Search results for: nature-based solutions
966 Issues in Travel Demand Forecasting
Authors: Huey-Kuo Chen
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Travel demand forecasting including four travel choices, i.e., trip generation, trip distribution, modal split and traffic assignment constructs the core of transportation planning. In its current application, travel demand forecasting has associated with three important issues, i.e., interface inconsistencies among four travel choices, inefficiency of commonly used solution algorithms, and undesirable multiple path solutions. In this paper, each of the three issues is extensively elaborated. An ideal unified framework for the combined model consisting of the four travel choices and variable demand functions is also suggested. Then, a few remarks are provided in the end of the paper
Keywords: Travel choices, B algorithm, entropy maximization, dynamic traffic assignment.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2337965 Solutions to Probabilistic Constrained Optimal Control Problems Using Concentration Inequalities
Authors: Tomoaki Hashimoto
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Recently, optimal control problems subject to probabilistic constraints have attracted much attention in many research field. Although probabilistic constraints are generally intractable in optimization problems, several methods haven been proposed to deal with probabilistic constraints. In most methods, probabilistic constraints are transformed to deterministic constraints that are tractable in optimization problems. This paper examines a method for transforming probabilistic constraints into deterministic constraints for a class of probabilistic constrained optimal control problems.Keywords: Optimal control, stochastic systems, discrete-time systems, probabilistic constraints.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1361964 The Positive Solution for Singular Eigenvalue Problem of One-dimensional p-Laplace Operator
Authors: Lv Yuhua
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In this paper, by constructing a special cone and using fixed point theorem and fixed point index theorem of cone, we get the existence of positive solution for a class of singular eigenvalue value problems with p-Laplace operator, which improved and generalized the result of related paper.
Keywords: Cone, fixed point index, eigenvalue problem, p-Laplace operator, positive solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1419963 Nonlinear Modelling of Sloshing Waves and Solitary Waves in Shallow Basins
Authors: Mohammad R. Jalali, Mohammad M. Jalali
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The earliest theories of sloshing waves and solitary waves based on potential theory idealisations and irrotational flow have been extended to be applicable to more realistic domains. To this end, the computational fluid dynamics (CFD) methods are widely used. Three-dimensional CFD methods such as Navier-Stokes solvers with volume of fluid treatment of the free surface and Navier-Stokes solvers with mappings of the free surface inherently impose high computational expense; therefore, considerable effort has gone into developing depth-averaged approaches. Examples of such approaches include Green–Naghdi (GN) equations. In Cartesian system, GN velocity profile depends on horizontal directions, x-direction and y-direction. The effect of vertical direction (z-direction) is also taken into consideration by applying weighting function in approximation. GN theory considers the effect of vertical acceleration and the consequent non-hydrostatic pressure. Moreover, in GN theory, the flow is rotational. The present study illustrates the application of GN equations to propagation of sloshing waves and solitary waves. For this purpose, GN equations solver is verified for the benchmark tests of Gaussian hump sloshing and solitary wave propagation in shallow basins. Analysis of the free surface sloshing of even harmonic components of an initial Gaussian hump demonstrates that the GN model gives predictions in satisfactory agreement with the linear analytical solutions. Discrepancies between the GN predictions and the linear analytical solutions arise from the effect of wave nonlinearities arising from the wave amplitude itself and wave-wave interactions. Numerically predicted solitary wave propagation indicates that the GN model produces simulations in good agreement with the analytical solution of the linearised wave theory. Comparison between the GN model numerical prediction and the result from perturbation analysis confirms that nonlinear interaction between solitary wave and a solid wall is satisfactorilly modelled. Moreover, solitary wave propagation at an angle to the x-axis and the interaction of solitary waves with each other are conducted to validate the developed model.
