Search results for: non-fickian diffusion

Authors: Ilkham Gafurovich Atabaev, Khimmatali Nomozovich Juraev

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The activation energy of conductivity in p-i-n SiC structures fabricated by doping with Aluminum using the new low-temperature diffusion method is investigated. In this method, diffusion is stimulated by the flux of carbon and silicon vacancies created by surface oxidation. The activation energy of conductivity in the p - layer is 0.25 eV and it is close to the ionization energy of Aluminum in 4H-SiC from 0.21 to 0.27 eV for the hexagonal and cubic positions of aluminum in the silicon sublattice for weakly doped crystals. The conductivity of the i-layer (measured in the reverse biased diode) shows 2 activation energies: 0.02 eV and 0.62 eV. Apparently, the 0.62 eV level is a deep trap level and it is a complex of Aluminum with a vacancy. According to the published data, an analogous level system (with activation energies of 0.05, 0.07, 0.09 and 0.67 eV) was observed in the ion Aluminum doped 4H-SiC samples.

Keywords: activation energy, aluminum, low temperature diffusion, SiC

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Authors: H. Namazi, H. T. N. Kuan

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Fick's first law relates the diffusive flux to the concentration field, by postulating that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative). It is clear that the diffusion of flux cannot be instantaneous and should be some time delay in this propagation. But Fick’s first law doesn’t consider this delay which results in some errors especially when there is a considerable time delay in the process. In this paper, we introduce a time delay to Fick’s first law. By this modification, we consider that the diffusion of flux cannot be instantaneous. In order to verify this claim an application sample in fluid diffusion is discussed and the results of modified Fick’s first law, Fick’s first law and the experimental results are compared. The results of this comparison stand for the accuracy of the modified model. The modified model can be used in any application where the time delay has considerable value and neglecting its effect reflects in undesirable results.

Keywords: Fick's first law, flux, diffusion, time delay, modified Fick’s first law

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

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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: Anna Keuchenius

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Broadly speaking, scientific development is studied in either a qualitative manner with a focus on the behavior and interpretations of academics, such as the sociology of science and science studies or in a quantitative manner with a focus on the analysis of publications, such as scientometrics and bibliometrics. Both come with a different set of methodologies and few cross-references. This paper contributes to the bridging of this divide, by on the on hand approaching the process of scientific progress from a qualitative sociological angle and using on the other hand quantitative and computational techniques. As a case study, we analyze the diffusion of Granovetter's hypothesis from his 1973 paper 'On The Strength of Weak Ties.' A network is constructed of all scientists that have referenced this particular paper, with directed edges to all other researchers that are concurrently referenced with Granovetter's 1973 paper. Studying the structure and growth of this network over time, it is found that Granovetter's hypothesis is used by distinct communities of scientists, each with their own key-narrative into which the hypothesis is fit. The diffusion within the communities shares similarities with the diffusion of an innovation in which innovators, early adopters, and an early-late majority can clearly be distinguished. Furthermore, the network structure shows that each community is clustered around one or few hub scientists that are disproportionately often referenced and seem largely responsible for carrying the hypothesis into their scientific subfield. The larger implication of this case study is that the diffusion of scientific hypotheses and ideas are not the spreading of well-defined objects over a network. Rather, the diffusion is a process in which the object itself dynamically changes in concurrence with its spread. Therefore it is argued that the methodology presented in this paper has potential beyond the scientific domain, in the study of diffusion of other not well-defined objects, such as opinions, behavior, and ideas.

Keywords: diffusion of innovations, network analysis, scientific development, sociology of science

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Authors: Betim Bahtiri, B. Arash, R. Rolfes

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Epoxy-based materials are frequently exposed to high-humidity environments in many engineering applications. As a result, their material properties would be degraded by water absorption. A full characterization of the material properties under hygrothermal conditions requires time- and cost-consuming experimental tests. To gain insights into the physics of diffusion mechanisms, atomistic simulations have been shown to be effective tools. Concerning the diffusion of water in polymers, spatial trajectories of water molecules are obtained from molecular dynamics (MD) simulations allowing the interpretation of diffusion pathways at the nanoscale in a polymer network. Conventional MD simulations of water diffusion in amorphous polymers lead to discrepancies at low temperatures due to the short timescales of the simulations. In the proposed model, this issue is solved by using a combined scheme of autonomous basin climbing (ABC) with kinetic Monte Carlo and reactive MD simulations to investigate the diffusivity of water molecules in epoxy resins across a wide range of temperatures. It is shown that the proposed simulation framework estimates kinetic properties of water diffusion in epoxy resins that are consistent with experimental observations and provide a predictive tool for investigating the diffusion of small molecules in other amorphous polymers.

