Search results for: modified cubic B-spline differential quadrature method

Authors: N. Al-Orfi, M. S. El-Shahawi, A. S. Bashammakh

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The electrochemical response of glassy carbon electrode (GCE) for the sensitive and selective determination of dianabol steroid (DS) in phosphate, Britton-Robinson (B-R) and HEPES buffers of pH 2.0 - 11, 2.0 - 11 and 6.2 - 8.0, respectively using cyclic voltammetry (CV) and differential pulse- adsorptive cathodic stripping voltammetry (DP-CSV) at bare GCE was studied. The dependence of the CV response of the developed cathodic peak potential (Ep, c), peak current (ip, c) and the current function (ip, c / υ1/2) on the scan rate (υ) at the bare GCE revealed the occurrence of electrode coupled chemical reaction of EC type mechanism. The selectivity of the proposed method was assessed in the presence of high concentrations of major interfering species e.g. uric acid, ascorbic acid, citric acid, glucose, fructose, sucrose, starch and ions Na+, K+, PO4-3, NO3- and SO42-. The recovery of the method was not significant where t(critical)=2.20 > texp=1.81-1.93 at 95% confidence. The analytical application of the sensor for the quantification of DS in biological fluids as urine was investigated. The results were demonstrated as recovery percentages in the range 95±2.5-97±4.7% with relative standard deviation (RSD) of 0.5-1.5%.

Keywords: dianabol, determination, modified electrode, urine

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Authors: Mohamed Abdel-Monem, Gamal Sowilam, Omar Hegazy

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This paper presents a technical assessment of an electric vehicle with two independent rear-wheel motor and an improved traction control system. The electric differential and the control strategy have been implemented to assure that in a straight trajectory, the two rear-wheels run exactly at the same speed, considering the same/different road conditions under the left and right side of the wheels. In case of turning to right/left, the difference between the two rear-wheels speeds assures a vehicle trajectory without sliding, thanks to a harmony between the electric differential and the control strategy. The present article demonstrates a complete model and analysis of a traction control system, considering four different traction scenarios, for two independent rear-wheels motors for electric vehicles. Furthermore, the vehicle model, including wheel dynamics, load forces, electric differential, and control strategy, is designed and verified by using MATLAB/Simulink environment.

Keywords: electric vehicle, energy saving, multi-motor, electric differential, simulation and control

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Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

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This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: interpolation, approximate solution, collocation, differential system, half step, converges, block method, efficiency

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Authors: Patricia Mikchaela D. L. Feliciano, Ciela Kadeshka A. Fuentes, Bea Trixia B. Gales, Ethel Princess A. Gepulango, Martin R. Hernandez, Elina Andrea S. Lantion, Jhoe Cynder P. Legaspi, Peter F. Quilala, Gina C. Castro

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Propolis is a resin-like material used by bees to fill large gap holes in the beehive. It has been found to possess anti-inflammatory property, which stimulates hair growth in rats by inducing hair keratinocytes proliferation, causing water retention and preventing damage caused by heat, ultraviolet rays, and other microorganisms without abnormalities in hair follicles. The present study aimed to formulate 10% and 30% Propolis Hair Cream for use in enhancing hair properties. Raw propolis sample was tested for heavy metals using Atomic Absorption Spectroscopy; zinc and chromium were found to be present. Likewise, propolis was extracted in a percolator using 70% ethanol and concentrated under vacuum using a rotary evaporator. The propolis extract was analyzed for total flavonoid content. Compatibility of the propolis extract with excipients was evaluated using Differential Scanning Calorimetry (DSC). No significant changes in organoleptic properties, pH and viscosity of the formulated creams were noted after four weeks of storage at 2-8°C, 30°C, and 40°C. The formulated creams were found to be non-irritating based on the Modified Draize Rabbit Test. In vivo efficacy was evaluated based on thickness and tensile strength of hair grown on previously shaved rat skin. Results show that the formulated 30% propolis-based cream had greater hair enhancing properties than the 10% propolis cream, which had a comparable effect with minoxidil.

