Search results for: nonlinear excited system

Authors: Ali Raheli, Rahim Habibifar, Behzad Mohammadi-Alasti, Mahdi Abbasgholipour

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This paper presents vibration behavior of a FGM micro-beam and its pull-in instability under a nonlinear electrostatic pressure. An exponential function has been applied to show the continuous gradation of the properties along thickness. Nonlinear integro-differential-electro-mechanical equation based on Euler–Bernoulli beam theory has been derived. The governing equation in the static analysis has been solved using Step-by-Step Linearization Method and Finite Difference Method. Fixed points or equilibrium positions and singular points have been shown in the state control space. In order to find the response to a step DC voltage, the nonlinear equation of motion has been solved using Galerkin-based reduced-order model and time histories and phase portrait for different applied voltages have been shown. The effects of electrostatic pressure on stability of FGM micro-beams having various amounts of the ceramic constituent have been investigated.

Keywords: FGM, MEMS, nonlinear vibration, electrical, dynamic pull-in voltage

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Authors: Hisham M. Soliman, Hassan Yousef

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This manuscript presents new results on design saturated power system stabilizers (PSS) to assign system poles within a desired region for achieving good dynamic performance. The regional pole placement is accomplished against model uncertainties caused by different load conditions. The design is based on a sufficient condition in the form of linear matrix inequalities (LMI) which forces the saturated nonlinear controller to lie within the linear zone. The controller effectiveness is demonstrated on a single machine infinite bus system.

Keywords: power system stabilizer, saturated control, robust control, regional pole placement, linear matrix inequality (LMI)

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Authors: A. Torokhti

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A new method of mathematical modeling of the distributed nonlinear system is developed. The system is represented by a combination of the set of spatially distributed sensors and the fusion center. Its mathematical model is obtained from the iterative procedure that converges to the model which is optimal in the sense of minimizing an associated cost function.

Keywords: mathematical modeling, non-linear system, spatially distributed sensors, fusion center

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Authors: Ebrahim H. Kapeel, Ahmed M. Kamel, Hossam Hendy, Yehia Z. Elhalwagy

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Interest in autopilot design has been raised intensely as a result of recent advancements in Unmanned Aerial vehicles (UAVs). Due to the enormous number of applications that UAVs can achieve, the number of applied control theories used for them has increased in recent years. These small fixed-wing UAVs are suffering high non-linearity, sensitivity to disturbances, and coupling effects between their channels. In this work, the nonlinear dynamic inversion (NDI) control law is designed for a nonlinear small fixed-wing UAV model. The NDI is preferable for varied operating conditions, there is no need for a scheduling controller. Moreover, it’s applicable for high angles of attack. For the designed flight controller validation, a nonlinear Modified PI-D controller is performed with our model. A comparative study between both controllers is achieved to evaluate the NDI performance. Simulation results and analysis are proposed to illustrate the effectiveness of the designed controller based on NDI.

Keywords: attitude control, nonlinear PID, dynamic inversion

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Authors: Mohammad Reza Esmaili

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After the occurrence of blackouts, the most important subject is how fast the electric service is restored. Power system restoration is an immensely complex issue and there should be a plan to be executed within the shortest time period. This plan has three main stages of black start, network reconfiguration and load restoration. In the black start stage, operators and experts may face several problems, for instance, the unsuccessful connection of the long high-voltage transmission line connected to the electrical source. In this situation, the generator may be tripped because of the unsuitable setting of its line charging mode or high absorbed reactive power. In order to solve this problem, the line charging process is defined as a nonlinear programming problem, and it is optimized by using GAMS software in this paper. The optimized process is performed on a grid that includes a 250 MW hydroelectric unit and a 400 KV transmission system. Simulations and field test results show the effectiveness of optimal planning.

Keywords: power system restoration, black start, line charging mode, nonlinear programming

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Authors: O. Arikan, C. Kocatepe, G. Ucar, Y. Hacialiefendioglu

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In this paper, influence of harmonics on medium voltage distribution system of Bogazici Electricity Distribution Inc. (BEDAS) which takes place at Istanbul/Turkey is investigated. A ring network consisting of residential loads is taken into account for this study. Real system parameters and measurement results are used for simulations. Also, probable working conditions of the system are analyzed for %50, %75 and %100 loading of transformers with similar harmonic contents. Results of the study are exhibited the influence of nonlinear loads on %THDV, P.F. and technical losses of the medium voltage distribution system.

