Search results for: kinetic equation

Authors: Mohammad Ahmad, Dayalan Kasilingam

Abstract:

In this paper, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using the spectral domain (SD) analysis. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The study focuses on the application of SD-FMM to one-dimensional (1D) and two-dimensional (2D) electric field integral equation (EFIE). The case of perfectly conducting strip, circular and square cylinders are numerically analyzed and compared with the results from the standard method of moments (MoM).

Keywords: electric field integral equation, fast multipole method, method of moments, wave scattering, spectral domain

Procedia PDF Downloads 406

Authors: A. Bouriche, D. Merah, L.Alachaher-Bedjaoui, U. Maschke

Abstract:

Intensive research continues in the field of liquid crystals (LCs) for their potential use in modern display applications. Nematic LCs has been most commonly used due to the large birefringence and their sensitivity to even weak perturbation forces induced by electric, magnetic and optical fields. Polymer dispersed liquid crystals (PDLCs), composed of micron-sized nematic LC droplets dispersed in a polymer matrix is an important class of materials for applications in different domains of technology involving large area display devices, optical switches, phase modulators, variable attenuators, polarisers, flexible displays and smart windows. In this study the composites are prepared from mixtures of monofunctional acrylic monomers, (Butylacrylate (ABu), 2-Ethylhexylacrylate (2-EHA), 2-Hydroxyethyl methacrylate (HEMA) and hydroxybutylmethacrylate (HBMA)) and two liquid crystals: (4-cyano-4'-n-pentyl-biphenyl) (5CB) and E7 which is an eutectic mixtures of four cyanoparaphenylenes. These mixtures are prepared adding the Darocur 1173 as photoinitiateor, the 1.6-hexanediol diacrylate (HDDA) as cross-linker agent, and finally they are exposed to UV irradiation. The kinetic polymerization of monomer/LC mixture were investigated with the Fourier Transform Infra Red spectroscopy (FTIR). The electro-optical properties of the PDLC films were determined by measuring the voltage dependence on the transmitted light.

Keywords: acrylic monomers, films PDLC, liquid crystal, polymerisation

Procedia PDF Downloads 326

Authors: Saman Mostafazadeh-Fard, Zohrab Samani, Kenneth Suazo

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Agricultural ditch liners are used to prevent soil erosion and reduce seepage losses. This paper introduced an approach to validate a computational fluid dynamics (CFD) platform FLOW-3D code and its use to design a flow-regulating corrugated agricultural ditch liner system (Smart Ditch (SM)). Hydrodynamic and sediment transport analyses were performed on the proposed liner flow using the CFD platform FLOW-3D code. The code's hydrodynamic and scour and sediment transport models were calibrated and validated using lab data with an accuracy of 94 % and 95%, respectively. The code was then used to measure hydrodynamic parameters of sublayer turbulent intensity, kinetic energy, dissipation, and packed sediment mass normalized with respect to sublayer flow velocity. Sublayer turbulent intensity, kinetic energy, and dissipation in the SM flow were significantly higher than CR flow. An alternative corrugated liner was also designed, and sediment transport was measured and compared to SM and CR flows. Normalized packed sediment mass with respect to average sublayer flow velocity was 27.8 % lower in alternative flow compared to SM flow. CFD platform FLOW-3D code could effectively be used to design corrugated ditch liner systems and perform hydrodynamic and sediment transport analysis under various corrugation designs.

Keywords: CFD, hydrodynamic, sediment transport, ditch, liner design

Procedia PDF Downloads 122

Authors: Abhishek Mukherjee, Juan C. Cajas, Jenny Suckale, Guillaume Houzeaux, Oriol Lehmkuhl, Simone Marras

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The investigation of tsunami flow characteristics and the quantification of tsunami energy reduction through the coastal vegetation is important to understand the protective benefits of nature-based mitigation parks. In the present study, a three-dimensional non-hydrostatic incompressible Computational Fluid Dynamics model with a two-way coupling enabled fluid-structure interaction approach (FSI) is used. After validating the numerical model against experimental data, tsunami flow characteristics have been investigated by varying vegetation density, modulus of elasticity, the gap between stems, and arrangement or distribution of vegetation patches. Streamwise depth average velocity profiles, turbulent kinetic energy, energy flux reflection, and dissipation extracted by the numerical study will be presented in this study. These diagnostics are essential to assess the importance of different parameters to design the proper coastal defense systems. When a tsunami wave reaches the shore, it transforms into undular bores, which induce scour around offshore structures and sediment transport. The bed shear stress, instantaneous turbulent kinetic energy, and the vorticity near-bed will be presented to estimate the importance of vegetation to prevent tsunami-induced scour and sediment transport.

