Spectral discretization of Darcy’s equations with pressure dependent porosity

We consider the flow of a viscous incompressible fluid in a rigid homogeneous porous medium provided with boundary conditions on the pressure around a circular well. When the boundary pressure presents high variations, the permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a spectral discretization of the resulting system of equations which takes into account the axisymmetry of the domain and of the flow. We prove optimal error estimates and present some numerical experiments which confirm the interest of the discretization.     

Physics and applications of aligned carbon nanotubes

Ever since the discovery of carbon nanotubes (CNTs) by Iijima in 1991, there have been extensive research efforts on their synthesis, physics, electronics, chemistry, and applications due to the fact that CNTs were predicted to have extraordinary physical, mechanical, chemical, optical, and electronic properties. Among the various forms of CNTs, single-walled and multi-walled, random and aligned, semiconducting and metallic, aligned CNTs are especially important since fundamental physics studies and many important applications will not be possible without alignment. Even though there have been significant endeavors on growing CNTs in an aligned configuration since their discovery, little success had been realized before our first report on growing individually aligned CNTs on various substrates by plasma-enhanced chemical vapor deposition (PECVD) [Science 282 (1998) 1105–1108]. Our report spearheaded a new field on growth, characterization, physics, and applications of aligned CNTs. Up to now, there have been thousands of scientific publications on synthesizing, studying, and utilizing aligned CNTs in various aspects. In this communication, we review the current status of aligned CNTs, the physics for their alignment, their applications in field emission, optical antennas, subwavelength light transmission in CNT-based nanocoax structures, nanocoax arrays for novel solar cell structures, etc.

The focus of this review is to examine various aligned CNT systems, either as an individual or as an array, either the orientation is vertical, parallel, or at other angles to the substrate horizon, either the CNT core structures are mostly hollow channels or are composed of complex compartments. Major fabrication methods are illustrated in detail, particularly the most widely used PECVD growth technique on which various device integration schemes are based, followed by applications whereas current limitations and challenges will also be discussed to lay down the foundation for future developments.     

Superinsulator–superconductor duality in two dimensions

For nearly a half century the dominant orthodoxy has been that the only effect of the Cooper pairing is the state with zero resistivity at finite temperatures, superconductivity. In this work we demonstrate that by the symmetry of the Heisenberg uncertainty principle relating the amplitude and phase of the superconducting order parameter, Cooper pairing can generate the dual state with zero conductivity in the finite temperature range, superinsulation. We show that this duality realizes in the planar Josephson junction arrays (JJA) via the duality between the Berezinskii–Kosterlitz–Thouless (BKT) transition in the vortex–antivortex plasma, resulting in phase-coherent superconductivity below the transition temperature, and the charge-BKT transition occurring in the insulating state of JJA and marking formation of the low-temperature charge-BKT state, superinsulation. We find that in disordered superconducting films that are on the brink of superconductor–insulator transition the Coulomb forces between the charges acquire two-dimensional character, i.e. the corresponding interaction energy depends logarithmically upon charge separation, bringing the same vortex-charge-BKT transition duality, and realization of superinsulation in disordered films as the low-temperature charge-BKT state. Finally, we discuss possible applications and utilizations of superconductivity–superinsulation duality.     

Resonant ultrasound spectroscopy measurement of Young's modulus,shear modulus and Poisson's ratio as a function of porosity for alumina and hydroxyapatite

Modulus–porosity relationships are critical for engineered bone tissue scaffold materials such as hydroxyapatite (HA), where porosity is essential to biological function. Resonant ultrasound spectroscopy (RUS) measurements revealed that the Young's modulus, E, and shear modulus, G, of both alumina and HA decrease monotonically with increasing volume fraction porosity, P, for 0.06 < P < 0.39 (alumina) and 0.05 < P < 0.51 (HA). Although the elastic moduli of porous materials have been measured by a number of different ultrasonic resonance techniques (of which the RUS technique is one example) and over the last decade the elastic moduli of many solids have been measured by the RUS technique, this study is the first systematic RUS study of porous materials. Comparison of E versus P data for alumina (which has been studied extensively) with literature data from several measurement techniques indicates the RUS technique is effective for modulus–porosity measurements. Another key result is that although the HA specimens included in this study have a unimodal pore size distribution, the details of the decrease in E and G with increasing P agree well with literature data for HA with both unimodal and bimodal pore size distributions. In addition, Poisson's ratio exhibits a local minimum in the porosity range of 0.2 < P < 0.25 for both HA and alumina, which may be related to the pore morphology evolution during sintering.     