Keywords: atomic absorption spectroscopy, differential scanning calorimetry (DSC), modified draize rabbit test, propolis

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Authors: Ahmed Machmoum, Malika El Kyal

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We consider iterative parallel multi-splitting method for differential algebraic equations. The main feature of the proposed idea is to use the asynchronous form. We prove that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process. The main characteristic of an asynchronous mode is that the local algorithm not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays tobe substantial and unpredictable. Note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: computer, multi-splitting methods, asynchronous mode, differential algebraic systems

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Authors: Laith K. Abbas, Xiaoting Rui, Pier Marzocca

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Aerospace systems, generally speaking, are inherently nonlinear. These nonlinearities may modify the behavior of the system. However, nonlinearities in an aeroelastic system can be divided into structural and aerodynamic. Structural nonlinearities can be subdivided into distributed and concentrated ones. Distributed nonlinearities are spread over the whole structure representing the characteristic of materials and large motions. Concentrated nonlinearities act locally, representing loose of attachments, worn hinges of control surfaces, and the presence of external stores. The concentrated nonlinearities can be approximated by one of the classical structural nonlinearities, namely, cubic, free-play and hysteresis, or by a combination of these, for example, a free-play and a cubic one. Compressibility, aerodynamic heating, separated flows and turbulence effects are important aspects that result in nonlinear aerodynamic behavior. An issue related to the low-speed flutter and its catastrophic/benign character represented by Limit Cycle Oscillation (LCO) of all-movable fin, as well to their control is addressed in the present work. To the approach of this issue: (1) Quasi-Steady (QS) Theory and Computational Fluid Dynamics (CFD) of subsonic flow are implemented, (2) Flutter motion equations of a two-dimensional typical section with cubic nonlinear stiffness in the pitching direction and free play gap are established, (3) Uncoupled bending/torsion frequencies of the selected fin are computed using recently developed Transfer Matrix Method of Multibody System Dynamics (MSTMM), and (4) Time simulations are carried out to study the bifurcation behavior of the aeroelastic system. The main objective of this study is to investigate how the LCO and chaotic behavior are influenced by the coupled aeroelastic nonlinearities and intend to implement a control capability enabling one to control both the flutter boundary and its character. By this way, it may expand the operational envelop of the aerospace vehicle without failure.

Keywords: aeroelasticity, CFD, MSTMM, flutter, freeplay, fin

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Authors: Jiya Mohammed, Tsadu Shuaib, Yusuf Abdulhakeem

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The research work focuses on the cases of MHD boundary layer flow past a stretching plate with heat transfer and viscous dissipation. The non-linear of momentum and energy equation are transform into ordinary differential equation by using similarity transformation, the resulting equation are solved using Adomian Decomposition Method (ADM). An attempt has been made to show the potentials and wide range application of the Adomian decomposition method in the comparison with the previous one in solving heat transfer problems. The Pade approximates value (η= 11[11, 11]) is use on the difficulty at infinity. The results are compared by numerical technique method. A vivid conclusion can be drawn from the results that ADM provides highly precise numerical solution for non-linear differential equations. The result where accurate especially for η ≤ 4, a general equating terms of Eckert number (Ec), Prandtl number (Pr) and magnetic parameter ( ) is derived which was used to investigate velocity and temperature profiles in boundary layer.

Keywords: MHD, Adomian decomposition, boundary layer, viscous dissipation

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Authors: Eugene Stepanov, Arcady Ponosov

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To model gene regulatory networks one uses ordinary differential equations with switching nonlinearities, where the initial value problem is known to be well-posed if the trajectories cross the discontinuities transversally. Otherwise, the initial value problem is usually ill-posed, which lead to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid dynamical systems, rather than switched ones, to regularize the problem. 'Hybridization' of the switched system means that one attaches a dynamic discrete component ('automaton'), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness of the initial value problem making it well-posed. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. Several examples are provided in the presentation, which support the suggested analysis. The method can also be of interest in other applied fields, where differential equations contain switchings, e.g. in neural field models.