Keywords: epoxy resins, water diffusion, autonomous basin climbing, kinetic Monte Carlo, reactive molecular dynamics

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Authors: Giulio Mangano, Alberto De Marco, Giovanni Zenezini

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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: H. Namazi, H. T. N. Kuan

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It is known that in humans, the adaptation to a given odor occurs within a quite short span of time (typically one minute) after the odor is presented to the brain. Different models of human olfaction have been developed by scientists but none of these models consider the diffusion phenomenon in olfaction. A novel microscopic model of the human olfaction is presented in this paper. We develop this model by incorporating the transient diffusivity. In fact, the mathematical model is written based on diffusion of the odorant within the mucus layer. By the use of the model developed in this paper, it becomes possible to provide quantification of the objective strength of odor.

Keywords: diffusion, microscopic model, mucus layer, olfaction

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Authors: Barbora Chmelova, Radek Sachl

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Gangliosides are amphipathic membrane lipids. Due to the composition of bulky oligosaccharide chains containing one or more sialic acids linked to the hydrophobic ceramide base, gangliosides are classified among glycosphingolipids. This unique structure induces a high self-aggregating tendency of gangliosides and, therefore, the formation of nanoscopic clusters called nanodomains. Gangliosides are preferentially present in an extracellular membrane leaflet of all human tissues and thus have an impact on a huge number of biological processes, such as intercellular communication, cell signalling, membrane trafficking, and regulation of receptor activity. Defects in their metabolism, impairment of proper ganglioside function, or changes in their organization lead to serious health conditions such as Alzheimer´s and Parkinson´s diseases, autoimmune diseases, tumour growth, etc. This work mainly focuses on ganglioside organization into nanodomains and their dynamics within the plasma membrane. Current research investigates static ganglioside nanodomains characterization; nevertheless, the information about their diffusion is missing. In our study, fluorescence correlation spectroscopy is implemented together with stimulated emission depletion (STED-FCS), which combines the diffraction-unlimited spatial resolution with high temporal resolution. By comparison of the experiments performed on model vesicles containing 4 % of either GM1, GM2, or GM3 and Monte Carlo simulations of diffusion on the plasma membrane, the description of ganglioside clustering, diffusion of nanodomains, and even diffusion of ganglioside molecules inside investigated nanodomains are described.

Keywords: gangliosides, nanodomains, STED-FCS, flourescence microscopy, membrane diffusion

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Authors: Andrew Terhemen Tyowua, Zhibing Zhang, Michael J. Adams

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Water vapor sorption data at a range of temperatures (25–70 °C) have been obtained for starch (corn and wheat) and non-starch (carrageenan and xanthan gum) hydrocolloid particles in the form of a thin slab. The results reveal that the data may be more accurately described by an existing sigmoidal rather than a Fickian model. The sigmoidal model accounts for the initial surface sorption before the onset of bulk diffusion. At relatively small water activities (≤ 0.3), the absorption of the moisture caused the particles to be plasticized, but at greater activity values (> 0.3), anti-plasticization was induced. However, it was found that for the whole range of water activities and temperatures studied, the data could be characterized by a single non-dimensional number, which was termed the non-Fickian diffusion number where τ is the characteristic time of surface sorption, D is the bulk diffusion coefficient and L is the thickness of the layer of particles. The activation energy suggested that the anti-plasticization mechanism was the result of a reduction in the molecular free volume or an increase in crystallinity.

Keywords: anti-plasticization, arrhenius behavior, diffusion coefficient, hygroscopic polymers, moisture migration, non-fickian sigmoidal model

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Authors: Ihab Elaff

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Simulating the heart’s electrical stimulation is essential in modeling and evaluating the electrophysiology behavior of the heart. For achieving that, there are two structures in concern: the ventricles’ Myocardium, and the ventricles’ Conduction Network. Ventricles’ Myocardium has been modeled as anisotropic material from Diffusion Tensor Imaging (DTI) scan, and the Conduction Network has been extracted from DTI as a case-based structure based on the biological properties of the heart tissues and the working methodology of the Magnetic Resonance Imaging (MRI) scanner. Results of the produced activation were much similar to real measurements of the reference model that was presented in the literature.

