Search results for: generalised gradient approximation

Authors: Madina Hamiane

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Modelling and simulation of an analogy function generator is presented based on a polynomial expansion model. The proposed function generator model is based on a 10th order polynomial approximation of any of the required functions. The polynomial approximations of these functions can then be implemented using basic CMOS circuit blocks. In this paper, a circuit model is proposed that can simultaneously generate many different mathematical functions. The circuit model is designed and simulated with HSPICE and its performance is demonstrated through the simulation of a number of non-linear functions.

Keywords: modelling and simulation, analog function generator, polynomial approximation, CMOS transistors

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Authors: Li Chen

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For an aerofoil or hydrofoil in high Reynolds number flows, broadband noise is generated efficiently as the result of the turbulence convecting over the trailing edge. This noise can be related to the surface pressure fluctuations, which can be predicted by either CFD or empirical models. However, in reality, the aerofoil or hydrofoil often operates at an angle of attack. Under this situation, the flow is subjected to an Adverse-Pressure-Gradient (APG), and as a result, a flow separation may occur. This study is to assess trailing-edge noise models for such flows. In the present work, the trailing-edge noise from a 2D airfoil at 6 degree of angle of attach is investigated. Under this condition, the flow is experiencing a strong APG, and the flow separation occurs. The flow over the airfoil with a chord of 300 mm, equivalent to a Reynold Number 4x10⁵, is simulated using RANS with the SST k-ɛ turbulent model. The predicted surface pressure fluctuations are compared with the published experimental data and empirical models, and show a good agreement with the experimental data. The effect of the APG on the trailing edge noise is discussed, and the associated trailing edge noise is calculated.

Keywords: aero-acoustics, adverse-pressure gradient, computational fluid dynamics, trailing-edge noise

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Authors: Supriya Manikrao Ovhal

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In India, the summer monsoon rainfall occurs owing to large scale convection with reference to continental ITCZ. It was found that convection over tropical ocean increases with SST from 26 to 28 degree C, and when SST is above 29 degree C, it sharply decreases for warm pool areas of Indian and for monsoon areas of West Pacific Ocean. The reduction in convection can be influenced by large scale subsidence forced by nearby or remotely generated deep convection, thus it was observed that under the influence of strong large scale rising motion, convection does not decreases but increases monotonically with SST even if SST value is higher than 29.5 degree C. Since convection is related to SST gradient, that helps to generate low level moisture convergence and upward vertical motion in the atmosphere. Strong wind fields like cross equatorial low level jet stream on equator ward side of the warm pool are produced due to convection initiated by SST gradient. Areas having maximum SST have low SST gradient, and that result in feeble convection. Hence it is imperative to mention that the oceanic role (other than SST) could be prominent in influencing large Scale Atmospheric convection. Since warm oceanic surface somewhere or the other contributes to penetrate the heat radiation to the subsurface of the ocean, and as there is no studies seen related to oceanic subsurface role in large Scale Atmospheric convection, in the present study, we are concentrating on the oceanic subsurface contribution in large Scale Atmospheric convection by considering the SST gradient, mixed layer depth (MLD), thermocline, barrier layer. The present study examines the probable role of subsurface ocean parameters in influencing convection.

Keywords: sst, d20, olr, wind

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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: Hassan J. Al Salman, Ahmed A. Al Ghafli

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

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

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Authors: Jeries J. Abou-Hanna

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Several techniques exist for determining stress-intensity factors in linear elastic fracture mechanics analysis. These techniques are based on analytical, numerical, and empirical approaches that have been well documented in literature and engineering handbooks. However, not all techniques share the same merit. In addition to overly-conservative results, the numerical methods that require extensive computational effort, and those requiring copious user parameters hinder practicing engineers from efficiently evaluating stress-intensity factors. This paper investigates the prospects of reducing the complexity and required variables to determine stress-intensity factors through the utilization of the stress gradient and a weighting function. The heart of this work resides in the understanding that fracture emanating from stress concentration locations cannot be explained by a single maximum stress value approach, but requires use of a critical volume in which the crack exists. In order to understand the effectiveness of this technique, this study investigated components of different notch geometry and varying levels of stress gradients. Two forms of weighting functions were employed to determine stress-intensity factors and results were compared to analytical exact methods. The results indicated that the “exponential” weighting function was superior to the “absolute” weighting function. An error band +/- 10% was met for cases ranging from a steep stress gradient in a sharp v-notch to the less severe stress transitions of a large circular notch. The incorporation of the proposed method has shown to be a worthwhile consideration.

