Search results for: diffusion maps
1915 Combining Diffusion Maps and Diffusion Models for Enhanced Data Analysis
Authors: Meng Su
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High-dimensional data analysis often presents challenges in capturing the complex, nonlinear relationships and manifold structures inherent to the data. This article presents a novel approach that leverages the strengths of two powerful techniques, Diffusion Maps and Diffusion Probabilistic Models (DPMs), to address these challenges. By integrating the dimensionality reduction capability of Diffusion Maps with the data modeling ability of DPMs, the proposed method aims to provide a comprehensive solution for analyzing and generating high-dimensional data. The Diffusion Map technique preserves the nonlinear relationships and manifold structure of the data by mapping it to a lower-dimensional space using the eigenvectors of the graph Laplacian matrix. Meanwhile, DPMs capture the dependencies within the data, enabling effective modeling and generation of new data points in the low-dimensional space. The generated data points can then be mapped back to the original high-dimensional space, ensuring consistency with the underlying manifold structure. Through a detailed example implementation, the article demonstrates the potential of the proposed hybrid approach to achieve more accurate and effective modeling and generation of complex, high-dimensional data. Furthermore, it discusses possible applications in various domains, such as image synthesis, time-series forecasting, and anomaly detection, and outlines future research directions for enhancing the scalability, performance, and integration with other machine learning techniques. By combining the strengths of Diffusion Maps and DPMs, this work paves the way for more advanced and robust data analysis methods.Keywords: diffusion maps, diffusion probabilistic models (DPMs), manifold learning, high-dimensional data analysis
Procedia PDF Downloads 951914 A Study of Closed Sets and Maps with Ideals
Authors: Asha Gupta, Ramandeep Kaur
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The purpose of this paper is to study a class of closed sets, called generalized pre-closed sets with respect to an ideal (briefly Igp-closed sets), which is an extension of generalized pre-closed sets in general topology. Then, by using these sets, the concepts of Igp- compact spaces along with some classes of maps like continuous and closed maps via ideals have been introduced and analogues of some known results for compact spaces, continuous maps and closed maps in general topology have been obtained.Keywords: ideal, gp-closed sets, gp-closed maps, gp-continuous maps
Procedia PDF Downloads 2161913 Diffusion Magnetic Resonance Imaging and Magnetic Resonance Spectroscopy in Detecting Malignancy in Maxillofacial Lesions
Authors: Mohamed Khalifa Zayet, Salma Belal Eiid, Mushira Mohamed Dahaba
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Introduction: Malignant tumors may not be easily detected by traditional radiographic techniques especially in an anatomically complex area like maxillofacial region. At the same time, the advent of biological functional MRI was a significant footstep in the diagnostic imaging field. Objective: The purpose of this study was to define the malignant metabolic profile of maxillofacial lesions using diffusion MRI and magnetic resonance spectroscopy, as adjunctive aids for diagnosing of such lesions. Subjects and Methods: Twenty-one patients with twenty-two lesions were enrolled in this study. Both morphological and functional MRI scans were performed, where T1, T2 weighted images, diffusion-weighted MRI with four apparent diffusion coefficient (ADC) maps were constructed for analysis, and magnetic resonance spectroscopy with qualitative and semi-quantitative analyses of choline and lactate peaks were applied. Then, all patients underwent incisional or excisional biopsies within two weeks from MR scans. Results: Statistical analysis revealed that not all the parameters had the same diagnostic performance, where lactate had the highest areas under the curve (AUC) of 0.9 and choline was the lowest with insignificant diagnostic value. The best cut-off value suggested for lactate was 0.125, where any lesion above this value is supposed to be malignant with 90 % sensitivity and 83.3 % specificity. Despite that ADC maps had comparable AUCs still, the statistical measure that had the final say was the interpretation of likelihood ratio. As expected, lactate again showed the best combination of positive and negative likelihood ratios, whereas for the maps, ADC map with 500 and 1000 b-values showed the best realistic combination of likelihood ratios, however, with lower sensitivity and specificity than lactate. Conclusion: Diffusion weighted imaging and magnetic resonance spectroscopy are state-of-art in the diagnostic arena and they manifested themselves as key players in the differentiation process of orofacial tumors. The complete biological profile of malignancy can be decoded as low ADC values, high choline and/or high lactate, whereas that of benign entities can be translated as high ADC values, low choline and no lactate.Keywords: diffusion magnetic resonance imaging, magnetic resonance spectroscopy, malignant tumors, maxillofacial
