Application of a continuum theory to vertical vibrations of a layer of granular material

Many interesting phenomena have been observed in layers of granular materials subjected to vertical oscillations; these include the formation of a variety of standing wave patterns, and the occurrence of isolated features called oscillons, which alternately form conical heaps and craters oscillating at one-half of the forcing frequency. No continuum-based explanation of these phenomena has previously been proposed. We apply a continuum theory, termed the double-shearing theory, which has had success in analyzing various problems in the flow of granular materials, to the problem of a layer of granular material on a vertically vibrating rigid base undergoing vertical oscillations in plane strain. There exists a trivial solution in which the layer moves as a rigid body. By investigating linear perturbations of this solution, we find that at certain amplitudes and frequencies this trivial solution can bifurcate. The time dependence of the perturbed solution is governed by Mathieu’s equation, which allows stable, unstable and periodic solutions, and the observed period-doubling behaviour. Several solutions for the spatial velocity distribution are obtained; these include one in which the surface undergoes vertical velocities that have sinusoidal dependence on the horizontal space dimension, which corresponds to the formation of striped standing waves, and is one of the observed patterns. An alternative continuum theory of granular material mechanics, in which the principal axes of stress and rate-of-deformation are coincident, is shown to be incapable of giving rise to similar instabilities.

New stress and velocity fields for highly frictional granular materials

The idealised theory for the quasi-static flow of granular materials which satisfy the Coulomb-Mohr hypothesis is considered. This theory arises in the limit that the angle of internal friction approaches $\pi/2$, and accordingly these materials may be referred to as being `highly frictional'. In this limit, the stress field for both two-dimensional and axially symmetric flows may be formulated in terms of a single nonlinear second order partial differential equation for the stress angle. To obtain an accompanying velocity field, a flow rule must be employed. Assuming the non-dilatant double-shearing flow rule, a further partial differential equation may be derived in each case, this time for the streamfunction. Using Lie symmetry methods, a complete set of group-invariant solutions is derived for both systems, and through this process new exact solutions are constructed. Only a limited number of exact solutions for gravity driven granular flows are known, so these results are potentially important in many practical applications. The problem of mass flow through a two-dimensional wedge hopper is examined as an illustration.

Perturbation solutions for flow through symmetrical hoppers with inserts and asymmetrical wedge hoppers

Under certain circumstances, an industrial hopper which operates under the "funnel-flow" regime can be converted to the "mass-flow" regime with the addition of a flow-corrective insert. This paper is concerned with calculating granular flow patterns near the outlet of hoppers that incorporate a particular type of insert, the cone-in-cone insert. The flow is considered to be quasi-static, and governed by the Coulomb-Mohr yield condition together with the non-dilatant double-shearing theory. In two dimensions, the hoppers are wedge-shaped, and as such the formulation for the wedge-in-wedge hopper also includes the case of asymmetrical hoppers. A perturbation approach, valid for high angles of internal friction, is used for both two-dimensional and axially symmetric flows, with analytic results possible for both leading order and correction terms. This perturbation scheme is compared with numerical solutions to the governing equations, and is shown to work very well for angles of internal friction in excess of 45 degree.

Vibrational spectroscopy of phthalocyanine and naphthalocyanine in sandwich-type (na)phthalocyaninato and porphyrinato rare earth complexes: Part 14. The infrared and Raman characteristics of phthalocyanine in “pinwheel-like” homoleptic bis[1,8,15,22-tetrakis(3-pentyloxy)phthalocyaninato] rare earth(III) double-decker complexes