Keywords: distribution system, harmonic, technical losses, power factor, total harmonic distortion, residential load, medium voltage

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Authors: Shaban Aly, Ali Al-Qahtani, Houari B. Khenous

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Synchronization is an important phenomenon commonly observed in nature. A system of periodically forced complex Duffings oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. In this paper, we study the remarkable phenomenon of chaotic synchronization on these oscillator systems, using impulsive synchronization techniques. We derive analytical expressions for impulsive control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set initial conditions, the differences between the drive and response systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.

Keywords: complex nonlinear oscillators, impulsive synchronization, chaotic systems, global exponential synchronization

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Authors: Mohamed Omar

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Steel bracing members are widely used in steel structures to reduce lateral displacement and dissipate energy during earthquake motions. Concentric steel bracing provide an excellent approach for strengthening and stiffening steel buildings. Using these braces the designer can hardly adjust the stiffness together with ductility as needed because of buckling of braces in compression. In this study the use of SMA bracing and steel bracing (Mega) utilized in steel frames are investigated. The effectiveness of these two systems in rehabilitating a mid-rise eight-storey steel frames were examined using time-history nonlinear analysis utilizing Seismo-Struct software. Results show that both systems improve the strength and stiffness of the original structure but due to excellent behavior of SMA in nonlinear phase and under compressive forces this system shows much better performance than the rehabilitation system of Mega bracing.

Keywords: finite element analysis, seismic response, shapes memory alloy, steel frame, mega bracing

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Authors: Meraj Ali Khan, Falleh R. Al-Solamy

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In the present paper, second order duality for multiobjective nonlinear programming are investigated under the second order generalized (F, b, φ, ρ, θ)− univex functions. The weak, strong and converse duality theorems are proved. Further, we also illustrated an example of (F, b, φ, ρ, θ)− univex functions. Results obtained in this paper extend some previously known results of multiobjective nonlinear programming in the literature.

Keywords: duality, multiobjective programming, univex functions, univex

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Authors: Sarun Phibanchon, Yuttakarn Rattanachai

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The quadratic-cubic nonlinear Schrodinger equation can be explained the weakly ion-acoustic waves in magnetized plasma with a slightly non-Maxwellian electron distribution by using the Madelung's fluid picture. However, the soliton solution to the quadratic-cubic nonlinear Schrodinger equation is determined by using the direct integration. By the characteristics of a soliton, the solution can be claimed that it's a soliton by considering its time evolution and their collisions between two solutions. These results are shown by applying the spectral method.

Keywords: soliton, ion-acoustic waves, plasma, spectral method

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Authors: Dehini Rachid, Ferdi Brahim

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The shunt active power filter (SAPF) is not destined only to improve the power factor, but also to compensate the unwanted harmonic currents produced by nonlinear loads. This paper presents a SAPF with identification and control method based on artificial neural network (ANN). To identify harmonics, many techniques are used, among them the conventional p-q theory and the relatively recent one the artificial neural network method. It is difficult to get satisfied identification and control characteristics by using a normal (ANN) due to the nonlinearity of the system (SAPF + fast nonlinear load variations). This work is an attempt to undertake a systematic study of the problem to equip the (SAPF) with the harmonics identification and DC link voltage control method based on (ANN). The latter has been applied to the (SAPF) with fast nonlinear load variations. The results of computer simulations and experiments are given, which can confirm the feasibility of the proposed active power filter.

Keywords: artificial neural networks (ANN), p-q theory, harmonics, total harmonic distortion

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Authors: Davood Yazdani Cherati, Hussein Hashemi Senejani

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In this paper, a convenient analytical solution for a system of coupled differential equations, derived from thermo-hydro-mechanical analysis of three-phase porous media such as unsaturated soils is developed. This kind of analysis can be used in various fields such as geothermal energy systems and seepage of leachate from buried municipal and domestic waste in geomaterials. Initially, a system of coupled differential equations, including energy, mass, and momentum conservation equations is considered, and an analytical method called AGM is employed to solve the problem. The method is straightforward and comprehensible and can be used to solve various nonlinear partial differential equations (PDEs). Results indicate the accuracy of the applied method for solving nonlinear partial differential equations.