Keywords: diffusion tensor, DTI, heart, conduction network, excitation propagation

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Authors: Shayma Munqith Al-Baker, Fadhl Ahmed Saeed Al-Gasha’a, Samira Hamid Hanash, Ahmed Ali Al-Hazmi

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A total of 200 samples (180 fecal materials and 20 organ samples) were collected from (5 different poultry farms, 10 local poultry shops, 5 houses poultry, 5 Eggs stores shops and 5 hand slaughters centers) in Ibb city, Yemen, 2014. According to morphological, cultural, as well as biochemical characterization and serological tests, 59 29.5% isolates were identified as Salmonella spp. and all Salmonella isolates were categorized by serotype, which comprised of, 37 62.71% Salmonella Typhimurium serovar, 21 35.59%. Salmonella Enteritidis serovar and 11.69% Salmonella Heidelberg serovar. Antibiotic sensitivity test was done for bacterial isolates and the results showed there were clear differences in antibiotic resistant. Antimicrobial susceptibility of the isolates varies as follows: Ofloxacin 79.66%, Ciprofloxacin 67.80%, Colistin 59.32% and Gentamycin 52.54%. All of isolates were resistant to Erythromycin, Penicillin and Lincomycin. Antibacterial activity was done for both aqueous and ethanol extracts of Dodonaea viscosa plant by using well and disc diffusion assay. The results indicated that well diffusion assay had best results than disc diffusion assay, the highest inhibition zone was 22 mm for well diffusion and 15 mm for disc diffusion assay, the results observed that ethanol extract had best antibacterial effect than aqueous extract which the percentage of bacterial isolates affected with ethanol extract was 71.19% comparing with aqueous extract 28.81% by using disc diffusion assay, while the percentage of bacterial isolates affected with ethanol extract was 88.13% comparing with aqueous extract 52.54% by using will diffusion assay.

Keywords: Salmonella spp, Dodonaea viscosa, antimicrobial and salmonellosis

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Authors: John Knight, Fuchun Li, Yan Xu

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Based on a new method of the nonparametric estimator of the drift function, we propose a consistent test for the parametric specification of the drift function in the short rate diffusion process using observations from a panel of yields. The test statistic is shown to follow an asymptotic normal distribution under the null hypothesis that the parametric drift function is correctly specified, and converges to infinity under the alternative. Taking the daily 7-day European rates as a proxy of the short rate, we use our test to examine whether the drift of the short rate diffusion process is linear or nonlinear, which is an unresolved important issue in the short rate modeling literature. The testing results indicate that none of the drift functions in this literature adequately captures the dynamics of the drift, but nonlinear specification performs better than the linear specification.

Keywords: diffusion process, nonparametric estimation, derivative security price, drift function and volatility function

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

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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: Mohammad Shams Esfand Abadi, Mohammad Ranjbar, Reza Ebrahimpour

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This work presents the distributed processing solution problem in a diffusion network based on the adapt then combine (ATC) and combine then adapt (CTA)selective partial update normalized least mean squares (SPU-NLMS) algorithms. Also, we extend this approach to dynamic selection affine projection algorithm (DS-APA) and ATC-DS-APA and CTA-DS-APA are established. The purpose of ATC-SPU-NLMS and CTA-SPU-NLMS algorithm is to reduce the computational complexity by updating the selected blocks of weight coefficients at every iteration. In CTA-DS-APA and ATC-DS-APA, the number of the input vectors is selected dynamically. Diffusion cooperation strategies have been shown to provide good performance based on these algorithms. The good performance of introduced algorithm is illustrated with various experimental results.

Keywords: selective partial update, affine projection, dynamic selection, diffusion, adaptive distributed networks

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Authors: Ankur Dixit, Hiroaki Wagatsuma

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The crack detection on a concrete bridge is an important and constant task in civil engineering. Chronically, humans are checking the bridge for inspection of cracks to maintain the quality and reliability of bridge. But this process is very long and costly. To overcome such limitations, we have used a drone with a digital camera, which took some images of bridge deck and these images are processed by morphological component analysis (MCA). MCA technique is a very strong application of sparse coding and it explores the possibility of separation of images. In this paper, MCA has been used to decompose the image into coarse and fine components with the effectiveness of two dictionaries namely anisotropic diffusion and wavelet transform. An anisotropic diffusion is an adaptive smoothing process used to adjust diffusion coefficient by finding gray level and gradient as features. These cracks in image are enhanced by subtracting the diffused coarse image into the original image and the results are treated by Sobel edge detector and binary filtering to exhibit the cracks in a fine way. Our results demonstrated that proposed MCA framework using anisotropic diffusion followed by Sobel operator and binary filtering may contribute to an automation of crack detection even in open field sever conditions such as bridge decks.

