Search results for: numerical solving method

Authors: Ho-Nyeon Lee

Abstract:

We propose to use a gradual-refractive-index dielectric (GRID) as a simple and efficient light-outcoupling method for organic light-emitting diodes (OLEDs). Using the simple GRIDs, we could improve the light outcoupling efficiency of OLEDs rather than relying on difficult nano-patterning processes. Through numerical simulations using a finite-difference time-domain (FDTD) method, the feasibility of the GRID structure was examined and the design parameters were extracted. The outcoupling enhancement effects due to the GRIDs were proved through severe experimental works. The GRIDs were adapted to bottom-emission OLEDs and top-emission OLEDs. For bottom-emission OLEDs, the efficiency was improved more than 20%, and for top-emission OLEDs, more than 40%. The detailed numerical and experimental results will be presented at the conference site.

Keywords: efficiency, GRID, light outcoupling, OLED

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Authors: Saeid Haghjoo, Ebrahim Reyhani, Fahimeh Kolahdouz

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The present study aimed to evaluate the understanding of the students in Tehran universities (Iran) about the numerical representation of the average rate of change based on the Structure of Observed Learning Outcomes (SOLO). In the present descriptive-survey research, the statistical population included undergraduate students (basic sciences and engineering) in the universities of Tehran. The samples were 604 students selected by random multi-stage clustering. The measurement tool was a task whose face and content validity was confirmed by math and mathematics education professors. Using Cronbach's Alpha criterion, the reliability coefficient of the task was obtained 0.95, which verified its reliability. The collected data were analyzed by descriptive statistics and inferential statistics (chi-squared and independent t-tests) under SPSS-24 software. According to the SOLO model in the prestructural, unistructural, and multistructural levels, basic science students had a higher percentage of understanding than that of engineering students, although the outcome was inverse at the relational level. However, there was no significant difference in the average understanding of both groups. The results indicated that students failed to have a proper understanding of the numerical representation of the average rate of change, in addition to missconceptions when using physics formulas in solving the problem. In addition, multiple solutions were derived along with their dominant methods during the qualitative analysis. The current research proposed to focus on the context problems with approximate calculations and numerical representation, using software and connection common relations between math and physics in the teaching process of teachers and professors.

Keywords: average rate of change, context problems, derivative, numerical representation, SOLO taxonomy

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Authors: Changgil Lee, Seunghee Park

Abstract:

Although vehicle driving test for the development of BWIM system is necessary, but it needs much cost and time in addition application of various driving condition. Thus, we need the numerical-simulation method resolving the cost and time problems of vehicle driving test and the way of measuring response of bridge according to the various driving condition. Using the precision analysis model reflecting the dynamic characteristic is contributed to increase accuracy in numerical simulation. In this paper, we conduct a numerical simulation to apply precision analysis model, which reflects the dynamic characteristic of bridge using Bridge Weigh-in-Motion technique and suggest overload vehicle enforcement technology using precision analysis model.

Keywords: bridge weigh-in-motion(BWIM) system, precision analysis model, dynamic characteristic of bridge, numerical simulation

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Authors: Mukhtari Hussaini Muhammad, Abba Adamu

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The paper will examine the approaches and solutions that will be offered by Senior Secondary School II Students (Demonstration Secondary School, Azare Bauchi State Northern Nigeria – Hausa/ Fulani predominant area) toward solving exercises related to the circle theorem. The angle that an arc of a circle subtends at the center is twice that which it subtends at any point on the remaining part of the circumference. The Students will be divided in to 2 groups by given them numbers 1, 2; 1, 2; 1, 2, then all 1s formed group I and all 2s formed group II. Group I will be considered as control group in which the traditional method will be applied during instructions. Thus, the researcher will revise the concept of circle, state the theorem, prove the theorem and then solve examples. Group II, experimental group in which the concept of circle will be revised to the students and then the students will be asked to draw different circles, mark arcs, draw angle at the center, angle at the circumference then measure the angles constructed. The students will be asked to explain what they can infer/deduce from the angles measured and lastly, examples will be solved. During the next contact day, both groups will be subjected to solving exercises in the classroom related to the theorem. The angle that an arc of a circle subtends at the center is twice that which it subtends at any point on the remaining part of circumference. The solution to the exercises will be marked, the scores compared/analysed using relevant statistical tool. It is expected that group II will perform better because of the method/ technique followed during instructions is more learner-centered. By exploiting the talents of the individual learners through listening to the views and asking them how they arrived at a solution will really improve learning and understanding.

