Search results for: Urbach method

Authors: Malik Sajjad Mehmood, Aisha Ali, Hamna Khan, Tariq Yasin, Masroor Ikram

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Ultra-high molecular weight polyethylene (UHMWPE) is one of the polymers belongs to polyethylene (PE) family having monomer –CH2– and average molecular weight is approximately 3-6 million g/mol. Due its chemical, mechanical, physical and biocompatible properties, it has been extensively used in the field of electrical insulation, medicine, orthopedic, microelectronics, engineering, chemistry and the food industry etc. In order to alter/modify the properties of UHMWPE for particular application of interest, certain various procedures are in practice e.g. treating the material with high energy irradiations like gamma ray, e-beam, and ion bombardment. Radiation treatment of UHMWPE induces free radicals within its matrix, and these free radicals are the precursors of chain scission, chain accumulation, formation of double bonds, molecular emission, crosslinking etc. All the aforementioned physical and chemical processes are mainly responsible for the modification of polymers properties to use them in any particular application of our interest e.g. to fabricate LEDs, optical sensors, antireflective coatings, polymeric optical fibers, and most importantly for radiation dosimetry applications. It is therefore, to check the feasibility of using UHMWPE for radiation dosimetery applications, the compressed sheets of UHMWPE were irradiated at room temperature (~25°C) for total dose values of 30 kGy and 100 kGy, respectively while one were kept un-irradiated as reference. Transmittance data (from 400 nm to 800 nm) of e-beam irradiated UHMWPE and its hybrids were measured by using Muller matrix spectro-polarimeter. As a result significant changes occur in the absorption behavior of irradiated samples. To analyze these (radiation induced) changes in polymer matrix Urbach edge method and modified Tauc’s equation has been used. The results reveal that optical activation energy decreases with irradiation. The values of activation energies are 2.85 meV, 2.48 meV, and 2.40 meV for control, 30 kGy, and 100 kGy samples, respectively. Direct and indirect energy band gaps were also found to decrease with irradiation due to variation of C=C unsaturation in clusters. We believe that the reported results would open new horizons for radiation dosimetery applications.

Keywords: electron beam, radiation dosimetry, Tauc’s equation, UHMWPE, Urbach method

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Authors: S. Abdullahi, M. Momoh, K. U. Isah

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Zinc oxide (ZnO) thin films of 75.5 nm and 130.5 nm were deposited at room temperature onto chemically and ultrasonically cleaned corning glass substrate by radio frequency technique and annealed at 150°C under nitrogen atmosphere for 60 minutes. The optical properties of the films were ascertained by UV-VIS-NIR spectrophotometry. Influence of the thickness of the films on the optical properties was studied keeping other deposition parameters constant. The optical transmittance spectra reveal a maximum transmittance of 81.49% and 84.26% respectively. The band gap of the films is found to be direct allowed transition and decreases with the increase in thickness of the films. The band gap energy (Eg) is in the range of 3.28 eV to 3.31 eV, respectively. These thin films are suitable for solar cell applications.

Keywords: optical constants, RF sputtering, Urbach energy, zinc oxide thin film

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Authors: Mohammed Omar

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Using Chenopodium murale leaf, gold nanoparticles (Au NP's) were biosynthesized effectively in an amicable strategy. The casting process was used to create composite layers of sodium alginate and polyvinyl pyrrolidone. Gold nanoparticles were incorporated into the polyvinyl pyrrolidone (PVP)/ sodium alginate (NaAlg) polymer blend by casting technique. Before and after exposure to different doses of gamma irradiation (2, 4, 6 Mrad), thin films of synthesized nanocomposites were analyzed. XRD revealed the amorphous nature of polymer blends (PVP/ NaAlg), which decreased by both Au NP's embedding and consecutive doses of irradiation. FT-IR spectra revealed interactions and differences within the functional groups of their respective pristine components and dopant nano-fillers. The optical properties of PVP/NaAlg – Au NP thin films (refractive index n, energy gap Eg, Urbach energy Eu) were examined before and after the irradiation procedure. Transmission electron micrographs (TEM) demonstrated a decrease in the size of Au NP’s and narrow size distribution as the gamma irradiation dose was increased. Gamma irradiation was found to influence the electrical conductivity of synthesized composite films, as well as dielectric permittivity (ɛ′) and dielectric losses (ε″).