Keywords: coastal defense, energy flux, fluid-structure interaction, natural hazards, sediment transport, tsunami mitigation

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Authors: Ralpian Randolian

Abstract:

Eighty-five Romanian teachers and principals participated on this study to examine their perspectives of different leadership styles. Demographic variables such as the source of degree (Romania, Europe institutes, USA institutes, etc.), gender, region, level taught, years of experience, and specialty were identified. The researcher developed a questionnaire that consisted of 4 leadership styles. The data were analyzed using structural equation modeling (SEM) to identify which of the variables best predict the leadership styles. Results indicated that the democracy style was the most preferred leadership style by Jordanian parents, while the authoritarian styles ranked second. The results also found statistically significant differences were found related to the study variables. This study ends by putting forward a number of suggestions and recommendation.

Keywords: teachers’ perspectives, leadership styles, gender, structural equation modeling

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Authors: Beghdadi Lotfi, Bouziane Abdelhafid

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A finite volume method for quadrilaterals unstructured mesh is developed to predict the two dimensional steady-state solutions of conduction equation. In this scheme, based on the integration around the polygonal control volume, the derivatives of conduction equation must be converted into closed line integrals using same formulation of the Stokes theorem. To valid the accuracy of the method two numerical experiments s are used: conduction in a regular block (with known analytical solution) and conduction in a rotated block (case with curved boundaries).The numerical results show good agreement with analytical results. To demonstrate the accuracy of the method, the absolute and root-mean square errors versus the grid size are examined quantitatively.

Keywords: Stokes theorem, unstructured grid, heat transfer, complex geometry

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Authors: Xu Runzhang, Yang Yanbing, Niu Yi, Zhang Mingyou, Liu Yu

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For a class of semilinear parabolic equations with linear dynamical boundary conditions in a bounded domain, we obtain both global solutions and finite time blow-up solutions when the initial data varies in the phase space H1(Ω). Our main tools are the comparison principle, the potential well method and the concavity method. In particular, we discuss the behavior of the solutions with the initial data at critical and high energy level.

Keywords: high energy level, critical energy level, linear dynamical boundary condition, semilinear parabolic equation

Procedia PDF Downloads 436

Authors: Anon Paserakung, Chaloemphon Muangyen, Suban Foiklang, Yanin Opatpatanakit

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Improving nutritive values and digestibility of maize stover is an alternative way to increase their utilization in ruminant and reduce air pollution from open burning of maize stover in the northern Thailand. The present study, 2x3 factorial arrangements in completely randomized design was conducted to investigate the effect of maize stover components (whole and upper stover; cut above 5th node). Urea treatment at levels 0, 3, and 6% DM on dry matter digestibility and fermentation kinetics of maize stover using in vitro gas production. After 21 days of urea treatment, results illustrated that there was no interaction between maize stover components and urea treatment on 48h in vitro dry matter digestibility (IVDMD). IVDMD was unaffected by maize stover components (P > 0.05), average IVDMD was 55%. However, using whole maize stover gave higher cumulative gas and gas kinetic parameters than those of upper stover (P<0.05). Treating maize stover by ensiling with urea resulted in a significant linear increase in IVDMD (P<0.05). IVDMD increased from 42.6% to 53.9% when increased urea concentration from 0 to 3% and maximum IVDMD (65.1%) was observed when maize stover was ensiled with 6% urea. Maize stover treated with urea at levels of 0, 3, and 6% linearly increased cumulative gas production at 96h (31.1 vs 50.5 and 59.1 ml, respectively) and all gas kinetic parameters excepted the gas production from the immediately soluble fraction (P<0.50). The results indicate that maize stover treated with 6% urea enhance in vitro dry matter digestibility and fermentation kinetics. This study provides a practical approach to increasing utilization of maize stover in feeding ruminant animals.