Keywords: circle theorem, control group, experimental group, traditional method

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Authors: Mahdad M’hamed, Belaidi Idir

Abstract:

This paper develops a meshless approach, called Element Free Galerkin (EFG) method, which is based on the weak form Moving Least Squares (MLS) of the partial differential governing equations and employs the interpolation to construct the meshless shape functions. The variation weak form is used in the EFG where the trial and test functions are approximated bye the MLS approximation. Since the shape functions constructed by this discretization have the weight function property based on the randomly distributed points, the essential boundary conditions can be implemented easily. The local weak form of the partial differential governing equations is obtained by the weighted residual method within the simple local quadrature domain. The spline function with high continuity is used as the weight function. The presently developed EFG method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak form. Several numerical examples of two-dimensional static structural analysis are presented to illustrate the performance of the present EFG method. They show that the EFG method is highly efficient for the implementation and highly accurate for the computation. The present method is used to analyze the static deflection of beams and plate hole

Keywords: numerical computation, element-free Galerkin (EFG), moving least squares (MLS), meshless methods

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Authors: Gleda Kutrolli, Maksi Kutrolli, Etjon Meco

Abstract:

SARS-CoV-2 virus is currently one of the most infectious pathogens for humans. It started in China at the end of 2019 and now it is spread in all over the world. The origin and diffusion of the SARS-CoV-2 epidemic, is analysed based on the discussion of viral phylogeny theory. With the aim of understanding the spread of infection in the affected countries, it is crucial to modelize the spread of the virus and simulate its activity. In this paper, the prediction of coronavirus outbreak is done by using SIR model without vital dynamics, applying different numerical technique solving ordinary differential equations (ODEs). We find out that ABM and MRT methods perform better than other techniques and that the activity of the virus will decrease in April but it never cease (for some time the activity will remain low) and the next cycle will start in the middle July 2020 for Norway and Denmark, and October 2020 for Sweden, and September for Finland.

Keywords: forecasting, ordinary differential equations, SARS-COV-2 epidemic, SIR model

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Authors: Praveen Kumar, R. Uma, R. P. Sharma

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This study investigates the generation of turbulence in a deep-fluid environment using a damped 1D-modified nonlinear Schrödinger equation model. The well-known damped modified nonlinear Schrödinger equation (d-MNLS) is solved using numerical methods. Artificial damping is added to the MNLS equation, and turbulence generation is investigated through a numerical simulation. The numerical simulation employs a finite difference method for temporal evolution and a pseudo-spectral approach to characterize spatial patterns. The results reveal a recurring periodic pattern in both space and time when the nonlinear Schrödinger equation is considered. Additionally, the study shows that the modified nonlinear Schrödinger equation disrupts the localization of structure and the recurrence of the Fermi-Pasta-Ulam (FPU) phenomenon. The energy spectrum exhibits a power-law behavior, closely following Kolmogorov's spectra steeper than k⁻⁵/³ in the inertial sub-range.

Keywords: water waves, modulation instability, hydrodynamics, nonlinear Schrödinger's equation

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Authors: Emmanuel Omokhuale

Abstract:

A mathematical model is presented to study free convective boundary layer flow in a semi-infinite vertical cylinder with heat sink effect in a porous medium. The governing dimensional governing partial differential equations (PDEs) with corresponding initial and boundary conditions are approximated and solved numerically employing finite difference method (FDM) the implicit type. Stability and convergence of the scheme are also established. Furthermore, the influence of significant physical parameters on the flow characteristics was analysed and shown graphically. The obtained results are benchmarked with previously published works in order to access the accuracy of the numerical method and found to be in good agreement.

Keywords: free convection flow, vertical cylinder, implicit finite difference method, heat sink and porous medium

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Authors: Aouaouche Elmaouhab, Hassina Beggar

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Solving multi-objective discrete optimization applications has always been limited by the resources of one machine: By computing power or by memory, most often both. To speed up the calculations, the grid computing represents a primary solution for the treatment of these applications through the parallelization of these resolution methods. In this work, we are interested in the study of some methods for solving multiple objective integer linear programming problem based on Branch-and-Bound and the study of grid computing technology. This study allowed us to propose an implementation of the method of Abbas and Al on the grid by reducing the execution time. To enhance our contribution, the main results are presented.