Keywords: fracture mechanics, finite element method, stress intensity factor, stress gradient

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Authors: Saeed Poormoaied, Zumbul Atan

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Emergency shipments provide a powerful mechanism to alleviate the risk of imminent stock-outs and can result in substantial benefits in an inventory system. Customer satisfaction and high service level are immediate consequences of utilizing emergency shipments. In this paper, we consider a single-echelon periodic review inventory system consisting of a single local warehouse, being replenished from a central warehouse with ample capacity in an infinite horizon setting. Since the structure of the optimal policy appears to be complicated, we analyze this problem under an order-up-to-S inventory control policy framework, the (S, T) policy, with the emergency shipment consideration. In each period of the periodic review policy, there is a single opportunity at any point of time for the emergency shipment so that in case of stock-outs, an emergency shipment is requested. The goal is to determine the timing and amount of the emergency shipment during a period (emergency shipment policy) as well as the base stock periodic review policy parameters (replenishment policy). We show that how taking advantage of having an emergency shipment during periods improves the performance of the classical (S, T) policy, especially when fixed and unit emergency shipment costs are small. Investigating the structure of the objective function, we develop an exact algorithm for finding the optimal solution. We also provide a heuristic and an approximation algorithm for the periodic review inventory system problem. The experimental analyses indicate that the heuristic algorithm is computationally more efficient than the approximation algorithm, but in terms of the solution efficiency, the approximation algorithm performs very well. We achieve up to 13% cost savings in the (S, T) policy if we apply the proposed emergency shipment policy. Moreover, our computational results reveal that the approximated solution is often within 0.21% of the globally optimal solution.

Keywords: emergency shipment, inventory, periodic review policy, approximation algorithm.

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Authors: Vijaya K. Srivastava, Davide Spinello

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This paper presents performance of two robust gradient-based heuristic optimization procedures based on 3ⁿ enumeration and tunneling approach to seek global optimum of constrained integer problems. Both these procedures consist of two distinct phases for locating the global optimum of integer problems with a linear or non-linear objective function subject to linear or non-linear constraints. In both procedures, in the first phase, a local minimum of the function is found using the gradient approach coupled with hemstitching moves when a constraint is violated in order to return the search to the feasible region. In the second phase, in one optimization procedure, the second sub-procedure examines 3ⁿ integer combinations on the boundary and within hypercube volume encompassing the result neighboring the result from the first phase and in the second optimization procedure a tunneling function is constructed at the local minimum of the first phase so as to find another point on the other side of the barrier where the function value is approximately the same. In the next cycle, the search for the global optimum commences in both optimization procedures again using this new-found point as the starting vector. The search continues and repeated for various step sizes along the function gradient as well as that along the vector normal to the violated constraints until no improvement in optimum value is found. The results from both these proposed optimization methods are presented and compared with one provided by popular MS Excel solver that is provided within MS Office suite and other published results.

Keywords: constrained integer problems, enumerative search algorithm, Heuristic algorithm, Tunneling algorithm

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Authors: Hassan Al Salman, Ahmed Al Ghafli

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

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

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Authors: Likewin Thomas, M. V. Manoj Kumar, B. Annappa

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The aim of this study was to develop an Artificial Neural Network0 s recommendation model for an online process using the complexity of load, performance, and average servicing time of the resources. Here, the proposed model investigates the resource performance using stochastic gradient decent method for learning ranking function. A probabilistic cost function is implemented to identify the optimal θ values (load) on each resource. Based on this result the recommendation of resource suitable for performing the currently executing task is made. The test result of CoSeLoG project is presented with an accuracy of 72.856%.