Keywords: PVP, SPR, γ-radiations, XRD

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Authors: Rawan Aljabbari, Thamer Alomayri, Faisal G. Al-Maqate, Abeer Al Suwat

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For environmentally friendly innovative technologies and a sustainable future, fly ash/TiO₂ thin film nanocomposites are essential. Fly ash will be doped with titanium dioxide in this work in order to better understand its optical characteristics and employ it in semiconductor electrical devices. This study focused on the structure, morphology, and optical properties of fly ash/TiO₂ thin films. The spin-coating technique was used to create thin coatings of fly ash/TiO₂. For the first time, the doping of TiO₂ in the fly ash host at ratios of 1, 2, and 3 wt% was investigated with the thickness of all samples fixed. When compared to undoped thin films, the surface morphology of the doped thin films was improved. The weakly crystalline structure of the doped fly ash films was verified by XRD. The optical bandgap energy of these films was successfully reduced by the TiO₂ doping, going from 3.9 to 3.5 eV. With increasing dopant concentration, the value of Urbach energy is increasing. The optical band gap is clearly in opposition to the disorder. While it considerably improved the optical conductivity to a value of 4.1 x 10^9 s^(-1), it also raised the refractive index and extinction coefficient. Depending on the TiO₂ doping ratio, the transmittance decreased, and the reflection increased. As the TiO₂ concentration rises, the absorption of photon energy rises, and the absorption coefficient of photon energy is reduced. results in their possible use as solar energy and semiconductor materials.

Keywords: fly ash, structural analysis, optical properties, morphology

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Authors: M. Monisha, Sudha D. Kamath

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We investigate the optical and photoluminescence properties from Dy³+ singly doped and Dy³+ co-doped with Ce³+alumino borosilicate glasses prepared using high temperature melt-quenching technique. The glass composition formula is 25SiO₂-(40-x-y)B2O₃-10Al₂O₃-15NaF-10ZnO-xDy₂O₃ yCe₂O₃ where, x = 0.5 mol% and y = 0, 0.1, and 0.5 mol%. The XRD study reveals the amorphous nature of both singly doped and co-doped glasses. Absorption study on Dy3+ singly doped glass shows nearly twelve absorption peaks arising from the ground level of Dy³+ ions (⁶H₁₅/₂) to various upper levels, and for Dy³+/Ce³+ co-doped glasses, few of the transitions in the visible region are suppressed. The absorption band edge is shifted towards the higher wavelength region on increasing Ce3+concentration. The decrease in indirect energy bandgap and increase in Urbach energy of the prepared glasses is observed due to codoping with Ce3+ ions. The photoluminescence studies on singly doped glass under 350 nm excitation showed three peaks at the blue (482 nm), yellow (575 nm), and red (663 nm) region. For codoped glasses, the emission peak at 403 nm is raised due to the 4d to 5f transition of Ce3+ ions. Lifetime values (ms) of co-doped glass is found to be higher than singly doped glass. Under 350 nm excitation, CIE coordinates of the co-doped glasses moved towards the bright white light region. The correlated color temperature (CCT) values were obtained in the range 4500 – 4700 K. Thus, the prepared glasses can be used for photonics device applications.

Keywords: absorption spectra, borosilicate glasses, Ce³+, Dy³+, photoluminescence

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Authors: Muhammad Jawwad, Riffat Iqbal

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The Socratic method, also known as the dialectical method and elenctic method, has significant relevance in the contemporary educational system. It can be incorporated into modern-day educational systems theoretically as well as practically. Being interactive and dialogue-based in nature, this teaching approach is followed by critical thinking and innovation. The pragmatic value of the Dialectical Method has been discussed in this article, and the limitations of the Socratic method have also been highlighted. The interactive Method of Socrates can be used in many subjects for students of different grades. The Limitations and delimitations of the Method have also been discussed for its proper implementation. This article has attempted to elaborate and analyze the teaching method of Socrates with all its pre-suppositions and Epistemological character.