Keywords: anisotropic diffusion, coarse component, fine component, MCA, Sobel edge detector and wavelet transform

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Authors: Tudor Barbu

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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: anisotropic diffusion, finite differences, image denoising and restoration, nonlinear PDE model, anisotropic diffusion, numerical approximation schemes

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Authors: Varun A Baheti, Sanjay Kashyap, Kamanio Chattopadhyay, Praveen Kumar, Aloke Paul

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Ni–Sn system finds applications in the microelectronics industry, especially with respect to flip–chip or direct chip, attach technology. Here the region of interest is under bump metallization (UBM), and solder bump (Sn) interface due to the formation of brittle intermetallic phases there. Understanding the growth of these phases at UBM/Sn interface is important, as in many cases it controls the electro–mechanical properties of the product. Cu and Ni are the commonly used UBM materials. Cu is used for good bonding because of fast reaction with solder and Ni often acts as a diffusion barrier layer due to its inherently slower reaction kinetics with Sn–based solders. Investigation on the growth kinetics of phases in Ni–Sn system is reported in this study. Just for simplicity, Sn being major solder constituent is chosen. Ni–Sn electroplated diffusion couples are prepared by electroplating pure Sn on Ni substrate. Bulk diffusion couples prepared by the conventional method are also studied along with Ni–Sn electroplated diffusion couples. Diffusion couples are annealed for 25–1000 h at 50–215°C to study the phase evolutions and growth kinetics of various phases. The interdiffusion zone was analysed using field emission gun equipped scanning electron microscope (FE–SEM) for imaging. Indexing of selected area diffraction (SAD) patterns obtained from transmission electron microscope (TEM) and composition measurements done in electron probe micro−analyser (FE–EPMA) confirms the presence of various product phases grown across the interdiffusion zone. Time-dependent experiments indicate diffusion controlled growth of the product phase. The estimated activation energy in the temperature range 125–215°C for parabolic growth constants (and hence integrated interdiffusion coefficients) of the Ni₃Sn₄ phase shed light on the growth mechanism of the phase; whether its grain boundary controlled or lattice controlled diffusion. The location of the Kirkendall marker plane indicates that the Ni₃Sn₄ phase grows mainly by diffusion of Sn in the binary Ni–Sn system.

Keywords: diffusion, equilibrium phase, metastable phase, the Ni-Sn system

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Authors: Michael Tupý, Vít Petránek

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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: Mary Ann U. Baradi, Arnold R. Elepaño, Manuel Jose C. Regalado

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Aromatic rice has become popular and continues to command higher price than ordinary rice because of its distinctive scent that makes it special. Freshly harvested aromatic rice exhibits strong aromatic scent but decreases with time and conditions during storage. Of the many volatile compounds in aromatic rice, 2-acetyl-1-pyrroline (2AP) is a major compound that gives rice its popcorn-like aroma. The diffusion mechanism of 2AP in rice was investigated. Semi-empirical models explaining 2AP diffusion as affected by temperature and duration were developed. Storage time and temperature affected 2AP loss via diffusion. The amount of 2AP in rice decreased with time. Free 2AP, being volatile, is lost due to diffusion. Storage experiment indicated rapid 2AP loss during the first five weeks and subsequently leveled off afterwards; attaining level of starch bound 2AP. Decline of 2AP during storage followed exponential equation and exhibited four stages; i.e. the initial, second, third and final stage. Free 2AP is easily lost while bound 2AP is left, only to be released upon exposure to high temperature such as cooking. Both free and bound 2AP is found in endosperm while free 2AP is in the bran. Around 63–67% of total 2AP was lost in brown and milled rice of MS 6 paddy kept at ambient. Samples stored at higher temperature (27°C) recorded higher 2AP loss than those kept at lower temperature (15°C). The study should be able to guide processors in understanding and controlling parameters in storage to produce high quality rice.

