Real rank boundaries and loci of forms

In this article we study forbidden loci and typical ranks of forms with respect to the embeddings of $\mathbb P^1\times \mathbb P^1$ given by the line bundles $(2,2d)$. We introduce the Ranestad-Schreyer locus corresponding to supports of non-reduced apolar schemes. We show that, in those cases, this is contained in the forbidden locus. Furthermore, for these embeddings, we give a component of the real rank boundary, the hypersurface dividing the minimal typical rank from higher ones. These results generalize to a class of embeddings of $\mathbb P^n\times \mathbb P^1$. Finally, in connection with real rank boundaries, we give a new interpretation of the $2\times n \times n$ hyperdeterminant.Comment: 17 p

Continuous non-perturbative regularization of QED

We regularize in a continuous manner the path integral of QED by construction of a non-local version of its action by means of a regularized form of Dirac's $\delta$ functions. Since the action and the measure are both invariant under the gauge group, this regularization scheme is intrinsically non-perturbative. Despite the fact that the non-local action converges formally to the local one as the cutoff goes to infinity, the regularized theory keeps trace of the non-locality through the appearance of a quadratic divergence in the transverse part of the polarization operator. This term which is uniquely defined by the choice of the cutoff functions can be removed by a redefinition of the regularized action. We notice that as for chiral fermions on the lattice, there is an obstruction to construct a continuous and non ambiguous regularization in four dimensions. With the help of the regularized equations of motion, we calculate the one particle irreducible functions which are known to be divergent by naive power counting at the one loop order.Comment: 23 pages, LaTeX, 5 Encapsulated Postscript figures. Improved and revised version, to appear in Phys. Rev.

Residual strain mapping through pair distribution function analysis of the porcelain veneer within a yttria partially stabilised zirconia dental prosthesis

OBJECTIVE: Residually strained porcelain is influential in the early onset of failure in Yttria Partially Stabilised Zirconia (YPSZ) - porcelain dental prosthesis. In order to improve current understanding it is necessary to increase the spatial resolution of residual strain analysis in these veneers. METHODS: Few techniques exist which can resolve residual stress in amorphous materials at the microscale resolution required. For this reason, recent developments in Pair Distribution Function (PDF) analysis of X-ray diffraction data of dental porcelain have been exploited. This approach has facilitated high-resolution (70μm) quantification of residual strain in a YPSZ-porcelain dental prosthesis. In order to cross-validate this technique, the sequential ring-core focused ion beam and digital image correlation approach was implemented at a step size of 50μm. This semi-destructive technique exploits microscale strain relief to provide quantitative estimates of the near-surface residual strain. RESULTS: The two techniques were found to show highly comparable results. The residual strain within the veneer was found to be primarily tensile, with the highest magnitude stresses located at the YPSZ-porcelain interface where failure is known to originate. Oscillatory tensile and compressive stresses were also found in a direction parallel to the interface, likely to be induced by the multiple layering used during fabrication. SIGNIFICANCE: This study provides the insights required to improve prosthesis modelling, to develop new processing routes that minimise residual stress and ultimately to reduce prosthesis failure rates. The PDF approach also offers a powerful new technique for microscale strain quantification in amorphous materials.</p

Production Process Modelling Architecture to Support Improved Cyber-Physical Production Systems

With the proliferation of intelligent networks in industrial environments, manufacturing SME’s have been in a continuous search for integrating and retrofitting existing assets with modern technologies that could provide low-cost solutions for optimizations in their production processes. Their willingness to support a technological evolution is firmly based on the perception that, in the future, better tools will guarantee process control, surveillance and maintenance. For this to happen, the digitalization of valuable and extractable information must be held in a cost-effective manner, through contemporary approaches such as IoT, creating the required fluidity between hardware and software, for implementing Cyber-Physical modules in the manufacturing process. The goal of this work is to develop an architecture that will support companies to digitize their machines and processes through an MDA approach, by modeling their production processes and physical resources, and transforming into an implementation model, using contemporary CPS and IoT concepts, to be continuously improved using forecasting/predictive algorithms and analytics.authorsversionpublishe

Goal-Based Selection of Visual Representations for Big Data Analytics

The H2020 TOREADOR Project adopts a model-driven architecture to streamline big data analytics and make it widely available to companies as a service. Our work in this context focuses on visualization, in particular on how to automate the translation of the visualization objectives declared by the user into a suitable visualization type. To this end we first define a visualization context based on seven prioritizable coordinates for assessing the user's objectives and describing the data to be visualized; then we propose a skyline-based technique for automatically translating a visualization context into a set of suitable visualization types. Finally, we evaluate our approach on a real use case excerpted from the pilot applications of TOREADOR

Regularization as quantization in reducible representations of CCR

A covariant quantization scheme employing reducible representations of canonical commutation relations with positive-definite metric and Hermitian four-potentials is tested on the example of quantum electrodynamic fields produced by a classical current. The scheme implies a modified but very physically looking Hamiltonian. We solve Heisenberg equations of motion and compute photon statistics. Poisson statistics naturally occurs and no infrared divergence is found even for pointlike sources. Classical fields produced by classical sources can be obtained if one computes coherent-state averages of Heisenberg-picture operators. It is shown that the new form of representation automatically smears out pointlike currents. We discuss in detail Poincar\'e covariance of the theory and the role of Bogoliubov transformations for the issue of gauge invariance. The representation we employ is parametrized by a number that is related to R\'enyi's $\alpha$. It is shown that the ``Shannon limit" $\alpha\to 1$ plays here a role of correspondence principle with the standard regularized formalism.Comment: minor extensions, version submitted for publicatio

Rich Polymorphism of a Metal-Organic Framework in Pressure-Temperature Space.

We present an in situ powder X-ray diffraction study on the phase stability and polymorphism of the metal-organic framework ZIF-4, Zn(imidazolate)2, at simultaneous high pressure and high temperature, up to 8 GPa and 600 °C. The resulting pressure-temperature phase diagram reveals four, previously unknown, high-pressure-high-temperature ZIF phases. The crystal structures of two new phases-ZIF-4-cp-II and ZIF-hPT-II-were solved by powder diffraction methods. The total energy of ZIF-4-cp-II was evaluated using density functional theory calculations and was found to lie in between that of ZIF-4 and the most thermodynamically stable polymorph, ZIF- zni. ZIF-hPT-II was found to possess a doubly interpenetrated diamondoid topology and is isostructural with previously reported Cd(Imidazolate)2 and Hg(Imidazolate)2 phases. This phase exhibited extreme resistance to both temperature and pressure. The other two new phases could be assigned with a unit cell and space group, although their structures remain unknown. The pressure-temperature phase diagram of ZIF-4 is strikingly complicated when compared with that of the previously investigated, closely related ZIF-62 and demonstrates the ability to traverse complex energy landscapes of metal-organic systems using the combined application of pressure and temperature