Keywords: multi-objective optimization, integer linear programming, grid computing, parallel computing

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Authors: Norma Binti Alias, Che Rahim Che The, Norfarizan Mohd Said, Sakinah Abdul Hanan, Akhtar Ali

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This paper discusses on the transportation of magnetic drug targeting through blood within vessels, tissues and cells. There are three integrated mathematical models to be discussed and analyze the concentration of drug and blood flow through magnetic nanoparticles. The cell therapy brought advancement in the field of nanotechnology to fight against the tumors. The systematic therapeutic effect of Single Cells can reduce the growth of cancer tissue. The process of this nanoscale phenomena system is able to measure and to model, by identifying some parameters and applying fundamental principles of mathematical modeling and simulation. The mathematical modeling of single cell growth depends on three types of cell densities such as proliferative, quiescent and necrotic cells. The aim of this paper is to enhance the simulation of three types of models. The first model represents the transport of drugs by coupled partial differential equations (PDEs) with 3D parabolic type in a cylindrical coordinate system. This model is integrated by Non-Newtonian flow equations, leading to blood liquid flow as the medium for transportation system and the magnetic force on the magnetic nanoparticles. The interaction between the magnetic force on drug with magnetic properties produces induced currents and the applied magnetic field yields forces with tend to move slowly the movement of blood and bring the drug to the cancer cells. The devices of nanoscale allow the drug to discharge the blood vessels and even spread out through the tissue and access to the cancer cells. The second model is the transport of drug nanoparticles from the vascular system to a single cell. The treatment of the vascular system encounters some parameter identification such as magnetic nanoparticle targeted delivery, blood flow, momentum transport, density and viscosity for drug and blood medium, intensity of magnetic fields and the radius of the capillary. Based on two discretization techniques, finite difference method (FDM) and finite element method (FEM), the set of integrated models are transformed into a series of grid points to get a large system of equations. The third model is a single cell density model involving the three sets of first order PDEs equations for proliferating, quiescent and necrotic cells change over time and space in Cartesian coordinate which regulates under different rates of nutrients consumptions. The model presents the proliferative and quiescent cell growth depends on some parameter changes and the necrotic cells emerged as the tumor core. Some numerical schemes for solving the system of equations are compared and analyzed. Simulation and computation of the discretized model are supported by Matlab and C programming languages on a single processing unit. Some numerical results and analysis of the algorithms are presented in terms of informative presentation of tables, multiple graph and multidimensional visualization. As a conclusion, the integrated of three types mathematical modeling and the comparison of numerical performance indicates that the superior tool and analysis for solving the complete set of magnetic drug delivery system which give significant effects on the growth of the targeted cancer cell.

Keywords: mathematical modeling, visualization, PDE models, magnetic nanoparticle drug delivery model, drug release model, single cell effects, avascular tumor growth, numerical analysis

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Authors: Balgaisha Mukanova, Tolkyn Mirgalikyzy

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Theory of interpretation of electromagnetic fields studied in the electrical prospecting with direct current is mainly developed for the case of a horizontal surface observation. However in practice we often have to work in difficult terrain surface. Conducting interpretation without the influence of topography can cause non-existent anomalies on sections. This raises the problem of studying the impact of different shapes of ground surface relief on the results of electrical prospecting's research. This research examines the numerical solutions of the direct problem of electrical prospecting for two-dimensional and three-dimensional media, taking into account the terrain. The problem is solved using the method of integral equations. The density of secondary currents on the relief surface is obtained.