Keywords: Even harmonic components of sloshing waves, Green–Naghdi equations, nonlinearity, solitary waves.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 856962 Self-Organizing Maps in Evolutionary Approachmeant for Dimensioning Routes to the Demand
Authors: J.-C. Créput, A. Koukam, A. Hajjam
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We present a non standard Euclidean vehicle routing problem adding a level of clustering, and we revisit the use of self-organizing maps as a tool which naturally handles such problems. We present how they can be used as a main operator into an evolutionary algorithm to address two conflicting objectives of route length and distance from customers to bus stops minimization and to deal with capacity constraints. We apply the approach to a real-life case of combined clustering and vehicle routing for the transportation of the 780 employees of an enterprise. Basing upon a geographic information system we discuss the influence of road infrastructures on the solutions generated.Keywords: Evolutionary algorithm, self-organizing map, clustering and vehicle routing.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1376961 Accounting Information Systems of Kuwaiti Companies: Obstacles and Barriers
Authors: Haya Y Alobaid
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The aim of this paper is to identify and discuss the obstacles to the ability of the accounting information systems of Kuwaiti companies to deal with electronic commerce, and then to propose appropriate solutions to overcome the barriers. The study revealed a remarkable decrease in external auditors who have professional certification. The results also showed an agreement regarding the accounting systems and the ability to deal with e-commerce, with a different degree of importance, despite the presence of obstacles to the ability of accounting systems in dealing with different companies.Keywords: Accounting information systems, obstacle, barriers, electronic commerce, Kuwait companies.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1392960 Comparison of Evolutionary Algorithms and their Hybrids Applied to MarioAI
Authors: Hidehiko Okada, Yuki Fujii
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Researchers have been applying artificial/ computational intelligence (AI/CI) methods to computer games. In this research field, further researchesare required to compare AI/CI methods with respect to each game application. In thispaper, we report our experimental result on the comparison of evolution strategy, genetic algorithm and their hybrids, applied to evolving controller agents for MarioAI. GA revealed its advantage in our experiment, whereas the expected ability of ES in exploiting (fine-tuning) solutions was not clearly observed. The blend crossover operator and the mutation operator of GA might contribute well to explore the vast search space.
Keywords: Evolutionary algorithm, autonomous game controller agent, neuroevolutions, MarioAI
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1715959 The Synthetic T2 Quality Control Chart and its Multi-Objective Optimization
Authors: Francisco Aparisi, Marco A. de Luna
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In some real applications of Statistical Process Control it is necessary to design a control chart to not detect small process shifts, but keeping a good performance to detect moderate and large shifts in the quality. In this work we develop a new quality control chart, the synthetic T2 control chart, that can be designed to cope with this objective. A multi-objective optimization is carried out employing Genetic Algorithms, finding the Pareto-optimal front of non-dominated solutions for this optimization problem.Keywords: Multi-objective optimization, Quality Control, SPC, Synthetic T2 control chart.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1546958 Extended Least Squares LS–SVM
Authors: József Valyon, Gábor Horváth
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Among neural models the Support Vector Machine (SVM) solutions are attracting increasing attention, mostly because they eliminate certain crucial questions involved by neural network construction. The main drawback of standard SVM is its high computational complexity, therefore recently a new technique, the Least Squares SVM (LS–SVM) has been introduced. In this paper we present an extended view of the Least Squares Support Vector Regression (LS–SVR), which enables us to develop new formulations and algorithms to this regression technique. Based on manipulating the linear equation set -which embodies all information about the regression in the learning process- some new methods are introduced to simplify the formulations, speed up the calculations and/or provide better results.Keywords: Function estimation, Least–Squares Support VectorMachines, Regression, System Modeling
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1996957 Laplace Decomposition Approximation Solution for a System of Multi-Pantograph Equations
Authors: M. A. Koroma, C. Zhan, A. F. Kamara, A. B. Sesay
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In this work we adopt a combination of Laplace transform and the decomposition method to find numerical solutions of a system of multi-pantograph equations. The procedure leads to a rapid convergence of the series to the exact solution after computing a few terms. The effectiveness of the method is demonstrated in some examples by obtaining the exact solution and in others by computing the absolute error which decreases as the number of terms of the series increases.
Keywords: Laplace decomposition, pantograph equations, exact solution, numerical solution, approximate solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1633956 Analytical Solution for the Zakharov-Kuznetsov Equations by Differential Transform Method
Authors: Saeideh Hesam, Alireza Nazemi, Ahmad Haghbin
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This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.