Keywords: ADALINE, neural network, gradient decent, process mining, resource behaviour, polynomial regression model

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Authors: Julius M. Ndambuki, Gislar E. Kifanyi, Samuel N. Odai, Charles Gyamfi

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Conjunctive management of surface and groundwater resources is a challenging task due to the spatial and temporal variability nature of hydrology as well as hydrogeology of the water storage systems. Surface water-groundwater hydrogeology is highly uncertain; thus it is imperative that this uncertainty is explicitly accounted for, when managing water resources. Various methodologies have been developed and applied by researchers in an attempt to account for the uncertainty. For example, simulation-optimization models are often used for conjunctive water resources management. However, direct application of such an approach in which all realizations are considered at each iteration of the optimization process leads to a very expensive optimization in terms of computational time, particularly when the number of realizations is large. The aim of this paper, therefore, is to introduce and apply an efficient approach referred to as Retrospective Optimization Approximation (ROA) that can be used for optimizing conjunctive use of surface water and groundwater over a multiple hydrogeological model simulations. This work is based on stochastic simulation-optimization framework using a recently emerged technique of sample average approximation (SAA) which is a sampling based method implemented within the Retrospective Optimization Approximation (ROA) approach. The ROA approach solves and evaluates a sequence of generated optimization sub-problems in an increasing number of realizations (sample size). Response matrix technique was used for linking simulation model with optimization procedure. The k-means clustering sampling technique was used to map the realizations. The methodology is demonstrated through the application to a hypothetical example. In the example, the optimization sub-problems generated were solved and analysed using “Active-Set” core optimizer implemented under MATLAB 2014a environment. Through k-means clustering sampling technique, the ROA – Active Set procedure was able to arrive at a (nearly) converged maximum expected total optimal conjunctive water use withdrawal rate within a relatively few number of iterations (6 to 7 iterations). Results indicate that the ROA approach is a promising technique for optimizing conjunctive water use of surface water and groundwater withdrawal rates under hydrogeological uncertainty.

Keywords: conjunctive water management, retrospective optimization approximation approach, sample average approximation, uncertainty

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Authors: Maria Miranda-Medina, Sara Salopek, Andras Vernes, Martin Jech

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Sliding lubricated surfaces induce the formation of tribofilms that reduce friction, wear and prevent large-scale damage of contact parts. Engine oils and lubricants use antiwear and antioxidant additives such as zinc dialkyldithiophosphate (ZDDP) from where protective tribofilms are formed by degradation. The ZDDP tribofilms are described as a two-layer structure composed of inorganic polymer material. On the top surface, the long chain polyphosphate is a zinc phosphate and in the bulk, the short chain polyphosphate is a mixed Fe/Zn phosphate with a gradient concentration. The polyphosphate chains are partially adherent to steel surface through a sulfide and work as anti-wear pads. In this contribution, ZDDP tribofilms formed on gray cast iron surfaces are studied. The tribofilms were generated in a reciprocating sliding tribometer with a piston ring-cylinder liner configuration. Fully formulated oil of SAE grade 5W-30 was used as lubricant during two tests at 40Hz and 50Hz. For the estimation of the tribofilm thicknesses, spectroscopic ellipsometry was used due to its high accuracy and non-destructive nature. Ellipsometry works under an optical principle where the change in polarisation of light reflected by the surface, is associated with the refractive index of the surface material or to the thickness of the layer deposited on top. Ellipsometrical responses derived from tribofilms are modelled by effective medium approximation (EMA), which includes the refractive index of involved materials, homogeneity of the film and thickness. The materials composition was obtained from x-ray photoelectron spectroscopic studies, where the presence of ZDDP, O and C was confirmed. From EMA models it was concluded that tribofilms formed at 40 Hz are thicker and more homogeneous than the ones formed at 50 Hz. In addition, the refractive index of each material is mixed to derive an effective refractive index that describes the optical composition of the tribofilm and exhibits a maximum response in the UV range, being a characteristic of glassy semitransparent films.

