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Prabhakar</a>, <a href="https://publications.waset.org/abstracts/search?q=Prem%20P.%20Srivastav"> Prem P. Srivastav</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Rohu (Labeo rohita) is an Indian major carp and highly relished freshwater food for its unique flavor, texture, and culinary properties. It is highly perishable and, spoilage occurs as a result of series of complicated biochemical changes brought about by enzymes which are the function of time and storage temperature also. The influence of storage temperature (5, 0, and -5 °C) on colour and texture of fish were studied during 14 days storage period in order to analyze kinetics of colour and textural changes. The rate of total colour change was most noticeable at the highest storage temperature (5°C), and these changes were well described by the first order reaction. Texture is an important variable of quality of the fish and is increasing concern to aquaculture industries. Textural parameters such as hardness, toughness and stiffness were evaluated on a texture analyzer for the different day of stored fish. The significant reduction (P ≤ 0.05) in hardness was observed after 2nd, 4th and 8th day for the fish stored at 5, 0, and -5 °C respectively. The textural changes of fish during storage followed a first order kinetic model and fitted well with this model (R2 > 0.95). However, the textural data with respect to time was also fitted to modified Maxwell model and found to be good fit with R2 value ranges from 0.96 to 0.98. Temperature dependence of colour and texture change was adequately modelled with the Arrhenius type equation. This fitted model may be used for the determination of shelf life of Rohu Rohu (Labeo rohita) Fish. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=first%20order%20kinetics" title="first order kinetics">first order kinetics</a>, <a href="https://publications.waset.org/abstracts/search?q=biochemical%20changes" title=" biochemical changes"> biochemical changes</a>, <a href="https://publications.waset.org/abstracts/search?q=Maxwell%20model" title=" Maxwell model"> Maxwell model</a>, <a href="https://publications.waset.org/abstracts/search?q=colour" title=" colour"> colour</a>, <a href="https://publications.waset.org/abstracts/search?q=texture" title=" texture"> texture</a>, <a href="https://publications.waset.org/abstracts/search?q=Arrhenius%20type%20equation" title=" Arrhenius type equation"> Arrhenius type equation</a> </p> <a href="https://publications.waset.org/abstracts/57115/kinetic-modeling-of-colour-and-textural-properties-of-stored-rohu-labeo-rohita-fish" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/57115.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">240</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8677</span> Multiple-Lump-Type Solutions of the 2D Toda Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jian-Ping%20Yu">Jian-Ping Yu</a>, <a href="https://publications.waset.org/abstracts/search?q=Wen-Xiu%20Ma"> Wen-Xiu Ma</a>, <a href="https://publications.waset.org/abstracts/search?q=Yong-Li%20Sun"> Yong-Li Sun</a>, <a href="https://publications.waset.org/abstracts/search?q=Chaudry%20Masood%20Khalique"> Chaudry Masood Khalique</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a 2d Toda equation is studied, which is a classical integrable system and plays a vital role in mathematics, physics and other areas. New lump-type solution is constructed by using the Hirota bilinear method. One interesting feature of this research is that this lump-type solutions possesses two types of multiple-lump-type waves, which are one- and two-lump-type waves. Moreover, the corresponding 3d plots, density plots and contour plots are given to show the dynamical features of the obtained multiple-lump-type solutions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=2d%20Toda%20equation" title="2d Toda equation">2d Toda equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Hirota%20bilinear%20method" title=" Hirota bilinear method"> Hirota bilinear method</a>, <a href="https://publications.waset.org/abstracts/search?q=Lump-type%20solution" title=" Lump-type solution"> Lump-type solution</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple-lump-type%20solution" title=" multiple-lump-type solution"> multiple-lump-type solution</a> </p> <a href="https://publications.waset.org/abstracts/104938/multiple-lump-type-solutions-of-the-2d-toda-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/104938.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">227</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8676</span> Useful Lifetime Prediction of Rail Pads for High Speed Trains</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chang%20Su%20Woo">Chang Su Woo</a>, <a href="https://publications.waset.org/abstracts/search?q=Hyun%20Sung%20Park"> Hyun Sung Park</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Useful lifetime evaluations of rail-pads were very important in design procedure to assure the safety and reliability. It is, therefore, necessary to establish a suitable criterion for the replacement period of rail pads. In this study, we performed properties and accelerated heat aging tests of rail pads considering degradation factors and all environmental conditions including operation, and then derived a lifetime prediction equation according to changes in hardness, thickness, and static spring constants in the Arrhenius plot to establish how to estimate the aging of rail pads. With the useful lifetime prediction equation, the lifetime of e-clip pads was 2.5 years when the change in hardness was 10% at 25°C; and that of f-clip pads was 1.7 years. When the change in thickness was 10%, the lifetime of e-clip pads and f-clip pads is 2.6 years respectively. The results obtained in this study to estimate the useful lifetime of rail pads for high speed trains can be used for determining the maintenance and replacement schedule for rail pads. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=rail%20pads" title="rail pads">rail pads</a>, <a href="https://publications.waset.org/abstracts/search?q=accelerated%20test" title=" accelerated test"> accelerated test</a>, <a href="https://publications.waset.org/abstracts/search?q=Arrhenius%20plot" title=" Arrhenius plot"> Arrhenius plot</a>, <a href="https://publications.waset.org/abstracts/search?q=useful%20lifetime%20prediction" title=" useful lifetime prediction"> useful lifetime prediction</a>, <a href="https://publications.waset.org/abstracts/search?q=mechanical%20engineering%20design" title=" mechanical engineering design"> mechanical engineering design</a> </p> <a href="https://publications.waset.org/abstracts/3182/useful-lifetime-prediction-of-rail-pads-for-high-speed-trains" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3182.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">329</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8675</span> Relativistic Energy Analysis for Some q Deformed Shape Invariant Potentials in D Dimensions Using SUSYQM Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Suparmi">A. Suparmi</a>, <a href="https://publications.waset.org/abstracts/search?q=C.