Search results for: nonlinear Takagi’s equations

Authors: S. Srednyak

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We study a class of functional partial differential equations(FPDEs). This class is suggested by Quantum Field Theory. We derive general properties of solutions to such equations. In particular, we demonstrate that they lead to systems of coupled integral equations with singular kernels. We show that solutions to such hierarchies can be sought among functions with regular singularities at a countable set of subvarieties of the physical space. We also develop a formal analogy of basic constructions of differential geometry on functional manifolds, as this is necessary for in depth study of FPDEs. We also consider the case of linear overdetermined systems of functional differential equations and show that it can be completely solved in terms of formal solutions of a functional equation that is a functional analogy of a system of determined algebraic equations. This development leads us to formally define the functional analogy of algebraic geometry, which we call functional algebraic geometry. We study basic properties of functional algebraic varieties. In particular, we investigate the case of a formally discrete set of solutions. We also define and study functional analogy of discriminants. In the case of fully determined systems such that the defining functionals have regular singularities, we demonstrate that formal solutions can be sought in the class of functions with regular singularities. This case provides a practical way to apply our results to physics problems.

Keywords: functional equations, quantum field theory, holomorphic functions, Yang Mills mass gap problem, quantum chaos

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Authors: Y. Pala, M. O. Ertas

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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.

Keywords: Riccati equation, analytical solution, proper solution, nonlinear

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Authors: Evln Ranga Charyulu, S. P. Venu Madhavarao, S. Udaya kumar, S. V. S. S. N. V. G. Krishna Murthy

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With the advent of new nanometer process technologies, it is possible to integrate billion transistors on a single substrate. When more and more functionality included there is the possibility of multi-million transistors switching simultaneously consuming more power and dissipating more power along with more leakage of current into the substrate of porous silicon or germanium material. These results in substrate heating and thermal noise generation coupled to signals of interest. The heating process is represented by coupled nonlinear partial differential equations in porous silicon and germanium. By identifying heat sources and heat fluxes may results in designing of ultra-low power circuits. The PDEs are solved by finite difference scheme assuming that boundary layer equations in porous silicon and germanium. Local heat fluxes along the vertical isothermal surface immersed in porous SI/Ge are considered. The parameters considered for optimization are thermal diffusivity, thermal expansion coefficient, thermal diffusion ratio, permeability, specific heat at constant temperatures, Rayleigh number, amplitude of wavy surface, mass expansion coefficient. The diffusion of heat was caused by the concentration gradient. Thermal physical properties are homogeneous and isotropic. By using L8, TAGUCHI method the parameters are optimized.

Keywords: heat transfer, pde, taguchi optimization, SI/Ge

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Authors: Haniye Dehestani, Yadollah Ordokhani

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In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.

Keywords: collocation method, fractional partial differential equations, legendre-laguerre functions, pseudo-operational matrix of integration

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Authors: Hossein Kabir, Mojtaba Sadeghi

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Finding the linear and nonlinear responses of a typical single-degree-of-freedom system (SDOF) is always being regarded as a time-consuming process. This study attempts to provide modifications in the renowned Newmark method in order to make it more time efficient than it used to be and make it more accurate by modifying the system in its own non-linear state. The efficacy of the presented method is demonstrated by assigning three base excitations such as Tabas 1978, El Centro 1940, and MEXICO CITY/SCT 1985 earthquakes to a SDOF system, that is, SDOF, to compute the strength reduction factor, yield pseudo acceleration, and ductility factor.

Keywords: single-degree-of-freedom system (SDOF), linear acceleration method, nonlinear excited system, equivalent displacement method, equivalent energy method

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Authors: Hyun-Woo Cho

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Unexpected events may occur with serious impacts on industrial process. This work utilizes a data representation technique to model and to analyze process data pattern for the purpose of diagnosis. In this work, the use of triangular representation of process data is evaluated using simulation process. Furthermore, the effect of using different pre-treatment techniques based on such as linear or nonlinear reduced spaces was compared. This work extracted the fault pattern in the reduced space, not in the original data space. The results have shown that the non-linear technique based diagnosis method produced more reliable results and outperforms linear method.