Keywords: Socratic method, dialectical method, knowledge, teaching, virtue

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Authors: K. Swapna, Sk. Mahamuda, Ch, Annapurna, A. Srinivasa Rao, G. Vijaya Prakash

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Samarium ions doped Alkali Fluoro Tungsten Tellurite (AFTT) Glasses have been prepared by using the melt quenching technique and characterized through various spectroscopic techniques such as optical absorption, excitation, emission and decay spectral studies. From the measured absorption spectra of Sm3+ ions in AFTT glasses, the optical band gap and Urbach energies have been evaluated. The spectroscopic parameters such as oscillator strengths (f), Judd-Ofelt (J-O) intensity parameters (Ωλ), spontaneous emission probability (AR), branching ratios (βR) and radiative lifetimes (τR) of various excited levels have been determined from the absorption spectrum by using J-O analysis. A strong luminescence in the reddish-orange spectral region has been observed for all the Sm3+ ions doped AFTT glasses. It consisting four emission transitions occurring from the 4G5/2metastable state to the lower lying states 6H5/2, 6H7/2, 6H9/2 and 6H11/2 upon exciting the sample with a 478 nm line of an argon ion laser. The stimulated emission cross-sections (σe) and branching ratios (βmeas) were estimated from the emission spectra for all emission transitions. Correlation of the radiative lifetime with the experimental lifetime measured from the day curves allows us to measure the quantum efficiency of the prepared glasses. In order to know the colour emission of the prepared glasses under near UV excitation, the emission intensities were analyzed using CIE 1931 colour chromaticity diagram. The aforementioned spectral studies carried out on Sm3+ ions doped AFTT glasses allowed us to conclude that, these glasses are best suited for orange-red visible lasers.

Keywords: fluoro tungsten tellurite glasses, judd-ofelt intensity parameters, lifetime, stimulated emission cross-section

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Authors: Mohammad Reza Akhavan Khaleghi

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This paper shows changes done to the Reduced Finite Element Method (RFEM) that its result will be the most powerful numerical method that has been proposed so far (some forms of this method are so powerful that they can approximate the most complex equations simply Laplace equation!). Finite Element Method (FEM) is a powerful numerical method that has been used successfully for the solution of the existing problems in various scientific and engineering fields such as its application in CFD. Many algorithms have been expressed based on FEM, but none have been used in popular CFD software. In this section, full monopoly is according to Finite Volume Method (FVM) due to better efficiency and adaptability with the physics of problems in comparison with FEM. It doesn't seem that FEM could compete with FVM unless it was fundamentally changed. This paper shows those changes and its result will be a powerful method that has much better performance in all subjects in comparison with FVM and another computational method. This method is not to compete with the finite volume method but to replace it.

Keywords: reduced finite element method, new computational package, new finite element formulation, new higher-order form, new isogeometric analysis

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Authors: O. Acan, Y. Keskin

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In this study, we will carry out a comparative study between the reduced differential transform method, the adomian decomposition method, the variational iteration method and the homotopy analysis method. These methods are used in many fields of engineering. This is been achieved by handling a kind of 2-Dimensional and forth-order partial differential equations called the Kuramoto–Sivashinsky equations. Three numerical examples have also been carried out to validate and demonstrate efficiency of the four methods. Furthermost, it is shown that the reduced differential transform method has advantage over other methods. This method is very effective and simple and could be applied for nonlinear problems which used in engineering.

Keywords: reduced differential transform method, adomian decomposition method, variational iteration method, homotopy analysis method

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Authors: Elvis Adam Alhassan, Kaiyu Tian, Akos Konadu, Ernest Zamanah, Michael Jackson Adjabui, Ibrahim Justice Musah, Esther Agyeiwaa Owusu, Emmanuel K. A. Agyeman

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In this paper, how to solve simultaneous equations using the Elvis improved method is shown. The Elvis improved method says; to make one variable in the first equation the subject; make the same variable in the second equation the subject; equate the results and simplify to obtain the value of the unknown variable; put the value of the variable found into one equation from the first or second steps and simplify for the remaining unknown variable. The difference between our Elvis improved method and the substitution method is that: with Elvis improved method, the same variable is made the subject in both equations, and the two resulting equations equated, unlike the substitution method where one variable is made the subject of only one equation and substituted into the other equation. After describing the Elvis improved method, findings from 100 secondary students and the views of 5 secondary tutors to demonstrate the effectiveness of the method are presented. The study's purpose is proved by hypothetical examples.