Keywords: Zakharov-Kuznetsov equation, differential transform method, closed form solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1919955 A Fast Cyclic Reduction Algorithm for A Quadratic Matrix Equation Arising from Overdamped Systems
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We are concerned with a class of quadratic matrix equations arising from the overdamped mass-spring system. By exploring the structure of coefficient matrices, we propose a fast cyclic reduction algorithm to calculate the extreme solutions of the equation. Numerical experiments show that the proposed algorithm outperforms the original cyclic reduction and the structure-preserving doubling algorithm.Keywords: Fast algorithm, Cyclic reduction, Overdampedquadratic matrix equation, Structure-preserving doubling algorithm
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1320954 Sustainability in Space Composition of Traditional Architecture of Hot Arid Zones of Iran
Authors: Farshad Kheiri
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Iran Central Plateau encompasses a large proportion of this country. The weather in these flat plains is warm and arid with very little precipitation. Different attempts in architecture have been done to alleviate the weather severity of this area and create a living place compatible with humans’ comfort criteria. Investigations have showed that some of the most successful approaches in traditional architecture of the area has been forgotten or are not being used widely. As sustainability is defined as an appropriate solution for environmental, economical, and social disorders, this research is a try to demonstrate the sustainability in aforementioned architecture and based on these studies, propounds solutions for today architecture in hot arid zones.
Keywords: Hot arid climatic zone, Iranian Architecture, Sustainability, Vernacular architecture.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2728953 Frequency Domain Analysis for Hopf Bifurcation in a Delayed Competitive Web-site Model
Authors: Changjin Xu, Yusen Wu
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In this paper, applying frequency domain approach, a delayed competitive web-site system is investigated. By choosing the parameter α as a bifurcation parameter, it is found that Hopf bifurcation occurs as the bifurcation parameter α passes a critical values. That is, a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. Some numerical simulations are included to justify the theoretical analysis results. Finally, main conclusions are given.Keywords: Web-site system, stability, Nyquist criterion, Hopf bifurcation, frequency domain.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1454952 An Efficient Iterative Updating Method for Damped Structural Systems
Authors: Jiashang Jiang
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Model updating is an inverse eigenvalue problem which concerns the modification of an existing but inaccurate model with measured modal data. In this paper, an efficient gradient based iterative method for updating the mass, damping and stiffness matrices simultaneously using a few of complex measured modal data is developed. Convergence analysis indicates that the iterative solutions always converge to the unique minimum Frobenius norm symmetric solution of the model updating problem by choosing a special kind of initial matrices.
Keywords: Model updating, iterative algorithm, damped structural system, optimal approximation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2077951 Removal of Basic Blue 3 from Aqueous Solution by Adsorption Onto Durio Ziberthinus
Authors: Siew-Teng
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Durian husk (DH), a fruit waste, was studied for its ability to remove Basic blue 3 (BB3) from aqueous solutions. Batch kinetic studies were carried out to study the sorption characteristics under various experimental conditions. The optimum pH for the dye removal occurred in the pH range of 3-10. Sorption was found to be concentration and agitation dependent. The kinetics of dye sorption fitted a pseudo-second order rate expression. Both Langmuir and Freundlich models appeared to provide reasonable fittings for the sorption data of BB3 on durian husk. Maximum sorption capacity calculated from the Langmuir model is 49.50 mg g-1.
Keywords: Durian husk, Batch study, Sorption, Basic Blue 3
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1265950 The Use of Crisis Workplace Technology to Protect Communication Processes of Critical Infrastructure
Authors: Jiri Barta, Jiri F. Urbanek
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This paper deals with a protection of the national and European infrastructure. It is issue nowadays. The paper deals with the perspectives and possibilities of "smart solutions" to critical infrastructure protection. The research project deals with computers aided technologies are used from the perspective of new, better protection of selected infrastructure objects. Protection is focused on communication and information channels. These communication and information channels are very important for the functioning of the system of protection of critical infrastructure elements.
Keywords: Interoperability, Communication systems, Controlling Process, Critical Infrastructure, Crisis Workplaces. Continuity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1726949 Enhancing Security in Resource Sharing Using Key Holding Mechanism
Authors: M. Victor Jose, V. Seenivasagam
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This paper describes a logical method to enhance security on the grid computing to restrict the misuse of the grid resources. This method is an economic and efficient one to avoid the usage of the special devices. The security issues, techniques and solutions needed to provide a secure grid computing environment are described. A well defined process for security management among the resource accesses and key holding algorithm is also proposed. In this method, the identity management, access control and authorization and authentication are effectively handled.