Analysing the sintering of heterogeneous powder structures by in situ microtomography

This work analyses the microstructure changes of various copper-based powder systems during sintering from 3D images provided by in situ synchrotron microtomography. The investigated systems include a copper powder with a wide particle size distribution of 0–63 µm poured into a quartz capillary, a pre-sintered copper compact with artificially created large pores and a mixture of copper and alumina particles. The experiments were carried out at the European Synchrotron in Grenoble, France. Powders were sintered up to 1060°C under reducing atmosphere in a furnace located between the X-ray source and the detector. During each experiment, 3D images were taken at various times of the thermal cycle. We have obtained images with a resolution of 1.5 µm and the time of acquisition of every image was ～1 min. Quantitative analysis of these images allowed the changes of various important parameters to be followed. Such parameters characterise the sintering process at the particle length scale: interparticle coordination, pore size distribution and particle centre-to-centre distance. Moreover, by tracking the displacement of each particle centre and comparing it to the displacement predicted by classical mean field assumption, we have been able to assess the magnitude of particle rearrangement occurring during sintering. From these data, the sintering behaviour of heterogeneous powder systems is discussed with particular emphasis of collective particle phenomena.     

Light Emission and Scanning Electron Microscopic Characterization of Porous Silicon

Optical emission resulting from sputtered species during ion bombardment of porous and oxidized porous silicon targets has been studied. Samples were bombarded with 5‐keV Kr⁺ ions at an incidence angle of 70 degrees, and the light emitted was analyzed over the wavelength range 200–300 nm. The surface morphology was investigated, and the micrographs revealed grooves parallel to the plane of incidence when the porosity was surprisingly observed in the grooves under each pore. The results are discussed as a function of the incidence angle and the porosity of the silicon targets.     

Convergent Power Series for Fields in Positive or Negative High-Contrast Periodic Media

We obtain convergent power series representations for Bloch waves in periodic high-contrast media. The material coefficient in the inclusions can be positive or negative. The small expansion parameter is the ratio of period cell width to wavelength, and the coefficient functions are solutions of the cell problems arising from formal asymptotic expansion. In the case of positive coefficient, the dispersion relation has an infinite sequence of branches, each represented by a convergent even power series whose leading term is a branch of the dispersion relation for the homogenized medium. In the negative case, there is a single branch.     

Principles of the micromechanics of material damage. 1. Long-term damage

The principles of the theory of long-term damage based on the mechanics of stochastically inhomogeneous media are set out. The process of damage is modeled as randomly dispersed micropores resulting from the destruction of microvolumes. A failure criterion for a single microvolume is associated with its long-term strength dependent on the relationship of the time to brittle failure and the difference between the equivalent stress and the Huber-von Mises failure stress, which is assumed to be a random function of coordinates. The stochastic elasticity equations for porous media are used to determine the effective moduli and the stress-strain state of microdamaged materials. The porosity balance equation is derived in finite-time and differential-time forms for given macrostresses or macrostrains and arbitrary time using the properties of the distribution function and the ergodicity of the random field of short-term strength as well as the dependence of the time to brittle failure on the stress state and the short-term strength. The macrostress-macrostrain relationship and the porosity balance equation describe the coupled processes of deformation and long-term damage __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 2, pp. 108–121, February 2007. For the centenary of the birth of G. N. Savin.     

Strong water repellency effect on SiO<Subscript>2</Subscript> films processed at a nanometric scale

The present study deals with the creation of nano-rough surfaces with stable and controlled high hydrophobicity. These surfaces were obtained by combining the ion track etching technique with a simple functionalization by grafting perfluoroctyltrichlorosilane (PFOTS) molecules. Surface morphology was investigated by AFM observations which evidenced a self-affine fractal structure with a fractal dimension D_f ~ 2.6. The study of the wetting properties of these surfaces allowed to elucidate the conditions for observing a high hydrophobicity phenomenon and to predict the contact angle values for surfaces designed at a nanometric scale.