Dispersion in retentive pillar array columns

The method of volume averaging is applied to estimate the Taylor–Aris dispersion tensor of solute advected in columns consisting of ordered pillar arrays with wall retention of the type used in chromatographic separation. The appropriate closure equations are derived and solved in a unit cell with periodic boundary conditions to obtain the dispersion tensor (or the reduced plate height) as a function of the Peclet number (reduced velocity); pillar pattern, shape and size; partition coefficient; and resistance to mass transfer. The contributions of the velocity profile, the wall adsorption, and the mass transfer resistance to the dispersion tensor are identified and delineated. The model is verified by comparing its predictions and obtaining favorable agreement with results of direct numerical simulations and with experimental data for columns containing ordered pillars. The model is then used to study the effect of pillars’ shape and pattern on the longitudinal dispersion coefficient (plate height).     

Effect and importance of static-load on airflow resistivity determination and its consequences on dynamic stiffness

Airflow resistivity is a physical parameter which characterizes porous and fibrous sound absorbent materials. It is well-known that such property allows the evaluation of the acoustic behaviour of sound absorbent materials in various fields of application, including automotive noise mitigation, architectural acoustics and building acoustics. In structure-borne sound insulation, airflow resistivity is essential for the evaluation of the dynamic stiffness of porous and fibrous resilient insulating materials used as underlay in floating floors.However, an inconsistency between the dynamic stiffness and the airflow resistivity test conditions can be recognized. In order to evaluate dynamic stiffness of a resilient material, a static load of about 2 kPa is applied, while in airflow resistivity determination this condition is not explicitly required. As a result, the density of analyzed material, in dynamic stiffness and airflow measurements, is different. Since these two quantities are correlated, it is necessary to measure materials under the same conditions of applied static load.In this work the effects of static load (or density after compression) in airflow resistivity determination of various porous and fibrous resilient materials are investigated, and the consequent influence on dynamic stiffness is discussed. A simply empirical relation between density and airflow resistivity is also put forth.The main focus of this paper is to propose an harmonization among requirements of the Standards in order to prevent significant errors in dynamic stiffness determination and incorrect evaluations of the acoustic behaviour.     

Discrete vs. continuum-scale simulation of radiative transfer in semitransparent two-phase media

The mathematical formulation of the continuum approach to radiative transfer modeling in two-phase semi-transparent media is numerically validated by comparing radiative fluxes computed by (i) direct, discrete-scale and (ii) continuum-scale approaches. The analysis is based on geometrical optics. The discrete-scale approach uses the Monte Carlo ray-tracing applied directly to real 3D geometry measured by computed tomography. The continuum-scale approach is based on a set of continuum-scale radiative transfer equations and associated radiative properties, and employs the Monte Carlo ray-tracing for computations of radiative fluxes and for computations of the radiative properties. The model two-phase media are reticulate porous ceramics and a particle packed bed, each composed of semitransparent solid and fluid phases. The results obtained by the two approaches are in good agreement within the limits of statistical uncertainty. The continuum-scale approach leads to a reduction in computational time by approximately one order of magnitude, and is therefore suited to treat radiative transfer problems in two-phase media in a wide range of engineering applications.     

Propagation characteristics of annular laser beams passing through the reflection Bragg grating with deformation

When high-power annular laser beams produced by the unstable resonator pass through the volume Bragg grating (VBG), absorption of light in the VBG will induce a temperature increment, resulting in changes in surface distortion. Considering that the surface distortion of the grating induces index and period differences, the scalar wave equations for the annular laser beams propagating in the VBG have been solved numerically and iteratively using finite-difference and sparse matrix methods. The variation in intensity distributions, the total power reflection coefficient, and the power in the bucket (PIB) for the annular laser beams passing through the reflection VBG with deformation have been analyzed quantitatively. It can be shown that the surface distortion of the VBG and the beam orders of the annular beams affect evidently the intensity distributions, the power reflection coefficient, and the PIB of the output beam. The peak intensity decreases as the deformation of the VBG increases. The total power reflection efficiency decreases significantly with the increase in deformations of the VBG. The PIB of the output beam decreases as the obscuration ratio β and the deformation of the VBG increase. For the given obscuration ratio β, the influence of deformation of reflection VBG on the PIB of the annular beams is more sensitive with increase in distortion of the VBG and decrease in beam order.     

Effect of substitution of K ions on the structural and electrical properties of nanocrystalline MgAl2O4 spinel oxide

Potassium substituted nanosized magnesium aluminates having a nominal composition Mg_1−xK_xAl₂O₄ where x=0.0, 0.25, 0.5, 0.75, 1.0 have been synthesized by the chemical co-precipitation method. The samples have been characterized by means of X-ray diffraction (XRD), scanning electron microscope (SEM), and dc electrical resistivity measurements. The XRD results reveal that the samples are spinel single phase cubic close packed crystalline materials. The calculated crystallite size ranges between 6 and 8 nm. The behaviour of the lattice constant seems to deviate from the Vegard's law. While X-ray density clearly increases, the bulk density and consequently, the percentage porosity do not exhibit a significant change on increasing the K⁺ content. The SEM micrographs suggest homogeneous distribution of the nanocrystallites in the samples. The dc electrical resistivity exhibits a typical semiconducting behaviour. Substitution of a Mg²⁺ ion by a K⁺ ion provides an extra hole to the system, which forms small polaron. Thermally activated hopping of these small polarons is believed to be the conduction mechanism in the Mg_1−xK_xAl₂O₄. The activation energy of hopping of small polarons has been calculated and found K⁺ ions content dependent.     

