An improved finite element space for discontinuous pressures

We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L(2)(Omega)-norm is of order h(1/2)). We propose a modification of the P(1)-conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system. The unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element, so that the implementation of the proposed space into existing codes is straightforward. With this modification, numerical tests show that the interpolation order improves to O(h(3/2)). The new pressure space is implemented for the stable P(1)(+)/P(1) mini-element discretization, and for the stabilized equal-order P(1)/P(1) discretization. Assessment is carried out for Poiseuille flow with a forcing surface and for a static bubble. In all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard P(1) space. In addition, two Navier-Stokes simulations with moving interfaces (Rayleigh-Taylor instability and merging bubbles) are reported to show that the proposed space is robust enough to carry out realistic simulations. (c) 2009 Elsevier B.V. All rights reserved.

A note on finite determinacy for corank 2 map germs from surfaces to 3-space

We study properties of finitely determined corank 2 quasihomogeneous map germs f: (C(2), 0) -> (C(3), 0). Examples and counter examples of such map germs are presented.

Comparing finite state machine test coverage criteria

To plan testing activities, testers face the challenge of determining a strategy, including a test coverage criterion that offers an acceptable compromise between the available resources and test goals. Known theoretical properties of coverage criteria do not always help and, thus, empirical data are needed. The results of an experimental evaluation of several coverage criteria for finite state machines (FSMs) are presented, namely, state and transition coverage; initialisation fault and transition fault coverage. The first two criteria focus on FSM structure, whereas the other two on potential faults in FSM implementations. The authors elaborate a comparison approach that includes random generation of FSM, construction of an adequate test suite and test minimisation for each criterion to ensure that tests are obtained in a uniform way. The last step uses an improved greedy algorithm.

Checking Completeness of Tests for Finite State Machines

In testing from a Finite State Machine (FSM), the generation of test suites which guarantee full fault detection, known as complete test suites, has been a long-standing research topic. In this paper, we present conditions that are sufficient for a test suite to be complete. We demonstrate that the existing conditions are special cases of the proposed ones. An algorithm that checks whether a given test suite is complete is given. The experimental results show that the algorithm can be used for relatively large FSMs and test suites.

A new scale-invariant ratio and finite-size scaling for the stochastic susceptible-infected-recovered model

The critical behavior of the stochastic susceptible-infected-recovered model on a square lattice is obtained by numerical simulations and finite-size scaling. The order parameter as well as the distribution in the number of recovered individuals is determined as a function of the infection rate for several values of the system size. The analysis around criticality is obtained by exploring the close relationship between the present model and standard percolation theory. The quantity UP, equal to the ratio U between the second moment and the squared first moment of the size distribution multiplied by the order parameter P, is shown to have, for a square system, a universal value 1.0167(1) that is the same for site and bond percolation, confirming further that the SIR model is also in the percolation class.

Light-induced lens analysis in photorefractive crystals employing phase-shifting real-time holographic interferometry

The purpose of this work is to study the potentialities of phase-shifting real-time holographic interferometry for the analysis of light-induced lens in photoreffactive and nonlinear optical materials. We show that this technique can be used for quantitative evaluation of the phase distribution of a wavefront changed by a light-induced lens and, consequently, the refractive index changes in these materials. The basic principle of this technique combines real-time holographic interferometry with phase-shifting technique for interferogram analysis. This method is demonstrated with in situ visualization, monitoring and analysis in real-time and uses a Bi(12)SiO(20) crystal as the holographic medium and a Bi(12)TiO(20) as the test sample. (C) 2008 Elsevier B.V. All rights reserved.

Finite temperature effective actions

We present, from first principles, a direct method for evaluating the exact fermion propagator in the presence of a general background held at finite temperature, which can be used to determine the finite temperature effective action for the system. As applications, we determine the complete one loop finite temperature effective actions for (0 + 1)-dimensional QED as well as the Schwinger model. These effective actions, which are derived in the real time (closed time path) formalism, generate systematically all the Feynman amplitudes calculated in thermal perturbation theory and also show that the retarded (advanced) amplitudes vanish in these theories. (C) 2009 Elsevier B.V. All rights reserved.

Infrared chiral anomaly at finite temperature

We study the Schwinger model at finite temperature and show that a temperature dependent chiral anomaly may arise from the long distance behavior of the electric field. At high temperature this anomaly depends linearly on the temperature T and is present not only in the two point function, but also in all even point amplitudes. (C) 2011 Elsevier B.V. All rights reserved.

Number of particle creation and decoherence in the nonideal dynamical Casimir effect at finite temperature

In this work we investigate the dynamical Casimir effect in a nonideal cavity by deriving an effective Hamiltonian. We first compute a general expression for the average number of particle creation, applicable for any law of motion of the cavity boundary, under the only restriction of small velocities. We also compute a general expression for the linear entropy of an arbitrary state prepared in a selected mode, also applicable for any law of motion of a slow moving boundary. As an application of our results we have analyzed both the average number of particle creation and linear entropy within a particular oscillatory motion of the cavity boundary. On the basis of these expressions we develop a comprehensive analysis of the resonances in the number of particle creation in the nonideal dynamical Casimir effect. We also demonstrate the occurrence of resonances in the loss of purity of the initial state and estimate the decoherence times associated with these resonances. Since our results were obtained in the framework of the perturbation theory, they are restricted, under resonant conditions, to a short-time approximation. (C) 2009 Elsevier Inc. All rights reserved.