Keywords: ground surface relief, method of integral equations, numerical method, electromagnetic

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Authors: Michał Lidner, Zbigniew SzcześNiak

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The ability to estimate blast load overpressure properly plays an important role in safety design of buildings. The issue of studying of blast loading on structural elements has been explored for many years. However, in many literature reports shock wave overpressure is estimated with simplified triangular or exponential distribution in time. This indicates some errors when comparing real and numerical reaction of elements. Nonetheless, it is possible to further improve setting similar to the real blast load overpressure function versus time. The paper presents a method of numerical analysis of the phenomenon of the air shock wave propagation. It uses Finite Volume Method and takes into account energy losses due to a heat transfer with respect to an adiabatic process rule. A system of three equations (conservation of mass, momentum and energy) describes the flow of a volume of gaseous medium in the area remote from building compartments, which can inhibit the movement of gas. For validation three cases of a shock wave flow were analyzed: a free field explosion, an explosion inside a steel insusceptible tube (the 1D case) and an explosion inside insusceptible cube (the 3D case). The results of numerical analysis were compared with the literature reports. Values of impulse, pressure, and its duration were studied. Finally, an overall good convergence of numerical results with experiments was achieved. Also the most important parameters were well reflected. Additionally analyses of dynamic response of one of considered structural element were made.

Keywords: adiabatic process, air shock wave, explosive, finite volume method

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Authors: Teng Li, Kamran Mohseni

Abstract:

This paper presents an inviscid regularization technique for the incompressible two-phase flow simulations. This technique is known as observable method due to the understanding of observability that any feature smaller than the actual resolution (physical or numerical), i.e., the size of wire in hotwire anemometry or the grid size in numerical simulations, is not able to be captured or observed. Differ from most regularization techniques that applies on the numerical discretization, the observable method is employed at PDE level during the derivation of equations. Difficulties in the simulation and analysis of realistic fluid flow often result from discontinuities (or near-discontinuities) in the calculated fluid properties or state. Accurately capturing these discontinuities is especially crucial when simulating flows involving shocks, turbulence or sharp interfaces. Over the past several years, the properties of this new regularization technique have been investigated that show the capability of simultaneously regularizing shocks and turbulence. The observable method has been performed on the direct numerical simulations of shocks and turbulence where the discontinuities are successfully regularized and flow features are well captured. In the current paper, the observable method will be extended to two-phase interfacial flows. Multiphase flows share the similar features with shocks and turbulence that is the nonlinear irregularity caused by the nonlinear terms in the governing equations, namely, Euler equations. In the direct numerical simulation of two-phase flows, the interfaces are usually treated as the smooth transition of the properties from one fluid phase to the other. However, in high Reynolds number or low viscosity flows, the nonlinear terms will generate smaller scales which will sharpen the interface, causing discontinuities. Many numerical methods for two-phase flows fail at high Reynolds number case while some others depend on the numerical diffusion from spatial discretization. The observable method regularizes this nonlinear mechanism by filtering the convective terms and this process is inviscid. The filtering effect is controlled by an observable scale which is usually about a grid length. Single rising bubble and Rayleigh-Taylor instability are studied, in particular, to examine the performance of the observable method. A pseudo-spectral method is used for spatial discretization which will not introduce numerical diffusion, and a Total Variation Diminishing (TVD) Runge Kutta method is applied for time integration. The observable incompressible Euler equations are solved for these two problems. In rising bubble problem, the terminal velocity and shape of the bubble are particularly examined and compared with experiments and other numerical results. In the Rayleigh-Taylor instability, the shape of the interface are studied for different observable scale and the spike and bubble velocities, as well as positions (under a proper observable scale), are compared with other simulation results. The results indicate that this regularization technique can potentially regularize the sharp interface in the two-phase flow simulations

Keywords: Euler equations, incompressible flow simulation, inviscid regularization technique, two-phase flow

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Authors: Lydia Wahid, Mona F. Ahmed, Nevin Darwish

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The vehicle routing problem (VRP) consists of a group of customers that needs to be served. Each customer has a certain demand of goods. A central depot having a fleet of vehicles is responsible for supplying the customers with their demands. The problem is composed of two subproblems: The first subproblem is an assignment problem where the number of vehicles that will be used as well as the customers assigned to each vehicle are determined. The second subproblem is the routing problem in which for each vehicle having a number of customers assigned to it, the order of visits of the customers is determined. Optimal number of vehicles, as well as optimal total distance, should be achieved. In this paper, an approach for solving the first subproblem (the assignment problem) is presented. In the approach, a clustering algorithm is proposed for finding the optimal number of vehicles by grouping the customers into clusters where each cluster is visited by one vehicle. Finding the optimal number of clusters is NP-hard. This work presents a polynomial time clustering algorithm for finding the optimal number of clusters and solving the assignment problem.