Keywords: maize stover, urea treatment, ruminant feed, gas production

Procedia PDF Downloads 224

Authors: A. Bouriche, D. Merah, T. Bouchaour, L. Alachaher-Bedjaoui, U. Maschke

Abstract:

Intensive research continues in the field of liquid crystals (LCs) for their potential use in modern display applications. Nematic LCs has been most commonly used due to the large birefringence and their sensitivity to even weak perturbation forces induced by electric, magnetic and optical fields. Polymer dispersed liquid crystals (PDLCs), composed of micron-sized nematic LC droplets dispersed in a polymer matrix is an important class of materials for applications in different domains of technology involving large area display devices, optical switches, phase modulators, variable attenuators, polarisers, flexible displays and smart windows. In this study the composites are prepared from mixtures of mono functional acrylic monomers, (Butylacrylate (ABu), 2-Ethylhexylacrylate (2-EHA), 2-Hydroxyethyl methacrylate (HEMA) and hydroxybutylmethacrylate (HBMA)) and two liquid crystals: (4-cyano-4'-n-pentyl-biphenyl) (5CB) and E7 which is an eutectic mixtures of four cyanoparaphenylenes. These mixtures are prepared adding the Darocur 1173 as photoinitiator, the 1.6-hexanediol diacrylate (HDDA) as cross-linker agent, and finally they are exposed to UV irradiation. The kinetic polymerization of monomer/LC mixture were investigated with the Fourier Transform Infra Red spectroscopy (FTIR). The electro-optical properties of the PDLC films were determined by measuring the voltage dependence on the transmitted light.

Keywords: acrylic monomers, films PDLC, liquid crystal, polymerisation

Procedia PDF Downloads 293

Authors: Abdurrahim Dal, Tuncay Karaçay

Abstract:

Dynamics of a rotor supported by air bearings is strongly depends on the pressure distribution between the rotor and the bearing. In this study, internal pressure in air bearings is numerical and experimental analyzed for different radial clearances. Firstly the pressure distribution between rotor and bearing is modeled using Reynold's equation and this model is solved numerically. The rotor-bearing system is also modeled in four degree of freedom and it is simulated for different radial clearances. Then, in order to validate numerical results, a test rig is designed and the rotor bearing system is run under the same operational conditions. Pressure signals of left and right bearings are recorded. Internal pressure variations are compared for numerical and experimental results for different radial clearances.

Keywords: air bearing, internal pressure, Reynold’s equation, rotor

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Authors: Wanhyun Cho, Seongchae Seo, Soonja Kang

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In this work, we propose a variational technique for image contrast enhancement which utilizes global and local information around each pixel. The energy functional is defined by a weighted linear combination of three terms which are called on a local, a global contrast term and dispersion term. The first one is a local contrast term that can lead to improve the contrast of an input image by increasing the grey-level differences between each pixel and its neighboring to utilize contextual information around each pixel. The second one is global contrast term, which can lead to enhance a contrast of image by minimizing the difference between its empirical distribution function and a cumulative distribution function to make the probability distribution of pixel values becoming a symmetric distribution about median. The third one is a dispersion term that controls the departure between new pixel value and pixel value of original image while preserving original image characteristics as well as possible. Second, we derive the Euler-Lagrange equation for true image that can achieve the minimum of a proposed functional by using the fundamental lemma for the calculus of variations. And, we considered the procedure that this equation can be solved by using a gradient decent method, which is one of the dynamic approximation techniques. Finally, by conducting various experiments, we can demonstrate that the proposed method can enhance the contrast of colour images better than existing techniques.

Keywords: color image, contrast enhancement technique, variational approach, Euler-Lagrang equation, dynamic approximation method, EME measure

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Authors: Arcady Ponosov

Abstract:

Many well-known age-structured population models are derived from the celebrated McKendrick-von Foerster equation (MFE), also called the biological conservation law. A similar technique is suggested for the stochastically perturbed MFE. This technique is shown to produce stochastic versions of the deterministic population models, which appear to be very different from those one can construct by simply appending additive stochasticity to deterministic equations. In particular, it is shown that stochastic Nicholson’s blowflies model should contain both additive and multiplicative stochastic noises. The suggested transformation technique is similar to that used in the deterministic case. The difference is hidden in the formulas for the exact solutions of the simplified boundary value problem for the stochastically perturbed MFE. The analysis is also based on the theory of stochastic delay differential equations.

