Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

Motion compensation strategies in magnetic resonance imaging.

Image quality in magnetic resonance imaging (MRI) is considerably affected by motion. Therefore, motion is one of the most common sources of artifacts in contemporary cardiovascular MRI. Such artifacts in turn may easily lead to misinterpretations in the images and a subsequent loss in diagnostic quality. Hence, there is considerable research interest in strategies that help to overcome these limitations at minimal cost in time, spatial resolution, temporal resolution, and signal-to-noise ratio. This review summarizes and discusses the three principal sources of motion: the beating heart, the breathing lungs, and bulk patient movement. This is followed by a comprehensive overview of commonly used compensation strategies for these different types of motion. Finally, a summary and an outlook are provided.

Use of quantum dots in aqueous solution to detect blood fingermarks on non-porous surfaces.

A new and original reagent based on the use of highly fluorescent cadmium telluride (CdTe) quantum dots (QDs) in aqueous solution is proposed to detect weak fingermarks in blood on non-porous surfaces. To assess the efficiency of this approach, comparisons were performed with one of the most efficient blood reagents on non-porous surfaces, Acid Yellow 7 (AY7). To this end, four non-porous surfaces were studied, i.e. glass, transparent polypropylene, black polyethylene, and aluminium foil. To evaluate the sensitivity of both reagents, sets of depleted fingermarks were prepared, using the same finger, initially soaked with blood, which was then successively applied on the same surface without recharging it with blood or latent secretions. The successive marks were then cut in halves and the halves treated separately with each reagent. The results showed that QDs were equally efficient to AY7 on glass, polyethylene and polypropylene surfaces, and were superior to AY7 on aluminium. The use of QDs in new, sensitive and highly efficient latent and blood mark detection techniques appears highly promising. Health and safety issues related to the use of cadmium are also discussed. It is suggested that applying QDs in aqueous solution (and not as a dry dusting powder) considerably lowers the toxicity risks.

Participle Preposing and Other Related Phenomena in Old Spanish and Old Catalan

El participi i altres fenòmens relacionats en el Castellà i el Català antic

Towards economic and monetary union: changing trends in payment systems for new european members

The objective of this paper is preciselyto study the evolution of payment systems within the accession countries between 1996 and 2003 and compare them with those of the E.U. and the Eurozone countries

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay

Studying nanotoxic effects of CdTe quantum dots in Trypanosoma cruzi

Semiconductor nanoparticles, such as quantum dots (QDs), were used to carry out experiments in vivo and ex vivo with Trypanosoma cruzi. However, questions have been raised regarding the nanotoxicity of QDs in living cells, microorganisms, tissues and whole animals. The objective of this paper was to conduct a QD nanotoxicity study on living T. cruzi protozoa using analytical methods. This was accomplished using in vitro experiments to test the interference of the QDs on parasite development, morphology and viability. Our results show that after 72 h, a 200 μM cadmium telluride (CdTe) QD solution induced important morphological alterations in T. cruzi, such as DNA damage, plasma membrane blebbing and mitochondrial swelling. Flow cytometry assays showed no damage to the plasma membrane when incubated with 200 μM CdTe QDs for up to 72 h (propidium iodide cells), giving no evidence of classical necrosis. Parasites incubated with 2 μM CdTe QDs still proliferated after seven days. In summary, a low concentration of CdTe QDs (2 μM) is optimal for bioimaging, whereas a high concentration (200 μM CdTe) could be toxic to cells. Taken together, our data indicate that 2 μM QD can be used for the successful long-term study of the parasite-vector interaction in real time.

A survey on voltage sag events in power systems

This paper aims to survey the techniques and methods described in literature to analyse and characterise voltage sags and the corresponding objectives of these works. The study has been performed from a data mining point of view

Unusual voltage sag event detection in power systems

Three multivariate statistical tools (principal component analysis, factor analysis, analysis discriminant) have been tested to characterize and model the sags registered in distribution substations. Those models use several features to represent the magnitude, duration and unbalanced grade of sags. They have been obtained from voltage and current waveforms. The techniques are tested and compared using 69 registers of sags. The advantages and drawbacks of each technique are listed

Estimation of zero-sequence impedance of undergrounds cables for single-phase fault location in distribution systems with electric arc

This paper focus on the problem of locating single-phase faults in mixed distribution electric systems, with overhead lines and underground cables, using voltage and current measurements at the sending-end and sequence model of the network. Since calculating series impedance for underground cables is not as simple as in the case of overhead lines, the paper proposes a methodology to obtain an estimation of zero-sequence impedance of underground cables starting from previous single-faults occurred in the system, in which an electric arc occurred at the fault location. For this reason, the signal is previously pretreated to eliminate its peaks voltage and the analysis can be done working with a signal as close as a sinus wave as possible