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equations</title> <meta name="description" content="Search results for: dynamic equations"> <meta name="keywords" content="dynamic equations"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="dynamic equations"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 3357</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: dynamic equations</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3357</span> Effect of Delay on Supply Side on Market Behavior: A System Dynamic Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Khoshab">M. Khoshab</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20J.%20Sedigh"> M. J. Sedigh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Dynamic systems, which in mathematical point of view are those governed by differential equations, are much more difficult to study and to predict their behavior in comparison with static systems which are governed by algebraic equations. Economical systems such as market are among complicated dynamic systems. This paper tries to adopt a very simple mathematical model for market and to study effect of supply and demand function on behavior of the market while the supply side experiences a lag due to production restrictions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamic%20system" title="dynamic system">dynamic system</a>, <a href="https://publications.waset.org/abstracts/search?q=lag%20on%20supply%20demand" title=" lag on supply demand"> lag on supply demand</a>, <a href="https://publications.waset.org/abstracts/search?q=market%20stability" title=" market stability"> market stability</a>, <a href="https://publications.waset.org/abstracts/search?q=supply%20demand%20model" title=" supply demand model"> supply demand model</a> </p> <a href="https://publications.waset.org/abstracts/5147/effect-of-delay-on-supply-side-on-market-behavior-a-system-dynamic-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/5147.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">295</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">3356</span> Serious Digital Video Game for Solving Algebraic Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Liliana%20O.%20Mart%C3%ADnez">Liliana O. Martínez</a>, <a href="https://publications.waset.org/abstracts/search?q=Juan%20E%20Gonz%C3%A1lez"> Juan E González</a>, <a href="https://publications.waset.org/abstracts/search?q=Manuel%20Ram%C3%ADrez-Aranda"> Manuel Ramírez-Aranda</a>, <a href="https://publications.waset.org/abstracts/search?q=Ana%20Cervantes-Herrera"> Ana Cervantes-Herrera</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A serious game category mobile application called Math Dominoes is presented. The main objective of this applications is to strengthen the teaching-learning process of solving algebraic equations and is based on the board game "Double 6" dominoes. Math Dominoes allows the practice of solving first, second-, and third-degree algebraic equations. This application is aimed to students who seek to strengthen their skills in solving algebraic equations in a dynamic, interactive, and fun way, to reduce the risk of failure in subsequent courses that require mastery of this algebraic tool. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=algebra" title="algebra">algebra</a>, <a href="https://publications.waset.org/abstracts/search?q=equations" title=" equations"> equations</a>, <a href="https://publications.waset.org/abstracts/search?q=dominoes" title=" dominoes"> dominoes</a>, <a href="https://publications.waset.org/abstracts/search?q=serious%20games" title=" serious games"> serious games</a> </p> <a href="https://publications.waset.org/abstracts/156059/serious-digital-video-game-for-solving-algebraic-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/156059.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">130</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">3355</span> A Dynamic Equation for Downscaling Surface Air Temperature</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ch.%20Surawut">Ch. Surawut</a>, <a href="https://publications.waset.org/abstracts/search?q=D.%20Sukawat"> D. Sukawat</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In order to utilize results from global climate models, dynamical and statistical downscaling techniques have been developed. For dynamical downscaling, usually a limited area numerical model is used, with associated high computational cost. This research proposes dynamic equation for specific space-time regional climate downscaling from the Educational Global Climate Model (EdGCM) for Southeast Asia. The equation is for surface air temperature. These equations provide downscaling values of surface air temperature at any specific location and time without running a regional climate model. In the proposed equations, surface air temperature is approximated from ground temperature, sensible heat flux and 2m wind speed. Results from the application of the equation show that the errors from the proposed equations are less than the errors for direct interpolation from EdGCM. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamic%20equation" title="dynamic equation">dynamic equation</a>, <a href="https://publications.waset.org/abstracts/search?q=downscaling" title=" downscaling"> downscaling</a>, <a href="https://publications.waset.org/abstracts/search?q=inverse%20distance" title=" inverse distance"> inverse distance</a>, <a href="https://publications.waset.org/abstracts/search?q=weight%20interpolation" title=" weight interpolation"> weight interpolation</a> </p> <a href="https://publications.waset.org/abstracts/39670/a-dynamic-equation-for-downscaling-surface-air-temperature" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/39670.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">306</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">3354</span> A Sliding Model Control for a Hybrid Hyperbolic Dynamic System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Xuezhang%20Hou">Xuezhang Hou</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present paper, a hybrid hyperbolic dynamic system formulated by partial differential equations with initial and boundary conditions is considered. First, the system is transformed to an abstract evolution system in an appropriate Hilbert space, and spectral analysis and semigroup generation of the system operator is discussed. Subsequently, a sliding model control problem is proposed and investigated, and an equivalent control method is introduced and applied to the system. Finally, a significant result that the state of the system can be approximated by an ideal sliding mode under control in any accuracy is derived and examined. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hyperbolic%20dynamic%20system" title="hyperbolic dynamic system">hyperbolic dynamic system</a>, <a href="https://publications.waset.org/abstracts/search?q=sliding%20model%20control" title=" sliding model control"> sliding model control</a>, <a href="https://publications.waset.org/abstracts/search?q=semigroup%20of%20linear%20operators" title=" semigroup of linear operators"> semigroup of linear operators</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equations" title=" partial differential equations"> partial differential equations</a> </p> <a href="https://publications.waset.org/abstracts/148599/a-sliding-model-control-for-a-hybrid-hyperbolic-dynamic-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/148599.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">136</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">3353</span> Robust Control of a Parallel 3-RRR Robotic Manipulator via μ-Synthesis Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Abbasi%20Moshaii">A. Abbasi Moshaii</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Soltan%20Rezaee"> M. Soltan Rezaee</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Mohammadi%20Moghaddam"> M. Mohammadi Moghaddam</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Control of some mechanisms is hard because of their complex dynamic equations. If part of the complexity is resulting from uncertainties, an efficient way for solving that is robust control. By this way, the control procedure could be simple and fast and finally, a simple controller can be designed. One kind of these mechanisms is 3-<u>R</u>RR which is a parallel mechanism and has three revolute joints. This paper aims to robust control a 3-<u>R</u>RR planner mechanism and it presents that this could be used for other mechanisms. So, a significant problem in mechanisms control could be solved. The relevant diagrams are drawn and they show the correctness of control process. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=3-RRR" title="3-RRR">3-RRR</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamic%20equations" title=" dynamic equations"> dynamic equations</a>, <a href="https://publications.waset.org/abstracts/search?q=mechanisms%20control" title=" mechanisms control"> mechanisms control</a>, <a href="https://publications.waset.org/abstracts/search?q=structural%20uncertainty" title=" structural uncertainty"> structural uncertainty</a> </p> <a href="https://publications.waset.org/abstracts/51492/robust-control-of-a-parallel-3-rrr-robotic-manipulator-via-m-synthesis-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/51492.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">557</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">3352</span> Classification of Equations of Motion</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Amritpal%20Singh%20Nafria">Amritpal Singh Nafria</a>, <a href="https://publications.waset.org/abstracts/search?q=Rohit%20Sharma"> Rohit Sharma</a>, <a href="https://publications.waset.org/abstracts/search?q=Md.%20Shami%20Ansari"> Md. Shami Ansari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Up to now only five different equations of motion can be derived from velocity time graph without needing to know the normal and frictional forces acting at the point of contact. In this paper we obtained all possible requisite conditions to be considering an equation as an equation of motion. After that we classified equations of motion by considering two equations as fundamental kinematical equations of motion and other three as additional kinematical equations of motion. After deriving these five equations of motion, we examine the easiest way of solving a wide variety of useful numerical problems. At the end of the paper, we discussed the importance and educational benefits of classification of equations of motion. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=velocity-time%20graph" title="velocity-time graph">velocity-time graph</a>, <a href="https://publications.waset.org/abstracts/search?q=fundamental%20equations" title=" fundamental equations"> fundamental equations</a>, <a href="https://publications.waset.org/abstracts/search?q=additional%20equations" title=" additional equations"> additional equations</a>, <a href="https://publications.waset.org/abstracts/search?q=requisite%20conditions" title=" requisite conditions"> requisite conditions</a>, <a href="https://publications.waset.org/abstracts/search?q=importance%20and%20educational%20benefits" title=" importance and educational benefits"> importance and educational benefits</a> </p> <a href="https://publications.waset.org/abstracts/15102/classification-of-equations-of-motion" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15102.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">787</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">3351</span> Dynamic Behavior of Brain Tissue under Transient Loading</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Y.%20J.%20Zhou">Y. J. Zhou</a>, <a href="https://publications.waset.org/abstracts/search?q=G.%20Lu"> G. Lu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, an analytical study is made for the dynamic behavior of human brain tissue under transient loading. In this analytical model the Mooney-Rivlin constitutive law is coupled with visco-elastic constitutive equations to take into account both the nonlinear and time-dependent mechanical behavior of brain tissue. Five ordinary differential equations representing the relationships of five main parameters (radial stress, circumferential stress, radial strain, circumferential strain, and particle velocity) are obtained by using the characteristic method to transform five partial differential equations (two continuity equations, one motion equation, and two constitutive equations). Analytical expressions of the attenuation properties for spherical wave in brain tissue are analytically derived. Numerical results are obtained based on the five ordinary differential equations. The mechanical responses (particle velocity and stress) of brain are compared at different radii including 5, 6, 10, 15 and 25 mm under four different input conditions. The results illustrate that loading curves types of the particle velocity significantly influences the stress in brain tissue. The understanding of the influence by the input loading cures can be used to reduce the potentially injury to brain under head impact by designing protective structures to control the loading curves types. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=analytical%20method" title="analytical method">analytical method</a>, <a href="https://publications.waset.org/abstracts/search?q=mechanical%20responses" title=" mechanical responses"> mechanical responses</a>, <a href="https://publications.waset.org/abstracts/search?q=spherical%20wave%20propagation" title=" spherical wave propagation"> spherical wave propagation</a>, <a href="https://publications.waset.org/abstracts/search?q=traumatic%20brain%20injury" title=" traumatic brain injury"> traumatic brain injury</a> </p> <a href="https://publications.waset.org/abstracts/11805/dynamic-behavior-of-brain-tissue-under-transient-loading" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/11805.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">269</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">3350</span> On Boundary Value Problems of Fractional Differential Equations Involving Stieltjes Derivatives</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Baghdad%20Said">Baghdad Said</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Differential equations of fractional order have proved to be important tools to describe many physical phenomena and have been used in diverse fields such as engineering, mathematics as well as other applied sciences. On the other hand, the theory of differential equations involving the Stieltjes derivative (SD) with respect to a non-decreasing function is a new class of differential equations and has many applications as a unified framework for dynamic equations on time scales and differential equations with impulses at fixed times. The aim of this paper is to investigate the existence, uniqueness, and generalized Ulam-Hyers-Rassias stability (UHRS) of solutions for a boundary value problem of sequential fractional differential equations (SFDE) containing (SD). This study is based on the technique of noncompactness measures (MNCs) combined with Monch-Krasnoselski fixed point theorems (FPT), and the results are proven in an appropriate Banach space under sufficient hypotheses. We also give an illustrative example. In this work, we introduced a class of (SFDE) and the results are obtained under a few hypotheses. Future directions connected to this work could focus on another problem with different types of fractional integrals and derivatives, and the (SD) will be assumed under a more general hypothesis in more general functional spaces. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=SFDE" title="SFDE">SFDE</a>, <a href="https://publications.waset.org/abstracts/search?q=SD" title=" SD"> SD</a>, <a href="https://publications.waset.org/abstracts/search?q=UHRS" title=" UHRS"> UHRS</a>, <a href="https://publications.waset.org/abstracts/search?q=MNCs" title=" MNCs"> MNCs</a>, <a href="https://publications.waset.org/abstracts/search?q=FPT" title=" FPT"> FPT</a> </p> <a href="https://publications.waset.org/abstracts/187408/on-boundary-value-problems-of-fractional-differential-equations-involving-stieltjes-derivatives" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/187408.