Keywords: boundary value problems, population models, stochastic delay differential equations, stochastic partial differential equation

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Authors: Seema Kothari, Dinesh Panday

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An observed correlation of the reaction rates with the changes in the nature of substituent present on one of the reactants often reveals the nature of transition state. Selective oxidation of organic compounds under non-aqueous media is an important transformation in synthetic organic chemistry. Inorganic chromates and dichromates being drastic oxidant and are generally insoluble in most organic solvents, a number of different chromium (VI) derivatives have been synthesized. Benzimidazolium dichromate (BIDC) is one of the recently reported Cr(VI) reagents which is neither hygroscopic nor light sensitive being, therefore, much stable. Not many reports on the kinetics of the oxidations by BIDC are seemed to be available in the literature. In the present investigation, the kinetics and mechanism of benzyl alcohol (BA) and a number of para- and meta-substituted benzyl alcohols by benzimidazolium dichromate (BIDC), in dimethyl sulphoxide, is reported. The reactions were followed spectrophotometrically at 364 nm by monitoring the decrease in [BIDC] for up to 85-90% reaction, the temperature being constant. The observed oxidation product is the corresponding benzaldehyde. The reactions were of first order with respect to each the alcohol and BIDC. The reactions are catalyzed by proton, and the dependence is of the form: kobs = a + b[H+]. The reactions thus follow both, an acid-dependent and acid-independent paths. The oxidation of [1,1 2H2]benzyl alcohol exhibited the presence of a substantial kinetic isotope effect ( kH/kD = 6.20 at 298 K ). This indicated the cleavage of a α-C-H bond in the rate-determining step. An analysis of the temperature dependence of the deuterium isotope effect showed that the loss of hydrogen proceeds through a concerted cyclic process. The rate of oxidation of BA was determined in 19 organic solvents. An analysis of the solvent effect by Swain’s equation indicated that though both the anion and cation-solvating powers of the solvent contribute to the observed solvent effect, the role of cation-solvation is major. The rates of the para and meta compounds, at 298 K, failed to exhibit a significant correlation in terms of Hammett or Brown's substituent constants. The rates were then subjected to analyses in terms of dual substituent parameter (DSP) equations. The rates of oxidation of the para-substituted benzyl alcohols show an excellent correlation with Taft's σI and σRBA values. However, the rates for the meta-substituted benzyl alcohols show an excellent correlation with σI and σR0. The polar reaction constants are negative indicating an electron-deficient transition state. Hence the overall mechanism is proposed to involve the formation of a chromate ester in a fast pre-equilibrium and then a decomposition of the ester in a subsequent slow step via a cyclic concerted symmetrical transition state, involving hydride-ion transfer, leading to the product. The first order dependence on alcohol may be accounted in terms of the small value of the formation constant of the ester intermediate. An another reaction mechanism accounting the acid-catalysis involve the formation of a protonated BIDC prior to formation of an ester intermediate which subsequently decomposes in a slow step leading to the product.

Keywords: benzimidazolium dichromate, benzyl alcohols, correlation analysis, kinetics, oxidation

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

Abstract:

Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations

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Authors: Calister Wingang Makebe, Wilson Ambindei Agwanande, Emmanuel Jong Nso, P. Nisha

Abstract:

Traditional liquid-state fermentation processes of Annona muricata L. juice can result in fluctuating product quality and quantity due to difficulties in control and scale up. This work describes a laboratory-scale batch fermentation process to produce a probiotic Annona muricata L. enzymatically extracted juice, which was modeled using the Doehlert design with independent extraction factors being incubation time, temperature, and enzyme concentration. It aimed at a better understanding of the traditional process as an initial step for future optimization. Annona muricata L. juice was fermented with L. acidophilus (NCDC 291) (LA), L. casei (NCDC 17) (LC), and a blend of LA and LC (LCA) for 72 h at 37 °C. Experimental data were fitted into mathematical models (Monod, Logistic and Luedeking and Piret models) using MATLAB software, to describe biomass growth, sugar utilization, and organic acid production. The optimal fermentation time was obtained based on cell viability, which was 24 h for LC and 36 h for LA and LCA. The model was particularly effective in estimating biomass growth, reducing sugar consumption, and lactic acid production. The values of the determination coefficient, R2, were 0.9946, 0.9913 and 0.9946, while the residual sum of square error, SSE, was 0.2876, 0.1738 and 0.1589 for LC, LA and LCA, respectively. The growth kinetic parameters included the maximum specific growth rate, µm, which was 0.2876 h-1, 0.1738 h-1 and 0.1589 h-1 as well as the substrate saturation, Ks, with 9.0680 g/L, 9.9337 g/L and 9.0709 g/L respectively for LC, LA and LCA. For the stoichiometric parameters, the yield of biomass based on utilized substrate (YXS) was 50.7932, 3.3940 and 61.0202, and the yield of product based on utilized substrate (YPS) was 2.4524, 0.2307 and 0.7415 for LC, LA, and LCA, respectively. In addition, the maintenance energy parameter (ms) was 0.0128, 0.0001 and 0.0004 with respect to LC, LA and LCA. With the kinetic model proposed by Luedeking and Piret for lactic acid production rate, the growth associated, and non-growth associated coefficients were determined as 1.0028 and 0.0109, respectively. The model was demonstrated for batch growth of LA, LC, and LCA in Annona muricata L. juice. The present investigation validates the potential of Annona muricata L. based medium for heightened economical production of a probiotic medium.

Keywords: L. acidophilus, L. casei, fermentation, modelling, kinetics

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Authors: Siu-Siu Guo, Qingxuan Shi

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In this paper, single-degree-of-freedom (SDOF) systems to white noise and colored noise excitations are investigated. By expressing colored noise excitation as a second-order filtered white noise process and introducing colored noise as an additional state variable, the equation of motion for SDOF system under colored noise is then transferred artificially to multi-degree-of-freedom (MDOF) system under white noise excitations. As a consequence, corresponding Fokker-Planck-Kolmogorov (FPK) equation governing the joint probabilistic density function (PDF) of state variables increases to 4-dimension (4-D). Solution procedure and computer programme become much more sophisticated. The exponential-polynomial closure (EPC) method, widely applied for cases of SDOF systems under white noise excitations, is developed and improved for cases of systems under colored noise excitations and for solving the complex 4-D FPK equation. On the other hand, Monte Carlo simulation (MCS) method is performed to test the approximate EPC solutions. Two examples associated with Gaussian and non-Gaussian colored noise excitations are considered. Corresponding band-limited power spectral densities (PSDs) for colored noise excitations are separately given. Numerical studies show that the developed EPC method provides relatively accurate estimates of the stationary probabilistic solutions. Moreover, statistical parameter of mean-up crossing rate (MCR) is taken into account, which is important for reliability and failure analysis.

Keywords: filtered noise, narrow-banded noise, nonlinear dynamic, random vibration

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Authors: Merouane Salhi, Mohamed Roudane, Abdelkader Kirad

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In this work, we present a new form of characteristics method, which is a technique for solving partial differential equations. Typically, it applies to first-order equations; the aim of this method is to reduce a partial differential equation to a family of ordinary differential equations along which the solution can be integrated from some initial data. This latter developed under the real gas theory, because when the thermal and the caloric imperfections of a gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with the gas parameters. The gas doesn’t stay perfect. Its state equation change and it becomes for a real gas. The presented equations of the characteristics remain valid whatever area or field of study. Here we need have inserted the developed Prandtl Meyer function in the mathematical system to find a new model when the effect of stagnation pressure is taken into account. In this case, the effects of molecular size and intermolecular attraction forces intervene to correct the state equation, the thermodynamic parameters and the value of Prandtl Meyer function. However, with the assumptions that Berthelot’s state equation accounts for molecular size and intermolecular force effects, expressions are developed for analyzing the supersonic flow for thermally and calorically imperfect gas. The supersonic parameters depend directly on the stagnation parameters of the combustion chamber. The resolution has been made by the finite differences method using the corrector predictor algorithm. As results, the developed mathematical model used to design 2D minimum length nozzles under effect of the stagnation parameters of fluid flow. A comparison for air with the perfect gas PG and high temperature models on the one hand and our results by the real gas theory on the other of nozzles shapes and characteristics are made.