Keywords: process monitoring, data analysis, pattern modeling, fault, nonlinear techniques

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Authors: Daniil Karzanov

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This paper studies the effect of quarterly earnings reports on the stock price. The profitability of the stock is modeled by geometric Brownian diffusion and the Constant Elasticity of Variance model. We fit several variations of stochastic differential equations to the pre-and after-report period using the Maximum Likelihood Estimation and Grid Search of parameters method. By examining the change in the model parameters after reports’ publication, the study reveals that the reports have enough evidence to be a structural breakpoint, meaning that all the forecast models exploited are not applicable for forecasting and should be refitted shortly.

Keywords: stock market, earnings reports, financial time series, structural breaks, stochastic differential equations

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Authors: Reza Soleimanpour, Ching Tai Ng

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Fibre-composites are widely used in various structures due to their attractive properties such as higher stiffness to mass ratio and better corrosion resistance compared to metallic materials. However, one serious weakness of this composite material is delamination, which is a subsurface separation of laminae. A low level of this barely visible damage can cause a significant reduction in residual compressive strength. In the last decade, the application of guided waves for damage detection has been a topic of significant interest for many researches. Among all guided wave techniques, nonlinear guided wave has shown outstanding sensitivity and capability for detecting different types of damages, e.g. cracks and delaminations. So far, most of researches on applications of nonlinear guided wave have been dedicated to isotropic material, such as aluminium and steel, while only a few works have been done on applications of nonlinear characteristics of guided waves in anisotropic materials. This study investigates the nonlinear interactions of the fundamental antisymmetric lamb wave (A0) with delamination in composite laminates using three-dimensional (3D) explicit finite element (FE) simulations. The nonlinearity considered in this study arises from interactions of two interfaces of sub-laminates at the delamination region, which generates contact acoustic nonlinearity (CAN). The aim of this research is to investigate the phenomena of CAN in composite laminated beams by a series of numerical case studies. In this study interaction of fundamental antisymmetric lamb wave with delamination of different sizes are studied in detail. The results show that the A0 lamb wave interacts with the delaminations generating CAN in the form of higher harmonics, which is a good indicator for determining the existence of delaminations in composite laminates.

Keywords: contact acoustic nonlinearity, delamination, fibre reinforced composite beam, finite element, nonlinear guided waves

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Authors: N. Manoj

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The aeroelastic behavior of engine nacelle strake when subjected to unsteady aerodynamic flows is investigated in this paper. Geometric nonlinear characteristics and modal parameters of nacelle strake are studied when it is under dynamic loading condition. Here, an N-S based Finite Volume solver is coupled with Finite Element (FE) based nonlinear structural solver to investigate the nonlinear characteristics of nacelle strake over a range of dynamic pressures at various phases of flight like takeoff, climb, and cruise conditions. The combination of high fidelity models for both aerodynamics and structural dynamics is used to predict the nonlinearities of strake (chine). The methodology adopted for present aeroelastic analysis is partitioned-based time domain coupled CFD and CSD solvers and it is validated by the consideration of experimental and numerical comparison of aeroelastic data for a cropped delta wing model which has a proven record. The present strake geometry is derived from theoretical formulation. The amplitude and frequency obtained from the coupled solver at various dynamic pressures is discussed, which gives a better understanding of its impact on aerodynamic design-sizing of strake.

Keywords: aeroelasticity, finite volume, geometric nonlinearity, limit cycle oscillations, strake

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Authors: Maor Farid, Oleg Gendelman