Keywords: vehicle routing problems, clustering algorithms, Clarke and Wright Saving Method, agglomerative hierarchical clustering

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Authors: Kirill Trapezon, Alexandr Trapezon

Abstract:

A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

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Authors: Mevlüt Burak Dalmış, Kemal Yaman

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In this study, flutter characteristics of cantilever rectangular plate structure under incompressible flow regime are investigated by comparing the results of commercial flutter analysis program ZAERO^© with wind tunnel tests conducted in Ankara Wind Tunnel (ART). A rectangular polycarbonate (PC) plate, 5x125x1000 mm in dimensions, is used for both numerical and experimental investigations. Analysis and test results are very compatible with each other. A comparison between two different solution methods (g and k-method) of ZAERO^© is also done. It is seen that, k-method gives closer result than the other one. However, g-method results are on conservative side and it is better to use conservative results namely g-method results. Even if the modal analysis results are used for the flutter analysis for this simple structure, a modal test should be conducted in order to validate the modal analysis results to have accurate flutter analysis results for more complicated structures.

Keywords: flutter, plate, subsonic flow, wind tunnel

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Authors: A. A. Behroozpoor, M. M. Mazarei

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In this paper, a fuzzy recurrent neural network is proposed for solving the classical quadratic control problem subject to linear equality and bound constraints. The convergence of the state variables of the proposed neural network to achieve solution optimality is guaranteed.

Keywords: REFERENCES [1] Xia, Y, A new neural network for solving linear and quadratic programming problems. IEEE Transactions on Neural Networks, 7(6), 1996, pp.1544–1548. [2] Xia, Y., & Wang, J, A recurrent neural network for solving nonlinear convex programs subject to linear constraints. IEEE Transactions on Neural Networks, 16(2), 2005, pp. 379–386. [3] Xia, Y., H, Leung, & J, Wang, A projection neural network and its application to constrained optimization problems. IEEE Transactions Circuits and Systems-I, 49(4), 2002, pp.447–458.B. [4] Q. Liu, Z. Guo, J. Wang, A one-layer recurrent neural network for constrained seudoconvex optimization and its application for dynamic portfolio optimization. Neural Networks, 26, 2012, pp. 99-109.

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Authors: A. M. Tahsini

Abstract:

Computational study of two dimensional supersonic reacting hydrogen-air flows is performed to investigate the nitrogen effects on ignition delay time for premixed and diffusion flames. Chemical reaction is treated using detail kinetics and the advection upstream splitting method is used to calculate the numerical inviscid fluxes. The results show that only in the stoichiometric condition for both premixed and diffusion flames, there is monotone dependency of the ignition delay time to the nitrogen addition. In other situations, the optimal condition from ignition viewpoint should be found using numerical investigations.

Keywords: diffusion flame, ignition delay time, mixing layer, numerical simulation, premixed flame, supersonic flow

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Authors: Alexander Kospach, Fabian Benezeder, Jürgen Abraham

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E-mobility poses new challenges for inverters (e.g., higher switching frequencies) in terms of thermal behavior and thermal management. Due to even higher switching frequencies, thermal losses become greater, and the cooling of critical components (like insulated gate bipolar transistor and diodes) comes into focus. New manufacturing methods, such as 3D printing, enable completely new pin-fin structures that can handle higher waste heat to meet the new thermal requirements. Based on the geometrical specifications of the industrial partner regarding the manufacturing possibilities for 3D printing, different and completely new pin-fin structures were numerically investigated for their hydraulic and thermal behavior in fundamental studies assuming an indirect liquid cooling. For the 3D computational fluid dynamics (CFD) thermal simulations OpenFOAM was used, which has as numerical method the finite volume method for solving the conjugate heat transfer problem. A steady-state solver for turbulent fluid flow and solid heat conduction with conjugate heat transfer between solid and fluid regions was used for the simulations. In total, up to fifty pinfin structures and arrangements, some of them completely new, were numerically investigated. On the basis of the results of the principal investigations, the best two pin-fin structures and arrangements for the complete module cooling of an automotive inverter were numerically investigated and compared. There are clear differences in the maximum temperatures for the critical components, such as IGTBs and diodes. In summary, it was shown that 3D pin fin structures can significantly contribute to the improvement of heat transfer and cooling of an automotive inverter. This enables in the future smaller cooling designs and a better lifetime of automotive inverter modules. The new pin fin structures and arrangements can also be applied to other cooling applications where 3D printing can be used.