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">40</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">3349</span> Integrable Heisenberg Ferromagnet Equations with Self-Consistent Potentials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gulgassyl%20Nugmanova">Gulgassyl Nugmanova</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhanat%20Zhunussova"> Zhanat Zhunussova</a>, <a href="https://publications.waset.org/abstracts/search?q=Kuralay%20Yesmakhanova"> Kuralay Yesmakhanova</a>, <a href="https://publications.waset.org/abstracts/search?q=Galya%20Mamyrbekova"> Galya Mamyrbekova</a>, <a href="https://publications.waset.org/abstracts/search?q=Ratbay%20Myrzakulov"> Ratbay Myrzakulov </a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we consider some integrable Heisenberg Ferromagnet Equations with self-consistent potentials. We study their Lax representations. In particular we derive their equivalent counterparts in the form of nonlinear Schr\"odinger type equations. We present the integrable reductions of the Heisenberg Ferromagnet Equations with self-consistent potentials. These integrable Heisenberg Ferromagnet Equations with self-consistent potentials describe nonlinear waves in ferromagnets with some additional physical fields. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Heisenberg%20Ferromagnet%20equations" title="Heisenberg Ferromagnet equations">Heisenberg Ferromagnet equations</a>, <a href="https://publications.waset.org/abstracts/search?q=soliton%20equations" title=" soliton equations"> soliton equations</a>, <a href="https://publications.waset.org/abstracts/search?q=equivalence" title=" equivalence"> equivalence</a>, <a href="https://publications.waset.org/abstracts/search?q=Lax%20representation" title=" Lax representation"> Lax representation</a> </p> <a href="https://publications.waset.org/abstracts/27440/integrable-heisenberg-ferromagnet-equations-with-self-consistent-potentials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/27440.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">457</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">3348</span> Pressure-Controlled Dynamic Equations of the PFC Model: A Mathematical Formulation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jatupon%20Em-Udom">Jatupon Em-Udom</a>, <a href="https://publications.waset.org/abstracts/search?q=Nirand%20Pisutha-Arnond"> Nirand Pisutha-Arnond</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The phase-field-crystal, PFC, approach is a density-functional-type material model with an atomic resolution on a diffusive timescale. Spatially, the model incorporates periodic nature of crystal lattices and can naturally exhibit elasticity, plasticity and crystal defects such as grain boundaries and dislocations. Temporally, the model operates on a diffusive timescale which bypasses the need to resolve prohibitively small atomic-vibration time steps. The PFC model has been used to study many material phenomena such as grain growth, elastic and plastic deformations and solid-solid phase transformations. In this study, the pressure-controlled dynamic equation for the PFC model was developed to simulate a single-component system under externally applied pressure; these coupled equations are important for studies of deformable systems such as those under constant pressure. The formulation is based on the non-equilibrium thermodynamics and the thermodynamics of crystalline solids. To obtain the equations, the entropy variation around the equilibrium point was derived. Then the resulting driving forces and flux around the equilibrium were obtained and rewritten as conventional thermodynamic quantities. These dynamics equations are different from the recently-proposed equations; the equations in this study should provide more rigorous descriptions of the system dynamics under externally applied pressure. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=driving%20forces%20and%20flux" title="driving forces and flux">driving forces and flux</a>, <a href="https://publications.waset.org/abstracts/search?q=evolution%20equation" title=" evolution equation"> evolution equation</a>, <a href="https://publications.waset.org/abstracts/search?q=non%20equilibrium%20thermodynamics" title=" non equilibrium thermodynamics"> non equilibrium thermodynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=Onsager%E2%80%99s%20reciprocal%20relation" title=" Onsager’s reciprocal relation"> Onsager’s reciprocal relation</a>, <a href="https://publications.waset.org/abstracts/search?q=phase%20field%20crystal%20model" title=" phase field crystal model"> phase field crystal model</a>, <a href="https://publications.waset.org/abstracts/search?q=thermodynamics%20of%20single-component%20solid" title=" thermodynamics of single-component solid"> thermodynamics of single-component solid</a> </p> <a href="https://publications.waset.org/abstracts/45485/pressure-controlled-dynamic-equations-of-the-pfc-model-a-mathematical-formulation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/45485.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">305</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">3347</span> Dynamic Analysis of Differential Systems with Infinite Memory and Damping</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kun-Peng%20Jin">Kun-Peng Jin</a>, <a href="https://publications.waset.org/abstracts/search?q=Jin%20Liang"> Jin Liang</a>, <a href="https://publications.waset.org/abstracts/search?q=Ti-Jun%20Xiao"> Ti-Jun Xiao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we are concerned with the dynamic behaviors of solutions to some coupled systems with infinite memory, which consist of two partial differential equations where only one partial differential equation has damping. Such coupled systems are good mathematical models to describe the deformation and stress characteristics of some viscoelastic materials affected by temperature change, external forces, and other factors. By using the theory of operator semigroups, we give wellposedness results for the Cauchy problem for these coupled systems. Then, with the help of some auxiliary functions and lemmas, which are specially designed for overcoming difficulties in the proof, we show that the solutions of the coupled systems decay to zero in a strong way under a few basic conditions. The results in this dynamic analysis of coupled systems are generalizations of many existing results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamic%20analysis" title="dynamic analysis">dynamic analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=coupled%20system" title=" coupled system"> coupled system</a>, <a href="https://publications.waset.org/abstracts/search?q=infinite%20memory" title=" infinite memory"> infinite memory</a>, <a href="https://publications.waset.org/abstracts/search?q=damping." title=" damping."> damping.</a> </p> <a href="https://publications.waset.org/abstracts/93937/dynamic-analysis-of-differential-systems-with-infinite-memory-and-damping" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/93937.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">221</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">3346</span> Dynamic Analysis of a Moderately Thick Plate on Pasternak Type Foundation under Impact and Moving Loads</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Neslihan%20Genckal">Neslihan Genckal</a>, <a href="https://publications.waset.org/abstracts/search?q=Reha%20Gursoy"> Reha Gursoy</a>, <a href="https://publications.waset.org/abstracts/search?q=Vedat%20Z.