%20Cari"> C. Cari</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Yunianto"> M. Yunianto</a>, <a href="https://publications.waset.org/abstracts/search?q=B.%20N.%20Pratiwi"> B. N. Pratiwi </a> </p> <p class="card-text"><strong>Abstract:</strong></p> D-dimensional Dirac equations of q-deformed shape invariant potentials were solved using supersymmetric quantum mechanics (SUSY QM) in the case of exact spin symmetry. The D dimensional radial Dirac equation for shape invariant potential reduces to one-dimensional Schrodinger type equation by an appropriate variable and parameter change. The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial D dimensional Dirac equation that have reduced to one dimensional Schrodinger type equation. The SUSY operator was used to generate the D dimensional relativistic radial wave functions, the relativistic energy equation reduced to the non-relativistic energy in the non-relativistic limit. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=D-dimensional%20dirac%20equation" title="D-dimensional dirac equation">D-dimensional dirac equation</a>, <a href="https://publications.waset.org/abstracts/search?q=non-central%20potential" title=" non-central potential"> non-central potential</a>, <a href="https://publications.waset.org/abstracts/search?q=SUSY%20QM" title=" SUSY QM"> SUSY QM</a>, <a href="https://publications.waset.org/abstracts/search?q=radial%20wave%20function" title=" radial wave function"> radial wave function</a> </p> <a href="https://publications.waset.org/abstracts/43601/relativistic-energy-analysis-for-some-q-deformed-shape-invariant-potentials-in-d-dimensions-using-susyqm-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/43601.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">348</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8674</span> Second Order Solitary Solutions to the Hodgkin-Huxley Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tadas%20Telksnys">Tadas Telksnys</a>, <a href="https://publications.waset.org/abstracts/search?q=Zenonas%20Navickas"> Zenonas Navickas</a>, <a href="https://publications.waset.org/abstracts/search?q=Minvydas%20Ragulskis"> Minvydas Ragulskis</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Necessary and sufficient conditions for the existence of second order solitary solutions to the Hodgkin-Huxley equation are derived in this paper. The generalized multiplicative operator of differentiation helps not only to construct closed-form solitary solutions but also automatically generates conditions of their existence in the space of the equation's parameters and initial conditions. It is demonstrated that bright, kink-type solitons and solitary solutions with singularities can exist in the Hodgkin-Huxley equation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hodgkin-Huxley%20equation" title="Hodgkin-Huxley equation">Hodgkin-Huxley equation</a>, <a href="https://publications.waset.org/abstracts/search?q=solitary%20solution" title=" solitary solution"> solitary solution</a>, <a href="https://publications.waset.org/abstracts/search?q=existence%20condition" title=" existence condition"> existence condition</a>, <a href="https://publications.waset.org/abstracts/search?q=operator%20method" title=" operator method"> operator method</a> </p> <a href="https://publications.waset.org/abstracts/37370/second-order-solitary-solutions-to-the-hodgkin-huxley-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37370.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">389</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8673</span> Parametric Dependence of the Advection-Diffusion Equation in Two Dimensions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Matheus%20Fernando%20Pereira">Matheus Fernando Pereira</a>, <a href="https://publications.waset.org/abstracts/search?q=Varese%20Salvador%20Timoteo"> Varese Salvador Timoteo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we have solved the two-dimensional advection-diffusion equation numerically for a spatially dependent solute dispersion along non-uniform flow with a pulse type source in order to make a systematic study on the influence of medium heterogeneity, initial flow velocity, and initial dispersion coefficient parameters on the solutions of the equation. The behavior of the solutions is then investigated as we change the three parameters independently. Our results show that even though the parameters represent different physical features of the system, the effect on their variation is very similar. We also observe that the effects caused by the parameters on the concentration depend on the distance from the source. Finally, our numerical results are in good agreement with the exact solutions for all values of the parameters we used in our analysis. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=advection-diffusion%20equation" title="advection-diffusion equation">advection-diffusion equation</a>, <a href="https://publications.waset.org/abstracts/search?q=dispersion" title=" dispersion"> dispersion</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20methods" title=" numerical methods"> numerical methods</a>, <a href="https://publications.waset.org/abstracts/search?q=pulse-type%20source" title=" pulse-type source"> pulse-type source</a> </p> <a href="https://publications.waset.org/abstracts/94370/parametric-dependence-of-the-advection-diffusion-equation-in-two-dimensions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/94370.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">243</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8672</span> Formulation of Corrector Methods from 3-Step Hybid Adams Type Methods for the Solution of First Order Ordinary Differential Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Y.%20A.%20Yahaya">Y. A. Yahaya</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmad%20Tijjani%20Asabe"> Ahmad Tijjani Asabe</a> </p> <p class="card-text"><strong>Abstract:</strong></p> 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. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adam-moulton%20type%20%28amt%29" title="adam-moulton type (amt)">adam-moulton type (amt)</a>, <a href="https://publications.waset.org/abstracts/search?q=corrector%20method" title=" corrector method"> corrector method</a>, <a href="https://publications.waset.org/abstracts/search?q=off-grid" title=" off-grid"> off-grid</a>, <a href="https://publications.waset.org/abstracts/search?q=block%20method" title=" block method"> block method</a>, <a href="https://publications.waset.org/abstracts/search?q=convergence%20analysis" title=" convergence analysis"> convergence analysis</a> </p> <a href="https://publications.waset.org/abstracts/31263/formulation-of-corrector-methods-from-3-step-hybid-adams-type-methods-for-the-solution-of-first-order-ordinary-differential-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/31263.