Keywords: hybrid dynamical systems, ill-posed problems, singular perturbation analysis, switching nonlinearities

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Authors: Jenna Metera, Olivia Graeve

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Ceramic capacitor technologies using lead based materials is being phased out for its environmental and handling hazards. Bismuth ferrite (BiFeO₃) is the next best replacement for those lead-based technologies. Unfortunately, the electrical properties in bismuth systems are not as robust as the lead alternatives. The improvement of electrical properties such as charge density, charge anisotropy, relative permittivity, and dielectric loss are the parameters that will make BiFeO₃ a competitive alternative to lead-based ceramic materials. In order to maximize the utility of these properties, we propose the ordering and an evaporation-induced self-assembly of a cubic morphology powder. Evaporation-induced self-assembly is a template-less, bottom-up, self-assembly option. The capillary forces move the particles closer together when the solvent evaporates, promoting organized agglomeration at the particle faces. The assembly of particles into organized structures can lead to enhanced properties compared to unorganized structures or single particles themselves. The interactions between the particles can be controlled based on the long-range order in the organized structure. The cubic particle morphology is produced through a hydrothermal synthesis with changes in the concentration of potassium hydroxide, which changes the morphology of the powder. Once the assembly materializes, the powder is fabricated into workable substrates for electrical testing after consolidation.

Keywords: evaporation, lead-free, morphology, self-assembly

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Authors: A. S. Hakeem, B. Ahmed, M. Ehsan, A. Ibrahim, H. M. Irshad, T. Laoui

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Alumina (Al2O3) - cubic boron nitride (cBN) ceramic composites were sintered by spark plasma sintering (SPS) using α-Al2O3 particle sizes; 150 µm, 150 nm and cBN particle size of 42 µm. Alumina-cBN composites containing 10, 20 and 30wt% cBN with and without Ni coated were sintering at an elevated temperature of 1400°C at a constant uniaxial pressure of 50 MPa. The effect of matrix particle size, cBN and Ni content on mechanical properties and thermal properties, i.e., thermal conductivity, diffusivity, expansion, densification, phase transformation, microstructure, hardness and toughness of the Al2O3-cBN/(Ni) composites under specific sintering conditions were investigated. The highest relative densification of 150 nm-Al2O3 containing 30wt% cBN (Ni coated) composite was 99% at TSPS = 1400°C. In case of 150 µm- Al2O3 compositions, the phase transformation of cBN to hBN were observed, and the relative densification decreased. Thermal conductivity depicts maximum value in case of 150 nm- Al2O3-30wt% cBN-Ni composition. The Vickers hardness of this composition at TSPS = 1400°C also showed the highest value of 29 GPa.

Keywords: alumina composite, cubic boron nitride, mechanical properties, phase transformation, Spark plasma sintering

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Authors: S. Summart, C. Saetiaw, T. Thosdeekoraphat, C. Thongsopa

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This article presents new current-mode oscillator circuits using CDTAs which is designed from block diagram. The proposed circuits consist of two CDTAs and two grounded capacitors. The condition of oscillation and the frequency of oscillation can be adjusted by electronic method. The circuits have high output impedance and use only grounded capacitors without any external resistor which is very appropriate to future development into an integrated circuit. The results of PSPICE simulation program are corresponding to the theoretical analysis.

Keywords: current-mode, quadrature oscillator, block diagram, CDTA

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Authors: Sung-Sik Park, Han Chang, Kyung-Hun Chae, Sae-Byeok Lee

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In this study, a three-dimensional (3D) Particle method without using grid was developed for analyzing large deformation of soils instead of using ordinary finite element method (FEM) or finite difference method (FDM). In the 3D Particle method, the governing equations were discretized by various particle interaction models corresponding to differential operators such as gradient, divergence, and Laplacian. The Mohr-Coulomb failure criterion was incorporated into the 3D Particle method to determine soil failure. The yielding and hardening behavior of soil before failure was also considered by varying viscosity of soil. First of all, an unconfined compression test was carried out and the large deformation following soil yielding or failure was simulated by the developed 3D Particle method. The results were also compared with those of a commercial FEM software PLAXIS 3D. The developed 3D Particle method was able to simulate the 3D large deformation of soils due to soil yielding and calculate the variation of normal and shear stresses following clay deformation.

