cellular spaces. The movement of a molecule A from a region i to a region j of the space is described as a first order reaction Ai k- → Aj , where the rate constant k depends on the diffusion coefficient. Representing the diffusional motion as a chemical reaction allows to assimilate a reaction-diffusion system to a pure reaction system and to simulate it with Gillespie-inspired stochastic simulation algorithms. 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 specific speed of reaction and diffusion events. Redi is the software tool, developed to implement the model of reaction-diffusion kinetics and dynamics. It is a free software, that can be downloaded from http://www.cosbi.eu. To demonstrate the validity of the new reaction-diffusion model, the simulation results of the chaperone-assisted protein folding in cytoplasm obtained with Redi are reported. This case study is redrawing the attention of the scientific community due to current interests on protein aggregation as a potential cause for neurodegenerative diseases.

Keywords: Reaction-diffusion systems, Fick's law, stochastic simulation algorithm.

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Authors: Xinhua Zhang, Kelin Li

Abstract:

In this paper, a class of impulsive BAM fuzzy cellular neural networks with distributed delays and reaction-diffusion terms is formulated and investigated. By employing the delay differential inequality and inequality technique developed by Xu et al., some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM fuzzy cellular neural networks with distributed delays and reaction-diffusion terms are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters, diffusion effect and impulsive disturbed intention. It is believed that these results are significant and useful for the design and applications of BAM fuzzy cellular neural networks. An example is given to show the effectiveness of the results obtained here.

Keywords: Bi-directional associative memory, fuzzy cellular neuralnetworks, reaction-diffusion, delays, impulses, global exponentialstability.

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Authors: Salah Alrabeei, Mohammad Yousuf

Abstract:

The goal of option pricing theory is to help the investors to manage their money, enhance returns and control their financial future by theoretically valuing their options. However, most of the option pricing models have no analytical solution. Furthermore, not all the numerical methods are efficient to solve these models because they have nonsmoothing payoffs or discontinuous derivatives at the exercise price. In this paper, we solve the American option under jump diffusion models by using efficient time-dependent numerical methods. several techniques are integrated to reduced the overcome the computational complexity. Fast Fourier Transform (FFT) algorithm is used as a matrix-vector multiplication solver, which reduces the complexity from O(M2) into O(M logM). Partial fraction decomposition technique is applied to rational approximation schemes to overcome the complexity of inverting polynomial of matrices. The proposed method is easy to implement on serial or parallel versions. Numerical results are presented to prove the accuracy and efficiency of the proposed method.

Keywords: Integral differential equations, American options, jump–diffusion model, rational approximation.

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Authors: M. Kaggwa

Abstract:

Technology or lack of it will play an important role in Africa-s effort to achieve inclusive development. Although a key determinant of competitiveness, new technology can exacerbate exclusion of the majority from the mainstream economic activities. To minimise potential technology exclusion while leveraging its critical role in African-s development, requires insight into technology diffusion process. Using system dynamics approach, a technology diffusion model is presented. The frequency of interaction of people exposed to and those not exposed to technology, and the technology adoption rate - the fraction of people who embrace new technologies once they are exposed, are identified as the broad factors critical to technology diffusion to wider society enabling more people to be part of the economic growth process. Based on simulation results, it is recommends that these two broad factors should form part of national policy aimed at achieving inclusive and sustainable development in Africa.

Keywords: Inclusive Development, System Dynamics, Technology, Technology diffusion.

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Authors: N. Santatriniaina, J. Deseure, T.Q. Nguyen, H. Fontaine, C. Beitia, L. Rakotomanana

Abstract:

Nowadays, with the increasing of the wafer's size and the decreasing of critical size of integrated circuit manufacturing in modern high-tech, microelectronics industry needs a maximum attention to challenge the contamination control. The move to 300 [mm] is accompanied by the use of Front Opening Unified Pods for wafer and his storage. In these pods an airborne cross contamination may occur between wafers and the pods. A predictive approach using modeling and computational methods is very powerful method to understand and qualify the AMCs cross contamination processes. This work investigates the required numerical tools which are employed in order to study the AMCs cross-contamination transfer phenomena between wafers and FOUPs. Numerical optimization and finite element formulation in transient analysis were established. Analytical solution of one dimensional problem was developed and the calibration process of physical constants was performed. The least square distance between the model (analytical 1D solution) and the experimental data are minimized. The behavior of the AMCs intransient analysis was determined. The model framework preserves the classical forms of the diffusion and convection-diffusion equations and yields to consistent form of the Fick's law. The adsorption process and the surface roughness effect were also traduced as a boundary condition using the switch condition Dirichlet to Neumann and the interface condition. The methodology is applied, first using the optimization methods with analytical solution to define physical constants, and second using finite element method including adsorption kinetic and the switch of Dirichlet to Neumann condition.

Keywords: AMCs, FOUP, cross-contamination, adsorption, diffusion, numerical analysis, wafers, Dirichlet to Neumann, finite elements methods, Fick’s law, optimization.

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Authors: Basma M. Mohammad El-Basioni, Sherine M. Abd El-kader, Hussein S. Eissa

Abstract:

This paper proposes an implementation for the directed diffusion paradigm aids in studying this paradigm-s operations and evaluates its behavior according to this implementation. The directed diffusion is evaluated with respect to the loss percentage, lifetime, end-to-end delay, and throughput. From these evaluations some suggestions and modifications are proposed to improve the directed diffusion behavior according to this implementation with respect to these metrics. The proposed modifications reflect the effect of local path repair by introducing a technique called Loop-free Local Path Repair (LLPR) which improves the directed diffusion behavior especially with respect to packet loss percentage by about 92.69%. Also LLPR improves the throughput and end-to-end delay by about 55.31% and 14.06% respectively, while the lifetime decreases by about 29.79%.

Keywords: Attribute-value based naming scheme, data gathering, data-centric routing, energy-efficiency, locality, wireless sensor network.

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Authors: Guixia Lv, Longjun Shen

Abstract:

This paper presents a finite point method based on directional derivatives for diffusion equation on 2D scattered points. To discretize the diffusion operator at a given point, a six-point stencil is derived by employing explicit numerical formulae of directional derivatives, namely, for the point under consideration, only five neighbor points are involved, the number of which is the smallest for discretizing diffusion operator with first-order accuracy. A method for selecting neighbor point set is proposed, which satisfies the solvability condition of numerical derivatives. Some numerical examples are performed to show the good performance of the proposed method.

Keywords: Finite point method, directional derivatives, diffusionequation, method for selecting neighbor point set.

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Authors: Marzieh Dosti, Alireza Nazemi

Abstract:

Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper, a numerical solution for the one-dimensional hyperbolic telegraph equation by using the collocation method using the septic splines is proposed. The scheme works in a similar fashion as finite difference methods. Test problems are used to validate our scheme by calculate L2-norm and L∞-norm. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.

Keywords: B-spline, collocation method, second-order hyperbolic telegraph equation, difference schemes.

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Authors: Yanqin Chen, Chao Jiang, Chongdu Cho

Abstract:

This research presents the three-dimensional mechanical characteristics of a commercial gas diffusion layer by experiment and simulation results. Although the mechanical performance of gas diffusion layers has attracted much attention, its reliability and accuracy are still a major challenge. With the help of simulation analysis methods, it is beneficial to the gas diffusion layer’s extensive commercial development and the overall stress analysis of proton electrolyte membrane fuel cells during its pre-production design period. Therefore, in this paper, a three-dimensional constitutive model of a commercial gas diffusion layer, including its material stiffness matrix parameters, is developed and coded, in the user-defined material model of a commercial finite element method software for simulation. Then, the model is validated by comparing experimental results as well as simulation outcomes. As a result, both the experimental data and simulation results show a good agreement with each other, with high accuracy.

Keywords: Gas diffusion layer, proton electrolyte membrane fuel cell, stiffness matrix, three-dimensional mechanical characteristics, user-defined material model.