Procedia PDF Downloads 1661912 Dynamic Ad-hoc Topologies for Mobile Robot Navigation Based on Non-Uniform Grid Maps
Authors: Peter Sauer, Thomas Hinze, Petra Hofstedt
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To avoid obstacles in the surrounding environment and to navigate to a given target belong to the most important tasks for mobile robots. According to these tasks different data structures are suitable. To avoid near obstacles, occupancy grid maps are an ideal representation of the surroundings. For less fine grained tasks, such as navigating from one room to another in an apartment, pure grid maps are inappropriate. Grid maps are very detailed, calculating paths to navigate between rooms based on grid maps would take too long. Instead, graph-based data structures, so-called topologies, turn out to be a proper choice for such tasks. In this paper we present two methods to dynamically create topologies from grid maps. Both methods are based on non-uniform grid maps. The topologies are generated on-the-fly and can easily be modified to represent changes in the environment. This allows a hybrid approach to control mobile robots, where, depending on the situation and the current task, either the grid map or the generated topology may be used.Keywords: robot navigation, occupancy grids, topological maps, dynamic map creation
Procedia PDF Downloads 5551911 Solutions of Fractional Reaction-Diffusion Equations Used to Model the Growth and Spreading of Biological Species
Authors: Kamel Al-Khaled
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Reaction-diffusion equations are commonly used in population biology to model the spread of biological species. In this paper, we propose a fractional reaction-diffusion equation, where the classical second derivative diffusion term is replaced by a fractional derivative of order less than two. Based on the symbolic computation system Mathematica, Adomian decomposition method, developed for fractional differential equations, is directly extended to derive explicit and numerical solutions of space fractional reaction-diffusion equations. The fractional derivative is described in the Caputo sense. Finally, the recent appearance of fractional reaction-diffusion equations as models in some fields such as cell biology, chemistry, physics, and finance, makes it necessary to apply the results reported here to some numerical examples.Keywords: fractional partial differential equations, reaction-diffusion equations, adomian decomposition, biological species
Procedia PDF Downloads 3641910 A Study on Temperature and Drawing Speed for Diffusion Bonding Enhancement in Drawing of Hot Lined Pipes by FEM Analysis
Authors: M. T. Ahn, J. H. Park, S. H. Park, S. H. Ha
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Diffusion bonding has been continuously studied. Temperature and pressure are the most important factors to increase the strength between diffusion bonded interfaces. Diffusion bonding is an important factor affecting the bonding strength of the lined pipe. The increase of the diffusion bonding force results in a high formability clad pipe. However, in the case of drawing, it is difficult to obtain a high pressure between materials due to a relatively small reduction in cross-section, and it is difficult to prevent elongation or to tear of material in hot drawing even if the reduction in the section is increased. In this paper, to increase the diffusion bonding force, we derive optimal temperature and pressure to suppress material stretching and realize precise thickness precision.Keywords: diffusion bonding, temperature, pressure, drawing speed
Procedia PDF Downloads 3701909 Analysis of Vapor-Phase Diffusion of Benzene from Contaminated Soil
Authors: Asma A. Parlin, K. Nakamura, N. Watanabe, T. Komai
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Understanding the effective diffusion of benzene vapor in the soil-atmosphere interface is important as an intrusion of benzene into the atmosphere from the soil is largely driven by diffusion. To analyze the vertical one dimensional effective diffusion of benzene vapor in porous medium with high water content, diffusion experiments were conducted in soil columns using Andosol soil and Toyoura silica sand with different water content; for soil water content was from 0 to 30 wt.% and for sand it was from 0.06 to 10 wt.%. In soil, a linear relation was found between water content and effective diffusion coefficient while the effective diffusion coefficient didn’t change in the sand with increasing water. A numerical transport model following unsteady-state approaches based on Fick’s second law was used to match the required time for a steady state of the gas phase concentration profile of benzene to the experimentally measured concentration profile gas phase in the column. The result highlighted that both the water content and porosity might increase vertical diffusion of benzene vapor in soil.Keywords: benzene vapor-phase, effective diffusion, subsurface soil medium, unsteady state
Procedia PDF Downloads 1361908 A Simple Finite Element Method for Glioma Tumor Growth Model with Density Dependent Diffusion
Authors: Shangerganesh Lingeshwaran
