Asymptotic analysis and estimates of blow‐up time for the radial symmetric semilinear heat equation in the open‐spectrum case

We estimate the blow‐up time for the reaction diffusion equation u_t=Δu+ λf(u), for the radial symmetric case, where f is a positive, increasing and convex function growing fast enough at infinity. Here λ>λ^*, where λ^* is the ‘extremal’ (critical) value for λ, such that there exists an ‘extremal’ weak but not a classical steady‐state solution at λ=λ^* with ∥w(?, λ)∥_∞→∞ as 0<λ→λ^*?. Estimates of the blow‐up time are obtained by using comparison methods. Also an asymptotic analysis is applied when f(s)=e^s, for λ?λ^*?1, regarding the form of the solution during blow‐up and an asymptotic estimate of blow‐up time is obtained. Finally, some numerical results are also presented. Copyright © 2007 John Wiley & Sons, Ltd.     

Visualizing defects and pore connectivity within metal–organic frameworks by X-ray transmission tomography

Metal–Organic Frameworks (MOFs) have the potential to change the landscape of molecular separations in chemical processes owing to their ability of selectively binding molecules. Their molecular sorting properties generally rely on the micro- and meso-pore structure, as well as on the presence of coordinatively unsaturated sites that interact with the different chemical species present in the feed. In this work, we show a first-of-its-kind tomographic imaging of the crystal morphology of a metal–organic framework by means of transmission X-ray microscopy (TXM), including a detailed data reconstruction and processing approach. Corroboration with Focused Ion Beam-Scanning Electron Microscopy (FIB-SEM) images shows the potential of this strategy for further (non-destructively) assessing the inner architecture of MOF crystals. By doing this, we have unraveled the presence of large voids in the internal structure of a MIL-47(V) crystal, which are typically thought of as rather homogeneous lattices. This challenges the established opinion that hydrothermal syntheses yield relatively defect-free material and sheds further light on the internal morphology of crystals.

TXM-tomography unraveled large macropore defects within a MIL-47(V) MOF crystal. These pores do not seem to be well connected and they show a preferential orientation.     

Convolutional Neural Network Approach for Multispectral Facial Presentation Attack Detection in Automated Border Control Systems

Automated border control systems are the first critical infrastructure point when crossing a border country. Crossing border lines for unauthorized passengers is a high security risk to any country. This paper presents a multispectral analysis of presentation attack detection for facial biometrics using the learned features from a convolutional neural network. Three sensors are considered to design and develop a new database that is composed of visible (VIS), near-infrared (NIR), and thermal images. Most studies are based on laboratory or ideal conditions-controlled environments. However, in a real scenario, a subject’s situation is completely modified due to diverse physiological conditions, such as stress, temperature changes, sweating, and increased blood pressure. For this reason, the added value of this study is that this database was acquired in situ. The attacks considered were printed, masked, and displayed images. In addition, five classifiers were used to detect the presentation attack. Note that thermal sensors provide better performance than other solutions. The results present better outputs when all sensors are used together, regardless of whether classifier or feature-level fusion is considered. Finally, classifiers such as KNN or SVM show high performance and low computational level.     

On the feasibility of performing non-linear autocorrelation with attosecond pulse trains

We present experimental results in which a second-order effect, namely two-photon ionization of atomic He induced by a superposition of harmonics, is observed. The harmonics are generated in a Xe gas-jet using a 790-nm 10-Hz femtosecond Ti:sapphire laser and are subsequently focused into a He gas-jet with a Kirkpatrick–Baez arrangement. The superposition is formed by using a thin In filter and it comprises the 7th to 13th harmonics. Solving the time-dependent Schrödinger equation for He in a polychromatic laser field, the He ⁺ ion yield is calculated as a function of the total XUV intensity. Using the calculated yield and taking into account the focusing and transmission properties of the arrangement, the number of He ⁺ ions produced per laser pulse is estimated and is found to be in reasonable agreement with its measured value. The total number of ions produced non-resonantly follows a nearly quadratic dependence on the harmonic intensity, thus establishing the feasibility of a second-order auto-correlation measurement of the superposition of harmonics, i.e., of a direct temporal characterization of attosecond pulse trains.     

