Chaos synchronization of the master-slave generalized Lorenz systems via linear state error feedback control

This paper provides a unified method for analyzing chaos synchronization of the generalized Lorenz systems. The considered synchronization scheme consists of identical master and slave generalized Lorenz systems coupled by linear state error variables. A sufficient synchronization criterion for a general linear state error feedback controller is rigorously proven by means of linearization and Lyapunov's direct methods. When a simple linear controller is used in the scheme, some easily implemented algebraic synchronization conditions are derived based on the upper and lower bounds of the master chaotic system. These criteria are further optimized to improve their sharpness. The optimized criteria are then applied to four typical generalized Lorenz systems, i.e. the classical Lorenz system, the Chen system, the Lv system and a unified chaotic system, obtaining precise corresponding synchronization conditions. The advantages of the new criteria are revealed by analytically and numerically comparing their sharpness with that of the known criteria existing in the literature.Comment: 61 pages, 15 figures, 1 tabl

Temperature Dependent Empirical Pseudopotential Theory For Self-Assembled Quantum Dots

We develop a temperature dependent empirical pseudopotential theory to study the electronic and optical properties of self-assembled quantum dots (QDs) at finite temperature. The theory takes the effects of both lattice expansion and lattice vibration into account. We apply the theory to the InAs/GaAs QDs. For the unstrained InAs/GaAs heterostructure, the conduction band offset increases whereas the valence band offset decreases with increasing of the temperature, and there is a type-I to type-II transition at approximately 135 K. Yet, for InAs/GaAs QDs, the holes are still localized in the QDs even at room temperature, because the large lattice mismatch between InAs and GaAs greatly enhances the valence band offset. The single particle energy levels in the QDs show strong temperature dependence due to the change of confinement potentials. Because of the changes of the band offsets, the electron wave functions confined in QDs increase by about 1 - 5%, whereas the hole wave functions decrease by about 30 - 40% when the temperature increases from 0 to 300 K. The calculated recombination energies of exciton, biexciton and charged excitons show red shifts with increasing of the temperature, which are in excellent agreement with available experimental data

Study of the transfer between libration point orbits and lunar orbits in Earth–Moon system

This paper is devoted to the study of the transfer problem from a libration point orbit of the Earth–Moon system to an orbit around the Moon. The transfer procedure analysed has two legs: the first one is an orbit of the unstable manifold of the libration orbit and the second one is a transfer orbit between a certain point on the manifold and the final lunar orbit. There are only two manoeuvres involved in the method and they are applied at the beginning and at the end of the second leg. Although the numerical results given in this paper correspond to transfers between halo orbits around the L1 point (of several amplitudes) and lunar polar orbits with altitudes varying between 100 and 500 km, the procedure we develop can be applied to any kind of lunar orbits, libration orbits around the L1 or L2 points of the Earth–Moon system, or to other similar cases with different values of the mass ratio.Peer ReviewedPostprint (author's final draft