The infrared (IR) spectroscopic data and Raman spectroscopic properties for a series of 13 “pinwheel-like” homoleptic bis(phthalocyaninato) rare earth complexes M[Pc(α-OC5H11)4]2 [M = Y and Pr–Lu except Pm; H2Pc(α-OC5H11)4 = 1,8,15,22-tetrakis(3-pentyloxy)phthalocyanine] have been collected and comparatively studied. Both the IR and Raman spectra for M[Pc(α-OC5H11)4]2 are more complicated than those of homoleptic bis(phthalocyaninato) rare earth analogues, namely M(Pc)2 and M[Pc(OC8H17)8]2, but resemble (for IR) or are a bit more complicated (for Raman) than those of heteroleptic counterparts M(Pc)[Pc(α-OC5H11)4], revealing the decreased molecular symmetry of these double-decker compounds, namely S8. Except for the obvious splitting of the isoindole breathing band at 1110–1123 cm−1, the IR spectra of M[Pc(α-OC5H11)4]2 are quite similar to those of corresponding M(Pc)[Pc(α-OC5H11)4] and therefore are similarly assigned. With laser excitation at 633 nm, Raman bands derived from isoindole ring and aza stretchings in the range of 1300–1600 cm−1 are selectively intensified. The IR spectra reveal that the frequencies of pyrrole stretching and pyrrole stretching coupled with the symmetrical CH bending of –CH3 groups are sensitive to the rare earth ionic size, while the Raman technique shows that the bands due to the isoindole stretchings and the coupled pyrrole and aza stretchings are similarly affected. Nevertheless, the phthalocyanine monoanion radical Pc′− IR marker band of bis(phthalocyaninato) complexes involving the same rare earth ion is found to shift to lower energy in the order M(Pc)2 > M(Pc)[Pc(α-OC5H11)4] > M[Pc(α-OC5H11)4]2, revealing the weakened π–π interaction between the two phthalocyanine rings in the same order.

Tuning the valence of the cerium center in (Na)phthalocyaninato and porphyrinato cerium double-deckers by changing the nature of the tetrapyrrole ligands

A series of 7 cerium double-decker complexes with various tetrapyrrole ligands including porphyrinates, phthalocyaninates, and 2,3-naphthalocyaninates have been prepared by previously described methodologies and characterized with elemental analysis and a range of spectroscopic methods. The molecular structures of two heteroleptic \[(na)phthalocyaninato](porphyrinato) complexes have also been determined by X-ray diffraction analysis which exhibit a slightly distorted square antiprismatic geometry with two domed ligands. Having a range of tetrapyrrole ligands with very different electronic properties, these compounds have been systematically investigated for the effects of ligands on the valence of the cerium center. On the basis of the spectroscopic (UV−vis, near-IR, IR, and Raman), electrochemical, and structural data of these compounds and compared with those of the other rare earth(III) counterparts reported earlier, it has been found that the cerium center adopts an intermediate valence in these complexes. It assumes a virtually trivalent state in cerium bis(tetra-tert-butylnaphthalocyaninate) as a result of the two electron rich naphthalocyaninato ligands, which facilitate the delocalization of electron from the ligands to the metal center. For the rest of the cerium double-deckers, the cerium center is predominantly tetravalent. The valences (3.59−3.68) have been quantified according to their LIII-edge X-ray absorption near-edge structure (XANES) profiles.

Raman spectroscopic characteristics of phthalocyanine and naphthalocyanine in sandwich-type phthalocyaninato and porphyrinato rare earth complexes Part 5. – Raman spectroscopic characteristics of naphthalocyanine in mixed [tetrakis(4-tert-butylphenyl)porphyrinato]-(naphthalocyaninato) rare earth double-deckers

