Two-dimensional Time-dependent Point Interactions

We study the time-evolution of a quantum particle subjected to time-dependent zero-range forces in two dimensions. After establishing a conceivable ansatz for the solution to the Schr\"{o}dinger equation, we prove that the wave packet time-evolution is completely specified by the solutions of a system of Volterra-type equations -- the {\it charge equations} -- involving the coefficients of the singular part of the wave function, thus extending to the two-dimensional case known results in one and three dimensions.Comment: 17 pages, AMS-LaTex; presentation of the model changed, small changes to Lemma 2.1 and Proposition 2.

A Quantum Model of Feshbach Resonances

We consider a quantum model of two-channel scattering to describe the mechanism of a Feshbach resonance. We perform a rigorous analysis in order to count and localize the energy resonances in the perturbative regime, i.e., for small inter-channel coupling, and in the non-perturbative one. We provide an expansion of the effective scattering length near the resonances, via a detailed study of an effective Lippmann-Schwinger equation with energy-dependent potential.Comment: 29 pages, pdfLaTe

Multiple crack propagation in friction stir welded aluminium joints

This paper is concerned with the simulation of crack propagation in friction stir welded butt joints, in order to assess the influence of process induced microstructural alterations and residual stresses on the fatigue behaviour of the assembly. The approach employed is based on the coupled use of the finite element method and the dual boundary element method in order to take advantage of the main capabilities of the two methods. The distribution of the process induced residual stresses has been mapped by means of the contour method. Then, the computed residual stresses field has been superimposed, in a dual boundary element environment, to the stress field as a result of a remote fatigue traction load and the crack growth is simulated. A two-parameter crack growth law, based on the evaluation of two thresholds, for the material being analysed, is used for the crack propagation rate assessment. The stress intensity factors are evaluated using the J-integral technique. Computational results have been compared with experimental data, provided from constant amplitude crack propagation tests on welded samples, showing the subdivision of the overall fatigue life in the two periods of crack initiation and crack propagation

The assessment of dog welfare in the waiting room of a veterinary clinic

Veterinary visits are known to be stressful for many dogs. The aim of this study was to assess dog welfare in the waiting room of the veterinary clinic through a multi-modal, non-invasive approach. Forty-five dogs were each videoed for 3 min in the waiting room of a veterinary clinic where they went for a scheduled visit. The welfare of each dog was assessed using a thorough video analysis and two overall evaluations (low, medium and high stress); one performed by a veterinary behaviourist and one by the dog's owner. Two-thirds of dogs spent more than 20% of the time displaying at least one indicator of stress, and 53.3% showed four or more behavioural signs of stress. Assessments of stress by the behaviourist indicated that level of stress in the waiting room was high in 28.9% of cases. The agreement between owners' and behaviourist's overall evaluations was quite low. The behaviourist's evaluations were strongly correlated with the time spent by dogs showing signs of stress and moderately correlated with the number of displayed signs, whilst owners' evaluations were not closely correlated to those factors. Dogs rated as highly stressed by the behaviourist were more prone to display resistance (halting, refusing to budge) when moving from the waiting room to the consultation room. The results of this pilot study support the idea that the welfare of dogs in the veterinary waiting room is often impaired, and that owners are unable to accurately assess stress in their dogs in such situations

SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group

Many important geometric estimation problems naturally take the form of synchronization over the special Euclidean group: estimate the values of a set of unknown poses given noisy measurements of a subset of their pairwise relative transforms. Examples of this class include the foundational problems of pose-graph simultaneous localization and mapping (SLAM) (in robotics), camera motion estimation (in computer vision), and sensor network localization (in distributed sensing), among others. This inference problem is typically formulated as a nonconvex maximum-likelihood estimation that is computationally hard to solve in general. Nevertheless, in this paper we present an algorithm that is able to efficiently recover certifiably globally optimal solutions of the special Euclidean synchronization problem in a non-adversarial noise regime. The crux of our approach is the development of a semidefinite relaxation of the maximum-likelihood estimation whose minimizer provides an exact MLE so long as the magnitude of the noise corrupting the available measurements falls below a certain critical threshold; furthermore, whenever exactness obtains, it is possible to verify this fact a posteriori, thereby certifying the optimality of the recovered estimate. We develop a specialized optimization scheme for solving large-scale instances of this semidefinite relaxation by exploiting its low-rank, geometric, and graph-theoretic structure to reduce it to an equivalent optimization problem defined on a low-dimensional Riemannian manifold, and then design a Riemannian truncated-Newton trust-region method to solve this reduction efficiently. Finally, we combine this fast optimization approach with a simple rounding procedure to produce our algorithm, SE-Sync. Experimental evaluation on a variety of simulated and real-world pose-graph SLAM datasets shows that SE-Sync is capable of recovering certifiably globally optimal solutions when the available measurements are corrupted by noise up to an order of magnitude greater than that typically encountered in robotics and computer vision applications, and does so more than an order of magnitude faster than the Gauss-Newton-based approach that forms the basis of current state-of-the-art techniques

Turning renewable feedstocks into a valuable and efficient chiral phosphate salt catalyst

Solketal, the chiral acetonide of glycerol, has been employed as the starting material in the design of a novel punctually chiral phosphate sodium salt for catalytic applications in organic and asymmetric synthesis. The racemate and the two enantiomers of the substrate are economic and commercially available, straightforwardly prepared in high yields from naturally occurring feedstocks. Therefore, remarkably, both enantiomers of the final catalyst can be synthesized by simple procedures in high yield and in compliance with several principles of green chemistry. To further demonstrate the usefulness of the novel catalyst, its application in a solventless protocol for cyanohydrin synthesis from a series of aldehydes has been presented

Microstructural and Mechanical Properties of Al2O3 and Al2O3/TiB2 Ceramics Consolidated by Plasma Pressure Compaction

Alumina oxide ceramics were produced by plasma pressure compaction (P2C) sintering process. Two types of pure α-alumina (Al2O3) and a mixture of alumina and titanium diboride (TiB2) powders were used as starting materials. Microstructure and mechanical properties, namely hardness, elastic modulus, and fracture toughness, were analyzed and correlated to the type of the sintered powders and the adopted manufacturing route. The microstructural development and the chemical composition variation induced by the sintering process were assessed by using scanning electron microscopy and x-ray diffraction. Nano-indentation and Chevron notch beam techniques were adopted to estimate the mechanical properties of the sintered ceramics. The conducted analyses show the capability of P2C technique to produce sound alumina ceramics. Pure alumina bulks exhibit a good level of compaction and mechanical properties close to those achievable with conventional sintering processes, such as hot isostatic pressing or spark plasma sintering. No significant alterations in the chemical composition of the ceramics were observed. The addition of the titanium diboride in the alumina powders caused a moderate increase in the grain size lowering the hardness and Young’s modulus of the sintered alumina and, at the same time, increased its fracture toughness to the occurrence of toughening mechanisms, like crack bridging and crack deflection