Spectral theory for the failure of linear control in a nonlinear stochastic system

We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur in systems described by linearly stable but strongly nonnormal evolution operators. In spatially extended systems the nonnormality manifests itself in two different but complementary ways: transient amplification and spectral focusing of disturbances. We show that temporal and spatial aspects of the nonnormality and the type of nonlinearity are all crucially important to understanding and describing the mechanism of nonlinear instability. Presented results are expected to apply equally to other physical systems where strong nonnormality is due to the presence of mean flow rather than the action of control.Comment: Submitted to Physical Review

Electronic structure and superconductivity of Europium

We have calculated the electronic structure of Eu for the bcc, hcp, and fcc crystal structures for volumes near equilibrium up to a calculated 90 GPa pressure using the augmented-plane wave method in the local-density approximation. The frozen-core approximation was used with a semi-empirical shift of the f-states energies in the radial Schr$\ddot{o}$dinger equation to move the occupied 4f valence states below the $\Gamma_1$ energy and into the core. This shift of the highly localized f-states yields the correct europium phase ordering with lattice parameters and bulk moduli in good agreement with experimental data. The calculated superconductivity properties under pressure for the $\it bcc$ and $\it hcp$ structures are also found to agree with and follow a $T_c$ trend similar to recent measurement by Debessai et al.$^1$Comment: 8 page

Continuous trench, pulsed laser ablation for micro-machining applications

The generation of controlled 3D micro-features by pulsed laser ablation in various materials requires an understanding of the material's temporal and energetic response to the laser beam. The key enabler of pulsed laser ablation for micro-machining is the prediction of the removal rate of the target material, thus allowing real-life machining to be simulated mathematically. Usually, the modelling of micro-machining by pulsed laser ablation is done using a pulse-by-pulse evaluation of the surface modification, which could lead to inaccuracies when pulses overlap. To address these issues, a novel continuous evaluation of the surface modification that use trenches as a basic feature is presented in this paper. The work investigates the accuracy of this innovative continuous modelling framework for micro-machining tasks on several materials. The model is calibrated using a very limited number of trenches produced for a range of powers and feed speeds; it is then able to predict the change in topography with a size comparable to the laser beam spot that arises from essentially arbitrary toolpaths. The validity of the model has been proven by being able to predict the surface obtained from single trenches with constant feed speed, single trenches with variable feed speed and overlapped trenches with constant feed speed for three different materials (graphite, polycrystalline diamond and a metal-matrix diamond CMX850) with low error. For the three materials tested, it is found that the average error in the model prediction for a single trench at constant feed speed is lower than 5 % and for overlapped trenches the error is always lower than 10 %. This innovative modelling framework opens avenues to: (i) generate in a repeatable and predictable manner any desired workpiece microtopography; (ii) understand the pulsed laser ablation machining process, in respect of the geometry of the trench produced, therefore improving the geometry of the resulting parts; (iii) enable numerical optimisation for the beam path, thus supporting the development of accurate and flexible computer assisted machining software for pulsed laser ablation micro-machining applications

On the Normalization of the Neutrino-Deuteron Cross Section

As is well-known, comparison of the solar neutrino fluxes measured in SuperKamiokande (SK) by $\nu + e^- \to \nu + e^-$ and in the Sudbury Neutrino Observatory (SNO) by $\nu_e + d \to e^- + p + p$ can provide a ``smoking gun'' signature for neutrino oscillations as the solution to the solar neutrino puzzle. This occurs because SK has some sensitivity to all active neutrino flavors whereas SNO can isolate electron neutrinos. This comparison depends crucially on the normalization and uncertainty of the theoretical charged-current neutrino-deuteron cross section. We address a number of effects which are significant enough to change the interpretation of the SK--SNO comparison.Comment: 4 pages, 1 figure, submitted to PR

Comparison of Radiation Damage in Lead Tungstate Crystals under Pion and Gamma Irradiation

Studies of the radiation hardness of lead tungstate crystals produced by the Bogoroditsk Techno-Chemical Plant in Russia and the Shanghai Institute of Ceramics in China have been carried out at IHEP, Protvino. The crystals were irradiated by a 40-GeV pion beam. After full recovery, the same crystals were irradiated using a $^{137}Cs$ $\gamma$-ray source. The dose rate profiles along the crystal length were observed to be quite similar. We compare the effects of the two types of radiation on the crystals light output.Comment: 10 pages, 8 figures, Latex 2e, 28.04.04 - minor grammatical change

LED Monitoring System for the BTeV Lead Tungstate Crystal Calorimeter Prototype

We report on the performance of a monitoring system for a prototype calorimeter for the BTeV experiment that uses Lead Tungstate crystals coupled with photomultiplier tubes. The tests were carried out at the 70 GeV accelerator complex at Protvino, Russia.Comment: 12 pages, 8 figures, LaTeX2e, revised versio

Study of Radiation Damage in Lead Tungstate Crystals Using Intense High Energy Beams

We report on the effects of radiation on the light output of lead tungstate crystals. The crystals were irradiated by pure, intense high energy electron and hadron beams as well as by a mixture of hadrons, neutrons and gammas. The crystals were manufactured in Bogoroditsk, Apatity (both Russia), and Shanghai (China). These studies were carried out at the 70-GeV proton accelerator in Protvino

Ab initio Quantum and ab initio Molecular Dynamics of the Dissociative Adsorption of Hydrogen on Pd(100)

The dissociative adsorption of hydrogen on Pd(100) has been studied by ab initio quantum dynamics and ab initio molecular dynamics calculations. Treating all hydrogen degrees of freedom as dynamical coordinates implies a high dimensionality and requires statistical averages over thousands of trajectories. An efficient and accurate treatment of such extensive statistics is achieved in two steps: In a first step we evaluate the ab initio potential energy surface (PES) and determine an analytical representation. Then, in an independent second step dynamical calculations are performed on the analytical representation of the PES. Thus the dissociation dynamics is investigated without any crucial assumption except for the Born-Oppenheimer approximation which is anyhow employed when density-functional theory calculations are performed. The ab initio molecular dynamics is compared to detailed quantum dynamical calculations on exactly the same ab initio PES. The occurence of quantum oscillations in the sticking probability as a function of kinetic energy is addressed. They turn out to be very sensitive to the symmetry of the initial conditions. At low kinetic energies sticking is dominated by the steering effect which is illustrated using classical trajectories. The steering effects depends on the kinetic energy, but not on the mass of the molecules. Zero-point effects lead to strong differences between quantum and classical calculations of the sticking probability. The dependence of the sticking probability on the angle of incidence is analysed; it is found to be in good agreement with experimental data. The results show that the determination of the potential energy surface combined with high-dimensional dynamical calculations, in which all relevant degrees of freedon are taken into account, leads to a detailed understanding of the dissociation dynamics of hydrogen at a transition metal surface.Comment: 15 pages, 9 figures, subm. to Phys. Rev.

Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.Comment: 4 figures; version 3 minor changes; to appear in Statistics and Computin