Keywords: simultaneous equations, substitution method, elimination method, graphical method, Elvis improved method

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Authors: Arezoo Hakimi, Afshin Farahbakhsh

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Herein, we comparison synthesized Fe3O4 using, hydrothermal method, Mechanochemical processes and solvent thermal method. The Hydrothermal Technique has been the most popular one, gathering interest from scientists and technologists of different disciplines, particularly in the last fifteen years. In the hydrothermal method Fe3O4 microspheres, in which many nearly monodisperse spherical particles with diameters of about 400nm, in the mechanochemical method regular morphology indicates that the particles are well crystallized and in the solvent thermal method Fe3O4 nanoparticles have good properties of uniform size and good dispersion.

Keywords: Fe3O4 nanoparticles, hydrothermal method, mechanochemical processes, solvent thermal method

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Authors: Autcha Araveeporn

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This paper presents a study about a nonparametric regression model consisting of a smoothing spline method and a penalized spline regression method. We also compare the techniques used for estimation and prediction of nonparametric regression model. We tried both methods with crude oil prices in dollars per barrel and the Stock Exchange of Thailand (SET) index. According to the results, it is concluded that smoothing spline method performs better than that of penalized spline regression method.

Keywords: nonparametric regression model, penalized spline regression method, smoothing spline method, Stock Exchange of Thailand (SET)

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Authors: Bale Baidi Blaise, Gilles Marckmann, Liman Kaoye, Talaka Dya, Moustapha Bachirou, Gambo Betchewe, Tibi Beda

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This work highlights the capabilities of particles swarm optimization (PSO) method to identify parameters of hyperelastic models. The study compares this method with Genetic Algorithm (GA) method, Least Squares (LS) method, Pattern Search Algorithm (PSA) method, Beda-Chevalier (BC) method and the Levenberg-Marquardt (LM) method. Four classic hyperelastic models are used to test the different methods through parameters identification. Then, the study compares the ability of these models to reproduce experimental Treloar data in simple tension, biaxial tension and pure shear.

Keywords: particle swarm optimization, identification, hyperelastic, model

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Authors: M. K. Balyan

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The main principles of X-ray Fourier interferometric holography method are discussed. The object image is reconstructed by the mathematical method of Fourier transformation. The three methods are presented – method of approximation, iteration method and step by step method. As an example the complex amplitude transmission coefficient reconstruction of a beryllium wire is considered. The results reconstructed by three presented methods are compared. The best results are obtained by means of step by step method.

Keywords: dynamical diffraction, hologram, object image, X-ray holography

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Authors: N. Guruprasad

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This paper presents a modification of approximation method for transportation problems. The initial basic feasible solution can be computed using either Russel's or Vogel's approximation methods. Russell’s approximation method provides another excellent criterion that is still quick to implement on a computer (not manually) In most cases Russel's method yields a better initial solution, though it takes longer than Vogel's method (finding the next entering variable in Russel's method is in O(n1*n2), and in O(n1+n2) for Vogel's method). However, Russel's method normally has a lesser total running time because less pivots are required to reach the optimum for all but small problem sizes (n1+n2=~20). With this motivation behind we have incorporated a variation of the same – what we have proposed it has TMC (Total Modified Cost) to obtain fast and efficient solutions.

Keywords: computation, efficiency, modified cost, Russell’s approximation method, transportation, Vogel’s approximation method

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Authors: Bib Paruhum Silalahi, Djihad Wungguli, Sugi Guritman

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Steepest descent method is a simple gradient method for optimization. This method has a slow convergence in heading to the optimal solution, which occurs because of the zigzag form of the steps. Barzilai and Borwein modified this algorithm so that it performs well for problems with large dimensions. Barzilai and Borwein method results have sparked a lot of research on the method of steepest descent, including alternate minimization gradient method and Yuan method. Inspired by previous works, we modified the step size of the steepest descent method. We then compare the modification results against the Barzilai and Borwein method, alternate minimization gradient method and Yuan method for quadratic function cases in terms of the iterations number and the running time. The average results indicate that the steepest descent method with the new step sizes provide good results for small dimensions and able to compete with the results of Barzilai and Borwein method and the alternate minimization gradient method for large dimensions. The new step sizes have faster convergence compared to the other methods, especially for cases with large dimensions.