Keywords: particle method, large deformation, soil column, confined compressive stress

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Authors: Zhan Chen, Wenquan Bi, Xiaoyun Wang

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The Midori family of light weight block cipher is proposed in ASIACRYPT2015. It has attracted the attention of numerous cryptanalysts. There are two versions of Midori: Midori64 which takes a 64-bit block size and Midori128 the size of which is 128-bit. In this paper an improved 10-round impossible differential attack on Midori64 is proposed. Pre-whitening keys are considered in this attack. A better impossible differential path is used to reduce time complexity by decreasing the number of key bits guessed. A hash table is built in the pre-computation phase to reduce computational complexity. Partial abort technique is used in the key seiving phase. The attack requires 259 chosen plaintexts, 214.58 blocks of memory and 268.83 10-round Midori64 encryptions.

Keywords: cryptanalysis, impossible differential, light weight block cipher, Midori

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Authors: Jerzy F. Janik, Mariusz Drygas, Miroslaw M. Bucko

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A simple precursor system has been recently developed in our laboratory for the conversion of affordable microcrystalline gallium antimonide GaSb to a range of nanocrystalline powders of gallium nitride GaN – a wide bandgap semiconductor indispensable in modern optoelectronics. The process relies on high temperature nitridation reactions of GaSb with ammonia. Topochemical relationships set up by the cubic lattice of GaSb result in some metastable cubic GaN formed in addition to the stable hexagonal GaN. A prior application of high energy ball milling to the initially microcrystalline GaSb precursor is shown to alter the nitridation output.

Keywords: nanocrystalline, gallium nitride, GaN, gallium antimonide, GaSb, nitridation, ball milling

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Authors: M. A. Sedghamiz, S. Raeissi

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This study presents three different approaches to estimate bubble point pressures for the binary system of CO2 and ethyl palmitate fatty acid ethyl ester. The first method involves the Peng-Robinson (PR) Equation of State (EoS) with the conventional mixing rule of Van der Waals. The second approach involves the PR EOS together with the Wong Sandler (WS) mixing rule, coupled with the Uniquac Ge model. In order to model the bubble point pressures with this approach, the volume and area parameter for ethyl palmitate were estimated by the Hansen group contribution method. The last method involved the Peng-Robinson, combined with the Wong-Sandler Method, but using NRTL as the GE model. Results using the Van der Waals mixing rule clearly indicated that this method has the largest errors among all three methods, with errors in the range of 3.96–6.22 %. The Pr-Ws-Uniquac method exhibited small errors, with average absolute deviations between 0.95 to 1.97 percent. The Pr-Ws-Nrtl method led to the least errors where average absolute deviations ranged between 0.65-1.7%.

Keywords: bubble pressure, Gibbs excess energy model, mixing rule, CO2 solubility, ethyl palmitate

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Authors: Chompoonut Chaiyaraksa, Chanida Singbubpha, Kliaothong Angkabkingkaew, Thitikorn Boonyasawin

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Heavy metal contamination in an environment is an important problem in Thailand that needs to be addressed urgently, particularly contaminated with water. It can spread to other environments faster. This research aims to study the adsorption of cadmium ion by unmodified biochar and sodium dodecyl sulfate modified magnetic biochar derived from Eichhornia Crassipes. The determination of the adsorbent characteristics was by Scanning Electron Microscope, Fourier Transform Infrared Spectrometer, X-ray Diffractometer, and the pH drift method. This study also included the comparison of adsorption efficiency of both types of biochar, adsorption isotherms, and kinetics. The pH value at the point of zero charges of the unmodified biochar and modified magnetic biochar was 7.40 and 3.00, respectively. The maximum value of adsorption reached when using pH 8. The equilibrium adsorption time was 5 hours and 1 hour for unmodified biochar and modified magnetic biochar, respectively. The cadmium adsorption by both adsorbents followed Freundlich, Temkin, and Dubinin – Radushkevich isotherm model and the pseudo-second-order kinetic. The adsorption process was spontaneous at high temperatures and non-spontaneous at low temperatures. It was an endothermic process, physisorption in nature, and can occur naturally.