Keywords: pin fin heat sink optimization, 3D printed pin fins, CFD simulation, power electronic cooling, thermal management

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Authors: Zuodong Liang, Dong-Sheng Jeng

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Seabed instability around an offshore pipeline is one of key factors that need to be considered in the design of offshore infrastructures. Unlike previous investigations, a three-dimensional numerical model for the wave-induced soil response around an offshore pipeline is proposed in this paper. The numerical model was first validated with 2-D experimental data available in the literature. Then, a parametric study will be carried out to examine the effects of wave, seabed characteristics and confirmation of pipeline. Numerical examples demonstrate significant influence of wave obliquity on the wave-induced pore pressures and the resultant seabed liquefaction around the pipeline, which cannot be observed in 2-D numerical simulation.

Keywords: pore pressure, 3D wave model, seabed liquefaction, pipeline

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Authors: Abdul Halim Abdullah, Nur Liyana Zainal Abidin, Mahani Mokhtar

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Problem-solving is an activity which can encourage students to use Higher Order Thinking Skills (HOTS). Learning fractions can be challenging for students since empirical evidence shows that students experience difficulties in solving the fraction problems. However, visual methods can help students to overcome the difficulties since the methods help students to make meaningful visual representations and link abstract concepts in Mathematics. Therefore, the purpose of this study was to investigate whether there were any changes in students’ HOTS at the four highest levels when learning the fractions by using Thinking Blocks. 54 students participated in a quasi-experiment using pre-tests and post-tests. Students were divided into two groups. The experimental group (n=32) received a treatment to improve the students’ HOTS and the other group acted as the control group (n=22) which used a traditional method. Data were analysed by using Mann-Whitney test. The results indicated that during post-test, students who used Thinking Blocks showed significant improvement in their HOTS level (p=0.000). In addition, the results of post-test also showed that the students’ performance improved significantly at the four highest levels of HOTS; namely, application (p=0.001), analyse (p=0.000), evaluate (p=0.000), and create (p=0.000). Therefore, it can be concluded that Thinking Blocks can effectively encourage students to use the four highest levels of HOTS which consequently enable them to solve fractions problems successfully.

Keywords: Thinking Blocks, Higher Order Thinking Skills (HOTS), fractions, problem solving

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Authors: Ali Yasin, Ali Kamran, Muhammad Safdar

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In order to reduce the hefty cost involved in terms of time and project cost, the development and application of advanced numerical tools to address the burn-back analysis problem in solid rocket motor design and development is the need of time. Several advanced numerical schemes have been developed in recent times, but their usage in the design of propellant grain of solid rocket motors is very rare. In this paper, an advanced numerical technique named the Level-Set method has been utilized for the burn-back analysis of star grain to study the effect of geometrical parameters on ballistic performance indicators such as solid loading, neutrality, and sliver percentage. In the level set technique, simple finite difference methods may fail quickly and require more sophisticated non-oscillatory schemes for feasible long-time simulation. For internal ballistic calculations, a simplified equilibrium pressure method is utilized. Preliminary results of the operative conditions, for all the combustion time, of star grain burn-back using level set techniques are compared with published results using CAD technique to test the developed numerical model.

Keywords: solid rocket motor, internal ballistic, level-set technique, star grain

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Authors: Amal Maazoun, Abderrazak Mezghani, Ali Ben Moussa

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Aerogel consists of a ramified and inter-connected solid skeleton enclosing a very important number of nano-sized pores filled with air that occupies most of the volume and makes very low density. The thermal conductivity of this material can reach lower values than those of any other material, and it changes with the type of the aerogel and its composition. So, in order to explain the causes of the super-insulation of our material and to determine the factors in which depends on its conductivity we used a numerical simulation. We have developed a numerical code that generates random fractal structure of silica aerogel with pre-defined concentration, properties of the backbone and the gas in the pores as well as the size of the particles. The calculation of the conductivity at any point of domain shows that it is not constant and that it depends on the pore size and the location in the pore. A numerical method based on resolution by inversion of block tridiagonal matrices is used to calculate the equivalent thermal conductivity of the whole fractal structure. The average conductivity calculated for each concentration is in good agreement with those of typical aerogels. And we found that the equivalent thermal conductivity of a silica aerogel depends strongly not only on the porosity but also on the tortuosity of the solid backbone.