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Equivalent mechanical model of liquid sloshing in partially-filled cylindrical vessel is treated in the cases of free oscillations and of horizontal base excitation. The model is designed to cover both the linear and essentially nonlinear sloshing regimes. The latter fluid behaviour might involve hydraulic impacts interacting with the inner walls of the tank. These impulsive interactions are often modeled by high-power potential and dissipation functions. For the sake of analytical description, we use the traditional approach by modeling the impacts with velocity-dependent restitution coefficient. This modelling is similar to vibro-impact nonlinear energy sink (VI NES) which was recently explored for its vibration mitigation performances and nonlinear response regimes. Steady-state periodic regimes and chaotic strongly modulated responses (CSMR) are detected. Those dynamical regimes were described by the system's slow motion on the slow invariant manifold (SIM). There is a good agreement between the analytical results and numerical simulations. Subsequently, Finite-Element (FE) method is used to determine and verify the model parameters and to identify dominant dynamical regimes, natural modes and frequencies. The tank failure modes are identified and critical locations are identified. Mathematical relation is found between degrees-of-freedom (DOFs) motion and the mechanical stress applied in the tank critical section. This is the prior attempt to take under consideration large-amplitude nonlinear sloshing and tank structure elasticity effects for design, regulation definition and resistance analysis purposes. Both linear (tuned mass damper, TMD) and nonlinear (nonlinear energy sink, NES) passive energy absorbers contribution to the overall system mitigation is firstly examined, in terms of both stress reduction and time for vibration decay.

Keywords: nonlinear energy sink (NES), reduced-order modelling, liquid sloshing, vibration mitigation, vibro-impact dynamics

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Authors: P. G. Siddheshwar, R. K. Vanishree, C. Kanchana

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A local nonlinear stability analysis using a eight-mode expansion is performed in arriving at the coupled amplitude equations for Rayleigh-Bénard-Brinkman convection (RBBC) in the presence of LTNE effects. Streamlines and isotherms are obtained in the two-dimensional unsteady finite-amplitude convection regime. The parameters’ influence on heat transport is found to be more pronounced at small time than at long times. Results of the Rayleigh-Bénard convection is obtained as a particular case of the present study. Additional modes are shown not to significantly influence the heat transport thus leading us to infer that five minimal modes are sufficient to make a study of RBBC. The present problem that uses rolls as a pattern of manifestation of instability is a needed first step in the direction of making a very general non-local study of two-dimensional unsteady convection. The results may be useful in determining the preferred range of parameters’ values while making rheometric measurements in fluids to ascertain fluid properties such as viscosity. The results of LTE are obtained as a limiting case of the results of LTNE obtained in the paper.

Keywords: coupled Ginzburg–Landau model, local thermal non-equilibrium (LTNE), local thermal equilibrium (LTE), Rayleigh–Bénard-Brinkman convection

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Authors: Kazuhisa Takagi

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This paper is about movies and dynamic objects for mobile phones. Dynamic objects are the software programmed by JavaScript. They consist of geometric figures and work on HTML5-compliant browsers. Mobile phones are very popular among teenagers. They like watching movies and playing games on them. So, mathematics movies and dynamic objects would enhance teaching and learning processes. In the movies, manga characters speak with artificially synchronized voices. They teach trigonometry together with dynamic mathematical objects. Many movies are created. They are Windows Media files or MP4 movies. These movies and dynamic objects are not only used in the classroom but also distributed to students. By watching movies, students can study trigonometry before or after class.

Keywords: dynamic mathematical object, javascript, google drive, transfer jet

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Authors: Ilya Simanovskii

Abstract:

Nonlinear convective flows developed under the joint action of buoyant and thermo-capillary effects in a two-layer system with periodic boundary conditions on the lateral walls have been investigated. The influence of an interfacial heat release on oscillatory regimes has been studied. The computational regions with different lengths have been considered. It is shown that the development of oscillatory instability can lead to the appearance of different no steady flows.

Keywords: interface, instabilities, two-layer systems, bioinformatics, biomedicine

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Authors: Ahmad Forouzantabar, Mohammad Azadi, Alireza Alesaadi

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This paper describes a sliding mode controller for autonomous underwater vehicles (AUVs). The dynamic of AUV model is highly nonlinear because of many factors, such as hydrodynamic drag, damping, and lift forces, Coriolis and centripetal forces, gravity and buoyancy forces, as well as forces from thruster. To address these difficulties, a nonlinear sliding mode controller is designed to approximate the nonlinear dynamics of AUV and improve trajectory tracking. Moreover, the proposed controller can profoundly attenuate the effects of uncertainties and external disturbances in the closed-loop system. Using the Lyapunov theory the boundedness of AUV tracking errors and the stability of the proposed control system are also guaranteed. Numerical simulation studies of an AUV are included to illustrate the effectiveness of the presented approach.