Keywords: effective medium approximation, reciprocating sliding tribometer, spectroscopic ellipsometry, zinc dialkyldithiophosphate

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Authors: Mourad Hrizi

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In this paper, we study the inverse problem of reconstructing an interior interface D appearing in the elliptic partial differential equation: Δu+χ(D)u=0 from the knowledge of the boundary measurements. This problem arises from a semiconductor transistor model. We propose a new shape reconstruction procedure that is based on the Kohn-Vogelius formulation and the topological sensitivity method. The inverse problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from a function. The unknown subdomain D is reconstructed using a level-set curve of the topological gradient. Finally, we give several examples to show the viability of our proposed method.

Keywords: inverse problem, topological optimization, topological gradient, Kohn-Vogelius formulation

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Authors: Giovanni Merola

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Sparse Principal Components Analysis aims to find principal components with few non-zero loadings. We derive such sparse solutions by adding a genuine sparsity requirement to the original Principal Components Analysis (PCA) objective function. This approach differs from others because it preserves PCA's original optimality: uncorrelatedness of the components and least squares approximation of the data. To identify the best subset of non-zero loadings we propose a branch-and-bound search and an iterative elimination algorithm. This last algorithm finds sparse solutions with large loadings and can be run without specifying the cardinality of the loadings and the number of components to compute in advance. We give thorough comparisons with the existing sparse PCA methods and several examples on real datasets.

Keywords: SPCA, uncorrelated components, branch-and-bound, backward elimination

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Authors: Andrés C. Cuervo Pinilla, Christian G. Quintero M., Chinthaka Premachandra

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This paper considers people’s driving skills diagnosis under real driving conditions. In that sense, this research presents an approach that uses GPS signals which have a direct correlation with driving maneuvers. Besides, it is presented a novel expert-driving-criteria approximation using fuzzy logic which seeks to analyze GPS signals in order to issue an intelligent driving diagnosis. Based on above, this works presents in the first section the intelligent driving diagnosis system approach in terms of its own characteristics properties, explaining in detail significant considerations about how an expert-driving-criteria approximation must be developed. In the next section, the implementation of our developed system based on the proposed fuzzy logic approach is explained. Here, a proposed set of rules which corresponds to a quantitative abstraction of some traffics laws and driving secure techniques seeking to approach an expert-driving- criteria approximation is presented. Experimental testing has been performed in real driving conditions. The testing results show that the intelligent driving diagnosis system qualifies driver’s performance quantitatively with a high degree of reliability.

Keywords: driver support systems, intelligent transportation systems, fuzzy logic, real time data processing

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Authors: Raphael Zanella

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This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under the axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit march-in-time. The code is verified by space and time convergence tests using a manufactured solution. The solving of an example problem with an axisymmetric formulation is compared to that with a full-3D formulation. Both formulations lead to the same result, but the code based on the axisymmetric formulation is much faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest in using an axisymmetric formulation when it is possible.

Keywords: axisymmetric problem, continuous finite elements, heat equation, weak formulation

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Authors: E. G. Karvelas, C. Liosis, A. Theodorakakos, T. E. Karakasidis

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Magnetic navigation of the drug inside the human vessels is a very important concept since the drug is delivered to the desired area. Consequently, the quantity of the drug required to reach therapeutic levels is being reduced while the drug concentration at targeted sites is increased. Magnetic navigation of drug agents can be achieved with the use of magnetic nanoparticles where anti-tumor agents are loaded on the surface of the nanoparticles. The magnetic field that is required to navigate the particles inside the human arteries is produced by a magnetic resonance imaging (MRI) device. The main factors which influence the efficiency of the usage of magnetic nanoparticles for biomedical applications in magnetic driving are the size and the magnetization of the biocompatible nanoparticles. In this study, a computational platform for the simulation of the optimal gradient magnetic fields for the navigation of magnetic nanoparticles inside a carotid artery is presented. For the propulsion model of the particles, seven major forces are considered, i.e., the magnetic force from MRIs main magnet static field as well as the magnetic field gradient force from the special propulsion gradient coils. The static field is responsible for the aggregation of nanoparticles, while the magnetic gradient contributes to the navigation of the agglomerates that are formed. Moreover, the contact forces among the aggregated nanoparticles and the wall and the Stokes drag force for each particle are considered, while only spherical particles are used in this study. In addition, gravitational forces due to gravity and the force due to buoyancy are included. Finally, Van der Walls force and Brownian motion are taken into account in the simulation. The OpenFoam platform is used for the calculation of the flow field and the uncoupled equations of particles' motion. To verify the optimal gradient magnetic fields, a covariance matrix adaptation evolution strategy (CMAES) is used in order to navigate the particles into the desired area. A desired trajectory is inserted into the computational geometry, which the particles are going to be navigated in. Initially, the CMAES optimization strategy provides the OpenFOAM program with random values of the gradient magnetic field. At the end of each simulation, the computational platform evaluates the distance between the particles and the desired trajectory. The present model can simulate the motion of particles when they are navigated by the magnetic field that is produced by the MRI device. Under the influence of fluid flow, the model investigates the effect of different gradient magnetic fields in order to minimize the distance of particles from the desired trajectory. In addition, the platform can navigate the particles into the desired trajectory with an efficiency between 80-90%. On the other hand, a small number of particles are stuck to the walls and remains there for the rest of the simulation.