Keywords: steepest descent, line search, iteration, running time, unconstrained optimization, convergence

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Authors: S. Shahrooi, A. Talavari

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Numeral study on the crack and discontinuity using element-free methods has been widely spread in recent years. In this study, for stress intensity factor calculation of the cracked axis under torsional loading has been used from a new element-free method as MLPG method. Region range is discretized by some dispersed nodal points. From method of moving least square (MLS) utilized to create the functions using these nodal points. Then, results of meshless method and finite element method (FEM) were compared. The results is shown which the element-free method was of good accuracy.

Keywords: stress intensity factor, crack, torsional loading, meshless method

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Authors: Abu Hashan Md Mashud, M. Sharif Uddin, Aminur Rahman Khan

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In this paper, we formulate a new problem as a linear programming and Integer Programming problem and maximize profit within the limited budget and limited resources based on the construction of a tea garden problem. It describes a new idea about how to optimize profit and focuses on the practical aspects of modeling and the challenges of providing a solution to a complex real life problem. Finally, a comparative study is carried out among Graphical method, Simplex method and Branch and bound method.

Keywords: integer programming, tea garden, graphical method, simplex method, branch and bound method

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Authors: Osamu Igawa, Hiroshi Kouchiwa, Yuji Ito

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In recent years, a reconstruction project for sewer pipelines has been progressing in Japan with the aim of renewing old sewer culverts. However, it is difficult to secure a sufficient base area for shafts in an urban area because many streets are narrow with a complex layout. As a result, construction in such urban areas is generally very demanding. In urban areas, there is a strong requirement for a safe, reliable and economical construction method that does not disturb the public’s daily life and urban activities. With this in mind, we developed a new construction method called the 'shield switching type micro-tunneling method' which integrates the micro-tunneling method and shield method. In this method, pipeline is constructed first for sections that are gently curved or straight using the economical micro-tunneling method, and then the method is switched to the shield method for sections with a sharp curve or a series of curves without establishing an intermediate shaft. This paper provides the information, features and construction examples of this newly developed method.

Keywords: micro-tunneling method, secondary lining applied RC segment, sharp curve, shield method, switching type

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Authors: E. Popov, N. Yorino, Y. Zoka, Y. Sasaki, H. Sugihara

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This paper discusses the performance of critical trajectory method (CTrj) for power system transient stability analysis under various loading settings and heavy fault condition. The method obtains Controlling Unstable Equilibrium Point (CUEP) which is essential for estimation of power system stability margins. The CUEP is computed by applying the CTrjto the boundary controlling unstable equilibrium point (BCU) method. The Proposed method computes a trajectory on the stability boundary that starts from the exit point and reaches CUEP under certain assumptions. The robustness and effectiveness of the method are demonstrated via six power system models and five loading conditions. As benchmark is used conventional simulation method whereas the performance is compared with and BCU Shadowing method.

Keywords: power system, transient stability, critical trajectory method, energy function method

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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: 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: Nur Rokhman

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A mathematical function gives relationship between the variables composing the function. Interpolation can be viewed as a process of finding mathematical function which goes through some specified points. There are many interpolation methods, namely: Lagrange method, Newton method, Spline method etc. For some specific condition, such as, big amount of interpolation points, the interpolation function can not be written explicitly. This such function consist of computational steps. The solution of equations involving the interpolation function is a problem of solution of non linear equation. Newton method will not work on the interpolation function, for the derivative of the interpolation function cannot be written explicitly. This paper shows the use of Secton method to determine the numerical solution of the function involving the interpolation function. The experiment shows the fact that Secton method works better than Newton method in finding the root of Lagrange interpolation function.