Keywords: lyapunov stability, autonomous underwater vehicle, sliding mode controller, electronics engineering

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Authors: Ramdas Sonawane, Mahaveer Gadiya

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The control problem associated with nuclear dynamics is represented by nonlinear integro-differential equation with additive controls. To control chain reaction, certain amount of neutrons is added into (or withdrawn out of) chamber as and when required. It is not realistic. So, we can think of controlling the reactor dynamics by bilinear control, which enters the system as coefficient of state. In this paper, we study the approximate and exact controllability of parabolic integro-differential equation controlled by bilinear control with non-homogeneous boundary conditions in bounded domain. We prove the existence of control and propose an explicit control strategy.

Keywords: approximate control, exact control, bilinear control, nuclear dynamics, integro-differential equations

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Authors: Subha D. Puthankattil, Paul K. Joseph

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Analyzing brain signals of the patients suffering from the state of depression may lead to interesting observations in the signal parameters that is quite different from a normal control. The present study adopts two different methods: Time frequency domain and nonlinear method for the analysis of EEG signals acquired from depression patients and age and sex matched normal controls. The time frequency domain analysis is realized using wavelet entropy and approximate entropy is employed for the nonlinear method of analysis. The ability of the signal processing technique and the nonlinear method in differentiating the physiological aspects of the brain state are revealed using Wavelet entropy and Approximate entropy.

Keywords: EEG, depression, wavelet entropy, approximate entropy, relative wavelet energy, multiresolution decomposition

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Authors: Anton S. Perin, Vladimir M. Shandarov

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Compensation for the nonlinear diffraction of narrow laser beams with wavelength of 532 and the formation of photonic waveguides and waveguide circuits due to the contribution of pyroelectric effect to the nonlinear response of lithium niobate crystal have been experimentally demonstrated. Complete compensation for the linear and nonlinear diffraction broadening of light beams is obtained upon uniform heating of an undoped sample from room temperature to 55 degrees Celsius. An analysis of the light-field distribution patterns and the corresponding intensity distribution profiles allowed us to estimate the spacing for the channel waveguides. The observed behavior of bright soliton beams may be caused by their coherent interaction, which manifests itself in repulsion for anti-phase light fields and in attraction for in-phase light fields. The experimental results of this study showed a fundamental possibility of forming optically complex waveguide structures in lithium niobate crystals with pyroelectric mechanism of nonlinear response. The topology of these structures is determined by the light field distribution on the input face of crystalline sample. The optical induction of channel waveguide elements by interacting spatial solitons makes it possible to design optical systems with a more complex topology and a possibility of their dynamic reconfiguration.

Keywords: self-action, soliton, lithium niobate, piroliton, photorefractive effect, pyroelectric effect

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Authors: Shilpa Khobragade, Carlos Da Silva Granja, Niklas Sandström, Igor Efimov, Victor P. Ostanin, Wouter van der Wijngaart, David Klenerman, Sourav K. Ghosh

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Rapid, label-free and direct detection of pathogenic bacteria is critical for the prevention of disease outbreaks. This paper for the first time attempts to probe the nonlinear acoustic response of quartz crystal resonator (QCR) functionalized with specific DNA aptamers for direct detection and quantification of viable E. coli KCTC 2571 bacteria. DNA aptamers were immobilized through biotin and streptavidin conjugation, onto the gold surface of QCR to capture the target bacteria and the detection was accomplished by shift in amplitude of the peak 3f signal (3 times the drive frequency) upon binding, when driven near fundamental resonance frequency. The developed nonlinear acoustic aptasensor system demonstrated better reliability than conventional resonance frequency shift and energy dissipation monitoring that were recorded simultaneously. This sensing system could directly detect 10⁽⁵⁾ cells/mL target bacteria within 30 min or less and had high specificity towards E. coli KCTC 2571 bacteria as compared to the same concentration of S.typhi bacteria. Aptasensor response was observed for the bacterial suspensions ranging from 10⁽⁵⁾-10⁽⁸⁾ cells/mL. Conclusively, this nonlinear acoustic aptasensor is simple to use, gives real-time output, cost-effective and has the potential for rapid, specific, label-free direction detection of bacteria.

