Synchronization for chaotic systems and chaos-based secure communications via both reduced-order and step-by-step sliding mode observers

This paper considers the problems of the chaos synchronization and chaos-based secure communication when the observer matching condition is not satisfied. An auxiliary drive signal vector which may satisfy the observer matching condition is constructed. By using the drive signals of original system, a step-by-step sliding mode observer is considered to obtain the exact estimates of the auxiliary drive signals and their derivatives. A reduced-order observer is designed to asymptotically estimate the states of the drive system. By using the estimates of states and the derivatives of the auxiliary signals, an information signal recovery method which does not use any derivative information of original drive system is developed. Finally, a numerical simulation example is given to illustrate the effectiveness of the proposed methods.     

Synthesis,Characterization, and Electronic Structures of Porphyrins Fused with Polycyclic Aromatic Ring Systems

A series of porphyrins fused with acenaphthylene, phenanthroline, and benzofluoranthene polycyclic aromatic rings were prepared by means of a 3+1 porphyrin synthesis approach and subsequent retro‐Diels–Alder reaction of bicyclo[2.2.2]octadiene‐fused precursors. Analysis of the magnetic circular dichroism spectra and the results of time‐dependent DFT calculations are used to identify the reasons for the trends observed in the wavelengths and relative intensities of the Q bands of the products. Michl's perimeter model is used as a conceptual framework to explain the changes in the relative energies of the frontier π‐molecular orbitals.     

Three‐dimensional vortex simulation of unsteady flow in hydraulic turbines

On the basis of the Helmholtz decomposition, a grid‐free numerical scheme is provided for the solution of unsteady flow in hydraulic turbines. The Lagrangian vortex method is utilized to evaluate the convection and stretch of the vorticity, and the BEM is used to solve the Neumann problem to define the potential flow. The no‐slip boundary condition is satisfied by generating vortex sticks at the solid surface. A semi‐analytical regularization technique is applied to evaluate the singular boundary surface integrals of the potential velocity and its gradients accurately. The fast multipole method was extended to evaluate the velocity and velocity gradients induced by the discretized vortex blobs in the Lagrangian vortex method. The successful simulation for the unsteady flow through a hydraulic turbine's runner has manifested the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

Applying the canonical dual theory in optimal control problems

This paper presents some applications of the canonical dual theory in optimal control problems. The analytic solutions of several nonlinear and nonconvex problems are investigated by global optimizations. It turns out that the backward differential flow defined by the KKT equation may reach the globally optimal solution. The analytic solution to an optimal control problem is obtained via the expression of the co-state. Some examples are illustrated.     

The influences of amplified spontaneous emission,crystal temperature and round-trip loss on scaling of CW thin-disk laser

In this paper, a model is built to explore how the parameters (amplified spontaneous emission (ASE), temperature and round-trip loss) influence the output power in a thin-disk laser. It is found that optical efficiency of the disk laser is reduced with the increase of ASE, temperature or round-trip loss. The parameters are optimized to maximize the output power based on our model. We find that it is necessary to balance the need to lower the temperature with the need to control ASE during the optimization process. But the balance becomes more difficult to achieve with the increase of round-trip loss. We conclude that output power of more than 2.6 MW with a single disk can be achieved, but the necessary disk size (more than 0.5 m) is far beyond the actual technical limits. But it is possible to achieve output power of over a hundred kilowatts using a 10 cm disk in the near future.