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Authors: M. A. Basunia

Abstract:

Thirty three re-wetting tests were conducted at different combinations of temperatures (5.7- 46.30C) and relative humidites (48.2-88.6%) with barley. Two most commonly used thinlayer drying and rewetting models i.e. Page and Diffusion were compared for their ability to the fit the experimental re-wetting data based on the standard error of estimate (SEE) of the measured and simulated moisture contents. The comparison shows both the Page and Diffusion models fit the re-wetting experimental data of barley well. The average SEE values for the Page and Diffusion models were 0.176 % d.b. and 0.199 % d.b., respectively. The Page and Diffusion models were found to be most suitable equations, to describe the thin-layer re-wetting characteristics of barley over a typically five day re-wetting. These two models can be used for the simulation of deep-bed re-wetting of barley occurring during ventilated storage and deep bed drying.

Keywords: Thin-layer, barley, re-wetting parameters, temperature, relative humidity.

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Authors: Brajesh Kumar Jha, Neeru Adlakha, M. N. Mehta

Abstract:

Mathematical and computational modeling of calcium signalling in nerve cells has produced considerable insights into how the cells contracts with other cells under the variation of biophysical and physiological parameters. The modeling of calcium signaling in astrocytes has become more sophisticated. The modeling effort has provided insight to understand the cell contraction. Main objective of this work is to study the effect of voltage gated (Operated) calcium channel (VOC) on calcium profile in the form of advection diffusion equation. A mathematical model is developed in the form of advection diffusion equation for the calcium profile. The model incorporates the important physiological parameter like diffusion coefficient etc. Appropriate boundary conditions have been framed. Finite volume method is employed to solve the problem. A program has been developed using in MATLAB 7.5 for the entire problem and simulated on an AMD-Turion 32-bite machine to compute the numerical results.

Keywords: Ca2+ Profile, Advection Diffusion, VOC, FVM.

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Authors: Xinhua Zhang, Kelin Li

Abstract:

In this paper, the problem of stability analysis for a class of impulsive stochastic fuzzy neural networks with timevarying delays and reaction-diffusion is considered. By utilizing suitable Lyapunov-Krasovskii funcational, the inequality technique and stochastic analysis technique, some sufficient conditions ensuring global exponential stability of equilibrium point for impulsive stochastic fuzzy cellular neural networks with time-varying delays and diffusion are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters, diffusion effect and impulsive disturbed intention. It is believed that these results are significant and useful for the design and applications of fuzzy neural networks. An example is given to show the effectiveness of the obtained results.

Keywords: Exponential stability, stochastic fuzzy cellular neural networks, time-varying delays, impulses, reaction-diffusion terms.

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Authors: K. R. V. Manikantachari, Vasudevan Raghavan, K. Srinivasan

Abstract:

Present study focuses on studying the oscillatory behavior of jet diffusion flames. At a particular jet exit velocity, the flames are seen to exhibit natural flickering. Initially the flickering process is not continuous. In this transition region as well as in the continuous flickering regime, the flickering displays multiple frequency oscillations. The response of the flame to the exit velocity profile of the burner is also studied using three types of burners. The entire range of natural flickering is investigated by capturing high speed digital images and processing them using a MATLAB code.

Keywords: Diffusion flames, Natural flickering, flickering frequency, intermittent flickering

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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: Yasaman Tohidi, Rouzbeh Riazi, Shidvash Vakilipour, Masoud Mohammadi

Abstract:

The objective of the present study is to numerically investigate the effect of CO₂ replacement of N₂ in air stream on the flame characteristics of the CH₄ turbulent diffusion flame. The Open source Field Operation and Manipulation (OpenFOAM) has been used as the computational tool. In this regard, laminar flamelet and modified k-ε models have been utilized as combustion and turbulence models, respectively. Results reveal that the presence of CO₂ in air stream changes the flame shape and maximum flame temperature. Also, CO₂ dilution causes an increment in CO mass fraction.

Keywords: CH4 diffusion flame, CO2 dilution, OpenFOAM, turbulent flame.