Keywords: 2-acetyl-1-pyrroline, aromatic rice, diffusion mechanism, storage

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Authors: Thanisa Sirithaporn

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The study aims to examine the diffusion of social innovation among Thai Community Enterprises in conjunction with a singular case study of a medium-sized corporation that has successfully transitioned from a charitable foundation to a sustainable, profitable entity creating value for both shareholders and the communities in which it operates. It seeks to bridge the gap between different streams of aligned research in the fields of diffusion, social innovation, and community enterprises into a more cohesive conceptual framework and thus to better understand the historical and current impediments that have resulted in so many enterprises failing to be sustainable. The methodology is mixed and dual phased. The initial quantitative phase uses a questionnaire as the main research instrument distributed among community enterprises throughout Thailand which will provide the themes for the qualitative phase through semi-structured interviews with key stakeholders at a commercial enterprise actively engaged in social innovation. The findings seek to present a more comprehensive conceptual framework and actionable guidelines to aid community enterprises to develop social innovation in a sustainable manner that creates value to its beneficiaries.

Keywords: diffusion, community enterprises, social innovation, Thailand

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

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The present study introduces the folding technology to be utilized for the first time in vertical diffusion stills. This work represents a model of the distillation process by utilizing chevron pattern of folded structure. An experimental setup has been constructed, to investigate the performance of the folded sheets in the vertical effect diffusion still for a specific range of operating conditions. An experimental comparison between the folded type and the flat type sheets has been carried out. The folded pattern showed a higher performance and there is an increase in the condensate to feed ratio that ranges from 20-30 % through the operating hot plate temperature that ranges through 60-90°C. In addition, a parametric analysis of the system using Design of Experiments statistical technique, has been developed using the experimental results to determine the effect of operating conditions on the system's performance and the best operating conditions of the system has been evaluated.

Keywords: chevron pattern, fold structure, solar distillation, vertical diffusion still

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Authors: Zh. M. Blednova, P. O. Rusinov

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Results of research on the formation of the surface layers of a material with shape memory effect (SME) based on TiNi diffusion metallization in molten Pb-Bi under isothermal conditions in an argon atmosphere are presented. It is shown that this method allows obtaining of uniform surface layers in nanostructured state of internal surfaces on the articles of complex shapes with stress concentrators. Structure, chemical and phase composition of the surface layers provide a manifestation of TiNi shape memory. The average grain size of TiNi coatings ranges between 60 ÷ 160 nm.

Keywords: diffusion metallization, nikelid titanium surface layers, shape memory effect, nanostructures

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Authors: Sanaz Kavianpour, Zuraini Ismail, Bharanidharan Shanmugam

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Social Network Sites (SNSs) can be served as an invaluable platform to transfer the information across a large number of individuals. A substantial component of communicating and managing information is to identify which individual will influence others in propagating information and also whether dissemination of information in the absence of social signals about that information will be occurred or not. Classifying the final audience of social data is difficult as controlling the social contexts which transfers among individuals are not completely possible. Hence, undesirable information diffusion to an unauthorized individual on SNSs can threaten individuals’ privacy. This paper highlights the information diffusion in SNSs and moreover it emphasizes the most significant privacy issues to individuals of SNSs. The goal of this paper is to propose a privacy-preserving model that has urgent regards with individuals’ data in order to control availability of data and improve privacy by providing access to the data for an appropriate third parties without compromising the advantages of information sharing through SNSs.

Keywords: anonymization algorithm, classification algorithm, information diffusion, privacy, social network sites

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

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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 semi-analytical 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: Hassan J. Al Salman, Ahmed A. Al Ghafli

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In this study, we consider a nonlinear in time finite element approximation of a reaction diffusion system of lambda-omega type. We use a fixed-point theorem to prove existence of the approximations at each time level. Then, we derive some essential stability estimates and discuss the uniqueness of the approximations. In addition, we employ Nochetto mathematical framework to prove an optimal error bound in time for d= 1, 2 and 3 space dimensions. Finally, we present some numerical experiments to verify the obtained theoretical results.

Keywords: reaction diffusion system, finite element approximation, stability estimates, error bound

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Authors: Hassan Al Salman, Ahmed Al Ghafli

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In this study we consider a nonlinear in time finite element approximation of a reaction diffusion system of lambda-omega type. We use a fixed point theorem to prove existence of the approximations. Then, we derive some essential stability estimates and discuss the uniqueness of the approximations. Also, we prove an optimal error bound in time for d=1, 2 and 3 space dimensions. Finally, we present some numerical experiments to verify the theoretical results.

Keywords: reaction diffusion system, finite element approximation, fixed point theorem, an optimal error bound

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Authors: P. V. Pantyukhov, T. V. Monakhova, A. A. Popov

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The paper studies the diffusion of low molecular weight components from vegetable fillers into polyethylene matrix during the preparation of biocomposites. In order to identify the diffusible substances a model experiment used where the hexadecane acted as a model of polyethylene. It was determined that polyphenolic compounds and chlorophyll penetrate from vegetable fillers to hexadecane to the maximum extent. There was found a correlation between the amount of polyphenolic compounds diffusible from the fillers to hexadecane and thermal oxidation kinetics of real biocomposites based on polyethylene and vegetable fillers. Thus, it has been assumed the diffusion of polyphenols and chlorophyll from vegetable fillers into polyethylene matrix during the preparation of biocomposites.

