Internal and External Fluctuation Activated Non-equilibrium Reactive Rate Process

The activated rate process for non-equilibrium open systems is studied taking into account both internal and external noise fluctuations in a unified way. The probability of a particle diffusing passing over the saddle point and the rate constant together with the effective transmission coefficient are calculated via the method of reactive flux. We find that the complexity of internal noise is always harmful to the diffusion of particles. However the external modulation may be beneficial to the rate process.Comment: 10 pages, 1 figure (containing 2 subgraphs). arXiv admin note: text overlap with arXiv:cond-mat/9911028 by other author

Bandit Problems with Side Observations

An extension of the traditional two-armed bandit problem is considered, in which the decision maker has access to some side information before deciding which arm to pull. At each time t, before making a selection, the decision maker is able to observe a random variable X_t that provides some information on the rewards to be obtained. The focus is on finding uniformly good rules (that minimize the growth rate of the inferior sampling time) and on quantifying how much the additional information helps. Various settings are considered and for each setting, lower bounds on the achievable inferior sampling time are developed and asymptotically optimal adaptive schemes achieving these lower bounds are constructed.Comment: 16 pages, 3 figures. To be published in the IEEE Transactions on Automatic Contro

Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian

Based on the technique of integration within an ordered product (IWOP) of operators we introduce the Fresnel operator for converting Caldirola-Kanai Hamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresnel operator with the parameters A,B,C,D corresponds to classical optical Fresnel transformation, these parameters are the solution to a set of partial differential equations set up in the above mentioned converting process. In this way the exact wavefunction solution of the Schr\"odinger equation governed by the Caldirola-Kanai Hamiltonian is obtained, which represents a squeezed number state. The corresponding Wigner function is derived by virtue of the Weyl ordered form of the Wigner operator and the order-invariance of Weyl ordered operators under similar transformations. The method used here can be suitable for solving Schr\"odinger equation of other time-dependent oscillators.Comment: 6 pages, 2 figure

Optimum Shapes for Minimising Bond Stress in Scarf Repairs

Bonded scarf repairs are used in composite structures when high strength recovery is needed or when there is a requirement for a flush surface to satisfy aerodynamic or stealth requirements. However, scarf repairs are complex to design and require the removal of significant parent structure, particularly for thick skins. In this investigation, analytical and numerical approaches have been developed to investigate whether an optimum repair shape for a known biaxial load can be determined. The results clearly demonstrate that the strength of a repaired panel can be improved by optimising both the initial damage cut-out shape and the scarf angle distribution

δ\delta meson effects on neutron stars in the modified quark-meson coupling model

The properties of neutron stars are investigated by including $\delta$ meson field in the Lagrangian density of modified quark-meson coupling model. The $\Sigma^-$ population with $\delta$ meson is larger than that without $\delta$ meson at the beginning, but it becomes smaller than that without $\delta$ meson as the appearance of $\Xi^-$. The $\delta$ meson has opposite effects on hadronic matter with or without hyperons: it softens the EOSes of hadronic matter with hyperons, while it stiffens the EOSes of pure nucleonic matter. Furthermore, the leptons and the hyperons have the similar influence on $\delta$ meson effects. The $\delta$ meson increases the maximum masses of neutron stars. The influence of $(\sigma^*,\phi)$ on the $\delta$ meson effects are also investigated.Comment: 10 pages, 6 figures, 4 table