Search results for: numerical modeling

Authors: Ishara Madusanka, So Morikawa

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Natural disasters, particularly floods, pose severe challenges globally, affecting both developed and developing countries. In many regions, especially Asia, riverine floods are prevalent and devastating. Integrated flood management incorporates structural and non-structural measures, with preventive relocation emerging as a cost-effective and proactive strategy for areas repeatedly impacted by severe flooding. However, preventive relocation is often hindered by economic, psychological, social, and institutional barriers. This study investigates the factors influencing resistance to preventive relocation and evaluates the role of flood risk information in shaping relocation decisions through risk perception. A conceptual model was developed, incorporating variables such as Flood Risk Information (FRI), Place Attachment (PA), Good Living Conditions (GLC), and Adaptation to Flooding (ATF), with Flood Risk Perception (FRP) serving as a mediating variable. The research was conducted in Welipitiya in the Polwatta river basin, Matara district, Sri Lanka, a region experiencing recurrent flood damage. For this study, an experimental design involving a structured questionnaire survey was utilized, with 185 households participating. The treatment group received flood risk information, including flood risk maps and historical data, while the control group did not. Data were collected in 2023 and analyzed using independent sample t-tests and Partial Least Squares Structural Equation Modeling (PLS-SEM). PLS-SEM was chosen for its ability to model latent variables, handle complex relationships, and suitability for exploratory research. Multi-group Analysis (MGA) assessed variations across different flood risk areas. Findings indicate that flood risk information had a limited impact on flood risk perception and relocation decisions, though its effect was significant in specific high-risk areas. Place attachment was a significant factor influencing relocation decisions across the sample. One potential reason for the limited impact of flood risk information on relocation decisions could be the lack of specificity in the information provided. The results suggest that while flood risk information alone may not significantly influence relocation decisions, it is crucial in specific contexts. Future studies and practitioners should focus on providing more detailed risk information and addressing psychological factors like place attachments to enhance preventive relocation efforts.

Keywords: flood risk communication, flood risk perception, place attachment, preventive relocation, structural equation modeling

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Authors: Ibrahim A. Aref, Tarek El-Mihoub, Khadiga Ben Musa

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This paper presents Carrier Sense Multiple Access (CSMA) communication model based on SoC design methodology. Such model can be used to support the modelling of the complex wireless communication systems, therefore use of such communication model is an important technique in the construction of high performance communication. SystemC has been chosen because it provides a homogeneous design flow for complex designs (i.e. SoC and IP based design). We use a swarm system to validate CSMA designed model and to show how advantages of incorporating communication early in the design process. The wireless communication created through the modeling of CSMA protocol that can be used to achieve communication between all the agents and to coordinate access to the shared medium (channel).

Keywords: systemC, modelling, simulation, CSMA

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Authors: Uyanga Sukhbaatar, Ahmed Lbath, Mendamar Majig

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The Orienteering Problem is the most known example to start modeling tourist trip design problem. In order to meet tourist’s interest and constraint the OP is becoming more and more complicate to solve. The Multi Constraint Team Orienteering Problem with Time Windows is the last extension of the OP which differentiates from other extensions by including more extra associated constraints. The goal of the MCTOPTW is maximizing tourist’s satisfaction score in same time not to violate any of these constraints. This paper presents a genetic algorithmic approach to tackle the MCTOPTW. The benchmark data from literature is tested by our algorithm and the performance results are compared.

Keywords: multi constraint team orienteering problem with time windows, genetic algorithm, tour planning system

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Authors: Zdzislaw Kaminski, Zbigniew Czyz, Krzysztof Skiba