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In this presentation, we have performed numerical simulations for a reaction-diffusion equation with various nonlinear density-dependent diffusion operators and proliferation functions. The mathematical model represented by parabolic partial differential equation is considered to study the invasion of gliomas (the most common type of brain tumors) and to describe the growth of cancer cells and response to their treatment. The unknown quantity of the given reaction-diffusion equation is the density of cancer cells and the mathematical model based on the proliferation and migration of glioma cells. A standard Galerkin finite element method is used to perform the numerical simulations of the given model. Finally, important observations on the each of nonlinear diffusion functions and proliferation functions are presented with the help of computational results.Keywords: glioma invasion, nonlinear diffusion, reaction-diffusion, finite eleament method
Procedia PDF Downloads 2231907 Evaluate the Possibility of Using ArcGIS Basemaps as GCP for Large Scale Maps
Authors: Jali Octariady, Ida Herliningsih, Ade K. Mulyana, Annisa Fitria, Diaz C. K. Yuwana
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Awareness of the importance large-scale maps for development of a country is growing in all walks of life, especially for governments in Indonesia. Various parties, especially local governments throughout Indonesia demanded for immediate availability the large-scale maps of 1:5000 for regional development. But in fact, the large-scale maps of 1:5000 is only available less than 5% of the entire territory of Indonesia. Unavailability precise GCP at the entire territory of Indonesia is one of causes of slow availability the large scale maps of 1:5000. This research was conducted to find an alternative solution to this problem. This study was conducted to assess the accuracy of ArcGIS base maps coordinate when it shall be used as GCP for creating a map scale of 1:5000. The study was conducted by comparing the GCP coordinate from Field survey using GPS Geodetic than the coordinate from ArcGIS basemaps in various locations in Indonesia. Some areas are used as a study area are Lombok Island, Kupang City, Surabaya City and Kediri District. The differences value of the coordinates serve as the basis for assessing the accuracy of ArcGIS basemaps coordinates. The results of the study at various study area show the variation of the amount of the coordinates value given. Differences coordinate value in the range of millimeters (mm) to meters (m) in the entire study area. This is shown the inconsistency quality of ArcGIS base maps coordinates. This inconsistency shows that the coordinate value from ArcGIS Basemaps is careless. The Careless coordinate from ArcGIS Basemaps indicates that its cannot be used as GCP for large-scale mapping on the entire territory of Indonesia.Keywords: accuracy, ArcGIS base maps, GCP, large scale maps
Procedia PDF Downloads 3651906 Brokerage and Value-Creation: Trading Practices in the English Market of 20th-Century Maps
Authors: Shaun Lim
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This paper presents a 9-month ethnographic case study of the value creating strategies employed by an Oxford market-trader of 20th-century maps. Maps are usually valued and sold as either antique objets d’art or useful navigational tools, with 20th-century maps precariously lying between the boundary of the aesthetic and utilitarian value-regimes. Here, the brokerage practices involved in the framing of outdated, lowly valued maps into vintage commodities will be examined. Ethnographic material of the unstudied market of old maps is introduced and situated in the second-hand, antique and collectible spheres of exchange. The map-trader as a broker is the ethnographic and methodological starting point of this paper. Brokerage is understood through the activity of framing that defines and brackets the value-regimes of commodities with the aid of market and framing devices. The trader’s activities will be examined in three parts. (1) The post-sourcing industry: the altering, mounting and tagging of maps before putting them into market circulation. Mounts, frames and tags are seen as market devices that authenticates and frames maps with aesthetic and symbolic values along with the disentanglement of its use value. (2) The market-display: the constitution of space that encourages the relations of looking at maps as aesthetic objects, while the categorical arrangement of the display contributes to legitimising of the collectability of maps. (3) The salesmanship strategies of the trader: the match-making of customers with maps of meaningful value, and the mediating of knowledge through the verbal articulation of the map’s symbolic values. Ultimately, value is not created in an accumulative sense, but is layered and superimposed to cater to a wide spectrum of patrons. The trader creates demand for his goods by mediating and articulating value-regimes already coherent to potential patrons.Keywords: art and material culture, brokerage, commodification, framing, markets, value
Procedia PDF Downloads 1431905 A Study of Numerical Reaction-Diffusion Systems on Closed Surfaces
Authors: Mei-Hsiu Chi, Jyh-Yang Wu, Sheng-Gwo Chen
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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: closed surfaces, high-order approachs, numerical solutions, reaction-diffusion systems
Procedia PDF Downloads 3651904 Buzan Mind Mapping: An Efficient Technique for Note-Taking