Keywords: numerical methods, nozzles design, real gas, stagnation parameters, supersonic expansion, the characteristics method

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Authors: Ömer Aktaş, Olga A. Suvorova, Oleg Tretyakov

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The boundary value problem on non-canonical and arbitrary shaped contour is solved with a numerically effective method called Analytical Regularization Method (ARM) to calculate propagation parameters. As a result of regularization, the equation of first kind is reduced to the infinite system of the linear algebraic equations of the second kind in the space of L2. This equation can be solved numerically for desired accuracy by using truncation method. The parameters as cut-off wavenumber and cut-off frequency are used in waveguide evolutionary equations of electromagnetic theory in time-domain to illustrate the real-valued TM fields with lossy and lossless media.

Keywords: analytical regularization method, electromagnetic theory evolutionary equations of time-domain, TM Field

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Authors: Keltoum Bouherine, Olivier Leroy

Abstract:

The present work is dedicated to study a three–dimensional (3D) self-consistent fluid simulation of microwave discharges of argon plasma in PECVD reactor. The model solves the Maxwell’s equations, continuity equations for charged species and the electron energy balance equation, coupled with Poisson’s equation, and Navier-Stokes equations by finite element method, using COMSOL Multiphysics software. In this study, the simulations yield the profiles of plasma components as well as the charge densities and electron temperature, the electric field, the gas velocity, and gas temperature. The results show that the microwave plasma reactor is outside of local thermodynamic equilibrium.The present work is dedicated to study a three–dimensional (3D) self-consistent fluid simulation of microwave discharges of argon plasma in PECVD reactor. The model solves the Maxwell’s equations, continuity equations for charged species and the electron energy balance equation, coupled with Poisson’s equation, and Navier-Stokes equations by finite element method, using COMSOL Multiphysics software. In this study, the simulations yield the profiles of plasma components as well as the charge densities and electron temperature, the electric field, the gas velocity, and gas temperature. The results show that the microwave plasma reactor is outside of local thermodynamic equilibrium.

Keywords: electron density, electric field, microwave plasma reactor, gas velocity, non-equilibrium plasma

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Authors: Y. A. Yahaya, Ahmad Tijjani Asabe

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This paper focuses on the formulation of 3-step hybrid Adams type method for the solution of first order differential equation (ODE). The methods which was derived on both grid and off grid points using multistep collocation schemes and also evaluated at some points to produced Block Adams type method and Adams moulton method respectively. The method with the highest order was selected to serve as the corrector. The convergence was valid and efficient. The numerical experiments were carried out and reveal that hybrid Adams type methods performed better than the conventional Adams moulton method.

Keywords: adam-moulton type (amt), corrector method, off-grid, block method, convergence analysis

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Authors: Djemai Bara, Mohamed Faouzi Mahboub, Djamila Bennaceur-Doumaz

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In this work, the role of the preformed plasma created on the front face of a target, irradiated by a high intensity short pulse laser, in the framework of ion acceleration process, modeled by Target Normal Sheath Acceleration (TNSA) mechanism, is studied. This plasma is composed of cold ions governed by fluid equations and non-thermal & trapped with densities represented by a "Cairns-Gurevich" equation. The self-similar solution of the equations shows that electronic trapping and the presence of non-thermal electrons in the pre-plasma are both responsible in ion acceleration as long as the proportion of energetic electrons is not too high. In the case where the majority of electrons are energetic, the electrons are accelerated directly by the ponderomotive force of the laser without the intermediate of an accelerating plasma wave.