Improvement of the dynamic range of a fiber specklegram sensor based on volume speckle recording in photorefractive materials

In this work, the improvement of the dynamic range of a micro displacement sensor based on fiber specklegrams holographically stored in a photorefractive BSO (Bi₁₂SiO₂₀) crystal is reported. In our experimental setup, a plastic optical fiber (POF) was used to generate a subjective speckle pattern that was recorded in the crystal using a two-wave mixing arrangement. The speckle size was controlled by modifying the diameter of a pupil aperture adjacent to a lens producing the image of the speckle. Fringe patterns were obtained at the output of the system by producing micro displacements of the fiber output end. An increase in the visibility of the fringe patterns was appreciated when the pupil aperture diameter decreased even without controlling the average modulation of the intensity of the light pattern, i.e. when the speckle length increased and the average light modulation simultaneously decreased. This behavior allowed recovering the autocorrelation functions of fringe patterns associated with displacements that initially led to decorrelation, and therefore, significantly to improve the dynamic range of the metrological system. To the best of our knowledge this is the first report about the influence of speckle size on the dynamic range of fiber specklegrams sensors recorded on photorefractive materials.     

Differentiation between intra-axial metastatic tumor progression and radiation injury following fractionated radiation therapy or stereotactic radiosurgery using MR spectroscopy, perfusion MR imaging or volume progression modeling

Objective

To determine the accuracy of magnetic resonance spectroscopy (MRS), perfusion MR imaging (MRP), or volume modeling in distinguishing tumor progression from radiation injury following radiotherapy for brain metastasis.

Methods

Twenty-six patients with 33 intra-axial metastatic lesions who underwent MRS (n=41) with or without MRP (n=32) after cranial irradiation were retrospectively studied. The final diagnosis was based on histopathology (n=4) or magnetic resonance imaging (MRI) follow-up with clinical correlation (n=29). Cho/Cr (choline/creatinine), Cho/NAA (choline/N-acetylaspartate), Cho/nCho (choline/contralateral normal brain choline) ratios were retrospectively calculated for the multi-voxel MRS. Relative cerebral blood volume (rCBV), relative peak height (rPH) and percentage of signal-intensity recovery (PSR) were also retrospectively derived for the MRPs. Tumor volumes were determined using manual segmentation method and analyzed using different volume progression modeling. Different ratios or models were tested and plotted on the receiver operating characteristic curve (ROC), with their performances quantified as area under the ROC curve (AUC). MRI follow-up time was calculated from the date of initial radiotherapy until the last MRI or the last MRI before surgical diagnosis.

Results

Median MRI follow-up was 16 months (range: 2-33). Thirty percent of lesions (n=10) were determined to be radiation injury; 70% (n=23) were determined to be tumor progression. For the MRS, Cho/nCho had the best performance (AUC of 0.612), and Cho/nCho >1.2 had 33% sensitivity and 100% specificity in predicting tumor progression. For the MRP, rCBV had the best performance (AUC of 0.802), and rCBV >2 had 56% sensitivity and 100% specificity. The best volume model was percent increase (AUC of 0.891); 65% tumor volume increase had 100% sensitivity and 80% specificity.

Conclusion

Cho/nCho of MRS, rCBV of MRP, and percent increase of MRI volume modeling provide the best discrimination of intra-axial metastatic tumor progression from radiation injury for their respective modalities. Cho/nCho and rCBV appear to have high specificities but low sensitivities. In contrast, percent volume increase of 65% can be a highly sensitive and moderately specific predictor for tumor progression after radiotherapy. Future incorporation of 65% volume increase as a pretest selection criterion may compensate for the low sensitivities of MRS and MRP.     

Geometry of manifolds with densities

We study the geometry of complete Riemannian manifolds endowed with a weighted measure, where the weight function is of quadratic growth. Assuming the associated Bakry–Émery curvature is bounded from below, we derive a new Laplacian comparison theorem and establish various sharp volume upper and lower bounds. We also obtain some splitting type results by analyzing the Busemann functions. In particular, we show that a complete manifold with nonnegative Bakry–Émery curvature must split off a line if it is not connected at infinity and its weighted volume entropy is of maximal value among linear growth weight functions.     

Reply to the comment from Mamedov

Here, I present the reply to the comments from Mamedov regarding numerical solution of Bloch–Gruneisen function to determine the contribution of electron–phonon interaction in polycrystalline superconductor. Reply to the comments from Mamedov is discussed one by one.     

Enhancement of electrical properties due to Cr substitution in Co-ferrite nanoparticles synthesized by two chemical techniques

Nanocrystalline cobalt ferrites with nominal composition CoCr_xFe_2−xO₄ ranging from x=0.0 to 0.5 with step increment of 0.25 were prepared by sol–gel auto combustion and chemical co-precipitation techniques. A comparative study of structural, electrical and magnetic properties of these ferrites has been measured using different characterization techniques. Structural and micro-structural studies were measured using X-ray diffraction, Fourier transform infra-red spectroscopy (FTIR), scanning electron microscopy and atomic force microscopy. Crystallite sizes of the series are within the range of 12–29±2 nm. Lattice parameters decrease by increasing Cr³⁺ concentration. FTIR confirms the presence of two lattice absorption bands. DC electrical resistivity increases to a value of ∼10¹⁰ Ω-cm with increase in Cr³⁺ concentration, but the most significant increase is in samples prepared by sol–gel combustion. Dielectric properties have been measured as a function of frequency at room temperature. Dielectric loss decreases to 0.1037 and 0.0108 at 5 MHz for chemical co-precipitation and sol–gel combustion, respectively. Impedance measurements further helped in analyzing the electrical properties and to separate the grain and grain boundary resistance effects using a complex impedance analysis. Magnetic parameters were studied using a vibrating sample magnetometer in the applied field of 10 kOe. The saturation magnetization decreased from 63 to 10.8 emu/gm with increase in Cr³⁺ concentration.