Keywords: acoustic, aptasensor, detection, nonlinear

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Authors: Jorge Gonzalez Camus, Carlos Lizama

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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.

Keywords: attractive mild solutions, integral Volterra equations, neutral type equations, non-local in time equations

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Authors: X. Li, Y. Liu, H. Wong, B. Pardoen, A. Fabbri, F. McGregor, E. Liu

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The target of this paper is to investigate how saturated poroelastic soils subject to freezing temperatures behave and how different boundary conditions can intervene and affect the thermo-hydro-mechanical (THM) responses, based on a particular but classical configuration of a finite homogeneous soil layer studied by Terzaghi. The essential relations on the constitutive behavior of a freezing soil are firstly recalled: ice crystal - liquid water thermodynamic equilibrium, hydromechanical constitutive equations, momentum balance, water mass balance, and the thermal diffusion equation, in general, non-linear case where material parameters are state-dependent. The system of equations is firstly linearized, assuming all material parameters to be constants, particularly the permeability of liquid water, which should depend on the ice content. Two analytical solutions solved by the classic Laplace transform are then developed, accounting for two different sets of boundary conditions. Afterward, the general non-linear equations with state-dependent parameters are solved using a commercial code COMSOL based on finite elements method to obtain numerical results. The validity of this numerical modeling is partially verified using the analytical solution in the limiting case of state-independent parameters. Comparison between the results given by the linearized analytical solutions and the non-linear numerical model reveals that the above-mentioned linear computation will always underestimate the liquid pore pressure and displacement, whatever the hydraulic boundary conditions are. In the nonlinear model, the faster growth of ice crystals, accompanying the subsequent reduction of permeability of freezing soil layer, makes a longer duration for the depressurization of water liquid and slower settlement in the case where the ground surface is swiftly covered by a thin layer of ice, as well as a bigger global liquid pressure and swelling in the case of the impermeable ground surface. Nonetheless, the analytical solutions based on linearized equations give a correct order-of-magnitude estimate, especially at moderate temperature variations, and remain a useful tool for preliminary design checks.

Keywords: chemical potential, cryosuction, Laplace transform, multiphysics coupling, phase transformation, thermodynamic equilibrium

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Authors: Mohammad Vahedi Torshizi

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In this investigation, at first, bending stress, contact stress, Safety factor of bending and Safety factor of contact between sun gear and planet gear tooth was determined using mathematical equations. Also, The amount of Sun Revolution in, Speed carrier, power Transmitted of the sun, sun torque, sun peripheral speed, Enter the tangential force gears, was calculated using mathematical equations. According to the obtained results, maximum of bending stress and contact stress occurred in three plantary and low status of four plantary. Also, maximum of Speed carrier, sun peripheral speed, Safety factor of bending and Safety factor of contact obtained in four plantary and maximum of power Transmitted of the sun, Enter the tangential force gears, bending stress and contact stress was in three pantry and factors And other factors were equal in the two planets.

Keywords: bending stress, contact stress, plantary, mathematical equations

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Authors: Mustafa Bayram Gücen, Coşkun Yakar

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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability

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Authors: M. A. Anwar, K. Iqbal, M. Razzaq

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Background and Objectives: This numerical study reflects the magnetic field's effect on the reduction of plaque formation due to stenosis in a stenosed bifurcated artery. The entire arterythe wall is assumed as linearly elastic, and blood flow is modeled as a Newtonian, viscous, steady, incompressible, laminar, biomagnetic fluid. Methods: An Arbitrary Lagrangian-Eulerian (ALE) technique is employed to formulate the hemodynamic flow in a bifurcated artery under the effect of the asymmetric magnetic field by two-way Fluid-structure interaction coupling. A stable P2P1 finite element pair is used to discretize thenonlinear system of partial differential equations. The resulting nonlinear system of algebraic equations is solved by the Newton Raphson method. Results: The numerical results for displacement, velocity magnitude, pressure, and wall shear stresses for Reynolds numbers, Re = 500, 1000, 1500, 2000, in the presence of magnetic fields are presented graphically. Conclusions: The numerical results show that the presence of the magnetic field influences the displacement and flows velocity magnitude considerably. The magnetic field reduces the flow separation, recirculation area adjacent to stenosis and gives rise to wall shear stress.

