Symmetries of the heat equation on the lattice

Discrete versions of the heat equation on two-dimensional uniform lattices are shown to possess the same symmetry algebra as their continuum limits. Solutions with definite symmetry properties are presented.     

Structural distortion,charge modulation and local anisotropies in magnetite below the Verwey transition using resonant X‐ray scattering

The pattern of charge modulations and local anisotropies below the Verwey transition has been determined and quantified in high‐quality Fe₃O₄ single crystals and thin films grown on MgO by using resonant X‐ray scattering at the Fe K‐edge. The energy, polarization and azimuthal angle dependencies of an extensive set of reflections with potential sensitivity to charge or local anisotropy orderings have been analyzed to explore their origins. A charge disproportion on octahedral B sites of 0.20 ± 0.05 e^? with [0 0 1] and cubic periodicities has been confirmed, while no significant charge disproportion has been obtained with [0 0 1/2] cubic periodicity. Additional charge modulations in the monoclinic a–b plane are also present. In addition, the occurrence of new forbidden (1, 1, 0) and (0, 0, 2n + 1/2) cubic reflections that arise from the anisotropy of the local structure around different tetrahedral and octahedral Fe atoms is shown. This complex pattern of weak charge modulations and local anisotropies is fully compatible with the low‐temperature crystal structure refined in the non‐polar C2/c space group and disproves any bimodal charge disproportion of the octahedral Fe atoms.     

A closed model category for ()-connected spaces

For each integer , we give a distinct closed model category structure to the category of pointed spaces such that the corresponding localized category is equivalent to the standard homotopy category of -connected CW-complexes. The structure of closed model category given by Quillen to is based on maps which induce isomorphisms on all homotopy group functors and for any choice of base point. For each , the closed model category structure given here takes as weak equivalences those maps that for the given base point induce isomorphisms on for .

     

On the reactivity of naphthalene and biphenyl dianions: tying up loose ends concerning an SN2‐ET dichotomy in alkylation reactions

Naphthalene and biphenyl dianions are interesting compounds that can be obtained by double reduction of the corresponding arenes in solution with certain alkali metals. These dianions are highly reactive and rather elusive species with very high laying and highly delocalized electrons. They share many aspects of the reactivity of the alkali metal they originated from and consequently behave primarily as strong electron transfer (ET) reagents. We report here kinetic evidence for a different type of reactivity in their alkylation reactions with alkyl fluorides. By using cyclopropylmethyl fluoride (c‐C₃H₅CH₂F) as a very fast radical probe, we were able to settle that this alkylation does not involve the classical electron transfer reaction followed by radical coupling between diffusing radicals, but supports the alternative S_N2 concerted mechanism, discerning thus this mechanistic S_N2‐ET dichotomy. Copyright © 2015 John Wiley & Sons, Ltd.     

Correlations in the sand pile model: From the log-normal distribution to self-organized criticality

We have studied the approach of the Abelian sand pile model towards the stationary, self-organized criticality state. The uncorrelated limit is shown both numerically and by a simple analysis to follow the log-normal distribution. We introduce and evaluate several correlation fuctions to study the correlated region.     

Acoustic voice analysis in patients with essential tremor

To quantify several acoustic features of the voice in patients with essentialtremor (ET), 28 patients and 28 age- and sex-matched controls were studied. ET severity was assessed with the rating scale for tremor of Fahn, Tolosa, and Marín. The Computerized Speech Lab 4300 program (Kay Elemetrics) was used. Two-second samples of a sustained /a/ and a sentence were captured with a microphone and laryngograph equipment. Measures included fundamental frequency (F₀), frequency perturbation (fitter, Koike algorithm), intensity perturbation (shimmer, Horii algorithm), and harmonic-to-noise ratio (H/N, Yumoto algorithm) of the vowel /a/, and the frequency and intensity variability of the sentence, phonational range, and dynamic range at the natural frequency, maximum phonational time, and s/z ratio. All subjects underwent indirect laryngoscopy and/or laryngeal fibroscopy. When compared with controls, ET patients showed higher jitter, lower H/N ratio (the last one only with laryngographic signal), of the vowel /a/, lower frequency variability in the microphonc signal, lower intensity variability in the laryngographic signal of the sentence, and significantly lower dynamic range at natural frequency of phonation. ET patients reported higher frequency of the presence of high voice intensity, tremor, and struggle. Several acoustic parameters were influenced by the severity of the disease, including shimmer, jitter, H/N ratio, frequency variability of the sentence, and s/z ratio, although neither of the acoustic analysis values or the phonetometric measurements were affected by the presence of voice tremor or by a successful pharmacological treatment of ET.     

A computational modeling approach of the jet-like acoustic streaming and heat generation induced by low frequency high power ultrasonic horn reactors

High power ultrasound reactors have gained a lot of interest in the food industry given the effects that can arise from ultrasonic-induced cavitation in liquid foods. However, most of the new food processing developments have been based on empirical approaches. Thus, there is a need for mathematical models which help to understand, optimize, and scale up ultrasonic reactors. In this work, a computational fluid dynamics (CFD) model was developed to predict the acoustic streaming and induced heat generated by an ultrasonic horn reactor. In the model it is assumed that the horn tip is a fluid inlet, where a turbulent jet flow is injected into the vessel. The hydrodynamic momentum rate of the incoming jet is assumed to be equal to the total acoustic momentum rate emitted by the acoustic power source. CFD velocity predictions show excellent agreement with the experimental data for power densities higher than W(0)/V ≥ 25kWm(-3). This model successfully describes hydrodynamic fields (streaming) generated by low-frequency-high-power ultrasound.     

Design and performance of BOREAS,the beamline for resonant X‐ray absorption and scattering experiments at the ALBA synchrotron light source

The optical design of the BOREAS beamline operating at the ALBA synchrotron radiation facility is described. BOREAS is dedicated to resonant X‐ray absorption and scattering experiments using soft X‐rays, in an unusually extended photon energy range from 80 to above 4000 eV, and with full polarization control. Its optical scheme includes a fixed‐included‐angle, variable‐line‐spacing grating monochromator and a pair of refocusing mirrors, equipped with benders, in a Kirkpatrick–Baez arrangement. It is equipped with two end‐stations, one for X‐ray magnetic circular dichroism and the other for resonant magnetic scattering. The commissioning results show that the expected beamline performance is achieved both in terms of energy resolution and of photon flux at the sample position.     

The effect of metal dispersion on the resonance of antennas at infrared frequencies

In this paper the optical parameters at infrared frequencies of metallic thin films were obtained experimentally using a variable angle spectroscopic ellipsometer and used to simulate numerically the frequency response of antennas and antenna-coupled detectors at infrared frequencies (5–15 μm). The simulation results agree with previously published data and practical guidelines are presented for the design and fabrication of dipole and bowtie antennas at infrared frequencies.