%20Dogan"> Vedat Z. Dogan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, dynamic responses of composite plates on elastic foundations subjected to impact and moving loads are investigated. The first order shear deformation (FSDT) theory is used for moderately thick plates. Pasternak-type (two-parameter) elastic foundation is assumed. Elastic foundation effects are integrated into the governing equations. It is assumed that plate is first hit by a mass as an impact type loading then the mass continues to move on the composite plate as a distributed moving loading, which resembles the aircraft landing on airport pavements. Impact and moving loadings are modeled by a mass-spring-damper system with a wheel. The wheel is assumed to be continuously in contact with the plate after impact. The governing partial differential equations of motion for displacements are converted into the ordinary differential equations in the time domain by using Galerkin’s method. Then, these sets of equations are solved by using the Runge-Kutta method. Several parameters such as vertical and horizontal velocities of the aircraft, volume fractions of the steel rebar in the reinforced concrete layer, and the different touchdown locations of the aircraft tire on the runway are considered in the numerical simulation. The results are compared with those of the ABAQUS, which is a commercial finite element code. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=elastic%20foundation" title="elastic foundation">elastic foundation</a>, <a href="https://publications.waset.org/abstracts/search?q=impact" title=" impact"> impact</a>, <a href="https://publications.waset.org/abstracts/search?q=moving%20load" title=" moving load"> moving load</a>, <a href="https://publications.waset.org/abstracts/search?q=thick%20plate" title=" thick plate"> thick plate</a> </p> <a href="https://publications.waset.org/abstracts/51046/dynamic-analysis-of-a-moderately-thick-plate-on-pasternak-type-foundation-under-impact-and-moving-loads" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/51046.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">313</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">3345</span> Nonlinear Dynamic Response of Helical Gear with Torque-Limiter</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ahmed%20Guerine">Ahmed Guerine</a>, <a href="https://publications.waset.org/abstracts/search?q=Ali%20El%20Hafidi"> Ali El Hafidi</a>, <a href="https://publications.waset.org/abstracts/search?q=Bruno%20Martin"> Bruno Martin</a>, <a href="https://publications.waset.org/abstracts/search?q=Philippe%20Leclaire"> Philippe Leclaire</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper investigates the nonlinear dynamic response of a mechanical torque limiter which is used to protect drive parts from overload (helical transmission gears). The system is driven by four excitations: two external excitations (aerodynamics torque and force) and two internal excitations (two mesh stiffness fluctuations). In this work, we develop a dynamic model with lumped components and 28 degrees of freedom. We use the Runge Kutta step-by-step time integration numerical algorithm to solve the equations of motion obtained by Lagrange formalism. The numerical results have allowed us to identify the sources of vibration in the wind turbine. Also, they are useful to help the designer to make the right design and correctly choose the times for maintenance. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=two-stage%20helical%20gear" title="two-stage helical gear">two-stage helical gear</a>, <a href="https://publications.waset.org/abstracts/search?q=lumped%20model" title=" lumped model"> lumped model</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamic%20response" title=" dynamic response"> dynamic response</a>, <a href="https://publications.waset.org/abstracts/search?q=torque-limiter" title=" torque-limiter"> torque-limiter</a> </p> <a href="https://publications.waset.org/abstracts/142306/nonlinear-dynamic-response-of-helical-gear-with-torque-limiter" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/142306.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">353</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">3344</span> Analysis of a Self-Acting Air Journal Bearing: Effect of Dynamic Deformation of Bump Foil</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=H.%20Bensouilah">H. Bensouilah</a>, <a href="https://publications.waset.org/abstracts/search?q=H.%20Boucherit"> H. Boucherit</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Lahmar"> M. Lahmar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A theoretical investigation on the effects of both steady-state and dynamic deformations of the foils on the dynamic performance characteristics of a self-acting air foil journal bearing operating under small harmonic vibrations is proposed. To take into account the dynamic deformations of foils, the perturbation method is used for determining the gas-film stiffness and damping coefficients for given values of excitation frequency, compressibility number, and compliance factor of the bump foil. The nonlinear stationary Reynolds’ equation is solved by means of the Galerkins’ finite element formulation while the finite differences method are used to solve the first order complex dynamic equations resulting from the perturbation of the nonlinear transient compressible Reynolds’ equation. The stiffness of a bump is uniformly distributed throughout the bearing surface (generation I bearing). It was found that the dynamic properties of the compliant finite length journal bearing are significantly affected by the compliance of foils especially when the dynamic deformation of foils is considered in addition to the static one by applying the principle of superposition. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=elasto-aerodynamic%20lubrication" title="elasto-aerodynamic lubrication">elasto-aerodynamic lubrication</a>, <a href="https://publications.waset.org/abstracts/search?q=air%20foil%20bearing" title=" air foil bearing"> air foil bearing</a>, <a href="https://publications.waset.org/abstracts/search?q=steady-state%20deformation" title=" steady-state deformation"> steady-state deformation</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamic%20deformation" title=" dynamic deformation"> dynamic deformation</a>, <a href="https://publications.waset.org/abstracts/search?q=stiffness%20and%20damping%20coefficients" title=" stiffness and damping coefficients"> stiffness and damping coefficients</a>, <a href="https://publications.waset.org/abstracts/search?q=perturbation%20method" title=" perturbation method"> perturbation method</a>, <a href="https://publications.waset.org/abstracts/search?q=fluid-structure%20interaction" title=" fluid-structure interaction"> fluid-structure interaction</a>, <a href="https://publications.waset.org/abstracts/search?q=Galerk%20infinite%20element%20method" title=" Galerk infinite element method"> Galerk infinite element method</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20method" title=" finite difference method"> finite difference method</a> </p> <a href="https://publications.waset.org/abstracts/14356/analysis-of-a-self-acting-air-journal-bearing-effect-of-dynamic-deformation-of-bump-foil" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/14356.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">392</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">3343</span> New Insight into Fluid Mechanics of Lorenz Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yu-Kai%20Ting">Yu-Kai Ting</a>, <a href="https://publications.waset.org/abstracts/search?q=Jia-Ying%20Tu"> Jia-Ying Tu</a>, <a href="https://publications.waset.org/abstracts/search?q=Chung-Chun%20Hsiao"> Chung-Chun Hsiao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> New physical insights into the nonlinear Lorenz equations related to flow resistance is discussed in this work. The chaotic dynamics related to Lorenz equations has been studied in many papers, which is due to the sensitivity of Lorenz equations to initial conditions and parameter uncertainties. However, the physical implication arising from Lorenz equations about convectional motion attracts little attention in the relevant literature. Therefore, as a first step to understand the related fluid mechanics of convectional motion, this paper derives the Lorenz equations again with different forced conditions in the model. Simulation work of the modified Lorenz equations without the viscosity or buoyancy force is discussed. The time-domain simulation results may imply that the states of the Lorenz equations are related to certain flow speed and flow resistance. The flow speed of the underlying fluid system increases as the flow resistance reduces. This observation would be helpful to analyze the coupling effects of different fluid parameters in a convectional model in future work. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Galerkin%20method" title="Galerkin method">Galerkin method</a>, <a href="https://publications.waset.org/abstracts/search?q=Lorenz%20equations" title=" Lorenz equations"> Lorenz equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Navier-Stokes%20equations" title=" Navier-Stokes equations"> Navier-Stokes equations</a>, <a href="https://publications.waset.org/abstracts/search?q=convectional%20motion" title=" convectional motion"> convectional motion</a> </p> <a href="https://publications.waset.org/abstracts/21427/new-insight-into-fluid-mechanics-of-lorenz-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/21427.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">393</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">3342</span> Response of Pavement under Temperature and Vehicle Coupled Loading</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yang%20Zhong">Yang Zhong</a>, <a href="https://publications.waset.org/abstracts/search?q=Mei-Jie%20Xu"> Mei-Jie Xu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> To study the dynamic mechanics response of asphalt pavement under the temperature load and vehicle loading, asphalt pavement was regarded as multilayered elastic half-space system, and theory analysis was conducted by regarding dynamic modulus of asphalt mixture as the parameter. Firstly, based on the dynamic modulus test of asphalt mixture, function relationship between the dynamic modulus of representative asphalt mixture and temperature was obtained. In addition, the analytical solution for thermal stress in the single layer was derived by using Laplace integral transformation and Hankel integral transformation respectively by using thermal equations of equilibrium. The analytical solution of calculation model of thermal stress in asphalt pavement was derived by transfer matrix of thermal stress in multilayer elastic system. Finally, the variation of thermal stress in pavement structure was analyzed. The result shows that there is an obvious difference between the thermal stress based on dynamic modulus and the solution based on static modulus. Therefore, the dynamic change of parameter in asphalt mixture should be taken into consideration when the theoretical analysis is taken out. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asphalt%20pavement" title="asphalt pavement">asphalt pavement</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamic%20modulus" title=" dynamic modulus"> dynamic modulus</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20transformation" title=" integral transformation"> integral transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=transfer%20matrix" title=" transfer matrix"> transfer matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=thermal%20stress" title=" thermal stress"> thermal stress</a> </p> <a href="https://publications.waset.org/abstracts/31808/response-of-pavement-under-temperature-and-vehicle-coupled-loading" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/31808.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">502</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">3341</span> Online Estimation of Clutch Drag Torque in Wet Dual Clutch Transmission Based on Recursive Least Squares</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hongkui%20Li">Hongkui Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Tongli%20Lu"> Tongli Lu </a>, <a href="https://publications.waset.org/abstracts/search?q=Jianwu%20Zhang"> Jianwu Zhang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper focuses on developing an estimation method of clutch drag torque in wet DCT. The modelling of clutch drag torque is investigated. As the main factor affecting the clutch drag torque, dynamic viscosity of oil is discussed. The paper proposes an estimation method of clutch drag torque based on recursive least squares by utilizing the dynamic equations of gear shifting synchronization process. The results demonstrate that the estimation method has good accuracy and efficiency. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=clutch%20drag%20torque" title="clutch drag torque">clutch drag torque</a>, <a href="https://publications.waset.org/abstracts/search?q=wet%20DCT" title=" wet DCT"> wet DCT</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamic%20viscosity" title=" dynamic viscosity"> dynamic viscosity</a>, <a href="https://publications.waset.org/abstracts/search?q=recursive%20least%20squares" title=" recursive least squares"> recursive least squares</a> </p> <a href="https://publications.waset.org/abstracts/51881/online-estimation-of-clutch-drag-torque-in-wet-dual-clutch-transmission-based-on-recursive-least-squares" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/51881.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">3340</span> Study on The Pile Height Loss of Tunisian Handmade Carpets Under Dynamic Loading</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fatma%20Abidi">Fatma Abidi</a>, <a href="https://publications.waset.org/abstracts/search?q=Taoufik%20Harizi"> Taoufik Harizi</a>, <a href="https://publications.waset.org/abstracts/search?q=Slah%20Msahli"> Slah Msahli</a>, <a href="https://publications.waset.org/abstracts/search?q=Faouzi%20Sakli"> Faouzi Sakli</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Nine different Tunisian handmade carpets were used for the investigation. The raw material of the carpet pile yarns was wool. The influence of the different structure parameters (linear density and pile height) on the carpet compression was investigated. Carpets were tested under dynamic loading in order to evaluate and observe the thickness loss and carpet behavior under dynamic loads. To determine the loss of pile height under dynamic loading, the pile height carpets were measured. The test method was treated according to the Tunisian standard NT 12.165 (corresponds to the standard ISO 2094). The pile height measurements are taken and recorded at intervals up to 1000 impacts (measures of this study were made after 50, 100, 200, 500, and 1000 impacts). The loss of pile height is calculated using the variation between the initial height and those measured after the number of reported impacts. The experimental results were statistically evaluated using Design Expert Analysis of Variance (ANOVA) software. As regards the deformation, results showed that both of the structure parameters of the pile yarn and the pile height have an influence. The carpet with the higher pile and the less linear density of pile yarn showed the worst performance. Results of a polynomial regression analysis are highlighted. There is a good correlation between the loss of pile height and the impacts number of dynamic loads. These equations are in good agreement with measured data. Because the prediction is reasonably accurate for all samples, these equations can also be taken into account when calculating the theoretical loss of pile height for the considered carpet samples. Statistical evaluations of the experimen¬tal data showed that the pile material and number of impacts have a significant effect on mean thickness and thickness loss variations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tunisian%20handmade%20carpet" title="Tunisian handmade carpet">Tunisian handmade carpet</a>, <a href="https://publications.waset.org/abstracts/search?q=loss%20of%20pile%20height" title=" loss of pile height"> loss of pile height</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamic%20loads" title=" dynamic loads"> dynamic loads</a>, <a href="https://publications.waset.org/abstracts/search?q=performance" title=" performance"> performance</a> </p> <a href="https://publications.waset.org/abstracts/51785/study-on-the-pile-height-loss-of-tunisian-handmade-carpets-under-dynamic-loading" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/51785.