Authors: T. K. Tee, M. N. A. Azman, S. Mohamed, M. Muhammad, M. M. Mohamad, J. Md Yunos, M. H. Yee, W. Othman
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Buzan mind mapping is an efficient system of note-taking that makes revision a fun thing to do for students. Tony Buzan has been teaching children all over the world for the past thirty years and has proved that mind maps are the magic formula in the classroom for everyone. The purpose of this paper is to discuss the importance of Buzan mind mapping as a note-taking technique for the secondary school students. This paper also examines the mind mapping technique, advantages and disadvantages of hand-drawn mind maps. Samples of students’ mind maps were presented and discussed.Keywords: Buzan mind mapping, note-taking technique, hand-drawn, mind maps
Procedia PDF Downloads 5321903 A Novel Probabilistic Spatial Locality of Reference Technique for Automatic Cleansing of Digital Maps
Authors: A. Abdullah, S. Abushalmat, A. Bakshwain, A. Basuhail, A. Aslam
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GIS (Geographic Information System) applications require geo-referenced data, this data could be available as databases or in the form of digital or hard-copy agro-meteorological maps. These parameter maps are color-coded with different regions corresponding to different parameter values, converting these maps into a database is not very difficult. However, text and different planimetric elements overlaid on these maps makes an accurate image to database conversion a challenging problem. The reason being, it is almost impossible to exactly replace what was underneath the text or icons; thus, pointing to the need for inpainting. In this paper, we propose a probabilistic inpainting approach that uses the probability of spatial locality of colors in the map for replacing overlaid elements with underlying color. We tested the limits of our proposed technique using non-textual simulated data and compared text removing results with a popular image editing tool using public domain data with promising results.Keywords: noise, image, GIS, digital map, inpainting
Procedia PDF Downloads 3441902 Flood Disaster Prevention and Mitigation in Nigeria Using Geographic Information System
Authors: Dinebari Akpee, Friday Aabe Gaage, Florence Fred Nwaigwu
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Natural disasters like flood affect many parts of the world including developing countries like Nigeria. As a result, many human lives are lost, properties damaged and so much money is lost in infrastructure damages. These hazards and losses can be mitigated and reduced by providing reliable spatial information to the generality of the people through about flood risks through flood inundation maps. Flood inundation maps are very crucial for emergency action plans, urban planning, ecological studies and insurance rates. Nigeria experience her worst flood in her entire history this year. Many cities were submerged and completely under water due to torrential rainfall. Poor city planning, lack of effective development control among others contributes to the problem too. Geographic information system (GIS) can be used to visualize the extent of flooding, analyze flood maps to produce flood damaged estimation maps and flood risk maps. In this research, the under listed steps were taken in preparation of flood risk maps for the study area: (1) Digitization of topographic data and preparation of digital elevation model using ArcGIS (2) Flood simulation using hydraulic model and integration and (3) Integration of the first two steps to produce flood risk maps. The results shows that GIS can play crucial role in Flood disaster control and mitigation.Keywords: flood disaster, risk maps, geographic information system, hazards
Procedia PDF Downloads 2171901 A Study on the Relationship between Shear Strength and Surface Roughness of Lined Pipes by Cold Drawing
Authors: Mok-Tan Ahn, Joon-Hong Park, Yeon-Jong Jeong
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Diffusion bonding has been continuously studied. Temperature and pressure are the most important factors to increase the strength between diffusion bonded interfaces. Diffusion bonding is an important factor affecting the bonding strength of the lined pipe. The increase of the diffusion bonding force results in a high formability clad pipe. However, in the case of drawing, it is difficult to obtain a high pressure between materials due to a relatively small reduction in cross-section, and it is difficult to prevent elongation or to tear of material in heat drawing even if the reduction in section is increased. In this paper, to increase the diffusion bonding force, we derive optimal temperature and pressure to suppress material stretching and realize precise thickness precision.Keywords: drawing speed, FEM (Finite Element Method), diffusion bonding, temperature, heat drawing, lined pipe
Procedia PDF Downloads 3021900 Heat Transfer and Diffusion Modelling
Authors: R. Whalley
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The heat transfer modelling for a diffusion process will be considered. Difficulties in computing the time-distance dynamics of the representation will be addressed. Incomplete and irrational Laplace function will be identified as the computational issue. Alternative approaches to the response evaluation process will be provided. An illustration application problem will be presented. Graphical results confirming the theoretical procedures employed will be provided.Keywords: heat, transfer, diffusion, modelling, computation
