Research study of droplet sizing technology leading to the development of an advanced droplet sizing system

An instrument to measure the size and velocity of droplets was developed. The instrument uses one of two techniques, as appropriate. In the first technique two small laser beams of one color identify the center of a larger laser beam of a different color. This defines a region of almost uniform intensity where the light scattered by the individual droplets can be related to their size. The first technique uses the visibility of a Doppler burst and validates it against the peak intensity of the signal's pedestal. Results are presented for monodisperse, bimodal, trimodal, and polydisperse sprays produced by the Berglund-Liu droplet generator and a pressure nozzle. Size distributions of a given spray obtained using three different size ranges show excellent self-consistency in the overlapping region. Measurements of sprays of known characteristics exhibit errors in the order of 10%. The principles of operation and design criteria of the instrument are discussed in great detail

Flux-cutting and flux-transport effects in type-II superconductor slabs in a parallel rotating magnetic field

The magnetic response of irreversible type-II superconductor slabs subjected to in-plane rotating magnetic field is investigated by applying the circular, elliptic, extended-elliptic, and rectangular flux-line-cutting critical-state models. Specifically, the models have been applied to explain experiments on a PbBi rotating disk in a fixed magnetic field ${\bm H}_a$, parallel to the flat surfaces. Here, we have exploited the equivalency of the experimental situation with that of a fixed disk under the action of a parallel magnetic field, rotating in the opposite sense. The effect of both the magnitude $H_a$ of the applied magnetic field and its angle of rotation $\alpha_s$ upon the magnetization of the superconductor sample is analyzed. When $H_a$ is smaller than the penetration field $H_P$, the magnetization components, parallel and perpendicular to ${\bm H_a}$, oscillate with increasing the rotation angle. On the other hand, if the magnitude of the applied field, $H_a$, is larger than $H_P$, both magnetization components become constant functions of $\alpha_s$ at large rotation angles. The evolution of the magnetic induction profiles inside the superconductor is also studied.Comment: 12 pages, 29 figure

Moving embedded lattice solitons

It was recently proved that isolated unstable "embedded lattice solitons" (ELS) may exist in discrete systems. The discovery of these ELS gives rise to relevant questions such as the following: are there continuous families of ELS?, can ELS be stable?, is it possible for ELS to move along the lattice?, how do ELS interact?. The present work addresses these questions by showing that a novel differential-difference equation (a discrete version of a complex mKdV equation) has a two-parameter continuous family of exact ELS. The numerical tests reveal that these solitons are stable and robust enough to withstand collisions. The model may apply to the description of a Bose-Einstein condensate with dipole-dipole interactions between the atoms, trapped in a deep optical-lattice potential.Comment: 13 pages, 11 figure

Optimality of the Maximum Likelihood estimator in Astrometry

The problem of astrometry is revisited from the perspective of analyzing the attainability of well-known performance limits (the Cramer-Rao bound) for the estimation of the relative position of light-emitting (usually point-like) sources on a CCD-like detector using commonly adopted estimators such as the weighted least squares and the maximum likelihood. Novel technical results are presented to determine the performance of an estimator that corresponds to the solution of an optimization problem in the context of astrometry. Using these results we are able to place stringent bounds on the bias and the variance of the estimators in close form as a function of the data. We confirm these results through comparisons to numerical simulations under a broad range of realistic observing conditions. The maximum likelihood and the weighted least square estimators are analyzed. We confirm the sub-optimality of the weighted least squares scheme from medium to high signal-to-noise found in an earlier study for the (unweighted) least squares method. We find that the maximum likelihood estimator achieves optimal performance limits across a wide range of relevant observational conditions. Furthermore, from our results, we provide concrete insights for adopting an adaptive weighted least square estimator that can be regarded as a computationally efficient alternative to the optimal maximum likelihood solution. We provide, for the first time, close-form analytical expressions that bound the bias and the variance of the weighted least square and maximum likelihood implicit estimators for astrometry using a Poisson-driven detector. These expressions can be used to formally assess the precision attainable by these estimators in comparison with the minimum variance bound.Comment: 24 pages, 7 figures, 2 tables, 3 appendices. Accepted by Astronomy & Astrophysic

Higgs Inflation as a Mirage

We discuss a simple unitarization of Higgs inflation that is genuinely weakly coupled up to Planckian energies. A large non-minimal coupling between the Higgs and the Ricci curvature is induced dynamically at intermediate energies, as a simple ratio of mass scales. Despite not being dominated by the Higgs field, inflationary dynamics simulates the `Higgs inflation' one would get by blind extrapolation of the low-energy effective Lagrangian, at least qualitatively. Hence, Higgs inflation arises as an approximate `mirage' picture of the true dynamics. We further speculate on the generality of this phenomenon and show that, if Higgs-inflation arises as an effective description, the details of the UV completion are necessary to extract robust quantitative predictions.Comment: 21 pages, 2 figure

A No-Lose Theorem for Higgs Searches at a Future Linear Collider

Assuming perturbativity up to a high energy scale $\sim 10^{16}$ GeV, we demonstrate that a future $e^+e^-$ linear collider operating at $\sqrt{s} =$ 500 GeV with $\int{\cal L}=$ 500 fb$^{-1}$ per year (such as the recently proposed TESLA facility) will detect a Higgs boson signal regardless of the complexity of the Higgs sector and of how the Higgs bosons decay.Comment: 4 pages, LaTe

Conformal mapping of ultrasonic crystals: confining ultrasound and cochlear-like wave guiding

Conformal mapping of a slab of a two-dimensional ultrasonic crystal generate a closed geometrical arrangement of ultrasonic scatterers with appealing acoustic properties. This acoustic shell is able to confine ultrasonic modes. Some of these internal resonances can be induced from an external wave source. The mapping of a linear defect produces a wave-guide that exhibits a spatial-frequency selection analogous to that characteristic of a synthetic "cochlea". Both, experimental and theoretical results are reported here.Comment: 4 pages, 4 figure

Pair distribution function and structure factor of spherical particles

The availability of neutron spallation-source instruments that provide total scattering powder diffraction has led to an increased application of real-space structure analysis using the pair distribution function. Currently, the analytical treatment of finite size effects within pair distribution refinement procedures is limited. To that end, an envelope function is derived which transforms the pair distribution function of an infinite solid into that of a spherical particle with the same crystal structure. Distributions of particle sizes are then considered, and the associated envelope function is used to predict the particle size distribution of an experimental sample of gold nanoparticles from its pair distribution function alone. Finally, complementing the wealth of existing diffraction analysis, the peak broadening for the structure factor of spherical particles, expressed as a convolution derived from the envelope functions, is calculated exactly for all particle size distributions considered, and peak maxima, offsets, and asymmetries are discussed.Comment: 7 pages, 6 figure