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">321</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">3339</span> On the Relation between λ-Symmetries and μ-Symmetries of Partial Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Teoman%20Ozer">Teoman Ozer</a>, <a href="https://publications.waset.org/abstracts/search?q=Ozlem%20Orhan"> Ozlem Orhan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study deals with symmetry group properties and conservation laws of partial differential equations. We give a geometrical interpretation of notion of μ-prolongations of vector fields and of the related concept of μ-symmetry for partial differential equations. We show that these are in providing symmetry reduction of partial differential equations and systems and invariant solutions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=%CE%BB-symmetry" title="λ-symmetry">λ-symmetry</a>, <a href="https://publications.waset.org/abstracts/search?q=%CE%BC-symmetry" title=" μ-symmetry"> μ-symmetry</a>, <a href="https://publications.waset.org/abstracts/search?q=classification" title=" classification"> classification</a>, <a href="https://publications.waset.org/abstracts/search?q=invariant%20solution" title=" invariant solution"> invariant solution</a> </p> <a href="https://publications.waset.org/abstracts/59662/on-the-relation-between-l-symmetries-and-m-symmetries-of-partial-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59662.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">319</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">3338</span> Reduced Differential Transform Methods for Solving the Fractional Diffusion Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yildiray%20Keskin">Yildiray Keskin</a>, <a href="https://publications.waset.org/abstracts/search?q=Omer%20Acan"> Omer Acan</a>, <a href="https://publications.waset.org/abstracts/search?q=Murat%20Akkus"> Murat Akkus</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20diffusion%20equations" title="fractional diffusion equations">fractional diffusion equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Caputo%20fractional%20derivative" title=" Caputo fractional derivative"> Caputo fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=reduced%20differential%20transform%20method" title=" reduced differential transform method"> reduced differential transform method</a>, <a href="https://publications.waset.org/abstracts/search?q=partial" title=" partial"> partial</a> </p> <a href="https://publications.waset.org/abstracts/17526/reduced-differential-transform-methods-for-solving-the-fractional-diffusion-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17526.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">525</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">3337</span> Effect of Thickness and Solidity on the Performance of Straight Type Vertical Axis Wind Turbine</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jianyang%20Zhu">Jianyang Zhu</a>, <a href="https://publications.waset.org/abstracts/search?q=Lin%20Jiang"> Lin Jiang</a>, <a href="https://publications.waset.org/abstracts/search?q=Tixian%20Tian"> Tixian Tian</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Inspired by the increasing interesting on the wind power associated with production of clear electric power, a numerical experiment is applied to investigate the aerodynamic performance of straight type vertical axis wind turbine with different thickness and solidity, where the incompressible Navier-Stokes (N-S) equations coupled with dynamic mesh technique is solved. By analyzing the flow field, as well as energy coefficient of different thickness and solidity turbine, it is found that the thickness and solidity can significantly influence the performance of vertical axis wind turbine. For the turbine under low tip speed, the mean energy coefficient increase with the increasing of thickness and solidity, which may improve the self starting performance of the turbine. However for the turbine under high tip speed, the appropriate thickness and smaller solidity turbine possesses better performance. In addition, delay stall and no interaction of the blade and previous separated vortex are observed around appropriate thickness and solidity turbine, therefore lead better performance characteristics. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=vertical%20axis%20wind%20turbine" title="vertical axis wind turbine">vertical axis wind turbine</a>, <a href="https://publications.waset.org/abstracts/search?q=N-S%20equations" title=" N-S equations"> N-S equations</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamic%20mesh%20technique" title=" dynamic mesh technique"> dynamic mesh technique</a>, <a href="https://publications.waset.org/abstracts/search?q=thickness" title=" thickness"> thickness</a>, <a href="https://publications.waset.org/abstracts/search?q=solidity" title=" solidity"> solidity</a> </p> <a href="https://publications.waset.org/abstracts/54216/effect-of-thickness-and-solidity-on-the-performance-of-straight-type-vertical-axis-wind-turbine" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/54216.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">265</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">3336</span> Linear Dynamic Stability Analysis of a Continuous Rotor-Disk-Blades System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=F.%20Rahimi%20Dehgolan">F. Rahimi Dehgolan</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20E.%20Khadem"> S. E. Khadem</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Bab"> S. Bab</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Najafee"> M. Najafee</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Nowadays, using rotating systems like shafts and disks in industrial machines have been increased constantly. Dynamic stability is one of the most important factors in designing rotating systems. In this study, linear frequencies and stability of a coupled continuous flexible rotor-disk-blades system are studied. The Euler-Bernoulli beam theory is utilized to model the blade and shaft. The equations of motion are extracted using the extended Hamilton principle. The equations of motion have been simplified using the Coleman and complex transformations method. The natural frequencies of the linear part of the system are extracted, and the effects of various system parameters on the natural frequencies and decay rates (stability condition) are clarified. It can be seen that the centrifugal stiffening effect applied to the blades is the most important parameter for stability of the considered rotating system. This result highlights the importance of considering this stiffing effect in blades equation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=rotating%20shaft" title="rotating shaft">rotating shaft</a>, <a href="https://publications.waset.org/abstracts/search?q=flexible%20blades" title=" flexible blades"> flexible blades</a>, <a href="https://publications.waset.org/abstracts/search?q=centrifugal%20stiffness" title=" centrifugal stiffness"> centrifugal stiffness</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a> </p> <a href="https://publications.waset.org/abstracts/56540/linear-dynamic-stability-analysis-of-a-continuous-rotor-disk-blades-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56540.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">265</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">3335</span> Research of Amplitude-Frequency Characteristics of Nonlinear Oscillations of the Interface of Two-Layered Liquid</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Win%20Ko%20Ko">Win Ko Ko</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20N.