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">632</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8671</span> Influence of Rotation on Rayleigh-Type Wave in Piezoelectric Plate</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Soniya%20Chaudhary">Soniya Chaudhary</a>, <a href="https://publications.waset.org/abstracts/search?q=Sanjeev%20Sahu"> Sanjeev Sahu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Propagation of Rayleigh-type waves in a rotating piezoelectric plate is investigated. The materials are assumed to be transversely isotropic crystals. The frequency equation have been derived for electrically open and short cases. Effect of rotation and piezoelectricity have been shown. It is also found that piezoelectric material properties have an important effect on Rayleigh wave propagation. The result is relevant to the analysis and design of various acoustic surface wave devices constructed from piezoelectric materials also in SAW devices. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=rotation" title="rotation">rotation</a>, <a href="https://publications.waset.org/abstracts/search?q=frequency%20equation" title=" frequency equation"> frequency equation</a>, <a href="https://publications.waset.org/abstracts/search?q=piezoelectricity" title=" piezoelectricity"> piezoelectricity</a>, <a href="https://publications.waset.org/abstracts/search?q=rayleigh-type%20wave" title=" rayleigh-type wave"> rayleigh-type wave</a> </p> <a href="https://publications.waset.org/abstracts/60606/influence-of-rotation-on-rayleigh-type-wave-in-piezoelectric-plate" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/60606.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">318</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8670</span> Globally Attractive Mild Solutions for Non-Local in Time Subdiffusion Equations of Neutral Type</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Gonzalez%20Camus">Jorge Gonzalez Camus</a>, <a href="https://publications.waset.org/abstracts/search?q=Carlos%20Lizama"> Carlos Lizama</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work is proved the existence of at least one globally attractive mild solution to the Cauchy problem, for fractional evolution equation of neutral type, involving the fractional derivate in Caputo sense. An almost sectorial operator on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Hausdorff measure of noncompactness and fixed point theorems, specifically Darbo-type. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the analytic integral resolvent operator, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, each mild solution is globally attractive, a property that is desired in asymptotic behavior for that solution. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=attractive%20mild%20solutions" title="attractive mild solutions">attractive mild solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20Volterra%20equations" title=" integral Volterra equations"> integral Volterra equations</a>, <a href="https://publications.waset.org/abstracts/search?q=neutral%20type%20equations" title=" neutral type equations"> neutral type equations</a>, <a href="https://publications.waset.org/abstracts/search?q=non-local%20in%20time%20equations" title=" non-local in time equations"> non-local in time equations</a> </p> <a href="https://publications.waset.org/abstracts/99925/globally-attractive-mild-solutions-for-non-local-in-time-subdiffusion-equations-of-neutral-type" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/99925.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">165</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8669</span> Operational Matrix Method for Fuzzy Fractional Reaction Diffusion Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sachin%20Kumar">Sachin Kumar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20PDE" title="fractional PDE">fractional PDE</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20valued%20function" title=" fuzzy valued function"> fuzzy valued function</a>, <a href="https://publications.waset.org/abstracts/search?q=diffusion%20equation" title=" diffusion equation"> diffusion equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Legendre%20polynomial" title=" Legendre polynomial"> Legendre polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20method" title=" spectral method"> spectral method</a> </p> <a href="https://publications.waset.org/abstracts/125273/operational-matrix-method-for-fuzzy-fractional-reaction-diffusion-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/125273.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">207</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8668</span> Soliton Solutions of the Higher-Order Nonlinear Schrödinger Equation with Dispersion Effects</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=H.%20Triki">H. Triki</a>, <a href="https://publications.waset.org/abstracts/search?q=Y.%20Hamaizi"> Y. Hamaizi</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20El-Akrmi"> A. El-Akrmi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20Schr%C3%B6dinger%20equation" title="nonlinear Schrödinger equation">nonlinear Schrödinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=high-order%20effects" title=" high-order effects"> high-order effects</a>, <a href="https://publications.waset.org/abstracts/search?q=soliton%20solution" title=" soliton solution"> soliton solution</a> </p> <a href="https://publications.waset.org/abstracts/11564/soliton-solutions-of-the-higher-order-nonlinear-schrodinger-equation-with-dispersion-effects" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/11564.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">641</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8667</span> Teaching and Learning Dialectical Relationship between Thermodynamic Equilibrium and Reaction Rate Constant</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Anwar">Mohammad Anwar</a>, <a href="https://publications.waset.org/abstracts/search?q=Shah%20Waliullah"> Shah Waliullah</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The development of science and technology in the present era has an urgent demand for the training of thinking of undergraduates. This requirement actively promotes research and teaching of basic theories, beneficial to the career development of students. This study clarified the dialectical relation between the thermodynamic equilibrium constant and reaction rate constant through the contrast thinking method. Findings reveal that both the isobaric Van't Hoff equation and the Arrhenius equation had four similar forms, and the change in the trend of both constants showed a similar law. By the derivation of the formation rate constant of the product (KY) and the consumption rate constant of the reactant (KA), the ratio of both constants at the end state indicated the nature of the equilibrium state in agreement with that of the thermodynamic equilibrium constant (K^θ (T)). This study has thus presented that the thermodynamic equilibrium constant contained the characteristics of microscopic dynamics based on the analysis of the reaction mechanism, and both constants are organically connected and unified. The reaction enthalpy and activation energy are closely related to each other with the same connotation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=thermodynamic%20equilibrium%20constant" title="thermodynamic equilibrium constant">thermodynamic equilibrium constant</a>, <a href="https://publications.waset.org/abstracts/search?q=reaction%20rate%20constant" title=" reaction rate constant"> reaction rate constant</a>, <a href="https://publications.waset.org/abstracts/search?q=PBL%20teaching" title=" PBL teaching"> PBL teaching</a>, <a href="https://publications.waset.org/abstracts/search?q=dialectical%20relation" title=" dialectical relation"> dialectical relation</a>, <a href="https://publications.waset.org/abstracts/search?q=innovative%20thinking" title=" innovative thinking"> innovative thinking</a> </p> <a href="https://publications.waset.org/abstracts/161693/teaching-and-learning-dialectical-relationship-between-thermodynamic-equilibrium-and-reaction-rate-constant" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/161693.