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This paper discusses the CFD simulation of a flow around a rotor of a Vertical Axis Wind Turbine. Numerical simulation, unlike experiments, enables us to validate project assumptions when it is designed and avoid a costly preparation of a model or a prototype for a bench test. CFD simulation enables us to compare characteristics of aerodynamic forces acting on rotor working surfaces and define operational parameters like torque or power generated by a turbine assembly. This research focused on the rotor with the blades capable of modifying their working surfaces, i.e. absorbing wind kinetic energy. The operation of this rotor is based on adjusting angular aperture α of the top and bottom parts of the blades mounted on an axis. If this angular aperture α increases, the working surface which absorbs wind kinetic energy also increases. The operation of turbines is characterized by parameters like the angular aperture of blades, power, torque, speed for a given wind speed. These parameters have an impact on the efficiency of assemblies. The distribution of forces acting on the working surfaces in our turbine changes according to the angular velocity of the rotor. Moreover, the resultant force from the force acting on an advancing blade and retreating blade should be as high as possible. This paper is part of the research to improve an efficiency of a rotor assembly. Therefore, using simulation, the courses of the above parameters were studied in three full rotations individually for each of the blades for three angular apertures of blade working surfaces, i.e. 30 °, 60 °, 90 °, at three wind speeds, i.e. 4 m / s, 6 m / s, 8 m / s and rotor speeds ranging from 100 to 500 rpm. Finally, there were created the characteristics of torque coefficients and power as a function of time for each blade separately and for the entire rotor. Accordingly, the correlation between the turbine rotor power as a function of wind speed for varied values of rotor rotational speed. By processing this data, the correlation between the power of the turbine rotor and its rotational speed for each of the angular aperture of the working surfaces was specified. Finally, the optimal values, i.e. of the highest output power for given wind speeds were read. The research results in receiving the basic characteristics of turbine rotor power as a function of wind speed for the three angular apertures of the blades. Given the nature of rotor operation, the growth in the output turbine can be estimated if angular aperture of the blades increases. The controlled adjustment of angle α enables a smooth adjustment of power generated by a turbine rotor. If wind speed is significant, this type of adjustment enables this output power to remain at the same level (by reducing angle α) with no risk of damaging a construction. This work has been financed by the Polish Ministry of Science and Higher Education.

Keywords: computational fluid dynamics, numerical analysis, renewable energy, wind turbine

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Authors: Vinod Kumar Arya

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Creep analysis of a thick-walled composite anisotropic cylinder under internal pressure and considering large strains is presented. Using a threshold creep law for composite materials, expressions for stresses, strains, and strain rates are derived for several anisotropic cases. Numerical results, presented through several graphs and tables, depict the effect of anisotropy on the stress, strain, and strain rate distributions. Since for a specific type of material anisotropy described in the paper, these quantities are found to have the lowest values at the inner radius (the potential location of cylinder failure), it is concluded that by employing such an anisotropic material for the design of a thick-walled cylinder a longer service life for the cylinder may be achieved.

Keywords: creep, composites, large strains, thick-walled cylinders, anisotropy

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Authors: Safwan Kanan, Jonathan Dewsbury, Gregory Lane-Serff

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A salinity gradient solar pond is a free energy source system for collecting, converting and storing solar energy as heat. In this paper, the principles of solar pond are explained. A mathematical model is developed to describe and simulate heat and mass transfer behavior of salinity gradient solar pond. Matlab codes are programmed to solve the one dimensional finite difference method for heat and mass transfer equations. Temperature profiles and concentration distributions are calculated. The numerical results are validated with experimental data and the results are found to be in good agreement.

Keywords: finite difference method, salt-gradient solar-pond, solar energy, transient heat and mass transfer

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Authors: Michał Rogala, Jakub Gajewski

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As the automotive industry develops, passive safety is becoming an increasingly important aspect when designing motor vehicles. A commonly used solution is energy absorption by thin-walled construction. One such structure is a closed thin-walled profile fixed to the vehicle stringers. The article presents numerical tests of conical thin-walled profiles filled with aluminum foam. The columns were loaded axially with constant energy. On the basis of the results obtained, efficiency indicators were calculated. The efficiency of the foam filling was evaluated. Artificial neural networks were used for data analysis. The application of regression analysis was used as a tool to study the relationship between the quantities characteristic of the dynamic crush.

Keywords: aluminium foam, crashworthiness, neural networks, thin-walled structure

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Authors: Rim Ben Kalifa, Sabra Habli, Nejla Mahjoub Saïd, Hervé Bournot, Georges Le Palec

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The present study treats different phenomena taking place in a configuration of air jet impinging on a flat surface in a coflow stream. A Computational Fluid Dynamics study is performed using the Reynolds-averaged Navier–Stokes equations by means of the Reynolds Stress Model (RSM) second order turbulent closure model. The results include mean and turbulent velocities and quantify the large effects of the coflow stream on an impinging air jet. The study of the jet in a no-directed coflow stream shows the presence of a phenomenon of recirculation near the flat plate. The influence of the coflow velocity ratio on the behavior of an impinging plane jet was also numerically investigated. The coflow stream imposed noticeable restrictions on the spreading of the impinging jet. The results show that the coflow stream decreases considerably the entrainment of air jet.