Keywords: AGM, analytical solution, porous media, thermo-hydro-mechanical, unsaturated soils

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Authors: A. Zerarka, W. Djoudi

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We use some fractional transformations to obtain many types of new exact solutions of nonlinear lattice equation. These solutions include rational solutions, periodic wave solutions, and doubly periodic wave solutions.

Keywords: fractional transformations, nonlinear equation, travelling wave solutions, lattice equation

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Authors: Hendradi Hardhienata, Tony Sumaryada, Sri Setyaningsih

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Current progress in the field of nonlinear optics has enabled precise surface characterization in semiconductor materials. Nonlinear optical techniques are favorable due to their nondestructive measurement and ability to work in nonvacuum and ambient conditions. The advance of the bond hyperpolarizability models opens a wide range of nanoscale surface investigation including the possibility to detect molecular orientation at the surface of silicon and zincblende semiconductors, investigation of electric field induced second harmonic fields at the semiconductor interface, detection of surface impurities, and very recently, study surface defects such as twin boundary in wurtzite semiconductors. In this work, we show using nonlinear optical techniques, e.g. nonlinear bond models how arbitrary polarization of the incoming electric field in Rotational Anisotropy Spectroscopy experiments can provide more information regarding the origin of the nonlinear sources in zincblende and wurtzite semiconductor structure. In addition, using hyperpolarizability consideration, we describe how the nonlinear susceptibility tensor describing SHG can be well modelled using only few parameter because of the symmetry of the bonds. We also show how the third harmonic intensity feature shows considerable changes when the incoming field polarization angle is changed from s-polarized to p-polarized. We also propose a method how to investigate surface reconstruction and defects in wurtzite and zincblende structure at the nanoscale level.

Keywords: surface characterization, bond model, rotational anisotropy spectroscopy, effective hyperpolarizability

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Authors: P. Selyshchev

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Construction materials for nuclear facilities are operated under extreme thermal and radiation conditions. First of all, they are nuclear fuel, fuel assemblies, and reactor vessel. It places high demands on the control of their state, stability of their state, and their operating conditions. An irradiated material is a typical example of an open non-equilibrium system with nonlinear feedbacks between its elements. Fluxes of energy, matter and entropy maintain states which are far away from thermal equilibrium. The links that arise under irradiation are inherently nonlinear. They form the mechanisms of feed-backs that can lead to instability. Due to this instability the temperature of the sample, heat transfer, and the defect density can exceed the steady-state value in several times. This can lead to change of typical operation and an accident. Therefore, it is necessary to take into account the thermal instability to avoid the emergency situation. The point is that non-thermal energy can be accumulated in materials because irradiation produces defects (first of all these are vacancies and interstitial atoms), which are metastable. The stored energy is about energy of defect formation. Thus, an annealing of the defects is accompanied by releasing of non-thermal stored energy into thermal one. Temperature of the material grows. Increase of temperature results in acceleration of defect annealing. Density of the defects drops and temperature grows more and more quickly. The positive feed-back is formed and self-reinforcing annealing of radiation defects develops. To describe these phenomena a theoretical approach to thermal instability is developed via formalism of complex systems. We consider system of nonlinear differential equations for different components of microstructure and temperature. The qualitative analysis of this non-linear dynamical system is carried out. Conditions for development of instability have been obtained. Points of bifurcation have been found. Convenient way to represent obtained results is a set of phase portraits. It has been shown that different regimes of material state under irradiation can develop. Thus degradation of irradiated material can be limited by means of choice appropriate kind of evolution of materials under irradiation.

Keywords: irradiation, material, non-equilibrium state, nonlinear feed-back, thermal instability

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Authors: Woo Young Jung, Min Ho Kwon, Bu Seog Ju

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A failure of the non-structural component can cause significant damages in critical facilities such as nuclear power plants and hospitals. Historically, it was reported that the damage from the leakage of sprinkler systems, resulted in the shutdown of hospitals for several weeks by the 1971 San Fernando and 1994 North Ridge earthquakes. In most cases, water leakages were observed at the cross joints, sprinkler heads, and T-joint connections in piping systems during and after the seismic events. Hence, the primary objective of this study was to understand the seismic performance of T-joint connections and to develop an analytical Finite Element (FE) model for the T-joint systems of 2-inch fire protection piping system in hospitals subjected to seismic ground motions. In order to evaluate the FE models of the piping systems using OpenSees, two types of materials were used: 1) Steel 02 materials and 2) Pinching 4 materials. Results of the current study revealed that the nonlinear moment-rotation FE models for the threaded T-joint reconciled well with the experimental results in both FE material models. However, the system-level fragility determined from multiple nonlinear time history analyses at the threaded T-joint was slightly different. The system-level fragility at the T-joint, determined by Pinching 4 material was more conservative than that of using Steel 02 material in the piping system.