Keywords: artery, drug, nanoparticles, navigation

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Authors: Takuro Kida, Yuichi Kida

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We show a base of the new trend of algorithm mathematically that treats a historical reason of continuous discrimination in the world as well as its solution by introducing new concepts of parallel world that includes an invisible set of errors as its companion. With respect to a matrix operator-filter bank that the matrix operator-analysis-filter bank H and the matrix operator-sampling-filter bank S are given, firstly, we introduce the detailed algorithm to derive the optimum matrix operator-synthesis-filter bank Z that minimizes all the worst-case measures of the matrix operator-error-signals E(ω) = F(ω) − Y(ω) between the matrix operator-input-signals F(ω) and the matrix operator-output signals Y(ω) of the matrix operator-filter bank at the same time. Further, feedback is introduced to the above approximation theory and it is indicated that introducing conversations with feedback does not superior automatically to the accumulation of existing knowledge of signal prediction. Secondly, the concept of category in the field of mathematics is applied to the above optimum signal approximation and is indicated that the category-based approximation theory is applied to the set-theoretic consideration of the recognition of humans. Based on this discussion, it is shown naturally why the narrow perception that tends to create isolation shows an apparent advantage in the short term and, often, why such narrow thinking becomes intimate with discriminatory action in a human group. Throughout these considerations, it is presented that, in order to abolish easy and intimate discriminatory behavior, it is important to create a parallel world of conception where we share the set of invisible error signals, including the words and the consciousness of both worlds.

Keywords: signal prediction, pseudo inverse matrix, artificial intelligence, conditional optimization

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Authors: Elimhan N. Mahmudov

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The paper concerns the necessary and sufficient conditions of optimality for Cauchy problem of fourth order discrete (PD) and discrete-approximate (PDA) inclusions. The main problem is formulation of the fourth order adjoint discrete and discrete-approximate inclusions and transversality conditions, which are peculiar to problems including fourth order derivatives and approximate derivatives. Thus the necessary and sufficient conditions of optimality are obtained incorporating the Euler-Lagrange and Hamiltonian forms of inclusions. Derivation of optimality conditions are based on the apparatus of locally adjoint mapping (LAM). Moreover in the application of these results we consider the fourth order linear discrete and discrete-approximate inclusions.

Keywords: difference, optimization, fourth, approximation, transversality

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Authors: Abdul Hakim Chikho

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Most international codes allow the use of an equivalent lateral load method for designing practical buildings to withstand earthquake actions. This method requires calculating an approximation to the fundamental mode period of vibrations of these buildings. Several empirical equations have been suggested to calculate approximations to the fundamental periods of different types of structures. Most of these equations are knowing to provide an only crude approximation to the required fundamental periods and repeating the calculation utilizing a more accurate formula is usually required. In this paper, a new formula to calculate a satisfactory approximation of the fundamental period of a practical building is proposed. This formula takes into account the mass and the stiffness of the building therefore, it is more logical than the conventional empirical equations. In order to verify the accuracy of the proposed formula, several examples have been solved. In these examples, calculating the fundamental mode periods of several farmed buildings utilizing the proposed formula and the conventional empirical equations has been accomplished. Comparing the obtained results with those obtained from a dynamic computer has shown that the proposed formula provides a more accurate estimation of the fundamental periods of practical buildings. Since the proposed method is still simple to use and requires only a minimum computing effort, it is believed to be ideally suited for design purposes.