Finite temperature correction to the Thomas-Fermi approximation for a Bose-Einstein condensate: comparison between theory and experiment

We observe experimentally a deviation of the radius of a Bose-Einstein condensate from the standard Thomas-Fermi prediction, after free expansion, as a function of temperature. A modified Hartree-Fock model is used to explain the observations, mainly based on the influence of the thermal cloud on the condensate cloud.

Transition to quantum turbulence in finite-size superfluids

A novel concept of quantum turbulence in finite size superfluids, such as trapped bosonic atoms, is discussed. We have used an atomic (87)Rb Bose-Einstein condensate (BEC) to study the emergence of this phenomenon. In our experiment, the transition to the quantum turbulent regime is characterized by a tangled vortex lines formation, controlled by the amplitude and time duration of the excitation produced by an external oscillating field. A simple model is suggested to account for the experimental observations. The transition from the non-turbulent to the turbulent regime is a rather gradual crossover. But it takes place in a sharp enough way, allowing for the definition of an effective critical line separating the regimes. Quantum turbulence emerging in a finite-size superfluid may be a new idea helpful for revealing important features associated to turbulence, a more general and broad phenomenon. [GRAPHICS] Amplitude versus elapsed time diagram of magnetically excited BEC superfluid, presenting the evolution from the non-turbulent regime, with well separated vortices, to the turbulent regimes, with tangled vortices (C) 2011 by Astro Ltd. Published exclusively by WILEY-VCH Verlag GmbH & Co. KGaA

Trigger and aperture of the surface detector array of the Pierre Auger Observatory

The surface detector array of the Pierre Auger Observatory consists of 1600 water-Cherenkov detectors, for the study of extensive air showers (EAS) generated by ultra-high-energy cosmic rays. We describe the trigger hierarchy, from the identification of candidate showers at the level of a single detector, amongst a large background (mainly random single cosmic ray muons), up to the selection of real events and the rejection of random coincidences. Such trigger makes the surface detector array fully efficient for the detection of EAS with energy above 3 x 10(18) eV, for all zenith angles between 0 degrees and 60 degrees, independently of the position of the impact point and of the mass of the primary particle. In these range of energies and angles, the exposure of the surface array can be determined purely on the basis of the geometrical acceptance. (C) 2009 Elsevier B.V. All rights reserved.

Thermo-optics parameters measurements in photorefractive sillenite Bi(12)SiO(20) crystals by thermal lens technique

The present work reports on the thermo-optical properties of photorefractive sillenite Bi(12)SiO(20) (BSO) crystals obtained by applying the Thermal Lens Spectrometry technique (TLS). This crystals presents one high photorefractive sensitivity in the region blue-green spectra, since the measurements were carried out at two pump beam wavelengths (514.5 nm and 750 nm) to study of the light-induced effects in this material (thermal and/or photorefractive). We determine thermo-optical parameters like thermal diffusivity (D), thermal conductivity (K) and temperature coefficient of the optical path length change (ds/dT) in sillenite crystals. These aspects, for what we know, not was studied in details up to now using the lens spectrometry technique and are very important against of the promising potentiality of applications these crystals in non linear optics, real time holography and optical processing data.

Thermal lens spectrometry in pyroelectric lithium niobate crystals

In this work, the light-induced lens effect due to thermal and/or photorefractive processes was studied in pyroelectric (undoped and Fe(2+)-doped) lithium niobate crystals (LiNbO(3)) using thermal lens spectrometry with a two-beam (pump-probe) mode-mismatched configuration. The measurements were carried out at two pump beam wavelengths (514.5 and 750 nm) to establish a full understanding of the present effects in this material (thermal and/or photorefractive). We present an easy-to-implement method to determine quantitative values of the pyroelectric coefficient (dPs/dT), its contribution to the thermal effect and other thermo-optical parameters like thermal diffusivity (D), thermal conductivity (K) and temperature coefficient of the optical path length change (ds/dT). These measurements were performed in LiNbO(3) and LiNbO(3): Fe (0.1 ppm Fe(2+)) crystals with c axis along the direction of laser propagation.

Very low optical absorptions and analyte concentrations in water measured by Optimized Thermal Lens Spectrometry

Thermal Lens Spectrometry has traditionally been carried out in the single-beam and the mode-mismatched dual-beam configurations. Recently, a much more sensitive dual-beam TL setup was developed, where the probe beam is expanded and collimated. This feature optimizes Thermal Lens (TL) signal and allows the use of thicker samples, further improving the sensitivity. In this paper, we have made comparisons between the conventional and optimized TL configurations, and presented applications such as measurements of very low absorptions and concentrations in water and Cr(III) aqueous solution in the UV-vis range. For pure water we found linear absorption coefficients as low as the Raman scattering one due to the stretching vibrational modes of OH group. The detection limit was estimated 1 x 10(-6) cm(-1) with a 180-mW excitation power using a 100-mm cell length. This sensitivity is very high, considering that water has a photothermal enhancement factor similar to 33 times smaller than CCl(4), for example. For Cr(III) species in aqueous solution, the limit of detection (LOD) was estimated in similar to 40 ng mL(-1) at 514 nm, or similar to 10ng mL(-1) at 405 nm, which is similar to 30 times smaller than the LOD achieved with conventional transmission techniques. The more recent TL configuration is very attractive to obtain absorption spectra, since the result does not depend critically on the beam parameters, unlike the other configurations. The main drawbacks of this optimized TL configuration are the longer acquisition time and the need for larger samples. (C) 2011 Published by Elsevier B.V.