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">116</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8666</span> Numerical Solution of Manning's Equation in Rectangular Channels</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abdulrahman%20Abdulrahman">Abdulrahman Abdulrahman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> When the Manning equation is used, a unique value of normal depth in the uniform flow exists for a given channel geometry, discharge, roughness, and slope. Depending on the value of normal depth relative to the critical depth, the flow type (supercritical or subcritical) for a given characteristic of channel conditions is determined whether or not flow is uniform. There is no general solution of Manning's equation for determining the flow depth for a given flow rate, because the area of cross section and the hydraulic radius produce a complicated function of depth. The familiar solution of normal depth for a rectangular channel involves 1) a trial-and-error solution; 2) constructing a non-dimensional graph; 3) preparing tables involving non-dimensional parameters. Author in this paper has derived semi-analytical solution to Manning's equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning's equation in non-dimensional form, then expanding this form using Maclaurin's series. In order to simplify the solution, terms containing power up to 4 have been considered. The resulted equation is a quartic equation with a standard form, where its solution was obtained by resolving this into two quadratic factors. The proposed solution for Manning's equation is valid over a large range of parameters, and its maximum error is within -1.586%. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=channel%20design" title="channel design">channel design</a>, <a href="https://publications.waset.org/abstracts/search?q=civil%20engineering" title=" civil engineering"> civil engineering</a>, <a href="https://publications.waset.org/abstracts/search?q=hydraulic%20engineering" title=" hydraulic engineering"> hydraulic engineering</a>, <a href="https://publications.waset.org/abstracts/search?q=open%20channel%20flow" title=" open channel flow"> open channel flow</a>, <a href="https://publications.waset.org/abstracts/search?q=Manning%27s%20equation" title=" Manning's equation"> Manning's equation</a>, <a href="https://publications.waset.org/abstracts/search?q=normal%20depth" title=" normal depth"> normal depth</a>, <a href="https://publications.waset.org/abstracts/search?q=uniform%20flow" title=" uniform flow"> uniform flow</a> </p> <a href="https://publications.waset.org/abstracts/72618/numerical-solution-of-mannings-equation-in-rectangular-channels" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/72618.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">226</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8665</span> A Boundary Backstepping Control Design for 2-D, 3-D and N-D Heat Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Aziz%20Sezgin">Aziz Sezgin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We consider the problem of stabilization of an unstable heat equation in a 2-D, 3-D and generally n-D domain by deriving a generalized backstepping boundary control design methodology. To stabilize the systems, we design boundary backstepping controllers inspired by the 1-D unstable heat equation stabilization procedure. We assume that one side of the boundary is hinged and the other side is controlled for each direction of the domain. Thus, controllers act on two boundaries for 2-D domain, three boundaries for 3-D domain and ”n” boundaries for n-D domain. The main idea of the design is to derive ”n” controllers for each of the dimensions by using ”n” kernel functions. Thus, we obtain ”n” controllers for the ”n” dimensional case. We use a transformation to change the system into an exponentially stable ”n” dimensional heat equation. The transformation used in this paper is a generalized Volterra/Fredholm type with ”n” kernel functions for n-D domain instead of the one kernel function of 1-D design. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=backstepping" title="backstepping">backstepping</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20control" title=" boundary control"> boundary control</a>, <a href="https://publications.waset.org/abstracts/search?q=2-D" title=" 2-D"> 2-D</a>, <a href="https://publications.waset.org/abstracts/search?q=3-D" title="3-D">3-D</a>, <a href="https://publications.waset.org/abstracts/search?q=n-D%20heat%0D%0Aequation" title="n-D heat equation">n-D heat equation</a>, <a href="https://publications.waset.org/abstracts/search?q=distributed%20parameter%20systems" title=" distributed parameter systems"> distributed parameter systems</a> </p> <a href="https://publications.waset.org/abstracts/34150/a-boundary-backstepping-control-design-for-2-d-3-d-and-n-d-heat-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/34150.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">407</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8664</span> State Estimation Based on Unscented Kalman Filter for Burgers’ Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Takashi%20Shimizu">Takashi Shimizu</a>, <a href="https://publications.waset.org/abstracts/search?q=Tomoaki%20Hashimoto"> Tomoaki Hashimoto</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Controlling the flow of fluids is a challenging problem that arises in many fields. Burgers’ equation is a fundamental equation for several flow phenomena such as traffic, shock waves, and turbulence. The optimal feedback control method, so-called model predictive control, has been proposed for Burgers’ equation. However, the model predictive control method is inapplicable to systems whose all state variables are not exactly known. In practical point of view, it is unusual that all the state variables of systems are exactly known, because the state variables of systems are measured through output sensors and limited parts of them can be only available. In fact, it is usual that flow velocities of fluid systems cannot be measured for all spatial domains. Hence, any practical feedback controller for fluid systems must incorporate some type of state estimator. To apply the model predictive control to the fluid systems described by Burgers’ equation, it is needed to establish a state estimation method for Burgers’ equation with limited measurable state variables. To this purpose, we apply unscented Kalman filter for estimating the state variables of fluid systems described by Burgers’ equation. The objective of this study is to establish a state estimation method based on unscented Kalman filter for Burgers’ equation. The effectiveness of the proposed method is verified by numerical simulations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=observer%20systems" title="observer systems">observer systems</a>, <a href="https://publications.waset.org/abstracts/search?q=unscented%20Kalman%20filter" title=" unscented Kalman filter"> unscented Kalman filter</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20systems" title=" nonlinear systems"> nonlinear systems</a>, <a href="https://publications.waset.org/abstracts/search?q=Burgers%27%20equation" title=" Burgers' equation"> Burgers' equation</a> </p> <a href="https://publications.waset.org/abstracts/99541/state-estimation-based-on-unscented-kalman-filter-for-burgers-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/99541.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">155</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8663</span> Analytical Solution of Non–Autonomous Discrete Non-Linear Schrodinger Equation With Saturable Non-Linearity</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mishu%20Gupta">Mishu Gupta</a>, <a href="https://publications.waset.org/abstracts/search?q=Rama%20Gupta"> Rama Gupta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It has been elucidated here that non- autonomous discrete non-linear Schrödinger equation is associated with saturable non-linearity through photo-refractive media. We have investigated the localized solution of non-autonomous saturable discrete non-linear Schrödinger equations. The similarity transformation has been involved in converting non-autonomous saturable discrete non-linear Schrödinger equation to constant-coefficient saturable discrete non-linear Schrödinger equation (SDNLSE), whose exact solution is already known. By back substitution, the solution of the non-autonomous version has been obtained. We have analysed our solution for the hyperbolic and periodic form of gain/loss term, and interesting results have been obtained. The most important characteristic role is that it helps us to analyse the propagation of electromagnetic waves in glass fibres and other optical wave mediums. Also, the usage of SDNLSE has been seen in tight binding for Bose-Einstein condensates in optical mediums. Even the solutions are interrelated, and its properties are prominently used in various physical aspects like optical waveguides, Bose-Einstein (B-E) condensates in optical mediums, Non-linear optics in photonic crystals, and non-linear kerr–type non-linearity effect and photo refracting medium. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=B-E-Bose-Einstein" title="B-E-Bose-Einstein">B-E-Bose-Einstein</a>, <a href="https://publications.waset.org/abstracts/search?q=DNLSE-Discrete%20non%20linear%20schrodinger%20equation" title=" DNLSE-Discrete non linear schrodinger equation"> DNLSE-Discrete non linear schrodinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=NLSE-non%20linear%20schrodinger%20equation" title=" NLSE-non linear schrodinger equation"> NLSE-non linear schrodinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=SDNLSE%20-%20saturable%20discrete%20non%20linear%20Schrodinger%20equation" title=" SDNLSE - saturable discrete non linear Schrodinger equation"> SDNLSE - saturable discrete non linear Schrodinger equation</a> </p> <a href="https://publications.waset.org/abstracts/121074/analytical-solution-of-non-autonomous-discrete-non-linear-schrodinger-equation-with-saturable-non-linearity" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/121074.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">163</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8662</span> Existence of Minimal and Maximal Mild Solutions for Non-Local in Time Subdiffusion Equations of Neutral Type</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Gonzalez-Camus">Jorge Gonzalez-Camus</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work is proved the existence of at least one minimal and maximal mild solutions to the Cauchy problem, for fractional evolution equation of neutral type, involving a general kernel. An operator A generating a resolvent family and integral resolvent family on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Kuratowski measure of noncompactness and fixed point theorems, specifically Darbo-type, and an iterative method of lower and upper solutions, based in an order in X induced by a normal cone P. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the theory of resolvent families, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, the existence of minimal and maximal mild solutions was proved through in an iterative method of lower and upper solutions, using the Azcoli-Arzela Theorem, and the Gronwall’s inequality. Finally, we recovered the case derivate in Caputo sense. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20evolution%20equations" title="fractional evolution equations">fractional evolution equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Volterra%20integral%20equations" title=" Volterra integral equations"> Volterra integral equations</a>, <a href="https://publications.waset.org/abstracts/search?q=minimal%20and%20maximal%20mild%20solutions" title=" minimal and maximal mild solutions"> minimal and maximal mild solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=neutral%20type%20equations" title=" neutral type equations"> neutral type equations</a>, <a href="https://publications.waset.org/abstracts/search?q=non-local%20in%20time%20equations" title=" non-local in time equations"> non-local in time equations</a> </p> <a href="https://publications.waset.org/abstracts/105179/existence-of-minimal-and-maximal-mild-solutions-for-non-local-in-time-subdiffusion-equations-of-neutral-type" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/105179.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">181</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8661</span> Fokas-Lenells Equation Conserved Quantities and Landau-Lifshitz System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Riki%20Dutta">Riki Dutta</a>, <a href="https://publications.waset.org/abstracts/search?q=Sagardeep%20Talukdar"> Sagardeep Talukdar</a>, <a href="https://publications.waset.org/abstracts/search?q=Gautam%20Kumar%20Saharia"> Gautam Kumar Saharia</a>, <a href="https://publications.waset.org/abstracts/search?q=Sudipta%20Nandy"> Sudipta Nandy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fokas-Lenells equation (FLE) is one of the integrable nonlinear equations use to describe the propagation of ultrashort optical pulses in an optical medium. A 2x2 Lax pair has been introduced for the FLE and from that solving the Riccati equation yields infinitely many conserved quantities. Thereafter for a new field function (S) of the Landau-Lifshitz (LL) system, a gauge equivalence of the FLE with the generalised LL equation has been derived. We hope our findings are useful for the application purpose of FLE in optics and other branches of physics. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conserved%20quantities" title="conserved quantities">conserved quantities</a>, <a href="https://publications.waset.org/abstracts/search?q=fokas-lenells%20equation" title=" fokas-lenells equation"> fokas-lenells equation</a>, <a href="https://publications.waset.org/abstracts/search?q=landau-lifshitz%20equation" title=" landau-lifshitz equation"> landau-lifshitz equation</a>, <a href="https://publications.waset.org/abstracts/search?q=lax%20pair" title=" lax pair"> lax pair</a> </p> <a href="https://publications.waset.org/abstracts/165239/fokas-lenells-equation-conserved-quantities-and-landau-lifshitz-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/165239.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">125</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8660</span> Solving Stochastic Eigenvalue Problem of Wick Type</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hassan%20Manouzi">Hassan Manouzi</a>, <a href="https://publications.waset.org/abstracts/search?q=Taous-Meriem%20Laleg-Kirati"> Taous-Meriem Laleg-Kirati</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Ito chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=eigenvalue%20problem" title="eigenvalue problem">eigenvalue problem</a>, <a href="https://publications.waset.org/abstracts/search?q=Wick%20product" title=" Wick product"> Wick product</a>, <a href="https://publications.waset.org/abstracts/search?q=SPDEs" title=" SPDEs"> SPDEs</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element" title=" finite element"> finite element</a>, <a href="https://publications.waset.org/abstracts/search?q=Wiener-Ito%20chaos%20expansion" title=" Wiener-Ito chaos expansion"> Wiener-Ito chaos expansion</a> </p> <a href="https://publications.waset.org/abstracts/7652/solving-stochastic-eigenvalue-problem-of-wick-type" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/7652.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">363</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8659</span> Relaxation Behavior of Biorenewable Waterborne Castor Oil-Based Polyurethane-Lignin Thin Films</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Samy%20Madbouly">Samy Madbouly</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The relaxation behavior of biorenewable castor oil-based polyurethane-lignin thin films synthesized in homogenous waterborne dispersions was investigated as a function of concentration at different temperatures and frequencies using broadband dielectric relaxation spectroscopy (BDRS). The molecular dynamics of the glass relaxation process and the local relaxation process of the PU-LS thin films were studied over a wide range of temperatures (-70 to 30 ℃) and frequencies (5 × 10−2 to 0.5 × 107 Hz) for different lignin concentration. Four relaxation processes have been observed namely; ?-, β-, γ-relaxations and ionic conductivity for pure castor oil-based PU and castor oil-lignin-based PU thin films at different temperatures and frequencies ranges. The Vogel-Fulcher-Tammann equation was found to be well described the temperature dependence of the characteristic relaxation times of the ?-relaxation process. However, on the other hand, the molecular dynamics of both β- and γ-relaxation processes were given by the Arrhenius equation. The incorporation of lignin into the castor oil-based PU significantly increased the glass transition temperature and primitivity of the thin films. In addition, the broadness, intensity, and molecular dynamics of the only observed ?-relaxation process were found to be strongly dependent on lignin concentration. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=castor%20oil" title="castor oil">castor oil</a>, <a href="https://publications.waset.org/abstracts/search?q=lignin" title=" lignin"> lignin</a>, <a href="https://publications.waset.org/abstracts/search?q=polyurethane" title=" polyurethane"> polyurethane</a>, <a href="https://publications.waset.org/abstracts/search?q=dielectric" title=" dielectric"> dielectric</a>, <a href="https://publications.waset.org/abstracts/search?q=dispersions" title=" dispersions"> dispersions</a> </p> <a href="https://publications.waset.org/abstracts/140796/relaxation-behavior-of-biorenewable-waterborne-castor-oil-based-polyurethane-lignin-thin-films" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/140796.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">207</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8658</span> Asymptotic Expansion of the Korteweg-de Vries-Burgers Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jian-Jun%20Shu">Jian-Jun Shu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It is common knowledge that many physical problems (such as non-linear shallow-water waves and wave motion in plasmas) can be described by the Korteweg-de Vries (KdV) equation, which possesses certain special solutions, known as solitary waves or solitons. As a marriage of the KdV equation and the classical Burgers (KdVB) equation, the Korteweg-de Vries-Burgers (KdVB) equation is a mathematical model of waves on shallow water surfaces in the presence of viscous dissipation. Asymptotic analysis is a method of describing limiting behavior and is a key tool for exploring the differential equations which arise in the mathematical modeling of real-world phenomena. By using variable transformations, the asymptotic expansion of the KdVB equation is presented in this paper. The asymptotic expansion may provide a good gauge on the validation of the corresponding numerical scheme. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20expansion" title="asymptotic expansion">asymptotic expansion</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20equation" title=" differential equation"> differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Korteweg-de%20Vries-Burgers%20%28KdVB%29%20equation" title=" Korteweg-de Vries-Burgers (KdVB) equation"> Korteweg-de Vries-Burgers (KdVB) equation</a>, <a href="https://publications.waset.org/abstracts/search?q=soliton" title=" soliton"> soliton</a> </p> <a href="https://publications.waset.org/abstracts/78883/asymptotic-expansion-of-the-korteweg-de-vries-burgers-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/78883.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">262</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8657</span> Mapping Methods to Solve a Modified Korteweg de Vries Type Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=E.%20V.%20Krishnan">E. V. Krishnan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we employ mapping methods to construct exact travelling wave solutions for a modified Korteweg-de Vries equation. We have derived periodic wave solutions in terms of Jacobi elliptic functions, kink solutions and singular wave solutions in terms of hyperbolic functions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=travelling%20wave%20solutions" title="travelling wave solutions">travelling wave solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=Jacobi%20elliptic%20functions" title=" Jacobi elliptic functions"> Jacobi elliptic functions</a>, <a href="https://publications.waset.org/abstracts/search?q=solitary%20wave%20solutions" title=" solitary wave solutions"> solitary wave solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=Korteweg-de%20Vries%20equation" title=" Korteweg-de Vries equation"> Korteweg-de Vries equation</a> </p> <a href="https://publications.waset.org/abstracts/12150/mapping-methods-to-solve-a-modified-korteweg-de-vries-type-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/12150.