Keywords: turbulent jet, turbulence models, coflow stream, velocity ratio

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Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieha

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In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: polynomial constitutive equation, solitary, stress solitary waves, nonlinear constitutive law

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Authors: J. Racedo, J. Torres

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Globalization has led to a worldwide competition for participation in markets of goods and productive factors, with significant effects on transports requirements. The port industry has not been an exception to this event, in fact, it has received increasing attention in recent years due to its crucial role on international trade. Because of this, the measurement of port performance has become an important issue in transport policy. Port performance and port efficiency has been widely studied in the last decades, resulting in noteworthy contributions to improving the industry competitiveness. In this paper, we aim to present a review of the literature on port performance and the relation between this concept and transport policies. This study has the objective to describe the approaches that have been developed in recent years, and especially those that include the modeling of public policies. Finally, we highlight existing gaps in this field, as well as possible directions for future research.

Keywords: port performance, port efficiency, transport, policy

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Authors: Anteneh Getachew Gebrie, Rabian Wangkeeree

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The purpose of this paper is to introduce iterative algorithm solving split system of minimization problem given as a task of finding a common minimizer point of finite family of proper, lower semicontinuous convex functions and whose image under a bounded linear operator is also common minimizer point of another finite family of proper, lower semicontinuous convex functions. We obtain strong convergence of the sequence generated by our algorithm under some suitable conditions on the parameters. The iterative schemes are developed with a way of selecting the step sizes such that the information of operator norm is not necessary. Some applications and numerical experiment is given to analyse the efficiency of our algorithm.

Keywords: Hilbert Space, minimization problems, Moreau-Yosida approximate, split feasibility problem

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Authors: D. B. Gohil

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Closed die forging is a very complex process, and measurement of actual forces for real material is difficult and time consuming. Hence, the modelling technique has taken the advantage of carrying out the experimentation with the proper model material which needs lesser forces and relatively low temperature. The results of experiments on the model material then may be correlated with the actual material by using the theory of similarity. There are several methods available to resolve the complexity involved in the closed die forging process. Finite Element Method (FEM) and Finite Difference Method (FDM) are relatively difficult as compared to the slab method. The slab method is very popular and very widely used by the people working on shop floor because it is relatively easy to apply and reasonably accurate for most of the common forging load requirement computations.

Keywords: experimentation, forging, process modeling, strain distribution

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Authors: Richard Fairchild, Abdullah Al-Ghazali, Yilmaz Guney

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This study analyses the relationship between managerial overconfidence, dividends, and firm value by developing theoretical models that examine the condition under which managerial overconfident, dividends, and firm value may be positive or negative. Furthermore, the models incorporate moral hazard, in terms of managerial effort shirking, and the potential for the manager to choose negative NPV projects, due to private benefits. Our models demonstrate that overconfidence can lead to higher dividends (when the manager is overconfident about his current ability) or lower dividends (when the manager is overconfident about his future ability). The models also demonstrate that higher overconfidence may result in an increase or a decrease in firm value. Numerical examples are illustrated for both models which interestingly support the models’ propositions.

Keywords: behavioural corporate finance, dividend policy, overconfidence, moral hazard

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Authors: Harika Dasari, Eric Eisenbraun

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The present study models the role of electrode structural characteristics on the thermal behavior of lithium-ion batteries. Preliminary modeling runs have employed a 1D lithium-ion battery coupled to a two-dimensional axisymmetric model using silicon as the battery anode material. The two models are coupled by the heat generated and the average temperature. Our study is focused on the silicon anode particle sizes and it is observed that silicon anodes with nano-sized particles reduced the temperature of the battery in comparison to anodes with larger particles. These results are discussed in the context of the relationship between particle size and thermal transport properties in the electrode.

