Singular kernels, multiscale decomposition of microstructure, and dislocation models

We consider a model for dislocations in crystals introduced by Koslowski, Cuiti\~no and Ortiz, which includes elastic interactions via a singular kernel behaving as the $H^{1/2}$ norm of the slip. We obtain a sharp-interface limit of the model within the framework of $\Gamma$-convergence. From an analytical point of view, our functional is a vector-valued generalization of the one studied by Alberti, Bouchitt\'e and Seppecher to which their rearrangement argument no longer applies. Instead we show that the microstructure must be approximately one-dimensional on most length scales and exploit this property to derive a sharp lower bound

A simple abstraction of arrays and maps by program translation

We present an approach for the static analysis of programs handling arrays, with a Galois connection between the semantics of the array program and semantics of purely scalar operations. The simplest way to implement it is by automatic, syntactic transformation of the array program into a scalar program followed analysis of the scalar program with any static analysis technique (abstract interpretation, acceleration, predicate abstraction,.. .). The scalars invariants thus obtained are translated back onto the original program as universally quantified array invariants. We illustrate our approach on a variety of examples, leading to the " Dutch flag " algorithm

SBV regularity for Hamilton-Jacobi equations in Rn\mathbb R^n

In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$\partial_t u + H(D_{x} u)=0 \qquad \textrm{in} \Omega\subset \mathbb R\times \mathbb R^{n} .$$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb R^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.Comment: 15 page

Self-adaptive high-frequency injection based sensorless control for interior permanent magnet synchronous motor drives \u2020

Abstract: An auto-tuning and self-adaptation procedure for High Frequency Injection (HFI) based position and speed estimation algorithms in Interior Permanent Magnet Synchronous Motor (IPMSM) drives is proposed in this paper. Analytical developments show that, using conventional approaches, the dynamics of the high-frequency tracking loop varies with differential inductances, which in turn depend on the machine operating point. On-line estimation and adaptation of the small signal gain of the loop is proposed here, allowing accurate auto-tuning of the sensorless control scheme which does not rely on a priori knowledge of the machine parameters. On-line adaptation of Phase-Locked Loop (PLL) gains and of the injected voltage magnitude is also possible, leading to important advantages from the performance, loss and acoustic point of view. The theoretical basis of the method has been introduced first and the main concept demonstrated by means of simulations. Implementation has been carried out using the hardware of a commercial industrial drive and two Interior Permanent Magnet Synchronous Motors, namely a prototype and an off-the-shelf machine. Experimental tests demonstrate the feasibility and effectiveness of the proposal

Evaluation of Fresh Groundwater Lens Volume and Its Possible Use in Nauru Island

A proper management of fresh groundwater lenses in small islands is required in order to avoid or at least limit uncontrolled saltwater intrusion and guarantee the availability of the resource even during drought occurrences. An accurate estimation of the freshwater volume stored in the subsoil is a key step in the water management decision process. This study focused on understanding the hydrogeological system behaviour and on assessing the sustainable use of the groundwater resource in Nauru Atoll Island (Pacific Ocean). A first phase, concerning the hydrogeological characterization of the island, highlighted the occurrence of few drought-resilient freshwater lenses along the seashore. The second part of the study focused on the characterization of a freshwater lens found in the northern coastal area and identified such area as the most suitable for the development of groundwater infrastructures for water withdrawal. The characterization activities allowed quantifying the freshwater lens thickness and volume in order to assess the capability to satisfy the population water demand. A geo-electrical tomography survey was carried out, and a 3D density-dependent numerical model was implemented in SEAWAT. The model results demonstrated that in small islands freshwater can unexpectedly accumulate underground right along the seashore and not in the centre of the island as is commonly believed. Furthermore, the model can constitute a useful tool to manage the groundwater resources and would allow the design of sustainable groundwater exploitation systems, avoiding saltwater intrusion worsening

Spectral Conditions on the State of a Composite Quantum System Implying its Separability

For any unitarily invariant convex function F on the states of a composite quantum system which isolates the trace there is a critical constant C such that F(w)<= C for a state w implies that w is not entangled; and for any possible D > C there are entangled states v with F(v)=D. Upper- and lower bounds on C are given. The critical values of some F's for qubit/qubit and qubit/qutrit bipartite systems are computed. Simple conditions on the spectrum of a state guaranteeing separability are obtained. It is shown that the thermal equilbrium states specified by any Hamiltonian of an arbitrary compositum are separable if the temperature is high enough.Comment: Corrects 1. of Lemma 2, and the (under)statement of Proposition 7 of the earlier version

A decomposition theorem for BV functions

The Jordan decomposition states that a function f: R \u2192 R is of bounded variation if and only if it can be written as the dierence of two monotone increasing functions. In this paper we generalize this property to real valued BV functions of many variables, extending naturally the concept of monotone function. Our result is an extension of a result obtained by Alberti, Bianchini and Crippa. A counterexample is given which prevents further extensions

Influence of Diabetes on Implant Failure and Peri-Implant Diseases: A Retrospective Study

Diabetes is an important modifying factor of periodontitis, but its association with peri-implant diseases has not been fully explored and the existing literature reports controversial results. The aim of this retrospective study was to evaluate the influence of diabetes on peri-implantitis and implant failure. Smoking status, history of periodontal disease, presence of diabetes, diabetes type, therapy and glycaemia levels were collected in a total of 204 subjects treated with 929 implants, with a mean follow-up time of 5.7 \ub1 3.82 years after loading. Odds ratio (OR) for diabetes as a direct cause of peri-implantitis and implant failure were calculated, adjusted for smoking status and history of periodontitis. Nineteen patients were diabetic and most of them presented a good control of the disease at the time of surgery. The overall patient-level prevalence of peri-implantitis was 11.3%. Among diabetic patients, one developed peri-implantitis, whereas one experienced multiple implant failures. The calculated ORs, adjusted for smoking status and periodontitis, were not statistically significant. The results revealed no association between diabetes and peri-implantitis or implant failure coherently with the existing scientific literature. The actual influence of hyperglycemia on implant failure is still uncertain and new studies with larger cohorts of patients are needed

Seasonal budgets of ozone and oxidant precursors in an industrial coastal area of northern Italy

The seasonal budgets and evolution of photochemical oxidants reported for greater Ravenna's urban-industrial area in the present study were calculated using the combined data from on-site systematic surveys (1978-1989) and from the monitoring network of the local environmental authorities. The notable differences in the concentrations of ozone and nitrogen oxides depended on season, and meteorological variables showed a marked correlation to the seasonal budget of trace constituents. The weak local circulation, the land-sea breeze system, and high solar radiation in summer, which may persist at length because of the anticyclonic conditions, can produce episodes of intense photochemical reactions. In winter, by contrast, low solar radiation and the absence of the breeze system results in very different evolutions of both pollutant concentrations and their seasonal budget