%20Temnov"> A. N. Temnov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The problem of nonlinear oscillations of a two-layer liquid completely filling a limited volume is considered. Using two basic asymmetric harmonics excited in two mutually perpendicular planes, ordinary differential equations of nonlinear oscillations of the interface of a two-layer liquid are investigated. In this paper, hydrodynamic coefficients of linear and nonlinear problems in integral relations were determined. As a result, the instability regions of forced oscillations of a two-layered liquid in a cylindrical tank occurring in the plane of action of the disturbing force are constructed, as well as the dynamic instability regions of the parametric resonance for different ratios of densities of the upper and lower liquids depending on the amplitudes of liquids from the excitations frequencies. Steady-state regimes of fluid motion were found in the regions of dynamic instability of the initial oscillation form. The Bubnov-Galerkin method is used to construct instability regions for approximate solution of nonlinear differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20oscillations" title="nonlinear oscillations">nonlinear oscillations</a>, <a href="https://publications.waset.org/abstracts/search?q=two-layered%20liquid" title=" two-layered liquid"> two-layered liquid</a>, <a href="https://publications.waset.org/abstracts/search?q=instability%20region" title=" instability region"> instability region</a>, <a href="https://publications.waset.org/abstracts/search?q=hydrodynamic%20coefficients" title=" hydrodynamic coefficients"> hydrodynamic coefficients</a>, <a href="https://publications.waset.org/abstracts/search?q=resonance%20frequency" title=" resonance frequency"> resonance frequency</a> </p> <a href="https://publications.waset.org/abstracts/115967/research-of-amplitude-frequency-characteristics-of-nonlinear-oscillations-of-the-interface-of-two-layered-liquid" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/115967.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">219</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">3334</span> Solutions of Fractional Reaction-Diffusion Equations Used to Model the Growth and Spreading of Biological Species</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kamel%20Al-Khaled">Kamel Al-Khaled</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Reaction-diffusion equations are commonly used in population biology to model the spread of biological species. In this paper, we propose a fractional reaction-diffusion equation, where the classical second derivative diffusion term is replaced by a fractional derivative of order less than two. Based on the symbolic computation system Mathematica, Adomian decomposition method, developed for fractional differential equations, is directly extended to derive explicit and numerical solutions of space fractional reaction-diffusion equations. The fractional derivative is described in the Caputo sense. Finally, the recent appearance of fractional reaction-diffusion equations as models in some ﬁelds such as cell biology, chemistry, physics, and ﬁnance, makes it necessary to apply the results reported here to some numerical examples. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20partial%20differential%20equations" title="fractional partial differential equations">fractional partial differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=reaction-di%EF%AC%80usion%20equations" title=" reaction-diﬀusion equations"> reaction-diﬀusion equations</a>, <a href="https://publications.waset.org/abstracts/search?q=adomian%20decomposition" title=" adomian decomposition"> adomian decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=biological%20species" title=" biological species"> biological species</a> </p> <a href="https://publications.waset.org/abstracts/55994/solutions-of-fractional-reaction-diffusion-equations-used-to-model-the-growth-and-spreading-of-biological-species" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/55994.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">375</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">3333</span> Dynamic Analysis of Composite Doubly Curved Panels with Variable Thickness</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=I.%20Algul">I. Algul</a>, <a href="https://publications.waset.org/abstracts/search?q=G.%20Akgun"> G. Akgun</a>, <a href="https://publications.waset.org/abstracts/search?q=H.%20Kurtaran"> H. Kurtaran</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Dynamic analysis of composite doubly curved panels with variable thickness subjected to different pulse types using Generalized Differential Quadrature method (GDQ) is presented in this study. Panels with variable thickness are used in the construction of aerospace and marine industry. Giving variable thickness to panels can allow the designer to get optimum structural efficiency. For this reason, estimating the response of variable thickness panels is very important to design more reliable structures under dynamic loads. Dynamic equations for composite panels with variable thickness are obtained using virtual work principle. Partial derivatives in the equation of motion are expressed with GDQ and Newmark average acceleration scheme is used for temporal discretization. Several examples are used to highlight the effectiveness of the proposed method. Results are compared with finite element method. Effects of taper ratios, boundary conditions and loading type on the response of composite panel are investigated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=differential%20quadrature%20method" title="differential quadrature method">differential quadrature method</a>, <a href="https://publications.waset.org/abstracts/search?q=doubly%20curved%20panels" title=" doubly curved panels"> doubly curved panels</a>, <a href="https://publications.waset.org/abstracts/search?q=laminated%20composite%20materials" title=" laminated composite materials"> laminated composite materials</a>, <a href="https://publications.waset.org/abstracts/search?q=small%20displacement" title=" small displacement"> small displacement</a> </p> <a href="https://publications.waset.org/abstracts/74965/dynamic-analysis-of-composite-doubly-curved-panels-with-variable-thickness" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/74965.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">360</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">3332</span> Dynamic Shock Bank Liquidity Analysis</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=C.%20Recommand%C3%A9">C. Recommandé</a>, <a href="https://publications.waset.org/abstracts/search?q=J.%20C.%20Blind"> J. C. Blind</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Clavel"> A. Clavel</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20Gourichon"> R. Gourichon</a>, <a href="https://publications.waset.org/abstracts/search?q=V.%20Le%20Gal"> V. Le Gal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Simulations are developed in this paper with usual DSGE model equations. The model is based on simplified version of Smets-Wouters equations in use at European Central Bank which implies 10 macro-economic variables: consumption, investment, wages, inflation, capital stock, interest rates, production, capital accumulation, labour and credit rate, and allows take into consideration the banking system. Throughout the simulations, this model will be used to evaluate the impact of rate shocks recounting the actions of the European Central Bank during 2008. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=CC-LM" title="CC-LM">CC-LM</a>, <a href="https://publications.waset.org/abstracts/search?q=Central%20Bank" title=" Central Bank"> Central Bank</a>, <a href="https://publications.waset.org/abstracts/search?q=DSGE" title=" DSGE"> DSGE</a>, <a href="https://publications.waset.org/abstracts/search?q=liquidity%20shock" title=" liquidity shock"> liquidity shock</a>, <a href="https://publications.waset.org/abstracts/search?q=non-standard%20intervention" title=" non-standard intervention"> non-standard intervention</a> </p> <a href="https://publications.waset.org/abstracts/15074/dynamic-shock-bank-liquidity-analysis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15074.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">458</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">3331</span> Effect of Design Parameters on Porpoising Instability of a High Speed Planing Craft</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lokeswara%20Rao%20P.">Lokeswara Rao P.