Keywords: fragility, t-joint, piping, leakage, sprinkler

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Authors: George Mahalu

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The Chua diode has been configured over time in various ways, using electronic structures like as operational amplifiers (OAs) or devices with gas or semiconductors. When discussing the use of semiconductor devices, tunnel diodes (Esaki diodes) are most often considered, and more recently, transistorized configurations such as lambda diodes. The paper-work proposed here uses in the modeling a lambda diode type configuration consisting of two Junction Field Effect Transistors (JFET). The original scheme is created in the MULTISIM electronic simulation environment and is analyzed in order to identify the conditions for the appearance of evolutionary unpredictability specific to nonlinear dynamic systems with chaos-induced behavior. The chaotic deterministic oscillator is one autonomous type, a fact that places it in the class of Chua’s type oscillators, the only significant and most important difference being the presence of a nonlinear device like the one mentioned structure above. The chaotic behavior is identified both by means of strange attractor-type trajectories and visible during the simulation and by highlighting the hypersensitivity of the system to small variations of one of the input parameters. The results obtained through simulation and the conclusions drawn are useful in the further research of ways to implement such constructive electronic solutions in theoretical and practical applications related to modern small signal amplification structures, to systems for encoding and decoding messages through various modern ways of communication, as well as new structures that can be imagined both in modern neural networks and in those for the physical implementation of some requirements imposed by current research with the aim of obtaining practically usable solutions in quantum computing and quantum computers.

Keywords: chaos, lambda diode, strange attractor, nonlinear system

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Authors: Ali Ballouch, Nourelhouda Choukri, Zouhair Soufiani, Mohamed El Jouad, Mohamed Addou

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For several years, significant research has been developed in the areas of applications of semiconductor wide bandgap such as ZnO in optoelectronics. This oxide has the advantage of having a large exciton energy (60 meV) three times higher than that of GaN (21 meV) or ZnS (20 meV). This energy makes zinc oxide resistant for laser irradiations and very interesting for the near UV-visible optic, as well as for studying physical microcavities. A high-energy direct gap at room temperature (Eg > 1 eV) which makes it a potential candidate for emitting devices in the near UV and visible. Our work is to study the nonlinear optical properties, mainly the nonlinear third-order susceptibility of europium doped Zinc oxide thin films. The samples were prepared by chemical vapor spray method (Spray), XRD, SEM technique, THG were used for characterization. In this context, the influence of europium doping on the nonlinear optical response of the Zinc oxide was investigated. The nonlinear third-order properties depend on the physico-chemical parameters (crystallinity, strain, and surface roughness), the nature and the level of doping, temperature.

Keywords: ZnO, characterization, non-linear optical properties, optoelectronics

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Authors: Przemyslaw Nogly, Tobias Weinert, Daniel James, Sergio Carbajo, Dmitry Ozerov, Antonia Furrer, Dardan Gashi, Veniamin Borin, Petr Skopintsev, Kathrin Jaeger, Karol Nass, Petra Bath, Robert Bosman, Jason Koglin, Matthew Seaberg, Thomas Lane, Demet Kekilli, Steffen Brünle, Tomoyuki Tanaka, Wenting Wu, Christopher Milne, Thomas A. White, Anton Barty, Uwe Weierstall, Valerie Panneels, Eriko Nango, So Iwata, Mark Hunter, Igor Schapiro, Gebhard Schertler, Richard Neutze, Jörg Standfuss

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Ultrafast isomerization of retinal is the primary step in a range of photoresponsive biological functions including vision in humans and ion-transport across bacterial membranes. We studied the sub-picosecond structural dynamics of retinal isomerization in the light-driven proton pump bacteriorhodopsin using an X-ray laser. Twenty snapshots with near-atomic spatial and temporal resolution in the femtosecond regime show how the excited all-trans retinal samples conformational states within the protein binding pocket prior to passing through a highly-twisted geometry and emerging in the 13-cis conformation. The aspartic acid residues and functional water molecules in proximity of the retinal Schiff base respond collectively to formation and decay of the initial excited state and retinal isomerization. These observations reveal how the protein scaffold guides this remarkably efficient photochemical reaction.