Keywords: Grid security, Irregular binary series, Key holding mechanism, Resource identity, Secure resource access.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1721948 Utilizing 5G Mobile Connection as a Node in Layer 1 Proof of Authority Blockchain Used for Microtransaction
Authors: Frode van der Laak
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The paper contributes to the feasibility of using a 5G mobile connection as a node for a Proof of Authority (PoA) blockchain, which is used for microtransactions at the same time. It uses the phone number identity of the users that are linked to the crypto wallet address. It also proposed a consensus protocol based on PoA blockchain; PoA is a permission blockchain where consensus is achieved through a set of designated authority rather than through mining, as is the case with a Proof of Work (PoW) blockchain. This report will first explain the concept of a PoA blockchain and how it works. It will then discuss the potential benefits and challenges of using a 5G mobile connection as a node in such a blockchain, and finally, the main open problem statement and proposed solutions with the requirements.
Keywords: 5G, mobile, connection, node, PoA, blockchain, microtransaction.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 168947 The removal of Ni, Cu and Fe from a Mixed Metal System using Sodium Hypophosphite as a Reducing Agent
Authors: Promise Sethembiso Ngema, Freeman Ntuli, Mohamed Belaid
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The main objective of this study was to remove and recover Ni, Cu and Fe from a mixed metal system using sodium hypophosphite as a reducing agent and nickel powder as seeding material. The metal systems studied consisted of Ni-Cu, Ni-Fe and Ni-Cu-Fe solutions. A 5 L batch reactor was used to conduct experiments where 100 mg/l of each respective metal was used. It was found that the metals were reduced to their elemental form with removal efficiencies of over 80%. The removal efficiency decreased in the order Fe>Ni>Cu. The metal powder obtained contained between 97-99% Ni and was almost spherical and porous. Size enlargement by aggregation was the dominant particulate process.
Keywords: crystallization, electroless plating, heavy metal removal, wastewater treatment
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2027946 Research of Concentratibility of Low Quality Bauxite Raw Materials
Authors: Nadezhda Nikolaeva, Tatyana Alexandrova, Alexandr Alexandrov
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Processing of high-silicon bauxite on the base of the traditional clinkering method is related to high power consumption and capital investments, which makes production of alumina from those ores non-competitive in terms of basic economic showings. For these reasons, development of technological solutions enabling to process bauxites with various chemical and mineralogical structures efficiently with low level of thermal power consumption is important. Flow sheet of the studies on washability of ores from the Timanskoe and the Severo-Onezhskoe deposits is on the base of the flotation method.Keywords: Low-quality bauxite, resource-saving technology, optimization, aluminum, conditioning of composition, separation characteristics.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1934945 Combined Simulated Annealing and Genetic Algorithm to Solve Optimization Problems
Authors: Younis R. Elhaddad
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Combinatorial optimization problems arise in many scientific and practical applications. Therefore many researchers try to find or improve different methods to solve these problems with high quality results and in less time. Genetic Algorithm (GA) and Simulated Annealing (SA) have been used to solve optimization problems. Both GA and SA search a solution space throughout a sequence of iterative states. However, there are also significant differences between them. The GA mechanism is parallel on a set of solutions and exchanges information using the crossover operation. SA works on a single solution at a time. In this work SA and GA are combined using new technique in order to overcome the disadvantages' of both algorithms.
Keywords: Genetic Algorithm, Optimization problems, Simulated Annealing, Traveling Salesman Problem
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3427944 An Innovational Intermittent Algorithm in Networks-On-Chip (NOC)
Authors: Ahmad M. Shafiee, Mehrdad Montazeri, Mahdi Nikdast
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Every day human life experiences new equipments more automatic and with more abilities. So the need for faster processors doesn-t seem to finish. Despite new architectures and higher frequencies, a single processor is not adequate for many applications. Parallel processing and networks are previous solutions for this problem. The new solution to put a network of resources on a chip is called NOC (network on a chip). The more usual topology for NOC is mesh topology. There are several routing algorithms suitable for this topology such as XY, fully adaptive, etc. In this paper we have suggested a new algorithm named Intermittent X, Y (IX/Y). We have developed the new algorithm in simulation environment to compare delay and power consumption with elders' algorithms.Keywords: Computer architecture, parallel computing, NOC, routing algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1666943 Cognitive Virtual Exploration for Optimization Model Reduction
Authors: Livier Serna, Xavier Fischer, Fouad Bennis
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In this paper, a decision aid method for preoptimization is presented. The method is called “negotiation", and it is based on the identification, formulation, modeling and use of indicators defined as “negotiation indicators". These negotiation indicators are used to explore the solution space by means of a classbased approach. The classes are subdomains for the negotiation indicators domain. They represent equivalent cognitive solutions in terms of the negotiation indictors being used. By this method, we reduced the size of the solution space and the criteria, thus aiding the optimization methods. We present an example to show the method.Keywords: Optimization Model Reduction, Pre-Optimization, Negotiation Process, Class-Making, Cognition Based VirtualExploration.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1416942 Feature Subset Selection Using Ant Colony Optimization
