Strong （Weak） Exact Controllability and Strong （Weak） Exact Observability for Quasilinear Hyperbolic Systems

Numerical approximations of Cahn-Hilliard phase-field model for the two-phase incompressible flows are considered in this paper.Several efficient and energy stable time discretization schemes for the coupled nonlinear Cahn-Hilliard phase-field system for both the matched density case and the variable density case are constructed,and are shown to satisfy discrete energy laws which are analogous to the continuous energy laws.     

Global periodicity and complete integrability of discrete dynamical systems

Consider the discrete dynamical system generated by a map F. It is said that it is globally periodic if there exists a natural number p such that F ^p (x)=x for all x in the phase space. On the other hand, it is called completely integrable if it has as many functionally independent first integrals as the dimension of the phase space. In this paper, we relate both concepts. We also give a large list of globally periodic dynamical systems together with a complete set of their first integrals, emphasizing the ones coming from difference equations.     

Stochastic Dynamics for Passage Times and Diffusion Approximations for Finite Capacity Storage Models with Different Kinds of Barriers

In this article, we discuss a number of storage models of finite capacity with random inputs, random outputs, and linear release policy. They form a class of one-dimensional master equations with separable kernels. For this class of problems, the integral equations for first overflow or first emptiness can be transformed exactly into ordinary differential equations. Analysis is done with separable kernel. For all the stochastic models, two barriers are considered: one at X = 0 and the other at X = k, and the barriers are treated as absorbing or reflecting. The imbedding method is used to derive a third order differential equation. We consider first passage times for overflow without or with emptiness of the dam. We also study the passage times for first emptiness with and without overflows. The expected amount of overflows in a given time is also calculated. Finally, by suitable statistical features, all these models are converted into diffusion process with drift. Closed form solutions are obtained for all the problems in terms of Laplace transform functions. For the diffusion process with drift first passage time density is arrived at by treating X = 0 and X = k as absorbing barriers. One of the barriers as reflecting is also studied.     

Two hyperfinite constructions of the brownian bridge

Infinitesimal Analysis is used to give two constructions of the brownian bridge process. In the first construction a hyperfinite tied down random walk is used and a brownian bridge is obtained via the standard part map. As a consequence it is shown that the brownian bridge is the weak limit of a sequence of normalized tied down random walks. The second construction is based on a hyperfinite uniform empirical process. This construction gives an almost trivial proof of Donsker's Invariance Principle for the uniform empirical process     

Parallel and bootstrapped stochastic approximation

Parallelization of stochastic approximation procedures can reduce computation and total observation time of a system. Concerning the number of all observations used by the pure sequential and the suggested parallel method a weak invariance principle implies the asymptotic equivalence of both methods. A loglog invariance principle and a rate of a.s. convergence result describe the pathwise properties. Due to the parallel design asymptotic confidence regions can readily be constructed either by computing the bootstrap distribution or the Gaussian limit distribution determined by the empirical covariance     

Curvature identities derived from the integral formula for the first Pontrjagin number

We give an integral formula for the first Pontrjagin number of a compact almost Hermitian surface and derive curvature identities from the integral formula based on the fundamental fact that the first Pontrjagin number in the deRham cohomology group is a topological invariant. Further, we provide some applications of the identities.     

Testing of a scintillator and fibre optic based radiation sensor

We describe the optimisation of RadLine^®; a small, real time, remotely operated radiation detector, which consists of an inorganic scintillation crystal coupled to a fibre optic cable transporting produced photons to a CCD camera some distance away. RadLine^® is tested in a beta and gamma narrow radiation field of 2.4 GBq, from a Caesium-137 (662 KeV) source, at doses rates between 0.125 mSvhr⁻¹ and 10 mSvhr⁻¹. Our results establish that the lower limit of the device corresponds to a dose rate of 0.2 mSvhr⁻¹, constrained by the signal to noise ratio of the instrument. We also demonstrate the process of characterising the RadLine^® for utilisation underwater due to its partial electrical inactiveness; and to consider how the instrument might perform in aquatic environments and ultimately in a First Generation Magnox Storage Ponds (FGMSP). The RadLine^® brings a marked difference to actual underwater radiation monitoring devices such as; HPGe, CZT and GM detectors, which not only incorporate the whole electronics within and are more bulky, only perform over a short range. The RadLine^®’s design offers signification value for intermediate (>100 m) and long range detection.     

Electronic and lattice vibrational properties of cubic BaHfO3 from first principles calculations

Through first principles calculations, we investigated the electronic structure and lattice vibrational properties of BaHfO₃. The optimized lattice constant of BaHfO₃ is in agreement with experimental and theoretical results. Our results show that cubic BaHfO₃ is an insulator with an indirect band gap of 3.5 eV. Besides, the calculation using the screened exchange local density approximation (sX-LDA) has been performed with the predicted minimum gap of 5.3 eV. The phonon dispersion curves of BaHfO₃ were also calculated. All positive phonon frequencies in the Brillouin zone were found, indicating the stability of BaHfO₃ structure.     

Magnetic properties in zinc-blende CdS induced by Cd vacancies

The magnetic property induced by neutral Cd and S vacancies in CdS bulk and thin film are investigated, using first principles simulation. For bulk CdS, the magnetism originates from Cd, instead of S, vacancies. The ferromagnetism with a Curie temperature above room temperature can be expected. For CdS thin film, both Cd and S vacancies does not yield any magnetism at the (111) surface, while local magnetic moments at the outermost S plane of the (001) surface is ascribed to the surface effect. The ferromagnetism at S-terminated (001) surface can account for the experimental observation.