Keywords: particle size, NMC, silicon, heat generation, separator

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Authors: T. M. Ismail, M. A. El-Salam

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A mathematical model study was carried out to investigate gasification of biomass fuels using high-temperature air and steam as a gasifying agent using high-temperature air up to 1000°C. In this study, a 2D computational fluid dynamics model was developed to study the gasification process in an updraft gasifier, considering drying, pyrolysis, combustion, and gasification reactions. The gas and solid phases were resolved using a Euler−Euler multiphase approach, with exchange terms for the momentum, mass, and energy. The standard k−ε turbulence model was used in the gas phase, and the particle phase was modeled using the kinetic theory of granular flow. The results show that the present model giving a promising way in its capability and sensitivity for the parameter effects that influence the gasification process.

Keywords: computational fluid dynamics, gasification, biomass fuel, fixed bed gasifier

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Authors: Ming Luo

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In this real world, a manufacturer may produce more than one product. The products produced by the same manufacturer may share the same type of parts, similar design, and be produced in the same factory, i.e. some common causes. From the perspective of warranty management, the frequencies of those products’ warranty claims may have statistical dependence caused by the common causes. Warranty policy optimisation in the existing research, majorly, has not considered such dependence, which may increase bias in decision making. In the market, renewing warranty policies are provided to some unrepairable products and consumer electronic products. This paper optimises the renewing warranty policy collectively in a multi-product scenario with a consideration of the dependence among the warranty claims of the products produced by the same manufacturer. The existence of the optimal solution is proved. Numerical examples are used to validate the applicability of the proposed methods.

Keywords: mean-risk framework, modern portfolio theory, renewing warranty policy, warranty policy optimisation

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Authors: Jolly Puri, Shiv Prasad Yadav

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Multi-component data envelopment analysis (MC-DEA) is a popular technique for measuring aggregate performance of the decision making units (DMUs) along with their components. However, the conventional MC-DEA is limited to crisp input and output data which may not always be available in exact form. In real life problems, data may be imprecise or fuzzy. Therefore, in this paper, we propose (i) a fuzzy MC-DEA (FMC-DEA) model in which shared and undesirable fuzzy resources are incorporated, (ii) the proposed FMC-DEA model is transformed into a pair of crisp models using cut approach, (iii) fuzzy aggregate performance of a DMU and fuzzy efficiencies of components are defined to be fuzzy numbers, and (iv) a numerical example is illustrated to validate the proposed approach.

Keywords: multi-component DEA, fuzzy multi-component DEA, fuzzy resources, decision making units (DMUs)

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Authors: B. Sellami, M. Belloufi

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Conjugate gradient methods are an important class of methods for unconstrained optimization, especially for large-scale problems. Recently, they have been much studied. In this paper, we propose a new two-parameter family of conjugate gradient methods for unconstrained optimization. The two-parameter family of methods not only includes the already existing three practical nonlinear conjugate gradient methods, but also has other family of conjugate gradient methods as subfamily. The two-parameter family of methods with the Wolfe line search is shown to ensure the descent property of each search direction. Some general convergence results are also established for the two-parameter family of methods. The numerical results show that this method is efficient for the given test problems. In addition, the methods related to this family are uniformly discussed.

Keywords: unconstrained optimization, conjugate gradient method, line search, global convergence

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Authors: R. A. Petre, S. E. Nichifor, A. Craifaleanu, I. Stroe

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The relative motion of a robotic arm formed by homogeneous bars of different lengths and masses, hinged to each other is investigated. The first bar of the mechanism is articulated on a platform, considered initially fixed on the surface of the Earth, while for the second case the platform is considered to be in rotation with respect to the Earth. For both analyzed cases the motion equations are determined using the Lagrangian formalism, applied in its traditional form, valid with respect to an inertial reference system, conventionally considered as fixed. However, in the second case, a generalized form of the formalism valid with respect to a non-inertial reference frame will also be applied. The numerical calculations were performed using a MATLAB program.