Authors: Ahmed Al-Ani
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Feature selection is an important step in many pattern classification problems. It is applied to select a subset of features, from a much larger set, such that the selected subset is sufficient to perform the classification task. Due to its importance, the problem of feature selection has been investigated by many researchers. In this paper, a novel feature subset search procedure that utilizes the Ant Colony Optimization (ACO) is presented. The ACO is a metaheuristic inspired by the behavior of real ants in their search for the shortest paths to food sources. It looks for optimal solutions by considering both local heuristics and previous knowledge. When applied to two different classification problems, the proposed algorithm achieved very promising results.Keywords: Ant Colony Optimization, ant systems, feature selection, pattern recognition.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1584941 Socioculture and Cognitivist Perspectives on Language and Communication Barriers in Learning
Authors: David Hallberg
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It is believed that major account on language diversity must be taken in learning, and especially in learning using ICT. This paper-s objective is to exhibit language and communication barriers in learning, to approach the topic from socioculture and cognitivist perspectives, and to give exploratory solutions of handling such barriers. The review is mainly conducted by approaching the journal Computers & Education, but also an initially broad search was conducted. The results show that not much attention is paid on language and communication barriers in an immediate relation to learning using ICT. The results shows, inter alia, that language and communication barriers are caused because of not enough account is taken on both the individual-s background and the technology.
Keywords: communication barriers, cognitive, ICT, language barriers, learning, socioculture
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2347940 Group Similarity Transformation of a Time Dependent Chemical Convective Process
Authors: M. M. Kassem, A. S. Rashed
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The time dependent progress of a chemical reaction over a flat horizontal plate is here considered. The problem is solved through the group similarity transformation method which reduces the number of independent by one and leads to a set of nonlinear ordinary differential equation. The problem shows a singularity at the chemical reaction order n=1 and is analytically solved through the perturbation method. The behavior of the process is then numerically investigated for n≠1 and different Schmidt numbers. Graphical results for the velocity and concentration of chemicals based on the analytical and numerical solutions are presented and discussed.
Keywords: Time dependent, chemical convection, grouptransformation method, perturbation method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1611939 Towards Security in Virtualization of SDN
Authors: Wanqing You, Kai Qian, Xi He, Ying Qian
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In this paper, the potential security issues brought by the virtualization of a Software Defined Networks (SDN) would be analyzed. The virtualization of SDN is achieved by FlowVisor (FV). With FV, a physical network is divided into multiple isolated logical networks while the underlying resources are still shared by different slices (isolated logical networks). However, along with the benefits brought by network virtualization, it also presents some issues regarding security. By examining security issues existing in an OpenFlow network, which uses FlowVisor to slice it into multiple virtual networks, we hope we can get some significant results and also can get furtherdiscussions among the security of SDN virtualization.
Keywords: FlowVisor, Network virtualization, Potential threats, Possible solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2153938 Optimization of Unweighted Minimum Vertex Cover
Authors: S. Balaji, V. Swaminathan, K. Kannan
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The Minimum Vertex Cover (MVC) problem is a classic graph optimization NP - complete problem. In this paper a competent algorithm, called Vertex Support Algorithm (VSA), is designed to find the smallest vertex cover of a graph. The VSA is tested on a large number of random graphs and DIMACS benchmark graphs. Comparative study of this algorithm with the other existing methods has been carried out. Extensive simulation results show that the VSA can yield better solutions than other existing algorithms found in the literature for solving the minimum vertex cover problem.Keywords: vertex cover, vertex support, approximation algorithms, NP - complete problem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2469937 On the Determination of a Time-like Dual Curve in Dual Lorentzian Space
Authors: Emin Özyılmaz
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In this work, position vector of a time-like dual curve according to standard frame of D31 is investigated. First, it is proven that position vector of a time-like dual curve satisfies a dual vector differential equation of fourth order. The general solution of this dual vector differential equation has not yet been found. Due to this, in terms of special solutions, position vectors of some special time-like dual curves with respect to standard frame of D31 are presented.Keywords: Classical Differential Geometry, Dual Numbers, DualFrenet Equations, Time-like Dual Curve, Position Vector, DualLorentzian Space.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1462