Procedia PDF Downloads 5471899 Knowledge Diffusion via Automated Organizational Cartography (Autocart)
Authors: Mounir Kehal
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The post-globalization epoch has placed businesses everywhere in new and different competitive situations where knowledgeable, effective and efficient behavior has come to provide the competitive and comparative edge. Enterprises have turned to explicit - and even conceptualizing on tacit - knowledge management to elaborate a systematic approach to develop and sustain the intellectual capital needed to succeed. To be able to do that, you have to be able to visualize your organization as consisting of nothing but knowledge and knowledge flows, whilst being presented in a graphical and visual framework, referred to as automated organizational cartography. Hence, creating the ability of further actively classifying existing organizational content evolving from and within data feeds, in an algorithmic manner, potentially giving insightful schemes and dynamics by which organizational know-how is visualized. It is discussed and elaborated on most recent and applicable definitions and classifications of knowledge management, representing a wide range of views from mechanistic (systematic, data driven) to a more socially (psychologically, cognitive/metadata driven) orientated. More elaborate continuum models, for knowledge acquisition and reasoning purposes, are being used for effectively representing the domain of information that an end user may contain in their decision making process for utilization of available organizational intellectual resources (i.e. Autocart). In this paper, we present an empirical research study conducted previously to try and explore knowledge diffusion in a specialist knowledge domain.Keywords: knowledge management, knowledge maps, knowledge diffusion, organizational cartography
Procedia PDF Downloads 3011898 The Use of the Matlab Software as the Best Way to Recognize Penumbra Region in Radiotherapy
Authors: Alireza Shayegan, Morteza Amirabadi
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The y tool was developed to quantitatively compare dose distributions, either measured or calculated. Before computing ɣ, the dose and distance scales of the two distributions, referred to as evaluated and reference, are re-normalized by dose and distance criteria, respectively. The re-normalization allows the dose distribution comparison to be conducted simultaneously along dose and distance axes. Several two-dimensional images were acquired using a Scanning Liquid Ionization Chamber EPID and Extended Dose Range (EDR2) films for regular and irregular radiation fields. The raw images were then converted into two-dimensional dose maps. Transitional and rotational manipulations were performed for images using Matlab software. As evaluated dose distribution maps, they were then compared with the corresponding original dose maps as the reference dose maps.Keywords: energetic electron, gamma function, penumbra, Matlab software
Procedia PDF Downloads 2921897 Influence Maximization in Dynamic Social Networks and Graphs
Authors: Gkolfo I. Smani, Vasileios Megalooikonomou
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Social influence and influence diffusion have been studied in social networks. However, most existing tasks on this subject focus on static networks. 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 the 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, graphs
Procedia PDF Downloads 2281896 Data-Centric Anomaly Detection with Diffusion Models
Authors: Sheldon Liu, Gordon Wang, Lei Liu, Xuefeng Liu
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Anomaly detection, also referred to as one-class classification, plays a crucial role in identifying product images that deviate from the expected distribution. This study introduces Data-centric Anomaly Detection with Diffusion Models (DCADDM), presenting a systematic strategy for data collection and further diversifying the data with image generation via diffusion models. The algorithm addresses data collection challenges in real-world scenarios and points toward data augmentation with the integration of generative AI capabilities. The paper explores the generation of normal images using diffusion models. The experiments demonstrate that with 30% of the original normal image size, modeling in an unsupervised setting with state-of-the-art approaches can achieve equivalent performances. With the addition of generated images via diffusion models (10% equivalence of the original dataset size), the proposed algorithm achieves better or equivalent anomaly localization performance.Keywords: diffusion models, anomaly detection, data-centric, generative AI
Procedia PDF Downloads 771895 Knowledge Diffusion via Automated Organizational Cartography: Autocart
Authors: Mounir Kehal, Adel Al Araifi