Keywords: aerogel, fractal structure, numerical study, porous media, thermal conductivity

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Authors: Reza Ziaie Moayed, Ehsan Azini

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Jet grouting (JG) is one of the methods of improving and increasing the strength and bearing of soil in which the high pressure water or grout is injected through the nozzles into the soil. During this process, a part of the soil and grout particles comes out of the drill borehole, and the other part is mixed up with the grout in place, as a result of this process, a mass of modified soil is created. The purpose of this method is to change the soil into a mixture of soil and cement, commonly known as "soil-cement". In this paper, first, the principles of high pressure injection and then the effective parameters in the JG method are described. Then, the tests on the samples taken from the columns formed from the excavation around the soil-cement columns, as well as the static loading test on the created column, are discussed. In the other part of this paper, the soil behavior models for numerical modeling in PLAXIS software are mentioned. The purpose of this paper is to evaluate the results of numerical modeling based on in-situ static loading tests. The results indicate an acceptable agreement between the results of the tests mentioned and the modeling results. Also, modeling with this software as an appropriate option for technical feasibility can be used to soil improvement using JG.

Keywords: jet grouting column, soil improvement, numerical modeling, in-situ loading test

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Authors: Somveer Singh, Vineet Kumar Singh

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This work contributes a numerical method based on Legendre wavelet approximation for the treatment of partial integro-differential equation (PIDE). Operational matrices of Legendre wavelets reduce the solution of PIDE into the system of algebraic equations. Some useful results concerning the computational order of convergence and error estimates associated to the suggested scheme are presented. Illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method.

Keywords: legendre wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Chung To Kong, Siu Ming Yiu

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Rubik's cube was invented in 1974. Since then, speedcubers all over the world try their best to break the world record again and again. The newest record is 3.47 seconds. There are many factors that affect the timing, including turns per second (tps), algorithm, finger trick, hardware of the cube. In this paper, the lower bound of the cube solving time will be discussed using convex optimization. Extended analysis of the world records will be used to understand how to improve the timing. With the understanding of each part of the solving step, the paper suggests a list of speed improvement techniques. Based on the analysis of the world record, there is a high possibility that the 3 seconds mark will be broken soon.

Keywords: Rubik's Cube, speed, finger trick, optimization

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Authors: Y. Pala, M. O. Ertas

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In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

Keywords: Riccati equation, analytical solution, proper solution, nonlinear

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Authors: Mahmood Otadi, Maryam Mosleh

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: fuzzy number, fuzzy ODE, HAM, approximate method

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Authors: Kotaro Miura, Makoto Sakamoto, Yuji Tanabe

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We focus on internal stress and displacement of an elastic axisymmetric contact problem for indentation of a layer-substrate body. An elastic layer is assumed to be perfectly bonded to an elastic semi-infinite substrate. The elastic layer is smoothly indented with a flat-ended cylindrical indenter. The analytical and exact solutions were obtained by solving an infinite system of simultaneous equations using the method to express a normal contact stress at the upper surface of the elastic layer as an appropriate series. This paper presented the numerical results of internal stress and displacement distributions for hard-coating system with constant values of Poisson’s ratio and the thickness of elastic layer.

Keywords: indentation, contact problem, stress distribution, coating materials, layer-substrate body

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Authors: Nassima Sotehi

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This article presents experimental and numerical results concerning the thermal properties of the porous materials used as heat insulator in the buildings sector. Initially, the thermal conductivity of three types of studied walls (classic concrete, concrete with cork aggregate and polystyrene concrete) was measured in experiments by the method of the boxes. Then a numerical modeling of the heat and mass transfers which occur within porous materials was applied to these walls. This work shows the influence of the presence of water in building materials on their thermophysical properties, as well as influence of the nature of materials and dosage of fibers introduced within these materials on the thermal and mass transfers.

Keywords: modeling, porous media, thermal materials, thermal properties

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