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Authors: M-J. Huang, C-J. Huang, L-C. Chen

Abstract:

In a previously developed fast vortex method, the diffusion of the vortex sheet induced at the solid wall by the no-slip boundary conditions was modeled according to the approximation solution of Koumoutsakos and converted into discrete blobs in the vicinity of the wall. This scheme had been successfully applied to a simulation of the flow induced with an impulsively initiated circular cylinder. In this work, further modifications on this vortex method are attempted, including replacing the approximation solution by the boundary-element-method solution, incorporating a new algorithm for handling the over-weak vortex blobs, and diffusing the vortex sheet circulation in a new way suitable for high-curvature solid bodies. The accuracy is thus largely improved. The predictions of lift and drag coefficients for a uniform flow past a NASA airfoil agree well with the existing literature.

Keywords: Resurrected core-spreading vortex method, Boundaryelement method, Vortex sheet, Over-weak vortex blobs.

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Authors: Amir Rastegarnia, Mohammad Ali Tinati, Azam Khalili

Abstract:

In this paper we consider the issue of distributed adaptive estimation over sensor networks. To deal with more realistic scenario, different variance for observation noise is assumed for sensors in the network. To solve the problem of different variance of observation noise, the proposed method is divided into two phases: I) Estimating each sensor-s observation noise variance and II) using the estimated variances to obtain the desired parameter. Our proposed algorithm is based on a diffusion least mean square (LMS) implementation with linear combiner model. In the proposed algorithm, the step-size parameter the coefficients of linear combiner are adjusted according to estimated observation noise variances. As the simulation results show, the proposed algorithm considerably improves the diffusion LMS algorithm given in literature.

Keywords: Adaptive filter, distributed estimation, sensor network, diffusion.

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Authors: Giulio Mangano, Alberto De Marco, Giovanni Zenezini

Abstract:

The concept of City Logistics (CL) has emerged to improve the impacts of last mile freight distribution in urban areas. In this paper, a System Dynamics (SD) model exploring the dynamics of the diffusion of a ICT platform for CL management across different populations is proposed. For the development of the model two sources have been used. On the one hand, the major diffusion variables and feedback loops are derived from a literature review of existing diffusion models. On the other hand, the parameters are represented by the value propositions delivered by the platform as a response to some of the users’ needs. To extract the most important value propositions the Business Model Canvas approach has been used. Such approach in fact focuses on understanding how a company can create value for her target customers. These variables and parameters are thus translated into a SD diffusion model with three different populations namely municipalities, logistics service providers, and own account carriers. Results show that, the three populations under analysis fully adopt the platform within the simulation time frame, highlighting a strong demand by different stakeholders for CL projects aiming at carrying out more efficient urban logistics operations.

Keywords: City logistics, simulation, system dynamics, business model.

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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: 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: Elragig Aiman, Dreiwi Hanan, Townley Stuart, Elmabrook Idriss

Abstract:

In this paper, we reconsider the analysis of the Oregonator model. We highlight an error in this analysis which leads to an incorrect depiction of the parameter region in which diffusion driven instability is possible. We believe that the cause of the oversight is the complexity of stability analyses based on eigenvalues and the dependence on parameters of matrix minors appearing in stability calculations. We regenerate the parameter space where Turing patterns can be seen, and we use the common Lyapunov function (CLF) approach, which is numerically reliable, to further confirm the dependence of the results on diffusion coefficients intensities.

Keywords: Diffusion driven instability, common Lyapunov function (CLF), turing pattern, positive-definite matrix.

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Authors: Qiang Zhao, Yina Shi, Guangwei Yuan, Zhiwei Dong

Abstract:

A cell-centered finite volume scheme for discretizing diffusion operators on distorted quadrilateral meshes has recently been designed and added to APMFCG to enable that code to be used as a tool for studying explosive magnetic flux compression generators. This paper describes this scheme. Comparisons with analytic results for 2-D test cases are presented, as well as 2-D results from a test of a "realistic" generator configuration.

Keywords: Cell-centered FVM, distorted meshes, diffusion scheme, MFCG.