Keywords: Cairns-Gurevich Equation, ion acceleration, plasma expansion, pre-plasma

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Authors: Nana Adjoah Mbroh, Suares Clovis Oukouomi Noutchie

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Singularly perturbed problems are parameter dependent problems, and they play major roles in the modelling of real-life situational problems in applied sciences. Thus, designing efficient numerical schemes to solve these problems is of much interest since the exact solutions of such problems may not even exist. Generally, singularly perturbed problems are identified by a small parameter multiplying at least the highest derivative in the equation. The presence of this parameter causes the solution of these problems to be characterized by rapid oscillations. This unique feature renders classical numerical schemes inefficient since they are unable to capture the behaviour of the exact solution in the part of the domain where the rapid oscillations are present. In this paper, a numerical scheme is proposed to solve a singularly perturbed Volterra Integro-differential equation. The scheme is based on the midpoint rule and employs the non-standard finite difference scheme to solve the differential part whilst the composite trapezoidal rule is used for the integral part. A fully fledged error estimate is performed, and Richardson extrapolation is applied to accelerate the convergence of the scheme. Numerical simulations are conducted to confirm the theoretical findings before and after extrapolation.

Keywords: midpoint rule, non-standard finite difference schemes, Richardson extrapolation, singularly perturbed problems, trapezoidal rule, uniform convergence

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Authors: Divij Gupta

Abstract:

Pendular systems have a range of both mathematical and engineering applications, ranging from modelling the behaviour of a continuous mass-density rope to utilisation as Tuned Mass Dampers (TMD). Thus, it is of interest to study the differential equations governing the motion of such systems. Here we attempt to generalise these equations of motion for the plane compound pendulum with a finite number of N point masses. A Lagrangian approach is taken, and we attempt to find the generalised form for the Euler-Lagrange equations of motion for the i-th bob of the N -bob pendulum. The co-ordinates are parameterized as angular quantities to reduce the number of degrees of freedom from 2N to N to simplify the form of the equations. We analyse the form of these equations up to N = 4 to determine the general form of the equation. We also develop a MATLAB program to compute a solution to the system for a given input value of N and a given set of initial conditions.

Keywords: classical mechanics, differential equation, lagrangian analysis, pendulum

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Authors: H. Naderpour, R. C. Barros, S. M. Khatami

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Seismic excitation is naturally caused large horizontal relative displacements, which is able to provide collisions between two adjacent buildings due to insufficient separation distance and severe damages are occurred due to impact especially in tall buildings. In this paper, an impact is numerically simulated and two needed parameters are calculated, including impact force and energy absorption. In order to calculate mentioned parameters, mathematical study needs to model an unreal link element, which is logically assumed to be spring and dashpot to determine lateral displacement and damping ratio of impact. For the determination of dynamic response of impact, a new equation of motion is theoretically suggested to evaluate impact force and energy dissipation. In order to confirm the rendered equation, a series of parametric study are performed and the accuracy of formula is confirmed.

Keywords: pounding, impact, dissipated energy, coefficient of restitution

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Authors: Mohammadreza Akbari, Sara Akbari, Davood Domiri Ganji, Pooya Solimani, Reza Khalili

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As all experts know most of engineering system behavior in practical are nonlinear process (especially heat, fluid and mass, etc.) and analytical solving (no numeric) these problems are difficult, complex and sometimes impossible like (fluids and gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure a innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will be emerged after comparing the achieved solutions by Numerical method (Runge-Kutte 4th) and so compare to other methods such as HPM, ADM,… and exact solutions. Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations(ODE and PDE). In this paper, we investigate and solve 4 types of the nonlinear differential equation with AGM method : 1-Heat and fluid, 2-Unsteady state of nonlinear partial differential, 3-Coupled nonlinear partial differential in wave equation, and 4-Nonlinear integro-differential equation.

Keywords: new method AGM, sets of coupled nonlinear equations at engineering field, waves equations, integro-differential, fluid and thermal

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Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

Abstract:

In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration-free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results are in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes. Semi-Lagrangian method, iteration-free method, nonlinear advection-diffusion equation, second-order backward difference formula

Keywords: Semi-Lagrangian method, iteration free method, nonlinear advection-diffusion equation, second-order backward difference formula

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Authors: Clarinda Vitorino Nhangumbe, Fredericks Ebrahim, Betuel Canhanga

Abstract:

The price of an option weather derivatives can be approximated as a solution of the two-dimensional convection-diffusion dominant partial differential equation derived from the Ornstein-Uhlenbeck process, where one variable represents the weather dynamics and the other variable represent the underlying weather index. With appropriate financial boundary conditions, the solution of the pricing equation is approximated using a nonstandard finite difference method. It is shown that the proposed numerical scheme preserves positivity as well as stability and consistency. In order to illustrate the accuracy of the method, the numerical results are compared with other methods. The model is tested for real weather data.