Keywords: earthquake, fundamental mode period, design, building

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Authors: Rafik Baouche, Rabah Chaouchi

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This work reports the first comprehensive stress field interpretation from the eleven recently drilled wells in the Berkaoui Basin, Algerian Sahara. A cumulative length of 7000+m acoustic image logs from 06 vertical wells were investigated, and a mean NW-SE (128°-145° N) maximum horizontal stress (SHMax) orientation is inferred from the B-D quality wellbore breakouts. The study integrates log-based approach with the downhole measurements to infer pore pressure, in-situ stress magnitudes. Vertical stress (Sv), interpreted from the bulk-density profiles, has an average gradient of 22.36 MPa/km. The Ordovician and Cambrian reservoirs have a pore pressure gradient of 13.47-13.77 MPa/km, which is more than the hydrostatic pressure regime. A 17.2-18.3 MPa/km gradient of minimum horizontal stress (Shmin) is inferred from the fracture closure pressure in the reservoirs. Breakout widths constrained the SHMax magnitude in the 23.8-26.5 MPa/km range. Subsurface stress distribution in the central Saharan Algeria indicates that the present-day stress field in the Berkaoui Basin is principally strike-slip faulting (SHMax > Sv > Shmin). Inferences are drawn on the regional stress pattern and drilling and reservoir development.

Keywords: stress, imagery, breakouts, sahara

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Authors: Zhijun Ren, Zhang Lin, Zhao Ye, Zuo Xiangyu, Mei Dongxing

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As a pretreatment process of ballast water treatment, the performance of high gradient magnetic separation (HGMS) technology for the removal of particulates and microorganisms was studied. The results showed that HGMS process could effectively remove suspended particles larger than 5 µm and had ability to resist impact load. Microorganism could also be effectively removed by HGMS process, and the removal effect increased with increasing magnetic field strength. The maximum removal rates for Escherichia coli (E. coli) and Staphylococcus aureus (S. aureus) were 4016.1% and 9675.3% higher, respectively, than without the magnetic field. In addition, the superoxide dismutase (SOD) activity of the microbes decreased by 32.2% when the magnetic field strength was 15.4 mT for 72 min. The microstructure of the stainless steel wool was investigated, and the results showed that particle removal by HGMS has common function by the magnetic force of the high-strength, high-gradient magnetic field on weakly magnetic particles in the water, and on the stainless steel wool.

Keywords: HGMS, particulates, superoxide dismutase (SOD) activity, steel wool magnetic medium

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Authors: Gozel Judakova, Markus Bause

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We present and analyze reliable numerical techniques for simulating complex flow and transport phenomena related to natural gas transportation in pipelines. Such kind of problems are of high interest in the field of petroleum and environmental engineering. Modeling and understanding natural gas flow and transformation processes during transportation is important for the sake of physical realism and the design and operation of pipeline systems. In our approach a two fluid flow model based on a system of coupled hyperbolic conservation laws is considered for describing natural gas flow undergoing hydratization. The accurate numerical approximation of two-phase gas flow remains subject of strong interest in the scientific community. Such hyperbolic problems are characterized by solutions with steep gradients or discontinuities, and their approximation by standard finite element techniques typically gives rise to spurious oscillations and numerical artefacts. Recently, stabilized and discontinuous Galerkin finite element techniques have attracted researchers’ interest. They are highly adapted to the hyperbolic nature of our two-phase flow model. In the presentation a streamline upwind Petrov-Galerkin approach and a discontinuous Galerkin finite element method for the numerical approximation of our flow model of two coupled systems of Euler equations are presented. Then the efficiency and reliability of stabilized continuous and discontinous finite element methods for the approximation is carefully analyzed and the potential of the either classes of numerical schemes is investigated. In particular, standard benchmark problems of two-phase flow like the shock tube problem are used for the comparative numerical study.