Keywords: Lagrange equations, relative motion, inertial reference frame, non-inertial reference frame

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Authors: Juraj Beniak, Ľubomír Šooš, Peter Križan, Miloš Matúš

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Within Rapid Prototyping technologies are used many types of materials. Many of them are recyclable but there are still as plastic like, so practically they do not degrade in the landfill. Polylactic acid (PLA) is one of the special plastic materials which are biodegradable and also available for 3D printing within Fused Deposition Modelling (FDM) technology. The question is, if the mechanical properties of produced models are comparable to similar technical plastic materials which are usual for prototype production. Presented paper shows the experiments results for tensile strength measurements for specimens prepared with different 3D printer settings and model orientation. Paper contains also the comparison of tensile strength values with values measured on specimens produced by conventional technologies as injection moulding.

Keywords: 3D printing, biodegradable plastic, fused deposition modeling, PLA plastic, rapid prototyping

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Authors: Zhao Wang, Hong Yan

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In this paper, a unified-gas kinetic scheme (UGKS) for the gas-particle flow is constructed. UGKS is a direct modeling method for both continuum and rarefied flow computations. The dynamics of particle and gas are described as rarefied and continuum flow, respectively. Therefore, we use the Bhatnagar-Gross-Krook (BGK) equation for the particle distribution function. For the gas phase, the gas kinetic scheme for Navier-Stokes equation is solved. The momentum transfer between gas and particle is achieved by the acceleration term added to the BGK equation. The new scheme is tested by a 2cm-in-thickness dense bed comprised of glass particles with 1.5mm in diameter, and reasonable agreement is achieved.

Keywords: gas-particle flow, unified gas-kinetic scheme, momentum transfer, shock-induced fluidization

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Authors: Firooz Bakhtiari-Nejad, Hamidreza Rostami, Meysam Mirzaee, Mona Zandbaf

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Dynamic tests are an important step of the design of engineering structures, because the accuracy of predictions of theoretical–numerical procedures can be assessed. In experimental test of moving loads that is one of the major research topics, the load is modeled as a simple moving mass or a small vehicle. This paper deals with the applicability of Non-Contact Moving Load (NML) for vibration analysis. For this purpose, an experimental set-up is designed to generate the different types of NML including constant and harmonic. The proposed method relies on pressurized air which is useful, especially when dealing with fragile or sensitive structures. To demonstrate the performance of this system, the set-up is employed for a modal analysis of a beam and detecting crack of the beam. The obtained results indicate that the experimental set-up for NML can be an attractive alternative to the moving load problems.

Keywords: experimental analysis, moving load, non-contact excitation, materials engineering

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Authors: Nicodemus M. J. Mbwambo, Yu-Shan Sun, Murali Sitaraman, Joan Krone

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This paper presents a generic data abstraction that captures a navigable tree position. The mathematical modeling of the abstraction encapsulates the current tree position, which can be used to navigate and modify the tree. The encapsulation of the tree position in the data abstraction specification avoids the use of explicit references and aliasing, thereby simplifying verification of (imperative) client code that uses the data abstraction. To ease the tasks of such specification and verification, a general tree theory, rich with mathematical notations and results, has been developed. The paper contains an example to illustrate automated verification ramifications. With sufficient tree theory development, automated proving seems plausible even in the absence of a special-purpose tree solver.

Keywords: automation, data abstraction, maps, specification, tree, verification

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Authors: Jiao F. Huang, Shi Chen, Shu C. Duan, Gang H. Wang

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Due to its complex spatial structure as well as dynamic temporal evolution, an analytic solution of an X-pinch process is out of question, and numerical simulation becomes an important tool in X-pinch studies. Intrinsically, simulations of X-pinch are three-dimensional (3D) because of the specific structure of its load. Furthermore, in order to resolve both its μm-scales and ns-durations, fine spatial mesh grid and short time steps are usually adopted. The resulting large computational scales make the parallelization of codes a vital problem to be solved if any practical simulations are to be carried out. In this work, we report OpenMP parallelization of our 3D magnetohydrodynamic (MHD) code FOI-PERFECT. Results of test runs confirm that computational efficiency has been improved after parallelization, and both the sequential and parallel versions give the same physical results under the same initial conditions.

Keywords: MHD simulation, OpenMP, parallelization, X-pinch

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Authors: Daniia Nigmatullina, Vlada Kugurakova, Maxim Talanov

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We present a methodology and our plans of anthropomorphic social agent visualization. That includes creation of three-dimensional model of the virtual companion's head and its facial expressions. Talking Head is a cross-disciplinary project of developing of the human-machine interface with cognitive functions. During the creation of a realistic humanoid robot or a character, there might be the ‘uncanny valley’ problem. We think about this phenomenon and its possible causes. We are going to overcome the ‘uncanny valley’ by increasing of realism. This article discusses issues that should be considered when creating highly realistic characters (particularly the head), their facial expressions and speech visualization.