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The post-globalisation epoch has placed businesses everywhere in new and different competitive situations where knowledgeable, effective and efficient behaviour has come to provide the competitive and comparative edge. Enterprises have turned to explicit- and even conceptualising on tacit- Knowledge Management to elaborate a systematic approach to develop and sustain the Intellectual Capital needed to succeed. To be able to do that, you have to be able to visualize your organization as consisting of nothing but knowledge and knowledge flows, whilst being presented in a graphical and visual framework, referred to as automated organizational cartography. Hence, creating the ability of further actively classifying existing organizational content evolving from and within data feeds, in an algorithmic manner, potentially giving insightful schemes and dynamics by which organizational know-how is visualised. It is discussed and elaborated on most recent and applicable definitions and classifications of knowledge management, representing a wide range of views from mechanistic (systematic, data driven) to a more socially (psychologically, cognitive/metadata driven) orientated. More elaborate continuum models, for knowledge acquisition and reasoning purposes, are being used for effectively representing the domain of information that an end user may contain in their decision making process for utilization of available organizational intellectual resources (i.e. Autocart). In this paper we present likewise an empirical research study conducted previously to try and explore knowledge diffusion in a specialist knowledge domain.Keywords: knowledge management, knowledge maps, knowledge diffusion, organizational cartography
Procedia PDF Downloads 4131894 Influence of Photophysical Parameters of Photoactive Materials on Exciton Diffusion Length and Diffusion Coefficient in Bulk Heterojunction Organic Solar Cells
Authors: Douglas Yeboah, Jai Singh
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It has been experimentally demonstrated that exciton diffusion length in organic solids can be improved by fine-tuning the material parameters that govern exciton transfer. Here, a theoretical study is carried out to support this finding. We have therefore derived expressions for the exciton diffusion length and diffusion coefficient of singlet and triplet excitons using Förster resonance energy transfer and Dexter carrier transfer mechanisms and are plotted as a function of photoluminescence (PL) quantum yield, spectral overlap integral, refractive index and dipole moment of the photoactive material. We found that singlet exciton diffusion length increases with PL quantum yield and spectral overlap integral, and decreases with increase in refractive index. Likewise, the triplet exciton diffusion length increases when PL quantum yield increases and dipole moment decreases. The calculated diffusion lengths in different organic materials are compared with existing experimental values and found to be in reasonable agreement. The results are expected to provide insight in developing new organic materials for fabricating bulk heterojunction (BHJ) organic solar cells (OSCs) with better photoconversion efficiency.Keywords: Dexter carrier transfer, diffusion coefficient, exciton diffusion length, Föster resonance energy transfer, photoactive materials, photophysical parameters
Procedia PDF Downloads 3261893 Investigation of Mesoporous Silicon Carbonization Process
Authors: N. I. Kargin, G. K. Safaraliev, A. S. Gusev, A. O. Sultanov, N. V. Siglovaya, S. M. Ryndya, A. A. Timofeev
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In this paper, an experimental and theoretical study of the processes of mesoporous silicon carbonization during the formation of buffer layers for the subsequent epitaxy of 3C-SiC films and related wide-band-gap semiconductors is performed. Experimental samples were obtained by the method of chemical vapor deposition and investigated by scanning electron microscopy. Analytic expressions were obtained for the effective diffusion factor and carbon atoms diffusion length in a porous system. The proposed model takes into account the processes of Knudsen diffusion, coagulation and overgrowing of pores during the formation of a silicon carbide layer.Keywords: silicon carbide, porous silicon, carbonization, electrochemical etching, diffusion
Procedia PDF Downloads 2511892 Formation of Chemical Compound Layer at the Interface of Initial Substances A and B with Dominance of Diffusion of the A Atoms
Authors: Pavlo Selyshchev, Samuel Akintunde
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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
Procedia PDF Downloads 5641891 Operational Matrix Method for Fuzzy Fractional Reaction Diffusion Equation
Authors: Sachin Kumar
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Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method
Procedia PDF Downloads 1911890 Natural Gas Production Forecasts Using Diffusion Models
Authors: Md. Abud Darda