Keywords: discontinuous Galerkin method, Euler system, inviscid two-fluid model, streamline upwind Petrov-Galerkin method, twophase flow

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Authors: Benallou Yassine, Amara Kadda, Bouazza Boubakar, Soudini Belabbes, Arbouche Omar, M. Zemouli

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The study of the pressure effect on the materials, their functionality and their properties is very important, insofar as it provides the opportunity to identify others applications such the optical properties in the alkaline earth chalcogenides, as like the SrS. Here we present the first-principles calculations which have been performed using the full potential linearized augmented plane wave method (FP-LAPW) within the Generalized Gradient Approximation developed by Perdew–Burke–Ernzerhor for solids (PBEsol). The calculated structural parameters like the lattice parameters, the bulk modulus B and their pressure derivative B' are in reasonable agreement with the available experimental and theoretical data. In addition, the elastic properties such as elastic constants (C11, C12, and C44), the shear modulus G, the Young modulus E, the Poisson’s ratio ν and the B/G ratio are also given. The treatments of exchange and correlation effects were done by the Tran-Blaha modified Becke-Johnson (TB-mBJ) potential for the electronic. The pressure effect on the electronic properties was visualized by calculating the variations of the gap as a function of pressure. The obtained results are compared to available experimental data and to other theoretical calculations

Keywords: SrS, GGA-PBEsol+TB-MBJ, density functional, Perdew–Burke–Ernzerhor, FP-LAPW, pressure effect

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Authors: Stella C. Okenu, Stephen O. Adikwu, Martins E. Okoro

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The geothermal energy resource potential of the Lower Benue Trough (LBT) in Nigeria was evaluated in this study using spectral analysis of high-resolution aeromagnetic (HRAM) data. The reduced to the equator aeromagnetic data was divided into sixteen (16) overlapping blocks, and each of the blocks was analyzed to obtain the radial averaged power spectrum which enabled the computation of the top and centroid depths to magnetic sources. The values were then used to assess the Curie Point Depth (CPD), geothermal gradients, and heat flow variations in the study area. Results showed that CPD varies from 7.03 to 18.23 km, with an average of 12.26 km; geothermal gradient values vary between 31.82 and 82.50°C/km, with an average of 51.21°C/km, while heat flow variations range from 79.54 to 206.26 mW/m², with an average of 128.02 mW/m². Shallow CPD zones that run from the eastern through the western and southwestern parts of the study area correspond to zones of high geothermal gradient values and high subsurface heat flow distributions. These areas signify zones associated with anomalous subsurface thermal conditions and are therefore recommended for detailed geothermal energy exploration studies.

Keywords: geothermal energy, curie-point depth, geothermal gradient, heat flow, aeromagnetic data, LBT

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Authors: Anthony R. Hassan, Jacob A. Gbadeyan

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In this paper, the analysis of a reactive hydromagnetic Poiseuille fluid flow under each of sensitized, Arrhenius and bimolecular chemical kinetics through a channel in the presence of heat source is carried out. An exothermic reaction is assumed while the concentration of the material is neglected. Adomian Decomposition Method (ADM) together with Pade Approximation is used to obtain the solutions of the governing nonlinear non – dimensional differential equations. Effects of various physical parameters on the velocity and temperature fields of the fluid flow are investigated. The entropy generation analysis and the conditions for thermal criticality are also presented.

Keywords: chemical kinetics, entropy generation, thermal criticality, adomian decomposition method (ADM) and pade approximation

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Authors: Karkour Selma

Abstract:

We conducted first principles full potential calculations using the Wien2k code to explore the structural, electronic, magnetic, and optical properties of SiNi₂O₄, a cubic normal spinel oxide. Our calculations, based on the GGA-PBEsol of the generalized gradient approximation, revealed several key findings. The spinel oxides exhibited a stable cubic structure in the ferromagnetic phase and showed 100% spin polarization. We determined the equilibrium lattice constant and internal parameter values. In terms of the electronic properties, we observed a direct bandgap of 2.68 eV for the spin-up configuration, while the spin-down configuration exhibited an indirect bandgap of 0.82 eV. Additionally, we calculated the total density of states and partial densities for each atom, finding a magnetic moment spin density of states of 8.0 μB per formula unit. The optical properties have been calculated. The real, Ԑ₁(ω) and the imaginary, Ԑ₂(ω) parts of the complex dielectric constants, refractivity, reflection and energy loss when light scattered from the material. The absorption region spanned from 1.5 eV to 14 eV, with significant intensity. The calculated results confirm the suitability of this material for optical and spintronic devices application.