</a>, <a href="https://publications.waset.org/abstracts/search?q=Naga%20Venkata%20Rakesh%20N."> Naga Venkata Rakesh N.</a>, <a href="https://publications.waset.org/abstracts/search?q=V.%20Anantha%20Subramanian"> V. Anantha Subramanian</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It is important to estimate, predict, and avoid the dynamic instability of high speed planing crafts. It is known that design parameters like relative location of center of gravity with respect to the dynamic lift centre and length to beam ratio of the craft have influence on the tendency to porpoise. This paper analyzes the hydrodynamic performance on the basis of the semi-empirical Savitsky method and also estimates the same by numerical simulations based on Reynolds Averaged Navier Stokes (RANS) equations using a commercial code namely, STAR- CCM+. The paper examines through the same numerical simulation considering dynamic equilibrium, the changing running trim, which results in porpoising. Some interesting results emerge from the study and this leads to early detection of the instability. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=CFD" title="CFD">CFD</a>, <a href="https://publications.waset.org/abstracts/search?q=planing%20hull" title=" planing hull"> planing hull</a>, <a href="https://publications.waset.org/abstracts/search?q=porpoising" title=" porpoising"> porpoising</a>, <a href="https://publications.waset.org/abstracts/search?q=Savitsky%20method" title=" Savitsky method"> Savitsky method</a> </p> <a href="https://publications.waset.org/abstracts/97595/effect-of-design-parameters-on-porpoising-instability-of-a-high-speed-planing-craft" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/97595.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">180</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">3330</span> Representation of the Solution of One Dynamical System on the Plane</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kushakov%20Kholmurodjon">Kushakov Kholmurodjon</a>, <a href="https://publications.waset.org/abstracts/search?q=Muhammadjonov%20Akbarshox"> Muhammadjonov Akbarshox</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This present paper is devoted to a system of second-order nonlinear differential equations with a special right-hand side, exactly, the linear part and a third-order polynomial of a special form. It is shown that for some relations between the parameters, there is a second-order curve in which trajectories leaving the points of this curve remain in the same place. Thus, the curve is invariant with respect to the given system. Moreover, this system is invariant under a non-degenerate linear transformation of variables. The form of this curve, depending on the relations between the parameters and the eigenvalues of the matrix, is proved. All solutions of this system of differential equations are shown analytically. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamic%20system" title="dynamic system">dynamic system</a>, <a href="https://publications.waset.org/abstracts/search?q=ellipse" title=" ellipse"> ellipse</a>, <a href="https://publications.waset.org/abstracts/search?q=hyperbola" title=" hyperbola"> hyperbola</a>, <a href="https://publications.waset.org/abstracts/search?q=Hess%20system" title=" Hess system"> Hess system</a>, <a href="https://publications.waset.org/abstracts/search?q=polar%20coordinate%20system" title=" polar coordinate system"> polar coordinate system</a> </p> <a href="https://publications.waset.org/abstracts/140142/representation-of-the-solution-of-one-dynamical-system-on-the-plane" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/140142.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">193</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">3329</span> Numerical Solution for Integro-Differential Equations by Using Quartic B-Spline Wavelet and Operational Matrices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Khosrow%20Maleknejad">Khosrow Maleknejad</a>, <a href="https://publications.waset.org/abstracts/search?q=Yaser%20Rostami"> Yaser Rostami</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=%C4%B1ntegro-differential%20equations" title="ıntegro-differential equations">ıntegro-differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=quartic%20B-spline%20wavelet" title=" quartic B-spline wavelet"> quartic B-spline wavelet</a>, <a href="https://publications.waset.org/abstracts/search?q=operational%20matrices" title=" operational matrices"> operational matrices</a>, <a href="https://publications.waset.org/abstracts/search?q=dual%20functions" title=" dual functions"> dual functions</a> </p> <a href="https://publications.waset.org/abstracts/5002/numerical-solution-for-integro-differential-equations-by-using-quartic-b-spline-wavelet-and-operational-matrices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/5002.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">456</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">3328</span> Application of the Piloting Law Based on Adaptive Differentiators via Second Order Sliding Mode for a Fixed Wing Aircraft </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zaouche%20Mohammed">Zaouche Mohammed</a>, <a href="https://publications.waset.org/abstracts/search?q=Amini%20Mohammed"> Amini Mohammed</a>, <a href="https://publications.waset.org/abstracts/search?q=Foughali%20Khaled"> Foughali Khaled</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamissi%20Aicha"> Hamissi Aicha</a>, <a href="https://publications.waset.org/abstracts/search?q=Aktouf%20Mohand%20Arezki"> Aktouf Mohand Arezki</a>, <a href="https://publications.waset.org/abstracts/search?q=Boureghda%20Ilyes"> Boureghda Ilyes</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we present a piloting law based on the adaptive differentiators via high order sliding mode controller, by using an aircraft in virtual simulated environment. To deal with the design of an autopilot controller, we propose a framework based on Software in the Loop (SIL) methodology and we use Microsoft<sup>TM</sup> Flight Simulator (FS-2004) as the environment for plane simulation. The aircraft dynamic model is nonlinear, Multi-Input Multi-Output (MIMO) and tightly coupled. The nonlinearity resides in the dynamic equations and also in the aerodynamic coefficients' variability. In our case, two (02) aircrafts are used in the flight tests, the Zlin-142 and MQ-1 Predator. For both aircrafts and in a very low altitude flight, we send the piloting control inputs to the aircraft which has stalled due to a command disconnection. Then, we present the aircraft’s dynamic behavior analysis while reestablishing the command transmission. Finally, a comparative study between the two aircraft’s dynamic behaviors is presented. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adaptive%20differentiators" title="adaptive differentiators">adaptive differentiators</a>, <a href="https://publications.waset.org/abstracts/search?q=second%20order%20sliding%20modes" title=" second order sliding modes"> second order sliding modes</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamic%20adaptation%20of%20the%20gains" title=" dynamic adaptation of the gains"> dynamic adaptation of the gains</a>, <a href="https://publications.waset.org/abstracts/search?q=microsoft%20flight%20simulator" title=" microsoft flight simulator"> microsoft flight simulator</a>, <a href="https://publications.waset.org/abstracts/search?q=Zlin-142" title=" Zlin-142"> Zlin-142</a>, <a href="https://publications.waset.org/abstracts/search?q=MQ-1%20predator" title=" MQ-1 predator"> MQ-1 predator</a> </p> <a href="https://publications.waset.org/abstracts/44435/application-of-the-piloting-law-based-on-adaptive-differentiators-via-second-order-sliding-mode-for-a-fixed-wing-aircraft" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/44435.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">423</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=dynamic%20equations&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=dynamic%20equations&page=3">3</a></li> <li class="page-item"><a class="page-link" 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