Keywords: Eichhornia crassipes, magnetic biochar, sodium dodecyl sulfate, water treatment

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Authors: Salvatore Brischetto, Domenico Cesare

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Major improvements in future aircraft and spacecraft could be those dependent on an increasing use of conventional and unconventional multilayered structures embedding composite materials, functionally graded materials, piezoelectric or piezomagnetic materials, and soft foam or honeycomb cores. Layers made of such materials can be combined in different ways to obtain structures that are able to fulfill several structural requirements. The next generation of aircraft and spacecraft will be manufactured as multilayered structures under the action of a combination of two or more physical fields. In multifield problems for multilayered structures, several physical fields (thermal, hygroscopic, electric and magnetic ones) interact each other with different levels of influence and importance. An exact 3D shell model is here proposed for these types of analyses. This model is based on a coupled system including 3D equilibrium equations, 3D Fourier heat conduction equation, 3D Fick diffusion equation and electric and magnetic divergence equations. The set of partial differential equations of second order in z is written using a mixed curvilinear orthogonal reference system valid for spherical and cylindrical shell panels, cylinders and plates. The order of partial differential equations is reduced to the first one thanks to the redoubling of the number of variables. The solution in the thickness z direction is obtained by means of the exponential matrix method and the correct imposition of interlaminar continuity conditions in terms of displacements, transverse stresses, electric and magnetic potentials, temperature, moisture content and transverse normal multifield fluxes. The investigated structures have simply supported sides in order to obtain a closed form solution in the in-plane directions. Moreover, a layerwise approach is proposed which allows a 3D correct description of multilayered anisotropic structures subjected to field loads. Several results will be proposed in tabular and graphical formto evaluate displacements, stresses and strains when mechanical loads, temperature gradients, moisture content gradients, electric potentials and magnetic potentials are applied at the external surfaces of the structures in steady-state conditions. In the case of inclusions of piezoelectric and piezomagnetic layers in the multilayered structures, so called smart structures are obtained. In this case, a free vibration analysis in open and closed circuit configurations and a static analysis for sensor and actuator applications will be proposed. The proposed results will be useful to better understand the physical and structural behaviour of multilayered advanced composite structures in the case of multifield interactions. Moreover, these analytical results could be used as reference solutions for those scientists interested in the development of 3D and 2D numerical shell/plate models based, for example, on the finite element approach or on the differential quadrature methodology. The correct impositions of boundary geometrical and load conditions, interlaminar continuity conditions and the zigzag behaviour description due to transverse anisotropy will be also discussed and verified.

Keywords: composite structures, 3D shell model, stress analysis, multifield loads, exponential matrix method, layer wise approach

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Authors: Daljinder Singh, J.S.Dhillon, Balraj Singh

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According to no free lunch theorem, a single search technique cannot perform best in all conditions. Optimization method can be attractive choice to solve optimization problem that may have exclusive advantages like robust and reliable performance, global search capability, little information requirement, ease of implementation, parallelism, no requirement of differentiable and continuous objective function. In order to synergize between exploration and exploitation and to further enhance the performance of Bat algorithm, the paper proposed a modified bat algorithm that adds additional search procedure based on bat’s previous experience. The proposed algorithm is used for solving the economic load dispatch (ELD) problem. The practical constraint such valve-point loading along with power balance constraints and generator limit are undertaken. To take care of power demand constraint variable elimination method is exploited. The proposed algorithm is tested on various ELD problems. The results obtained show that the proposed algorithm is capable of performing better in majority of ELD problems considered and is at par with existing algorithms for some of problems.

Keywords: bat algorithm, economic load dispatch, penalty method, variable elimination method

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Authors: M. Qamarul Islam, Ergun Dogan, Mehmet Yazici

