The synchronizing properties of two diffusively coupled hyperchaotic Lorenz 4D systems are investigated by calculating the transverse Lyapunov exponents and by observing the phase space trajectories near the synchronization hyperplane. The effect of parameter mismatch is also observed. A simple electrical circuit described by the Lorenz 4D equations is proposed. Some results from laboratory experiments with two coupled circuits are presented.

Ruy Barboza

Diffusive Synchronization of Hyperchaotic Lorenz Systems

This paper presents a short overview of the flow around a slender circular cylinder, the purpose being to place it within the frame of the distributed Hopf bifurcation problems described by the Ginzburg-Landau equation (GLE). In particular, the chaotic behavior superposed to a well tuned harmonic oscillation observed in the range Re &gt; 270, with Re being the Reynolds number, is related to the defect-chaos regime of the GLE. Apparently new results, related to a Kolmogorov like length scale and the rms of the response amplitude, are derived in this defect-chaos regime and further related to the experimental rms of the lift coefficient measured in the range Re &gt; 270.

J. A. P. Aranha

K. P. Burr

I. C. Barbeiro

I. Korkischko

J. R. Meneghini

Flow Around a Slender Circular Cylinder: A Case Study on Distributed Hopf Bifurcation

This paper reviewed the research on the vibration of orthotropic membrane, which commonly applied in the membrane structural engineering. We applied the large deflection theory of membrane to derive the governing vibration equations of orthotropic membrane, solved it, and obtained the power series formula of nonlinear vibration frequency of rectangular membrane with four edges fixed. The paper gave the computational example and compared the two results from the large deflection theory and the small one, respectively. Results obtained from this paper provide some theoretical foundation for the measurement of pretension by frequency method; meanwhile, the results provide some theoretical foundation for the research of nonlinear vibration of membrane structures and the response solving of membrane structures under dynamic loads.

Zheng Zhou-Lian

Liu Chang-Jiang

He Xiao-Ting

Chen Shan-Lin

Free Vibration Analysis of Rectangular Orthotropic Membranes in Large Deflection

This paper is concerned with an evolutionary search for limit cycle operation in a class of nonlinear systems. In the first part, single input single output (SISO) systems are investigated and sinusoidal input describing function (SIDF) is extended to those cases where the key assumption in its derivation is violated. Describing function matrix (DMF) is employed to take into account the effects of higher harmonic signals and enhance the accuracy of predicting limit cycle operation.
In the second part, SIDF is extended to the class of nonlinear multiinput multioutput (MIMO) systems containing separable nonlinear elements of any general form. In both cases linearized harmonic balance equations are derived and the search for a limit cycle is formulated as a multiobjective problem. Multiobjective genetic algorithm (MOGA) is utilized to search the space of parameters of theoretically possible limit cycle operations. Case studies are presented to demonstrate the effectiveness of the proposed approach.

M. Katebi

H. Tawfik

S. D. Katebi

Limit Cycle Prediction Based on Evolutionary  Multiobjective Formulation

This article proposes a new approach to the construction of a linearization method based on the
iterative operator-splitting method for nonlinear differential equations. The convergence properties
of such a method are studied. The main features of the proposed idea are the linearization
of nonlinear equations and the application of iterative splitting methods. We present an iterative
operator-splitting method with embedded Newton methods to solve nonlinearity. We confirm
with numerical applications the effectiveness of the proposed iterative operator-splitting method
in comparison with the classical Newton methods. We provide improved results and convergence rates.

J&#252;rgen Geiser

Modified Jacobian Newton Iterative Method: Theory and Applications

The numerous technical applications in electronic and optoelectronic devices, such as lasers, diodes, and sensors, demand high-quality silicon carbide (SiC) bulk single crystal for industrial applications. We consider an SiC crystal growth process by physical vapor transport (PVT), called modified Lely method. We deal with a model for the micro- and  macroscales of the sublimation processes within the growth apparatus. The macroscopic model is based on the heat equation with heat sources due to induction heating and nonlocal interface conditions, representing the heat transfer by radiation. The microscopic model is based on the quantum interatomic potential and is computed with molecular dynamics. We study the temperature evolution in the apparatus and reflect the growth behavior of the microscopic model. We present results of some numerical simulations of
the micro- and macromodels of our growth apparatus.

Stephan Irle

Macro- and Microsimulations for a Sublimation Growth of SiC Single Crystals

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Mathematical Problems in Engineering is a broad-based journal publishing&nbsp;results of rigorous engineering research across all disciplines, carried out using mathematical tools.

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Chief Editor, Professor Guangming Xie, is currently a full professor of dynamics and control with the College of Engineering, Peking University. His research interests include complex system dynamics and control and intelligent and biomimetic robots.

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