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">335</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8656</span> Matrix Valued Difference Equations with Spectral Singularities</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Serifenur%20Cebesoy">Serifenur Cebesoy</a>, <a href="https://publications.waset.org/abstracts/search?q=Yelda%20Aygar"> Yelda Aygar</a>, <a href="https://publications.waset.org/abstracts/search?q=Elgiz%20Bairamov"> Elgiz Bairamov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, we examine some spectral properties of non-selfadjoint matrix-valued difference equations consisting of a polynomial type Jost solution. The aim of this study is to investigate the eigenvalues and spectral singularities of the difference operator L which is expressed by the above-mentioned difference equation. Firstly, thanks to the representation of polynomial type Jost solution of this equation, we obtain asymptotics and some analytical properties. Then, using the uniqueness theorems of analytic functions, we guarantee that the operator L has a finite number of eigenvalues and spectral singularities. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotics" title="asymptotics">asymptotics</a>, <a href="https://publications.waset.org/abstracts/search?q=continuous%20spectrum" title=" continuous spectrum"> continuous spectrum</a>, <a href="https://publications.waset.org/abstracts/search?q=difference%20equations" title=" difference equations"> difference equations</a>, <a href="https://publications.waset.org/abstracts/search?q=eigenvalues" title=" eigenvalues"> eigenvalues</a>, <a href="https://publications.waset.org/abstracts/search?q=jost%20functions" title=" jost functions"> jost functions</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20singularities" title=" spectral singularities"> spectral singularities</a> </p> <a href="https://publications.waset.org/abstracts/32256/matrix-valued-difference-equations-with-spectral-singularities" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32256.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">454</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8655</span> An Analytical Method for Solving General Riccati Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Y.%20Pala">Y. Pala</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20O.%20Ertas"> M. O. Ertas</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Riccati%20equation" title="Riccati equation">Riccati equation</a>, <a href="https://publications.waset.org/abstracts/search?q=analytical%20solution" title=" analytical solution"> analytical solution</a>, <a href="https://publications.waset.org/abstracts/search?q=proper%20solution" title=" proper solution"> proper solution</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear" title=" nonlinear"> nonlinear</a> </p> <a href="https://publications.waset.org/abstracts/64988/an-analytical-method-for-solving-general-riccati-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/64988.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">361</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8654</span> Operator Splitting Scheme for the Inverse Nagumo Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sharon-Yasotha%20Veerayah-Mcgregor">Sharon-Yasotha Veerayah-Mcgregor</a>, <a href="https://publications.waset.org/abstracts/search?q=Valipuram%20Manoranjan"> Valipuram Manoranjan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A backward or inverse problem is known to be an ill-posed problem due to its instability that easily emerges with any slight change within the conditions of the problem. Therefore, only a limited number of numerical approaches are available to solve a backward problem. This paper considers the Nagumo equation, an equation that describes impulse propagation in nerve axons, which also models population growth with the Allee effect. A creative operator splitting numerical scheme is constructed to solve the inverse Nagumo equation. Computational simulations are used to verify that this scheme is stable, accurate, and efficient. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=inverse%2Fbackward%20equation" title="inverse/backward equation">inverse/backward equation</a>, <a href="https://publications.waset.org/abstracts/search?q=operator-splitting" title=" operator-splitting"> operator-splitting</a>, <a href="https://publications.waset.org/abstracts/search?q=Nagumo%20equation" title=" Nagumo equation"> Nagumo equation</a>, <a href="https://publications.waset.org/abstracts/search?q=ill-posed" title=" ill-posed"> ill-posed</a>, <a href="https://publications.waset.org/abstracts/search?q=finite-difference" title=" finite-difference"> finite-difference</a> </p> <a href="https://publications.waset.org/abstracts/182287/operator-splitting-scheme-for-the-inverse-nagumo-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/182287.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">105</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8653</span> Steady-State Behavior of a Multi-Phase M/M/1 Queue in Random Evolution Subject to Catastrophe Failure</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Reni%20M.%20Sagayaraj">Reni M. Sagayaraj</a>, <a href="https://publications.waset.org/abstracts/search?q=Anand%20Gnana%20S.%20Selvam"> Anand Gnana S. Selvam</a>, <a href="https://publications.waset.org/abstracts/search?q=Reynald%20R.%20Susainathan"> Reynald R. Susainathan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we consider stochastic queueing models for Steady-state behavior of a multi-phase M/M/1 queue in random evolution subject to catastrophe failure. The arrival flow of customers is described by a marked Markovian arrival process. The service times of different type customers have a phase-type distribution with different parameters. To facilitate the investigation of the system we use a generalized phase-type service time distribution. This model contains a repair state, when a catastrophe occurs the system is transferred to the failure state. The paper focuses on the steady-state equation, and observes that, the steady-state behavior of the underlying queueing model along with the average queue size is analyzed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=M%2FG%2F1%20queuing%20system" title="M/G/1 queuing system">M/G/1 queuing system</a>, <a href="https://publications.waset.org/abstracts/search?q=multi-phase" title=" multi-phase"> multi-phase</a>, <a href="https://publications.waset.org/abstracts/search?q=random%20evolution" title=" random evolution"> random evolution</a>, <a href="https://publications.waset.org/abstracts/search?q=steady-state%20equation" title=" steady-state equation"> steady-state equation</a>, <a href="https://publications.waset.org/abstracts/search?q=catastrophe%20failure" title=" catastrophe failure"> catastrophe failure</a> </p> <a href="https://publications.waset.org/abstracts/53659/steady-state-behavior-of-a-multi-phase-mm1-queue-in-random-evolution-subject-to-catastrophe-failure" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/53659.