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There is a growing body of evidence that non-normal data is more prevalent in nature than the normal one. Examples can be quoted from, but not restricted to, the areas of Economics, Finance and Actuarial Science. The non-normality considered here is expressed in terms of fat-tailedness and asymmetry of the relevant distribution. In this study a skew t distribution that can be used to model a data that exhibit inherent non-normal behavior is considered. This distribution has tails fatter than a normal distribution and it also exhibits skewness. Although maximum likelihood estimates can be obtained by solving iteratively the likelihood equations that are non-linear in form, this can be problematic in terms of convergence and in many other respects as well. Therefore, it is preferred to use the method of modified maximum likelihood in which the likelihood estimates are derived by expressing the intractable non-linear likelihood equations in terms of standardized ordered variates and replacing the intractable terms by their linear approximations obtained from the first two terms of a Taylor series expansion about the quantiles of the distribution. These estimates, called modified maximum likelihood estimates, are obtained in closed form. Hence, they are easy to compute and to manipulate analytically. In fact the modified maximum likelihood estimates are equivalent to maximum likelihood estimates, asymptotically. Even in small samples the modified maximum likelihood estimates are found to be approximately the same as maximum likelihood estimates that are obtained iteratively. It is shown in this study that the modified maximum likelihood estimates are not only unbiased but substantially more efficient than the commonly used moment estimates or the least square estimates that are known to be biased and inefficient in such cases. Furthermore, in conventional regression analysis, it is assumed that the error terms are distributed normally and, hence, the well-known least square method is considered to be a suitable and preferred method for making the relevant statistical inferences. However, a number of empirical researches have shown that non-normal errors are more prevalent. Even transforming and/or filtering techniques may not produce normally distributed residuals. Here, a study is done for multiple linear regression models with random error having non-normal pattern. Through an extensive simulation it is shown that the modified maximum likelihood estimates of regression parameters are plausibly robust to the distributional assumptions and to various data anomalies as compared to the widely used least square estimates. Relevant tests of hypothesis are developed and are explored for desirable properties in terms of their size and power. The tests based upon modified maximum likelihood estimates are found to be substantially more powerful than the tests based upon least square estimates. Several examples are provided from the areas of Economics and Finance where such distributions are interpretable in terms of efficient market hypothesis with respect to asset pricing, portfolio selection, risk measurement and capital allocation, etc.

Keywords: least square estimates, linear regression, maximum likelihood estimates, modified maximum likelihood method, non-normality, robustness

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Authors: Siriwan Nantaphol, Robert B. Channon, Takeshi Kondo, Weena Siangproh, Orawon Chailapakul, Charles S. Henry

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In this work, we demonstrate a novel electrochemically reduced graphene oxide (ERGO) modified boron-doped diamond paste (BDDP) electrode on paper-based analytical devices (PADs) for simultaneous determination of norepinephrine (NE) and serotonin (5-HT). The BDD paste electrode was easily constructed by filling BDD paste in small channels, which made in transparency film sheets using a CO₂ laser etching 
system. The counter and reference electrodes were fabricated on paper by in-house screen-printing and then combined with BDD paste microelectrode. The electrochemical characterization of the device was investigated by cyclic voltammetry (CV). Differential pulse voltammetry (DPV) was employed for the simultaneous determination of NE and 5-HT. The ERGO-modified BDDP electrode displayed excellent electrocatalytic activities toward the oxidation of NE and 5-HT and strong function for resolving the overlapping voltammetric responses of NE and 5-HT into two well-defined voltammetric peaks. This device was capable of simultaneously detecting NE and 5-HT in wide concentration ranges and with a low limit of detections. In addition, it has the advantages in terms of ease of use, low cost, and disposability.

Keywords: boron-doped diamond paste electrode, electrochemically reduced graphene oxide, norepinephrine, paper-based analytical device, serotonin

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Authors: Hsu-Yung Cheng, Kuo-Chang Hsu, Chi-Chang Chan, Mei-Hui Tseng, Chih-Chang Yu, Ya-Sheng Liu

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Photovoltaics modules are usually not installed horizontally to avoid water or dust accumulation. However, the measured irradiance data on tilted surfaces are rarely available since installing pyranometers with various tilt angles induces high costs. Therefore, estimating solar irradiance on tilted surfaces is an important research topic. In this work, artificial neural networks (ANN) are utilized to construct the transfer model to estimate solar irradiance on tilted surfaces. Instead of predicting tilted irradiance directly, the proposed method estimates the differences between the horizontal irradiance and the irradiance on a tilted surface. The outputs of the ANNs in the proposed design are differential values. The experimental results have shown that the proposed ANNs with differential outputs can substantially improve the estimation accuracy compared to ANNs that estimate the titled irradiance directly.