Keywords: bacteriorhodopsin, free-electron laser, retinal isomerization mechanism, time-resolved crystallography

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Authors: T. A. Sakr, Hanaa E. Abd-El-Mottaleb

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Outrigger-braced wall systems are commonly used to provide high rise buildings with the required lateral stiffness for wind and earthquake resistance. The existence of outriggers adds to the stiffness and strength of walls as reported by several studies. The effects of different parameters on the elasto-plastic dynamic behavior of outrigger-braced wall systems to earthquakes are investigated in this study. Parameters investigated include outrigger stiffness, concrete strength, and reinforcement arrangement as the main design parameters in wall design. In addition to being significant to the wall behavior, such parameters may lead to the change of failure mode and the delay of crack propagation and consequently failure as the wall is excited by earthquakes. Bi-linear stress-strain relation for concrete with limited tensile strength and truss members with bi-linear stress-strain relation for reinforcement were used in the finite element analysis of the problem. The famous earthquake record, El-Centro, 1940 is used in the study. Emphasis was given to the lateral drift, normal stresses and crack pattern as behavior controlling determinants. Results indicated significant effect of the studied parameters such that stiffer outrigger, higher grade concrete and concentrating the reinforcement at wall edges enhance the behavior of the system. Concrete stresses and cracking behavior are sigbificantly enhanced while lesser drift improvements are observed.

Keywords: outrigger, shear wall, earthquake, nonlinear

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Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza khalili, Sara Akbari, Davood Domiri Ganji

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In this symposium, our aims are accuracy, capabilities and power at solving of the complicate non-linear differential at the reaction chemical in the catalyst reactor (heterogeneous reaction). Our purpose is to enhance the ability of solving the mentioned nonlinear differential equations at chemical engineering and similar issues with a simple and innovative approach which entitled ‘’Akbari-Ganji's Method’’ or ‘’AGM’’. In this paper we solve many examples of nonlinear differential equations of chemical reactions and its investigate. The chemical reactor with the energy changing (non-isotherm) in two reactors of mixed and plug are separately studied and the nonlinear differential equations obtained from the reaction behavior in these systems are solved by a new method. Practically, the reactions with the energy changing (heat or cold) have an important effect on designing and function of the reactors. This means that possibility of reaching the optimal conditions of operation for the maximum conversion depending on nonlinear nature of the reaction velocity toward temperature, results in the complexity of the operation in the reactor. In this case, the differential equation set which governs the reactors can be obtained simultaneous solution of mass equilibrium and energy and temperature changing at concentration.

Keywords: new method (AGM), nonlinear differential equation, tubular and mixed reactors, catalyst bed

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Authors: Juliette Harper, Yu Yang

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Biofuels have gained significant attention recently due to the new regulations and agreements regarding fossil fuels and greenhouse gases being made by countries around the globe. One of the most common types of biofuels is biodiesel, primarily made via the transesterification reaction. We model this nonlinear process in MATLAB using the standard kinetic equations. Then, a nonlinear Model predictive control (NMPC) was developed to regulate this process due to its capability to handle process constraints. The feeding flow uncertainty and kinetic disturbances are further incorporated in the model to capture the real-world operating conditions. The simulation results will show that the proposed NMPC can guarantee the final composition of fatty acid methyl esters (FAME) above the target threshold with a high chance by adjusting the process temperature and flowrate. This research will allow further understanding of NMPC under uncertainties and how to design the computational strategy for larger process with more variables.