Keywords: biocomposite, composite, diffusion, polyethylene, vegetable filler

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Authors: Sneha Samal, Iva Petrikova, Bohdana Marvalova

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Influence of grain size, shape and grain boundary diffusion at high temperature oxidation of pure metal is investigated as the function of microstructure evolution in this article. The oxidized scale depends on the geometrical parameter of the metal-scale system and grain shape, size, diffusion through boundary layers and influence of the contamination. The creation of the inner layer and the morphological structure develops from the internal stress generated during the growth of the scale. The oxidation rate depends on the cation and anion mobile transport of the metal in the inward and outward direction of the diffusion layer. Oxidation rate decreases with decreasing the grain size of the pure metal, whereas zinc deviates from this principle. A strong correlation between the surface roughness evolution, grain size, crystalline properties and oxidation mechanism of the oxidized metal was established.

Keywords: high temperature oxidation, pure metals, grain size, shape and grain boundary

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Authors: Ayan Chakraborty, BV. Rathish Kumar

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Off-late many models in viscoelasticity, signal processing or anomalous diffusion equations are formulated in fractional calculus. Tempered fractional calculus is the generalization of fractional calculus and in the last few years several important partial differential equations occurring in the different field of science have been reconsidered in this term like diffusion wave equations, Schr$\ddot{o}$dinger equation and so on. In the present paper, a time-dependent tempered fractional diffusion equation of order $\gamma \in (0,1)$ with forcing function is considered. Existence, uniqueness, stability, and regularity of the solution has been proved. Crank-Nicolson discretization is used in the time direction. B spline finite element approximation is implemented. Generally, B-splines basis are useful for representing the geometry of a finite element model, interfacing a finite element analysis program. By utilizing this technique a priori space-time estimate in finite element analysis has been derived and we proved that the convergent order is $\mathcal{O}(h²+T²)$ where $h$ is the space step size and $T$ is the time. A couple of numerical examples have been presented to confirm the accuracy of theoretical results. Finally, we conclude that the studied method is useful for solving tempered fractional diffusion equations.

Keywords: B-spline finite element, error estimates, Gronwall's lemma, stability, tempered fractional

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Authors: Boukhatem Mohamed Nadjib, Ferhat Mohamed Amine

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Essential Oils (EO) produced by medicinal plants have been traditionally used for respiratory tract infections and are used nowadays as ethical medicines for colds. The aim of this study was to test the efficacy of the Algerian EGEO against some respiratory tract pathogens by disc diffusion and vapour diffusion methods at different concentrations. The chemical composition of the EGEO was analysed by Gas Chromatography-Mass Spectrometry. Fresh leaves of E. globulus on steam distillation yielded 0.96% (v/w) of essential oil whereas the analysis resulted in the identification of a total of 11 constituents, 1.8 cineole (85.8%), α-pinene (7.2%) and β-myrcene (1.5%) being the main components. By disc diffusion method, EGEO showed potent antimicrobial activity against Gram-positive more than Gram-negative bacteria. The Diameter of Inhibition Zone (DIZ) varied from 69 mm to 75 mm for Staphylococcus aureus and Bacillus subtilis (Gram +) and from 13 to 42 mm for Enterobacter sp and Escherichia coli (Gram-), respectively. However, the results obtained by both agar diffusion and vapour diffusion methods were different. Significantly higher antibacterial activity was observed in the vapour phase at lower concentrations. A. baumanii and Klebsiella pneumoniae were the most susceptible strains to the oil vapour with DIZ varied from 38 to 42 mm. Therefore, smaller doses of EO in the vapour phase can be inhibitory to pathogenic bacteria. Else, the DIZ increased with increase in the concentration of the oil. There is growing evidence that EGEO in the vapour phase are effective antibacterial systems and appears worthy to be considered for practical uses in the treatment or prevention of patients with respiratory tract infections or as air decontaminants in the hospital. The present study indicates that EGEO has considerable antimicrobial activity, deserving further investigation for clinical applications.

Keywords: eucalyptus globulus, essential oils, respiratory tract pathogens, antimicrobial activity, vapour phase

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