Keywords: nonstandard finite differences, Ornstein-Uhlenbeck process, partial differential equations approach, weather derivatives

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Authors: Punit Kumar, Niraj Kumar

Abstract:

The influence of transverse surface roughness on EHL characteristics has been investigated numerically using an extensive set of full EHL line contact simulations for shear-thinning lubricants under pure sliding condition. The shear-thinning behavior of lubricant is modeled using Carreau viscosity equation along with Doolittle-Tait equation for lubricant compressibility. The surface roughness is assumed to be sinusoidal and it is present on the stationary surface. It is found that surface roughness causes sharp pressure peaks along with reduction in central and minimum film thickness. With increasing amplitude of surface roughness, the minimum film thickness decreases much more rapidly as compared to the central film thickness.

Keywords: EHL, Carreau, shear-thinning, surface roughness, amplitude, wavelength

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Authors: S. P. Raut, S. K. Soni, A. W. Kolhatkar

Abstract:

Denim is widely used by every age of people all over the world. As the use of denim is increasing progressively, till now the handle properties of denim fabric not reported at significant level. In the present study, five commercial denim fabric samples were used. Denim samples, weighing from 8.5oz/sq yds to 14.5 oz/sq yds, were processed as per standard commercial procedure for denim finishing. These finished denim samples were tested on Kawabata Evaluation System(KES) for low stress mechanical properties. The results of KES values are used for calculation of Total Hand value(THV) using equation for summer suit. The obtained result for THV using equation for summer suit for denim samples is in the range from 1.62 to 3.30. These values of low stress mechanical properties values given by KES, can be used to engineer the denim fabric for bottom wear.

Keywords: denim, handle value, Kawabata evaluation system, objective evaluation

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Authors: Soumyadip Banerjee, Tanmoy Maity

Abstract:

The recovery of power from waste air generated by mine ventilation fans presents a promising avenue for enhancing energy efficiency in mining operations. This abstract explores the feasibility and benefits of utilizing turbine generators to capture the kinetic energy present in waste air and convert it into electrical power. By integrating turbine generator systems into mine ventilation infrastructures, the potential to harness and utilize the previously untapped energy within the waste air stream is realized. This study examines the principles underlying turbine generator technology and its application within the context of mine ventilation systems. The process involves directing waste air from ventilation fans through specially designed turbines, where the kinetic energy of the moving air is converted into rotational motion. This mechanical energy is then transferred to connected generators, which convert it into electrical power. The recovered electricity can be employed for various on-site applications, including powering mining equipment, lighting, and control systems. The benefits of power recovery from waste air using turbine generators are manifold. Improved energy efficiency within the mining environment results in reduced dependence on external power sources and associated cost savings. Additionally, this approach contributes to environmental sustainability by utilizing a previously wasted resource for power generation. Resource conservation is further enhanced, aligning with modern principles of sustainable mining practices. However, successful implementation requires careful consideration of factors such as waste air characteristics, turbine design, generator efficiency, and integration into existing mine infrastructure. Maintenance and monitoring protocols are necessary to ensure consistent performance and longevity of the turbine generator systems. While there is an initial investment associated with equipment procurement, installation, and integration, the long-term benefits of reduced energy costs and environmental impact make this approach economically viable. In conclusion, the recovery of power from waste air from mine ventilation fans using turbine generators offers a tangible solution to enhance energy efficiency and sustainability within mining operations. By capturing and converting the kinetic energy of waste air into usable electrical power, mines can optimize resource utilization, reduce operational costs, and contribute to a greener future for the mining industry.

Keywords: waste to energy, wind power generation, exhaust air, power recovery

Procedia PDF Downloads 33