Keywords: NMPC, biodiesel, uncertainties, nonlinear, MATLAB

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Authors: Nicolò Vaiana, Filip C. Filippou, Giorgio Serino

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In order to reduce numerical computations in the nonlinear dynamic analysis of seismically base-isolated structures, a Mixed Explicit-Implicit time integration Method (MEIM) has been proposed. Adopting the explicit conditionally stable central difference method to compute the nonlinear response of the base isolation system, and the implicit unconditionally stable Newmark’s constant average acceleration method to determine the superstructure linear response, the proposed MEIM, which is conditionally stable due to the use of the central difference method, allows to avoid the iterative procedure generally required by conventional monolithic solution approaches within each time step of the analysis. The main aim of this paper is to investigate the stability and computational efficiency of the MEIM when employed to perform the nonlinear time history analysis of base-isolated structures with sliding bearings. Indeed, in this case, the critical time step could become smaller than the one used to define accurately the earthquake excitation due to the very high initial stiffness values of such devices. The numerical results obtained from nonlinear dynamic analyses of a base-isolated structure with a friction pendulum bearing system, performed by using the proposed MEIM, are compared to those obtained adopting a conventional monolithic solution approach, i.e. the implicit unconditionally stable Newmark’s constant acceleration method employed in conjunction with the iterative pseudo-force procedure. According to the numerical results, in the presented numerical application, the MEIM does not have stability problems being the critical time step larger than the ground acceleration one despite of the high initial stiffness of the friction pendulum bearings. In addition, compared to the conventional monolithic solution approach, the proposed algorithm preserves its computational efficiency even when it is adopted to perform the nonlinear dynamic analysis using a smaller time step.

Keywords: base isolation, computational efficiency, mixed explicit-implicit method, partitioned solution approach, stability

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Authors: Kang-Gyu Park, Sun-Jong Park, Hong Jae Yim, Hyo-Gyung Kwak

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This paper attempts to evaluate the effect of fire damage on concrete by using nonlinear resonance vibration method, one of the nonlinear nondestructive method. Concrete exhibits not only nonlinear stress-strain relation but also hysteresis and discrete memory effect which are contained in consolidated materials. Hysteretic materials typically show the linear resonance frequency shift. Also, the shift of resonance frequency is changed according to the degree of micro damage. The degree of the shift can be obtained through nonlinear resonance vibration method. Five exposure scenarios were considered in order to make different internal micro damage. Also, the effect of post-fire-curing on fire-damaged concrete was taken into account to conform the change in internal damage. Hysteretic non linearity parameter was obtained by amplitude-dependent resonance frequency shift after specific curing periods. In addition, splitting tensile strength was measured on each sample to characterize the variation of residual strength. Then, a correlation between the hysteretic non linearity parameter and residual strength was proposed from each test result.

Keywords: nonlinear resonance vibration method, non linearity parameter, splitting tensile strength, micro damage, post-fire-curing, fire damaged concrete

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Authors: Yasser Rammah, Wolf-Christian Mueller

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Nonlinear triad interactions in incompressible three-dimensional magnetohydrodynamic (3D-MHD) turbulence are studied by analyzing data from high-resolution direct numerical simulations of decaying isotropic (5123 grid points) and forced anisotropic (10242 x256 grid points) turbulence. An accurate numerical approach toward analyzing nonlinear turbulent energy transfer function and triad interactions is presented. It involves the direct numerical examination of every wavenumber triad that is associated with the nonlinear terms in the differential equations of MHD in the inertial range of turbulence. The technique allows us to compute the spectral energy transfer and energy fluxes, as well as the spectral locality property of energy transfer function. To this end, the geometrical shape of each underlying wavenumber triad that contributes to the statistical transfer density function is examined to infer the locality of the energy transfer. Results show that the total energy transfer is local via nonlocal triad interactions in decaying macroscopically isotropic MHD turbulence. In anisotropic MHD, turbulence subject to a strong mean magnetic field the nonlinear transfer is generally weaker and exhibits a moderate increase of nonlocality in both perpendicular and parallel directions compared to the isotropic case. These results support the recent mathematical findings, which also claim the locality of nonlinear energy transfer in MHD turbulence.

Keywords: magnetohydrodynamic (MHD) turbulence, transfer density function, locality function, direct numerical simulation (DNS)

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Authors: Tai-Ping Chang

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In the present study, the effects on chaotic motion of single-walled carbon nanotube (SWCNT) due to the linear and nonlinear damping are investigated. By using the Hamilton’s principle, the nonlinear governing equation of the single-walled carbon nanotube embedded in a matrix is derived. The Galerkin’s method is adopted to simplify the integro-partial differential equation into a nonlinear dimensionless governing equation for the SWCNT, which turns out to be a forced Duffing equation. The variations of the Lyapunov exponents of the SWCNT with damping and harmonic forcing amplitudes are investigated. Based on the computations of the top Lyapunov exponent, it is concluded that the chaotic motion of the SWCNT occurs when the amplitude of the periodic excitation exceeds certain value, besides, the chaotic motion of the SWCNT occurs with small linear damping and tiny nonlinear damping.