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">333</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8652</span> Performances Analysis of the Pressure and Production of an Oil Zone by Simulation of the Flow of a Fluid through the Porous Media</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Makhlouf%20Mourad">Makhlouf Mourad</a>, <a href="https://publications.waset.org/abstracts/search?q=Medkour%20Mihoub"> Medkour Mihoub</a>, <a href="https://publications.waset.org/abstracts/search?q=Bouchher%20Omar"> Bouchher Omar</a>, <a href="https://publications.waset.org/abstracts/search?q=Messabih%20Sidi%20Mohamed"> Messabih Sidi Mohamed</a>, <a href="https://publications.waset.org/abstracts/search?q=Benrachedi%20Khaled"> Benrachedi Khaled</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This work is the modeling and simulation of fluid flow (liquid) through porous media. This type of flow occurs in many situations of interest in applied sciences and engineering, fluid (oil) consists of several individual substances in pure, single-phase flow is incompressible and isothermal. The porous medium is isotropic, homogeneous optionally, with the rectangular format and the flow is two-dimensional. Modeling of hydrodynamic phenomena incorporates Darcy's law and the equation of mass conservation. Correlations are used to model the density and viscosity of the fluid. A finite volume code is used in the discretization of differential equations. The nonlinearity is treated by Newton's method with relaxation coefficient. The results of the simulation of the pressure and the mobility of liquid flowing through porous media are presented, analyzed, and illustrated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Darcy%20equation" title="Darcy equation">Darcy equation</a>, <a href="https://publications.waset.org/abstracts/search?q=middle%20porous" title=" middle porous"> middle porous</a>, <a href="https://publications.waset.org/abstracts/search?q=continuity%20equation" title=" continuity equation"> continuity equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Peng%20Robinson%20equation" title=" Peng Robinson equation"> Peng Robinson equation</a>, <a href="https://publications.waset.org/abstracts/search?q=mobility" title=" mobility"> mobility</a> </p> <a href="https://publications.waset.org/abstracts/102834/performances-analysis-of-the-pressure-and-production-of-an-oil-zone-by-simulation-of-the-flow-of-a-fluid-through-the-porous-media" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/102834.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">224</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8651</span> Closed Form Exact Solution for Second Order Linear Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Saeed%20Otarod">Saeed Otarod</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=explicit" title="explicit">explicit</a>, <a href="https://publications.waset.org/abstracts/search?q=linear" title=" linear"> linear</a>, <a href="https://publications.waset.org/abstracts/search?q=differential" title=" differential"> differential</a>, <a href="https://publications.waset.org/abstracts/search?q=closed%20form" title=" closed form"> closed form</a> </p> <a href="https://publications.waset.org/abstracts/185365/closed-form-exact-solution-for-second-order-linear-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/185365.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">72</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8650</span> Image Transform Based on Integral Equation-Wavelet Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yuan%20Yan%20Tang">Yuan Yan Tang</a>, <a href="https://publications.waset.org/abstracts/search?q=Lina%20Yang"> Lina Yang</a>, <a href="https://publications.waset.org/abstracts/search?q=Hong%20Li"> Hong Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=harmonic%20model" title="harmonic model">harmonic model</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equation%20%28PDE%29" title=" partial differential equation (PDE)"> partial differential equation (PDE)</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20equation" title=" integral equation"> integral equation</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20representation" title=" integral representation"> integral representation</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20measure%20formula" title=" boundary measure formula"> boundary measure formula</a>, <a href="https://publications.waset.org/abstracts/search?q=wavelet%20collocation" title=" wavelet collocation"> wavelet collocation</a> </p> <a href="https://publications.waset.org/abstracts/3920/image-transform-based-on-integral-equation-wavelet-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3920.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">570</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8649</span> Study of Cahn-Hilliard Equation to Simulate Phase Separation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nara%20Guimar%C3%A3es">Nara Guimarães</a>, <a href="https://publications.waset.org/abstracts/search?q=Marcelo%20Aquino%20Martorano"> Marcelo Aquino Martorano</a>, <a href="https://publications.waset.org/abstracts/search?q=Douglas%20Gouv%C3%AAa"> Douglas Gouvêa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An investigation into Cahn-Hilliard equation was carried out through numerical simulation to identify a possible phase separation for one and two dimensional domains. It was observed that this equation can reproduce important mass fluxes necessary for phase separation within the miscibility gap and for coalescence of particles. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Cahn-Hilliard%20equation" title="Cahn-Hilliard equation">Cahn-Hilliard equation</a>, <a href="https://publications.waset.org/abstracts/search?q=miscibility%20gap" title=" miscibility gap"> miscibility gap</a>, <a href="https://publications.waset.org/abstracts/search?q=phase%20separation" title=" phase separation"> phase separation</a>, <a href="https://publications.waset.org/abstracts/search?q=dimensional%20domains" title=" dimensional domains"> dimensional domains</a> </p> <a href="https://publications.waset.org/abstracts/17579/study-of-cahn-hilliard-equation-to-simulate-phase-separation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17579.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">520</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Arrhenius%20type%20equation&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Arrhenius%20type%20equation&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Arrhenius%20type%20equation&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Arrhenius%20type%20equation&page=5">5</a></li> <li class="page-item"><a class="page-link" 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