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Different options for natural gas production in wide geographic areas may be described through diffusion of innovation models. This type of modeling approach provides an indirect estimate of an ultimately recoverable resource, URR, capture the quantitative effects of observed strategic interventions, and allow ex-ante assessments of future scenarios over time. In order to ensure a sustainable energy policy, it is important to forecast the availability of this natural resource. Considering a finite life cycle, in this paper we try to investigate the natural gas production of Myanmar and Algeria, two important natural gas provider in the world energy market. A number of homogeneous and heterogeneous diffusion models, with convenient extensions, have been used. Models validation has also been performed in terms of prediction capability.Keywords: diffusion models, energy forecast, natural gas, nonlinear production
Procedia PDF Downloads 2221889 Diffusive Transport of VOCs Through Composite Liners
Authors: Christina Jery, R. K. Anjana, D. N. Arnepalli, R. Sobha
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Modern landfills employ a composite liner consisting of a geomembrane overlying a compacted clay liner (CCL) or a geosynthetic clay liner (GCL) as a barrier system. The primary function of a barrier system is to control the contaminant transport from the leachate (dissolved phase) and landfill gas (vapour phase) out of the landfill thereby minimizing the environmental impact. This study is undertaken to investigate the diffusive migration of VOCs through composite liners. VOCs are known hazardous air pollutants were often existing in both the vapour phase and dissolved phase. These compounds are known to diffuse readily through the polymeric geomembranes. The objective of the research is to develop a comprehensive data set of diffusive parameters involved in the diffusion of VOCs in the composite liner (1.5 mm HDPE geomembrane overlying a 30mm compacted clay layer). For this purpose, the study aims to develop a new experimental setup for determining the diffusion characteristics. The key parameters of diffusion (partitioning, diffusion and permeation coefficients) are examined. The diffusion tests are carried out both in aqueous and vapor phase. Finally, an attempt is also made to study the effect of low temperature on the diffusion characteristics.Keywords: diffusion, sorption, organic compounds, composite liners, geomembrane
Procedia PDF Downloads 3591888 A Very Efficient Pseudo-Random Number Generator Based On Chaotic Maps and S-Box Tables
Authors: M. Hamdi, R. Rhouma, S. Belghith
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Generating random numbers are mainly used to create secret keys or random sequences. It can be carried out by various techniques. In this paper we present a very simple and efficient pseudo-random number generator (PRNG) based on chaotic maps and S-Box tables. This technique adopted two main operations one to generate chaotic values using two logistic maps and the second to transform them into binary words using random S-Box tables. The simulation analysis indicates that our PRNG possessing excellent statistical and cryptographic properties.Keywords: Random Numbers, Chaotic map, S-box, cryptography, statistical tests
Procedia PDF Downloads 3591887 On Tarski’s Type Theorems for L-Fuzzy Isotone and L-Fuzzy Relatively Isotone Maps on L-Complete Propelattices
Authors: František Včelař, Zuzana Pátíková
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Recently a new type of very general relational structures, the so called (L-)complete propelattices, was introduced. These significantly generalize complete lattices and completely lattice L-ordered sets, because they do not assume the technically very strong property of transitivity. For these structures also the main part of the original Tarski’s fixed point theorem holds for (L-fuzzy) isotone maps, i.e., the part which concerns the existence of fixed points and the structure of their set. In this paper, fundamental properties of (L-)complete propelattices are recalled and the so called L-fuzzy relatively isotone maps are introduced. For these maps it is proved that they also have fixed points in L-complete propelattices, even if their set does not have to be of an awaited analogous structure of a complete propelattice.Keywords: fixed point, L-complete propelattice, L-fuzzy (relatively) isotone map, residuated lattice, transitivity
Procedia PDF Downloads 2711886 A Combinatorial Representation for the Invariant Measure of Diffusion Processes on Metric Graphs
Authors: Michele Aleandri, Matteo Colangeli, Davide Gabrielli
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We study a generalization to a continuous setting of the classical Markov chain tree theorem. In particular, we consider an irreducible diffusion process on a metric graph. The unique invariant measure has an atomic component on the vertices and an absolutely continuous part on the edges. We show that the corresponding density at x can be represented by a normalized superposition of the weights associated to metric arborescences oriented toward the point x. A metric arborescence is a metric tree oriented towards its root. The weight of each oriented metric arborescence is obtained by the product of the exponential of integrals of the form ∫a/b², where b is the drift and σ² is the diffusion coefficient, along the oriented edges, for a weight for each node determined by the local orientation of the arborescence around the node and for the inverse of the diffusion coefficient at x. The metric arborescences are obtained by cutting the original metric graph along some edges.Keywords: diffusion processes, metric graphs, invariant measure, reversibility
Procedia PDF Downloads 164