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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: A. Seleem, M. Mortada, M. El Morsi, M. Younan

Abstract:

Diffusion stills have been effective in water desalination. The present work represents a model of the distillation process by using vertical single-effect diffusion stills. A semianalytical model has been developed to model the process. A software computer code using Engineering Equation Solver EES software has been developed to solve the equations of the developed model. An experimental setup has been constructed, and used for the validation of the model. The model is also validated against former literature results. The results obtained from the present experimental test rig, and the data from the literature, have been compared with the results of the code to find its best range of validity. In addition, a parametric analysis of the system has been developed using the model to determine the effect of operating conditions on the system's performance. The dominant parameters that affect the productivity of the still are the hot plate temperature that ranges from (55- 90°C) and feed flow rate in range of (0.00694-0.0211 kg/m2-s).

Keywords: Analytical Model, Solar Distillation, Sustainable Water Systems, Vertical Diffusion Still.

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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: Michael Tupý, Vít Petránek

Abstract:

The paper is focused on testing of the poly(vinyl butyral) (PVB) layer which had the function of a CO₂ insulating protection against concrete and mortar carbonation. The barrier efficiency of PVB was verified by the measurement of diffusion characteristics. Two different types of PVB were tested; original extruded PVB sheet and PVB sheet made from PVB dispersion which was obtained from recycled windshields. The work deals with the testing CO₂ diffusion when polymer sheets were exposed to a CO₂ atmosphere (10% v/v CO₂) with 0% RH. The excellent barrier capability against CO₂ permeability of original and also recycled types of PVB layers was observed. This application of PVB waste can bring advantageous use in civil engineering and significant environmental contribution.

Keywords: Windshield, Poly(vinyl butyral), Mortar, Diffusion, Carbonatation, Polymer waste.

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Authors: Wan Nural Jawahir Wan Yussof, Hans Burkhardt

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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: Ujjal K Ghosh, Ling Teen

Abstract:

Pervaporation has the potential to be an alternative to the other traditional separation processes such as distillation, adsorption, reverse osmosis and extraction. This study investigates the separation of phenol from water using a polyurethane membrane by pervaporation by applying the modified Maxwell-Stephen model. The modified Maxwell-Stefan model takes into account the non-ideal multi-component solubility effect, nonideal diffusivity of all permeating components, concentration dependent density of the membrane and diffusion coupling to predict various fluxes. Four cases has been developed to investigate the process parameters effects on the flux and weight fraction of phenol in the permeate values namely feed concentration, membrane thickness, operating temperature and operating downstream pressure. The model could describe semi-quantitatively the performance of the pervaporation membrane for the given system as a very good agreement between the observed and theoretical fluxes was observed.

Keywords: Pervaporation, Phenol, Polyurethane, Modified Maxwell-Stefan equation, Solution Diffusion

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Authors: Jyh-Yang Wu, Sheng-Gwo Chen

Abstract:

In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: Conservation laws, diffusion equations, Cahn-Hilliard Equations, evolving surfaces.

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Authors: R. Rajeshkannan, M. Rajasimman, N. Rajamohan

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In this study, the sorption of Malachite green (MG) on Hydrilla verticillata biomass, a submerged aquatic plant, was investigated in a batch system. The effects of operating parameters such as temperature, adsorbent dosage, contact time, adsorbent size, and agitation speed on the sorption of Malachite green were analyzed using response surface methodology (RSM). The proposed quadratic model for central composite design (CCD) fitted very well to the experimental data that it could be used to navigate the design space according to ANOVA results. The optimum sorption conditions were determined as temperature - 43.5oC, adsorbent dosage - 0.26g, contact time - 200min, adsorbent size - 0.205mm (65mesh), and agitation speed - 230rpm. The Langmuir and Freundlich isotherm models were applied to the equilibrium data. The maximum monolayer coverage capacity of Hydrilla verticillata biomass for MG was found to be 91.97 mg/g at an initial pH 8.0 indicating that the optimum sorption initial pH. The external and intra particle diffusion models were also applied to sorption data of Hydrilla verticillata biomass with MG, and it was found that both the external diffusion as well as intra particle diffusion contributes to the actual sorption process. The pseudo-second order kinetic model described the MG sorption process with a good fitting.

Keywords: Response surface methodology, Hydrilla verticillata, malachite green, adsorption, central composite design

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