Keywords: Secton method, interpolation, non linear function, numerical solution

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Authors: B. Chikh, L. Moussa, H. Bechtoula, Y. Mehani, A. Zerzour

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This study presents a new method, applicable to evaluation and design of structures has been developed and illustrated by comparison with the capacity spectrum method (CSM, ATC-40). This method uses inelastic spectra and gives peak responses consistent with those obtained when using the nonlinear time history analysis. Hereafter, the seismic demands assessment method is called in this paper DSM, Ductility Spectrum Method. It is used to estimate the seismic deformation of Single-Degree-Of-Freedom (SDOF) systems based on DDRS, Ductility Demand Response Spectrum, developed by the author.

Keywords: seismic demand, capacity, inelastic spectra, design and structure

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Authors: Saheed A. Gbadegeshin

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Commercialization method is a means to make inventions available at the market for final consumption. It is described as an important tool for keeping business enterprises sustainable and improving national economic growth. Thus, there are several scholarly publications on it, either presenting or testing different methods for commercialization. However, young entrepreneurs, technologists and scientists would like to know the best method to commercialize their innovations. Then, this question arises: What is the best commercialization method? To answer the question, a systematic literature review was conducted, and practitioners were interviewed. The literary results revealed that there are many methods but new methods are needed to improve commercialization especially during these times of economic crisis and political uncertainty. Similarly, the empirical results showed there are several methods, but the best method is the one that reduces costs, reduces the risks associated with uncertainty, and improves customer participation and acceptability. Therefore, it was concluded that new commercialization method is essential for today's high technologies and a method was presented.

Keywords: commercialization method, technology, knowledge, intellectual property, innovation, invention

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Authors: Aicha Zohbie

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The purpose of this paper is to critically compare two teaching methods: the communicative method and the grammar-translation method. The paper presents the importance of language awareness as an approach to teaching and learning language and some challenges that language teachers face. In addition, the paper strives to determine whether the adoption of communicative teaching methods or the grammar teaching method would be more effective to teach a language. A variety of features are considered for comparing the two methods: the purpose of each method, techniques used, teachers’ and students’ roles, the use of L1, the skills that are emphasized, the correction of students’ errors, and the students’ assessments. Finally, the paper includes suggestions and recommendations for implementing an approach that best meets the students’ needs in a classroom.

Keywords: language teaching methods, language awareness, communicative method grammar translation method, advantages and disadvantages

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Authors: Kholod Mohammad Abualnaja

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A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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Authors: M. S. Baazzim, M. S. Al-Saud, M. A. El-Kady

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In this paper, steady-state ampacity (current carrying capacity) evaluation of underground power cable system by using analytical and numerical methods for different conditions (depth of cable, spacing between phases, soil thermal resistivity, ambient temperature, wind speed), for two system voltage level were used 132 and 380 kV. The analytical method or traditional method that was used is based on the thermal analysis method developed by Neher-McGrath and further enhanced by International Electrotechnical Commission (IEC) and published in standard IEC 60287. The numerical method that was used is finite element method and it was recourse commercial software based on finite element method.

Keywords: cable ampacity, finite element method, underground cable, thermal rating

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Authors: M. S. H. Chowdhury, Ishak Hashim

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In this paper, linear and non-linear stiff systems of ordinary differential equations are solved by the classical Adomian decomposition method (ADM) and the multi-stage Adomian decomposition method (MADM). The MADM is a technique adapted from the standard Adomian decomposition method (ADM) where standard ADM is converted into a hybrid numeric-analytic method called the multistage ADM (MADM). The MADM is tested for several examples. Comparisons with an explicit Runge-Kutta-type method (RK) and the classical ADM demonstrate the limitations of ADM and promising capability of the MADM for solving stiff initial value problems (IVPs).

Keywords: stiff system of ODEs, Runge-Kutta Type Method, Adomian decomposition method, Multistage ADM

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Authors: L. Fridrichova, R. Knížek, V. Bajzík

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Drape is one of the important visual characteristics of the fabric. This paper is introducing an innovative method of measurement and evaluation of the drape shape of the fabric. The measuring principle is based on the possibility of multiple vertical strain of the fabric. This method more accurately simulates the real behavior of the fabric in the process of draping. The method is fully automated, so the sample can be measured by using any number of cycles in any time horizon. Using the present method of measurement, we are able to describe the viscoelastic behavior of the fabric.

Keywords: drape, drape shape, automated drapemeter, fabric

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