Efficient wireless non-radiative mid-range energy transfer

We investigate whether, and to what extent, the physical phenomenon of long-lifetime resonant electromagnetic states with localized slowly-evanescent field patterns can be used to transfer energy efficiently over non-negligible distances, even in the presence of extraneous environmental objects. Via detailed theoretical and numerical analyses of typical real-world model-situations and realistic material parameters, we establish that such a non-radiative scheme can lead to “strong coupling” between two medium-range distant such states and thus could indeed be practical for efficient medium-range wireless energy transfer.     

A Simple Linear-Time Recognition Algorithm for Weakly Quasi-Threshold Graphs

Weakly quasi-threshold graphs form a proper subclass of the well-known class of cographs by restricting the join operation. In this paper we characterize weakly quasi-threshold graphs by a finite set of forbidden subgraphs: the class of weakly quasi-threshold graphs coincides with the class of {P ₄, co-(2P ₃)}-free graphs. Moreover we give the first linear-time algorithm to decide whether a given graph belongs to the class of weakly quasi-threshold graphs, improving the previously known running time. Based on the simplicity of our recognition algorithm, we can provide certificates of membership (a structure that characterizes weakly quasi-threshold graphs) or non-membership (forbidden induced subgraphs) in additional ${{\mathcal O}(n)}$ time. Furthermore we give a linear-time algorithm for finding the largest induced weakly quasi-threshold subgraph in a cograph.     

Light emission efficiency and imaging performance of Y3Al5O12: Ce (YAG: Ce) powder screens under diagnostic radiology conditions

In this study Y₃Al₅O₁₂: Ce powder scintillator was evaluated for use in X-ray imaging detectors. This phosphor, also known as YAG: Ce scintillator or P-46 phosphor, is a non-hygroscopic, emitting green light with very short decay time. These properties are very attractive for X-ray imaging. Y₃Al₅O₁₂: Ce powder was used to prepare various test screens (33–166 mg/cm²). Absolute luminescence efficiency measurements were performed for various X-ray tube voltages (50–130 kVp). In addition parameters related to image quality such as the modulation transfer function and the detective quantum efficiency were examined. A theoretical model, describing radiation and light transfer, was employed to fit experimental data and to estimate values of optical parameters. Absolute efficiency was found to decrease with X-ray tube voltage. Highest efficiency was obtained for the 107 mg/cm² screen. Light attenuation coefficients were close to those of green emitting rare earth scintillators. At low spatial frequencies the detective quantum efficiency was high for the 107–166 mg/cm² screens. The light emission efficiency and imaging performance of Y₃Al₅O₁₂: Ce was not better than currently employed scintillators. However due to its very fast response and high spectral compatibility to optical sensors it may be considered for use in digital imaging detectors.     

Calculation method for the continuum states of atomic systems

In the present work, we develop a calculational method of solving the scattering equations for spherically symmetric potentials by expanding the solutions on Coulomb functions. We utilize a multistep integration scheme together with the standard partial wave analysis in a region where the potential term dominates. The method applies to any physical problem expressed as [? ² + V(r) + k ²]ψ(r) = 0, while the extension of the method to more general scattering problems is briefly discussed. At present, we demonstrate a two-step Coulomb-fitted integration scheme by calculating the short-range scattering phase shifts for various potentials V (r).     

Leaf anatomy affects the extraction of photosynthetic pigments by DMSO

Dimethylsulfoxide (DMSO) is a widely used solvent for the extraction of chlorophylls (Chls) from leaves of higher plants. The method is preferred because the time-consuming steps of grinding and centrifuging are not required and the extracts are stable for a long time period. However, the extraction efficiency of this solvent is not comparable among plant species, whereas the particular leaf anatomical characteristics responsible for this unevenness remain unknown. In order to examine the influence of leaf anatomy on the extraction efficiency of DMSO (i.e. the concentration of Chls extracted with DMSO as % of the concentration of Chls extracted with 80% acetone), leaves of 19 plant species with different anatomical characteristics were incubated for 40min in DMSO at 65 degrees C. Under these conditions, heterobaric leaves, which are characterized by the occurrence of bundle sheath extensions in the mesophyll, showed lower extraction efficiency of DMSO compared to homobaric leaves and conifer needles. Microscopical observations of DMSO incubated leaf tissues showed that bundle sheath extensions behave as anatomical barriers which prevent the diffusion of DMSO within heterobaric leaves, even after prolonged incubation with the solvent. The effect was stronger in heterobaric leaves possessing thick bundle sheath extensions. The extraction efficiency of DMSO in these leaves was improved by vacuum infiltration of the samples in the presence of warm (65 degrees C) solvent.