Keywords: DFT, spintronic, GGA, spinel

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Authors: Kuniyoshi Abe

Abstract:

Bi-conjugate gradient (Bi-CG) is a well-known method for solving linear equations Ax = b, for x, where A is a given n-by-n matrix, and b is a given n-vector. Typically, the dimension of the linear equation is high and the matrix is sparse. A number of hybrid Bi-CG methods such as conjugate gradient squared (CGS), Bi-CG stabilized (Bi-CGSTAB), BiCGStab2, and BiCGstab(l) have been developed to improve the convergence of Bi-CG. Bi-CGSTAB has been most often used for efficiently solving the linear equation, but we have seen the convergence behavior with a long stagnation phase. In such cases, it is important to have Bi-CG coefficients that are as accurate as possible, and the stabilization strategy, which stabilizes the computation of the Bi-CG coefficients, has been proposed. It may avoid stagnation and lead to faster computation. Motivated by a large number of processors in present petascale high-performance computing hardware, the scalability of Krylov subspace methods on parallel computers has recently become increasingly prominent. The main bottleneck for efficient parallelization is the inner products which require a global reduction. The resulting global synchronization phases cause communication overhead on parallel computers. The parallel variants of Krylov subspace methods reducing the number of global communication phases and hiding the communication latency have been proposed. However, the numerical stability, specifically, the convergence speed of the parallel variants of Bi-CGSTAB may become worse than that of the standard Bi-CGSTAB. In this paper, therefore, we compare the convergence speed between the standard Bi-CGSTAB and the parallel variants by numerical experiments and show that the convergence speed of the standard Bi-CGSTAB is faster than the parallel variants. Moreover, we propose the stabilization strategy for the parallel variants.

Keywords: bi-conjugate gradient stabilized method, convergence speed, Krylov subspace methods, linear equations, parallel variant

Procedia PDF Downloads 138

Authors: Saikat Datta

Abstract:

Incompressible laminar time-varying flow is investigated over a rounded backward-facing step for a triangular piston motion at the inlet of a straight channel with very high acceleration, followed by a slow deceleration experimentally and through numerical simulation. The backward-facing step is an important test-case as it embodies important flow characteristics such as separation point, reattachment length, and recirculation of flow. A sliding piston imparts two successive triangular velocities at the inlet, constant acceleration from rest, 0≤t≤t0, and constant deceleration to rest, t0≤tKeywords: laminar boundary layer separation, rounded backward facing step, separation bubble, unsteady separation, unsteady vortex flows

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Authors: Jyoti Wadhwa, Arvinder Singh

Abstract:

This work presents the theoretical investigation of an enhanced second-harmonic generation of higher-order Gaussian laser beam in plasma having a density ramp. The mechanism responsible for the self-focusing of a laser beam in plasma is considered to be the relativistic mass variation of plasma electrons under the effect of a highly intense laser beam. Using the moment theory approach and considering the Wentzel-Kramers-Brillouin approximation for the non-linear Schrodinger wave equation, the differential equation is derived, which governs the spot size of the higher-order Gaussian laser beam in plasma. The nonlinearity induced by the laser beam creates the density gradient in the background plasma electrons, which is responsible for the excitation of the electron plasma wave. The large amplitude electron plasma wave interacts with the fundamental beam, which further produces the coherent radiations with double the frequency of the incident beam. The analysis shows the important role of the different modes of higher-order Gaussian laser beam and density ramp on the efficiency of generated harmonics.

Keywords: density rippled plasma, higher order Gaussian laser beam, moment theory approach, second harmonic generation.

Procedia PDF Downloads 143