Keywords: bifurcation, elastic walls, finite element, wall shear stress,

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Authors: Engin Metin Kaplan, Kemal Yaman

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In this study, the crash of a medium heavy vehicle onto a designed Road blocker (vehicle barrier) is studied numerically. Structural integrity of the Road blocker is studied by nonlinear dynamic methods under the loading conditions which are defined in the standards. NASTRAN® and LS-DYNA® which are commercial software are used to solve the problem. Outer geometry determination, alignment of the inner part and material properties of the road blocker are studied linearly to yield design parameters. Best design parameters are determined to achieve the most structurally optimized road blocker. Strain and stress values of the vehicle barrier are obtained by solving the partial differential equations.

Keywords: vehicle barrier, truck collision, road blocker, crash analysis

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Authors: Jatupon Em-Udom, Nirand Pisutha-Arnond

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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.

Keywords: driving forces and flux, evolution equation, non equilibrium thermodynamics, Onsager’s reciprocal relation, phase field crystal model, thermodynamics of single-component solid

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Authors: Bakur Gulua

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In this work, we consider some boundary value problems for the plate. The plate is the elastic material with voids. The state of plate equilibrium is described by the system of differential equations that is derived from three-dimensional equations of equilibrium of an elastic material with voids (Cowin-Nunziato model) by Vekua's reduction method. Its general solution is represented by means of analytic functions of a complex variable and solutions of Helmholtz equations. The problem is solved analytically by the method of the theory of functions of a complex variable.

Keywords: the elastic material with voids, boundary value problems, Vekua's reduction method, a complex variable

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Authors: Kazuma Okada, Tomoaki Hashimoto, Hirokazu Tahara

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Recently, the effectiveness of random dither quantization method for linear feedback control systems has been shown in several papers. However, the random dither quantization method has not yet been applied to nonlinear feedback control systems. The objective of this paper is to verify the effectiveness of random dither quantization method for nonlinear feedback control systems. For this purpose, we consider the attitude stabilization problem of satellites using discrete-level actuators. Namely, this paper provides a control method based on the random dither quantization method for stabilizing the attitude of satellites using discrete-level actuators.

Keywords: quantized control, nonlinear systems, random dither quantization

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α.

Keywords: Caputo, fractional calculation, hypergeometric, linear differential equations

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Authors: Keita Iwai, Isao Tomita

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To expand the optical spectrum for use in broadband optical communications, we study the properties of a semiconductor waveguide device with a tapered structure including its third-order optical nonlinearity. Spectral-broadened output by the tapered structure has the potential to create a compact, built-in device for optical communications. Here we deal with a compound semiconductor waveguide, the material of which is the same as that of laser diodes used in the communication systems, i.e., InₓGa₁₋ₓAsᵧP₁₋ᵧ, which has large optical nonlinearity. We confirm that our structure widens the output spectrum sufficiently by controlling its taper form factor while utilizing the large nonlinear refraction of InₓGa₁₋ₓAsᵧP₁₋ᵧ. We also examine the taper effect for nonlinear optical loss.

Keywords: InₓGa₁₋ₓAsᵧP₁₋ᵧ, waveguide, nonlinear refraction, spectral spreading, taper device

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Authors: Areeg Shermaddo

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Solar updraft power plants (SUPP) provide a great potential for green and environmentally friendly renewable power generation. An up to 1000 m high chimney represents one of the major parts of each SUPP, which consist of the main shell structure and the stiffening rings. Including the nonlinear material behavior in a simulation of the chimney is computationally a demanding task. However, allowing the formation of cracking in concrete leads to a more economical design of the structure. In this work, an FE model of a SUPP is presented incorporating the nonlinear material behavior. The effect of wind loading intensity on the structural response is explored. Furthermore, the influence of the stiffness of the ring beams on the global behavior is as well investigated. The obtained results indicate that the minimum reinforcement is capable of carrying the tensile stresses provided that the ring beams are rather stiff.

Keywords: ABAQUS, nonlinear analysis, ring beams, SUPP

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