Keywords: photovoltaics, artificial neural networks, tilted irradiance, solar energy

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Authors: Mohamed Suleiman, Zarina Bibi Ibrahim, Nor Ain Azeany, Khairil Iskandar Othman

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In this paper, a class of variable order fully implicit multistep Block Backward Differentiation Formulas (VOBBDF) using uniform step size for the numerical solution of stiff ordinary differential equations (ODEs) is developed. The code will combine three multistep block methods of order four, five and six. The order selection is based on approximation of the local errors with specific tolerance. These methods are constructed to produce two approximate solutions simultaneously at each iteration in order to further increase the efficiency. The proposed VOBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with single order Block Backward Differentiation Formula (BBDF). Numerical results shows the advantage of using VOBBDF for solving ODEs.

Keywords: block backward differentiation formulas, uniform step size, ordinary differential equations

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Authors: Belloufi Mohammed, Sellami Badreddine

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This paper deals with a new nonlinear modified three-term conjugate gradient algorithm for solving large-scale unstrained optimization problems. The search direction of the algorithms from this class has three terms and is computed as modifications of the classical conjugate gradient algorithms to satisfy both the descent and the conjugacy conditions. An example of three-term conjugate gradient algorithm from this class, as modifications of the classical and well known Hestenes and Stiefel or of the CG_DESCENT by Hager and Zhang conjugate gradient algorithms, satisfying both the descent and the conjugacy conditions is presented. Under mild conditions, we prove that the modified three-term conjugate gradient algorithm with Wolfe type line search is globally convergent. Preliminary numerical results show the proposed method is very promising.

Keywords: unconstrained optimization, three-term conjugate gradient, sufficient descent property, line search

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Authors: Weihua Ruan, Kuan-Chou Chen

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This paper is concerned with a system of Hamilton-Jacobi-Bellman equations coupled with an autonomous dynamical system. The mathematical system arises in the differential game formulation of political economy models as an infinite-horizon continuous-time differential game with discounted instantaneous payoff rates and continuously and discretely varying state variables. The existence of a weak solution of the PDE system is proven and a computational scheme of approximate solution is developed for a class of such systems. A model of democratization is mathematically analyzed as an illustration of application.

Keywords: Hamilton-Jacobi-Bellman equations, infinite-horizon differential games, continuous and discrete state variables, political-economy models

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Authors: J. A. Gbadeyan, R. A. Kareem

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In this paper, we investigated the effects of unsteady internal heat generation of a two-step exothermic reactive hydromagnetic fluid flow under different chemical kinetics namely: Sensitized, Arrhenius and Bimolecular kinetics through an isothermal wall temperature channel. The resultant modeled nonlinear partial differential equations were simplified and solved using a combined Laplace-Differential Transform Method (LDTM). The solutions obtained were discussed and presented graphically to show the salient features of the fluid flow and heat transfer characteristics.

Keywords: unsteady, reactive, hydromagnetic, couette ow, exothermi creactio

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Authors: Hakiki Kheira, Belhamiti Omar

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In this paper, we propose a new compartmental fractional order model for the simulation of epidemic obesity dynamics. Using the Legendre wavelet method combined with the decoupling and quasi-linearization technique, we demonstrate the validity and applicability of our model. We also present some fractional differential illustrative examples to demonstrate the applicability and efficiency of the method. The fractional derivative is described in the Caputo sense.

Keywords: Caputo derivative, epidemiology, Legendre wavelet method, obesity

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Authors: Pradeepa Teegala, Ramreddy Chitteti

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This article analyzes the mixed convection flow of chemically reacting micropolar fluid over a truncated cone embedded in non-Darcy porous medium with convective boundary condition. In addition, heat generation/absorption and Joule heating effects are taken into consideration. The similarity solution does not exist for this complex fluid flow problem, and hence non-similarity transformations are used to convert the governing fluid flow equations along with related boundary conditions into a set of nondimensional partial differential equations. Many authors have been applied the spectral quasi-linearization method to solve the ordinary differential equations, but here the resulting nonlinear partial differential equations are solved for non-similarity solution by using a recently developed method called the spectral quasi-linearization method (SQLM). Comparison with previously published work on special cases of the problem is performed and found to be in excellent agreement. The effect of pertinent parameters namely, Biot number, mixed convection parameter, heat generation/absorption, Joule heating, Forchheimer number, chemical reaction, micropolar and magnetic field on physical quantities of the flow are displayed through graphs and the salient features are explored in detail. Further, the results are analyzed by comparing with two special cases, namely, vertical plate and full cone wherever possible.