Keywords: anthropomorphic social agent, facial animation, uncanny valley, visualization, 3D modeling

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Authors: Alexandre Barbosa de Almeida, Telma Woerle de Lima Soares

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Protein structure prediction is a challenging task in the bioinformatics field. The biological function of all proteins majorly relies on the shape of their three-dimensional conformational structure, but less than 1% of all known proteins in the world have their structure solved. This work proposes a deep learning model to address this problem, attempting to predict some aspects of the protein conformations. Throughout a process of multiobjective dominance, a recurrent neural network was trained to abstract the particular bias of each individual multiobjective algorithm, generating a heuristic that could be useful to predict some of the relevant aspects of the three-dimensional conformation process formation, known as protein folding.

Keywords: Ab initio heuristic modeling, multiobjective optimization, protein structure prediction, recurrent neural network

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Authors: K. Khadidja

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Solitons are stable solution of nonlinear Schrodinger equation. Their stability is due to the exact combination between nonlinearity and dispersion which causes pulse broadening. Higher order solitons are born when nonlinear length is N multiple of dispersive length. Soliton order is determined by the number N itself. In this paper, evolution of higher order solitons is illustrated by simulation using Matlab. Results show that higher order solitons change their shape periodically, the reason why they are bad for transmission comparing to fundamental solitons which are constant. Partial analysis of a soliton of higher order explains that the periodic shape is due to the interplay between nonlinearity and dispersion which are not equal during a period. This class of solitons has many applications such as generation of supercontinuum and the impulse compression on the Femtosecond scale. As a conclusion, the periodicity which is harmful to transmission can be beneficial in other applications.

Keywords: dispersion, nonlinearity, optical fiber, soliton

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Authors: Ahmed A.D. Sarhan, Chong Feng Duan, Mum Wai Yip, M. Sayuti

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Rapid Prototyping (RP) technologies enable physical parts to be produced from various materials without depending on the conventional tooling. Fused Deposition Modeling (FDM) is one of the famous RP processes used at present. Tensile strength and compressive strength resistance will be identified for different sample structures and different layer orientations of ABS rapid prototype solid models. The samples will be fabricated by a FDM rapid prototyping machine in different layer orientations with variations in internal geometrical structure. The 0° orientation where layers were deposited along the length of the samples displayed superior strength and impact resistance over all the other orientations. The anisotropic properties were probably caused by weak interlayer bonding and interlayer porosity.

Keywords: building orientation, compression strength, rapid prototyping, tensile strength

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Authors: Dong Wook Lee, Adrian Mistreanu

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The authors have studied a method for analyzing containment and penetration using an explicit nonlinear Finite Element Analysis. This method may be used in the stage of concept design for the protection of external configurations or components of aircraft engines and nuclear power plant structures. This paper consists of the modeling method, the results obtained from the method and the comparison of the results with those calculated from simple analytical method. It shows that the containment capability obtained by proposed method matches well with analytically calculated containment capability.

Keywords: computer aided engineering, containment analysis, finite element analysis, impact analysis, penetration analysis

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Authors: Muhammad Azmain Abdullah, Ar Rashedul, Mohammad Ali

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This paper scrutinizes the influences of turbulence on heat transport rate, Nusselt number. The subject matter of this investigation also deals with the improvement of heat transfer efficiency of the swirl flow obtained by rotating a twisted tape in a circular pipe. The conditions to be fulfilled to observe the impact of Reynolds number and rotational speed of twisted tape are: a uniform temperature on the outer surface of the pipe, the magnitude of velocity of water varying from 0.1 m/s to 0.7 m/s in order to alter Reynolds number and a rotational speed of 200 rpm to 600 rpm. The gyration of twisted tape increase by 17%. It is also observed that heat transfer is exactly proportional to inlet gauge pressure and reciprocally proportional to increase of twist ratio.

Keywords: swirl flow, twisted tape, twist ratio, heat transfer

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