Robust adaptive synchronization for a general class of uncertain chaotic systems with application to Chua's circuit

The synchronization problem for a general class of uncertain chaotic systems is addressed. The underlying systems may be perturbed by unknown time-varying parameters, unstructured uncertainties, and external disturbances. Meanwhile, the time-varying parameters and disturbances are neither required to be periodic nor to have known bounds. Assuming the disturbances are L(2) signals, an adaptive control incorporated with H(∞) control technique is employed to construct a robust adaptive synchronization algorithm. Then, removing such assumption, a novel adaptive-based method is developed to achieve the goal of synchronization. In order to demonstrate the effectiveness of the proposed algorithms, such methods are applied to solve the synchronization problem of uncertain chaotic Chua's circuits.     

Asymptotical time response of time varying state space dynamic using homotopy perturbation method

The main goal of this study is to present a technique to find a state response of multivariable time varying systems. In this paper a novel Homotopy Perturbation based Method (HPM) will be presented to find a dynamic response of time varying system. According to this method, the linear part of the described system is partitioned into two time varying and invariant subsections. Time invariant part analytically constructs the state transition matrix. This matrix is a core of the rest of time varying differential equation without any further changes in a sequence order. The main advantage of this method is only the necessity to solve the time invariant part of the state transition matrix. Simulation results verify the significance of the proposed analytic and asymptotic method.     

Synchronization of unified chaotic system by sliding mode/mixed <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript>/<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control

This paper deals with the synchronization of uncertain unified chaotic system in the presence of two kinds of disturbances, white noise and bounded power signal. A sliding mode controller (SMC) is established to guarantee the sliding motion. Moreover, a proportional-integral (PI) switching surface is used to determine the performance of the system in the sliding motion. Also, by using a mixed H ₂/H _∞ approach, the effect of external disturbances on the sliding motion is reduced. The necessary parameters of constructing controller and switching surface are found via semidefinite programming (SDP) which can be solved effectively by a standard software. Finally, a numerical simulation is presented to show the effectiveness of the proposed method.     

New approaches to photocatalytic reaction of low concentrations of arylamines in alcohols

Photocatalytic interactions of a series of arylamines, for example 1,4-phenylenediamine, 1,2-phenylenediamine, 4-aminophenol, and 2-aminophenol, at low concentrations in typical primary alcohols have been investigated in the presence of anatase TiO₂ nanopowder. GC?CMS analysis of the irradiated solutions showed that, except for 1,2-phenylenediamine, 10?mmol/l alcoholic solutions of the arylamines gave predominately the corresponding imines. Irradiation of 2-aminophenol under these conditions, led to oxidation and dimerization to 2-amino-3H-phenoxazin-3-one.     

Photocatalytic reaction of arylamines/alcohols on TiO<Subscript>2</Subscript> nano-particles

In this article, the photocatalytic reaction of aniline and 4-amino N,N-dimethyl aniline with methanol, ethanol and isopropanol on anatase TiO₂ nano-particles under UV (365-nm wavelength) irradiation was examined. The concentration of unreacted arylamines and products was measured by gas chromatography picks integration, and then the products were identified by mass spectroscopy analysis. By making a comparison within the rates of photocatalysis of each arylamine in different alcohols under various irradiation times, it was revealed that, in all cases, the sequence of photocatalysis rate was methanol > ethanol > isopropanol. In reactions where the concentrations of arylamine were lower than 10 mmol/l, imines were the main products and the alkylation of amines was not observed. In the higher concentration of arylamines, oxidation and dimerization was occurred.     

Photocatalytic reaction of aryl amines/alcohols on TiO<Subscript>2</Subscript> nanoparticles

In this article, the photocatalytic reaction of aniline and 4-amino N, N dimethyl aniline with methanol, ethanol and isopropanol on anatase TiO₂ nano-particles under UV (365 nm wavelength) irradiation was examined. The concentration of unreacted aryl amines and products was measured by gas chromatography picks integration, and then the products were identified by mass spectroscopy analysis. By making a comparison within the rates of photocatalysis of each aryl amine in different alcohols under various irradiation times, it was revealed that, in all cases, the sequence of photocatalysis rate was methanol > ethanol > isopropanol. In reactions where the concentrations of aryl amine were lower than 10 mmol/L, imines were the main products and alkylation of amines was not observed. In the higher concentration of aryl amines, oxidation and dimerization occurred.     

The effect of heat treatment in the reducing atmosphere on the physical properties of TiO2 thin films prepared by sol–gel method

Multilayered nanostructured TiO₂ thin films were prepared by sol–gel and dipping deposition on quartz substrate followed by thermal treatment under reducing atmosphere (20 %H₂–80 %Ar). Heat treatment at progressively higher temperatures caused structural, morphological, and optical changes, which were investigated by X-ray diffraction (XRD), atomic force microscopy, scanning electron microscopy, and UV–Vis spectroscopy. The conductivities of the thin films were also measured by 4-point probe method. The XRD results showed that the calcined TiO₂ thin films consist of single anatase phase which was completely transformed into rutile phase after heat treatment at 1,000 °C. The grains of films grew by intra-agglomerate densification after heat treatment at higher temperatures. The root mean square roughness of the samples was found to be in the range of 0.58–3.36 nm. The partially reduced TiO₂ samples have red-shifted transmittance bands due to new energy band formed by oxygen vacancies. The electrical conductivity of the films was also enhanced after heat treatment in reducing atmosphere.     

Determination of complex modes in photonic crystal waveguides using the phase variation in characteristic coefficients

An efficient frequency-domain method, the phase variation monitoring (PVM) method, is proposed to determine the electromagnetic eigenmodes in two-dimensional photonic crystal waveguides. The proposed method is based on monitoring the reflection and transmission coefficients of incident plane waves. It is successfully applied to an illustrative line-defect photonic crystal waveguide and proved to be capable of calculating the in-plane leakage through the finite-size photonic crystal surrounding the line-defect. Calculation of the leakage loss is not only important for proper understanding of wave propagation within the defect but also for its significant role in applications of photonic structures.     

Water Promoted Michael Addition of Secondary Amines to α, β-Unsaturated Carbonyl Compounds Under Microwave Irradiation

A rapid Michael addition of secondary amines to α, β-unsaturated carbonyl compounds has been achieved in good to excellent yields in the presence of water under microwave irradiation. In the absence of water and under conventional method the reaction does not proceed or take place in very low yield after a long reaction time.     

Homotopy perturbation based linearization of nonlinear heat transfer dynamic

In this paper a new linearization procedure based on Homotopy Perturbation Method (HPM) will be presented. The procedure begins with solving nonlinear differential equation by HPM. This will be done by evaluation of the time response of a nonlinear dynamic. An equivalent Laplace transform of the time response will be obtained. In the preceding, the effect of an external excitation i.e. input, will be removed from the model to find an approximate linear model for the nonlinear dynamic. The effectiveness of the procedure is verified using a heat transfer nonlinear equation. Ultimately, both HPM based linear model and that of nonlinear have been controlled via a closed loop PID controller. The simulation result shows the significance of the proposed technique.