Time dependent analysis of finite buffer fluid flows and risk models with a dividend barrier

Based on the matrix-analytic approach to fluid flows initiated by Ramaswami, we develop an efficient time dependent analysis for a general Markov modulated fluid flow model with a finite buffer and an arbitrary initial fluid level at time 0. We also apply this to an insurance risk model with a dividend barrier and a general Markovian arrival process of claims with possible dependencies in successive inter-claim intervals and in claim sizes. We demonstrate the implementability and accuracy of our algorithms through a set of numerical examples that could also serve as test cases for comparing other solution approaches.      

On a generalization of Pólya’s theorem

We consider generalizations of Pólya’s theorem to the case of entire functions taking algebraic values at natural or integer points.     

Dimensional variation in production of high-aspect-ratio micro-pillars array by micro powder injection molding

Micro powder injection molding (μPIM) is one of the potential processes for the mass production of metallic microstructures and micro components. Here, μPIM is the miniaturization of conventional PIM, which involves four processing steps: mixing, injection molding, debinding and sintering. This paper looks into the feasibility and effectiveness of μPIM as a key mass production process for the fabrication of metallic micro components. For it to be an effective re-production process, it is imperative to examine how well parts can be duplicated/fabricated from a master mold. In this work, the dimensional variation of high-aspect-ratio micro-pillars arrays, in particular the dimensional shrinkage, global warpage, and surface roughness at each stage of the μPIM process for a range of molding pressures, are quantified and compared in detail. The sensitivity of the dimensional variation of the microstructures to the packing pressure is reported. The mechanism behind the dimensional variation is analyzed. PACS 81.20.Ev; 81.20.Hy; 81.70.Fy; 07.60.Ly; 81.05.-t     

The essential Lagrangian-Grassmannian and the homotopy type of the Fredholm Lagrangian-Grassmannian

Let H be a separable infinite dimensional Hilbert space endowed with a symplectic structure and let L₀⊂H be a Lagrangian subspace. Using the results of [A. Abbondandolo, P. Majer, Infinite dimensional Grassmannians, math.AT/0307192], we show that the Fredholm Lagrangian-Grassmannian FL₀(Λ) has the homotopy type of Gc(L₀), the Grassmannian of all Lagrangian subspaces of H that are compact perturbations of L₀. It is well known that the latter has the homotopy type of the quotient U(∞)/O(∞). As a corollary, we recover a result by B. Booss-Bavnbek and K. Furutani (see [B. Booss-Bavnbek, K. Furutani, Symplectic functional analysis and spectral invariants, Contemp. Math. 242 (1999) 53-83; K. Furutani, Fredholm-Lagrangian-Grassmannian and the Maslov index, J. Geom. Phys. 51 (2004) 269-331]) that the L₀-Maslov index is an isomorphism between the fundamental group of FL₀(Λ) and the integers.     

Advances in constant-velocity Mössbauer instrumentation

A prototype of a programmable constant-velocity scaler is presented. This instrument allows the acquisition of partial Mössbauer spectra in selected energy regions using standard drivers and transducers. It can be fully operated by a remote application, thus data acquisition can be automated. The instrument consists of a programmable counter and a constant-velocity reference. The reference waveform generator is amplitude modulated with 13-bit resolution, and is programmable in a wide range of frequencies and waveforms in order to optimize the performance of the transducer. The counter is compatible with most standard SCA, and is configured as a rate-meter that provides counts per selectable time slice at the programmed velocity. As a demonstration of the instrument applications, a partial Mössbauer spectrum of a natural iron foil was taken. Only positive energies were studied in 512 channels, accumulating 20 s per channel. A line width of 0.20 mm/s was achieved, performing with an efficiency of 80%.     

Some remarks on Newton–Sabatier methods

It is shown how Newton–Sabatier methods (arising in inverse scattering at fixed energy) can be related to spectral measures and typically when they correspond to regular potentials. A number of spectral formulae for various transmutation kernels are also given in terms of general Kontorovi?–Lebedev theory and connections to generating functions, generalized orthogonal polynomials, etc. are indicated.     

Coupled Thermo-Hydro-Mechanical and Chemical Analysis of Expansive Clay Subjected to Heating and Hydration

A fully coupled formulation combining reactive transport and an existing thermo-hydro-mechanical (THM) code is presented. Special attention has been given to phenomena likely to be encountered in clay barriers used as part of containment systems of nuclear waste. The types of processes considered include hydrolysis, complex formation, oxidation/reduction reactions, acid/base reactions, precipitation/dissolution of minerals and cation exchange. Both kinetically-controlled and equilibrium-controlled reactions have been incorporated. The total analytical concentrations (including precipitated minerals) are adopted as basic transport variables and chemical equilibrium is achieved by minimizing Gibbs Free Energy. The formulation has been incorporated in a general purpose computer code capable of performing numerical analysis of engineering problems. A validation exercise concerning a laboratory experiment involving the heating and hydration of an expansive compacted clay is described.     

On perfectly normal dense subspaces of products

Let M be a separable metric space consisting of more than one point. We construct perfectly normal dense subspaces Z⊂Mc² and (under additional set-theoretic assumption) Y⊂Mc which are not collectionwise Hausdorff.     

Time interval distributions of atoms in atomic beams

We report an experimental investigation of two-particle correlations between neutral atoms in a Hanbury Brown and Twiss experiment. Both an atom laser beam and a pseudo-thermal atomic beam are extracted from a Bose–Einstein condensate and the atom flux is measured with a single atom counter. We determine the conditional and the unconditional detection probabilities for the atoms in the beam and find good agreement with the theoretical predictions. PACS 03.75.Pp; 05.30.Jp; 07.77.Gx; 42.50.Pq     

A side-coupled photonic crystal filter with sidelobe suppression

This paper presents the theoretical model and the optimization method to suppress the sidelobes of side-coupled photonic crystal filters. Numerical verification shows a good agreement between the theoretical method and the finite-difference time-domain simulation, but the theoretic method does not involve the time-consuming computation. The theoretical method also presents a better physical image for choosing the critical parameters, such as the quality factor, phase shift and the number of resonators. Based on the theoretical model, two optimization methods (chirp and cascading) are proposed to deeply suppress the sidelobes. They also show more flexibility in controlling the bandwidth and steepness of the roll-off in the filter. PACS 42.70.Qs