Keywords: chaotic motion, damping, Lyapunov exponents, single-walled carbon nanotube

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Authors: Kuo-Teng Tsai, You-Min Huang

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In this study, the problem of a spiral fin with a period base temperature is analyzed by using the Adomian decomposition method. The Adomian decomposition method is a useful and practice method to solve the nonlinear energy equation which are associated with the heat radiation. The period base temperature is around a mean value. The results including the temperature distribution and the heat flux from the spiral fin base can be calculated directly. The results also discussed the effects of the dimensionless variables for the temperature variations and the total energy transferred from the spiral fin base.

Keywords: spiral fin, period, adomian decomposition method, nonlinear

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Authors: Tudor Barbu

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We present a robust nonlinear parabolic partial differential equation (PDE)-based denoising scheme in this article. Our approach is based on a second-order anisotropic diffusion model that is described first. Then, a consistent and explicit numerical approximation algorithm is constructed for this continuous model by using the finite-difference method. Finally, our restoration experiments and method comparison, which prove the effectiveness of this proposed technique, are discussed in this paper.

Keywords: anisotropic diffusion, finite differences, image denoising and restoration, nonlinear PDE model, anisotropic diffusion, numerical approximation schemes

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Authors: Aneek Kuila, Yaron Paz

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MIP 177 LT and HT are two-phase transformable metal organic frameworks consisting of a Ti12O15 oxocluster and a tetracarboxylate ligand that exhibits robust chemical stability and improved photoactivity. LT to HT only shows the changes in dimensionality from 0D to 1D without any change in the overall chemical structure. In terms of chemical and photoactivity MIP 177 LT is found to perform better than the MIP 177HT. Step-scan Fourier transform absorption difference time-resolved spectroscopy has been used to collect mid-IR time-resolved infrared spectra of the transient electronic excited states of a nano-porous metal–organic framework MIP 177-LT and HT with 2.5 ns time resolution. Analyzing the time-resolved vibrational data after 355nm LASER excitation reveals the presence of the temporal changes of ν (O-Ti-O) of Ti-O metal cluster and ν (-COO) of the ligand concluding the fact that these moieties are the ultimate acceptors of the excited charges which are localized over those regions on the nanosecond timescale. A direct negative correlation between the differential absorbance (Δ Absorbance) reveals the charge transfer relation among these two moieties. A longer-lived transient signal up to 180ns for MIP 177 LT compared to the 100 ns of MIP 177 HT shows the extended lifetime of the reactive charges over the surface that exerts in their effectivity. An ultrafast change of bidentate to monodentate bridging in the -COO-Ti-O ligand-metal coordination environment was observed after the photoexcitation of MIP 177 LT which remains and lives with for seconds after photoexcitation is halted. This phenomenon is very unique to MIP 177 LT but not observed with HT. This in-situ change in the coordination denticity during the photoexcitation was not observed previously which can rationalize the reason behind the ability of MIP 177 LT to accumulate electrons during continuous photoexcitation leading to a superior photocatalytic activity.

Keywords: time resolved FTIR, metal organic framework, denticity, photoacatalysis

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Authors: A. M. Gheitaghy, H. Saffari, G. Q. Zhang

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Numerical approach based on the electrical simulation method is proposed to solve a nonlinear transient heat conduction problem with nonlinear boundary for a spherical body. This problem represents a strong nonlinearity in both the governing equation for temperature dependent thermal property and the boundary condition for combined convective and radiative cooling. By analysing the equivalent electrical model using the electrical circuit simulation program HSPICE, transient temperature and heat flux distributions at sphere can be obtained easily and fast. The solutions clearly illustrate the effect of the radiation-conduction parameter Nrc, the Biot number and the linear coefficient of temperature dependent conductivity and heat capacity. On comparing the results with corresponding numerical solutions, the accuracy and efficiency of this computational method are found to be good.

Keywords: convective and radiative boundary, electrical simulation method, nonlinear heat conduction, spherical coordinate

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