Keywords: chemical reaction, convective boundary condition, joule heating, micropolar fluid, mixed convection, spectral quasi-linearization method

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Authors: Adamu S. Salawu, Ibrahim O. Isah

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Direct solution to several forms of fourth-order ordinary differential equations is not easily obtained without first reducing them to a system of first-order equations. Thus, numerical methods are being developed with the underlying techniques in the literature, which seeks to approximate some classes of fourth-order initial value problems with admissible error bounds. Multistep methods present a great advantage of the ease of implementation but with a setback of several functions evaluation for every stage of implementation. However, hybrid methods conventionally show a slightly higher order of truncation for any k-step linear multistep method, with the possibility of obtaining solutions at off mesh points within the interval of solution. In the light of the foregoing, we propose the continuous form of a hybrid multistep method with Chebyshev polynomial as a basis function for the numerical integration of fourth-order initial value problems of ordinary differential equations. The basis function is interpolated and collocated at some points on the interval [0, 2] to yield a system of equations, which is solved to obtain the unknowns of the approximating polynomial. The continuous form obtained, its first and second derivatives are evaluated at carefully chosen points to obtain the proposed block method needed to directly approximate fourth-order initial value problems. The method is analyzed for convergence. Implementation of the method is done by conducting numerical experiments on some test problems. The outcome of the implementation of the method suggests that the method performs well on problems with oscillatory or trigonometric terms since the approximations at several points on the solution domain did not deviate too far from the theoretical solutions. The method also shows better performance compared with an existing hybrid method when implemented on a larger interval of solution.

Keywords: Chebyshev polynomial, collocation, hybrid multistep method, initial value problems, interpolation

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Authors: Martin K. Steiger, Lukas Heisler, Hans-Georg Brachtendorf

Abstract:

Deep neural networks and their variants form the backbone of many AI applications. Based on the so-called residual networks, a continuous formulation of such models as ordinary differential equations (ODEs) has proven advantageous since different techniques may be applied that significantly increase the learning speed and enable controlled trade-offs with the resulting error at the same time. For the evaluation of such models, high-performance numerical differential equation solvers are used, which also provide the gradients required for training. However, whether classical gradient-based methods are even applicable or which one yields the best results has not been discussed yet. This paper aims to redeem this situation by providing empirical results for different applications.

Keywords: deep neural networks, gradient-based learning, image processing, ordinary differential equation networks

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Authors: Giorgio Visentin, Inna S. Kalinina, Alexei A. Buchachenko

Abstract:

In the ambit of intermolecular interactions, a combination rule is defined as a relation linking a potential parameter for the interaction of two unlike species with the same parameters for interaction pairs of like species. Some of their most exemplificative applications cover the construction of molecular dynamics force fields and dispersion-corrected density functionals. Here, an extended combination rule is proposed, relating the dipole-dipole dispersion coefficients for the interaction of like target species to the same coefficients for the interaction of the target and a set of partner species. The rule can be devised in two different ways, either by uniform discretization of the Casimir-Polder integral on a Gauss-Legendre quadrature or by relating the dynamic polarizabilities of the target and the partner species. Both methods return the same system of linear equations, which requires the knowledge of the dispersion coefficients for interaction between the partner species to be solved. The test examples show a high accuracy for dispersion coefficients (better than 1% in the pristine test for the interaction of Yb atom with rare gases and alkaline-earth metal atoms). In contrast, the rule does not ensure correct monotonic behavior of the dynamic polarizability of the target species. Acknowledgment: The work is supported by Russian Science Foundation grant # 17-13-01466.

Keywords: combination rule, dipole-dipole dispersion coefficient, Casimir-Polder integral, Gauss-Legendre quadrature

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