Raman spectra were recorded in the range 400–1800 cm−1 for a series of 15 mixed \[tetrakis(4-tert-butylphenyl)porphyrinato](2,3-naphthalocyaninato) rare earth double-deckers M(TBPP)(Nc) (M = Y; La–Lu except Pm) using laser excitation at 632.8 and 785 nm. Comparisons with bis(naphthalocyaninato) rare earth counterparts reveal that the vibrations of the metallonaphthalocyanine M(Nc) fragment dominate the Raman features of M(TBPP)(Nc). When excited with radiation of 632.8 nm, the most intense vibration appears at about 1595 cm−1, due to the naphthalene stretching. These complexes exhibit the marker Raman band for Nc•− as a medium-intense band in the range 1496–1507 cm−1, attributed to the coupling of pyrrole and aza stretching, while the marker Raman band of Nc2− in intermediate-valence Ce(TBPP)(Nc) appears as a strong band at 1493 cm−1 and is due to the isoindole stretchings. By contrast, when excited with radiation of 785 nm that is in close resonance with the main Q absorption band of the naphthalocyanine ligand, the ring radial vibrations at ca 680 and 735 cm−1 for MIII(TBPP)(Nc) are selectively intensified and are the most intense bands. For the cerium double-decker, the most intense vibration also acting as the marker Raman band of Nc2− appears at 1497 cm−1 with contributions from both pyrrole CC and aza CN stretches. The same vibrational modes show weak to medium intensity scattering at 1506–1509 cm−1 for MIII(TBPP)(Nc) and this is the marker Raman band of Nc•− when thus excited. The scatterings due to the Nc breathings, ring radial vibration, aza group stretchings, naphthalene stretchings, benzoisoindole stretchings and the coupling of pyrrole CC and aza CN stretchings in MIII(TBPP)(Nc) are all slightly blue shifted along with the decrease in rare earth ionic radius, confirming the effects of increased ring–ring interactions on the Raman characteristics of naphthalocyanine in the mixed ring double-deckers.

Characterization of commercial double-walled carbon nanotube material : composition, structure, and heat capacity

A purified commercial double-walled carbon nanotube (DWCNT) sample was investigated by transmission electron microscopy (TEM), thermogravimetry (TG), and Raman spectroscopy. Moreover, the heat capacity of the DWCNT sample was determined by temperature-modulated differential scanning calorimetry in the range of temperature between -50 and 290 °C. The main thermo-oxidation characterized by TG occurred at 474 °C with the loss of 90 wt% of the sample. Thermo-oxidation of the sample was also investigated by high-resolution TG, which indicated that a fraction rich in carbon nanotube represents more than 80 wt% of the material. Other carbonaceous fractions rich in amorphous coating and graphitic particles were identified by the deconvolution procedure applied to the derivative of TG curve. Complementary structural data were provided by TEM and Raman studies. The information obtained allows the optimization of composites based on this nanomaterial with reliable characteristics.

St. John’s wort and Kava in treating major depressive disorder with comorbid anxiety : a randomised double-blind placebo-controlled pilot trial

Objective - We report the first randomised controlled trial (RCT) using a combination of St. John’s wort (SJW) and Kava for the treatment of major depressive disorder (MDD) with comorbid anxiety. Methods - Twenty-eight adults with MDD and co-occurring anxiety were recruited for a double-blind RCT. After a placebo run-in of 2 weeks, the trial had a crossover design testing SJW and Kava against placebo over two controlled phases, each of 4 weeks. The primary analyses used intention-to-treat and completer analyses. Results - On both intention-to-treat ( p¼0.047) and completer analyses ( p¼0.003), SJW and Kava gave a significantly greater reduction in self-reported depression on the Beck Depression Inventory (BDI-II) over placebo in the first controlled phase. However, in the crossover phase, a replication of those effects in the delayed medication group did not occur. Nor were there significant effects on anxiety or quality of life. Conclusion - There was some evidence of antidepressant effects using SJW and Kava in a small sample with comorbid anxiety. Possible explanations for the absence of anxiolysis may include a potential interaction with SJW, the presence of depression, or an inadequate dose of Kava.

Silylation of layered double hydroxides via a calcination−rehydration route

Silylated layered double hydroxides (LDHs) were synthesized through a surfactant-free method involving an in situ condensation of silane with the surface hydroxyl group of LDHs during its reconstruction in carbonate solution. X-ray diffraction (XRD) patterns showed the silylation reaction occurred on the external surfaces of LDHs layers. The successful silylation was evidenced by 29Si cross-polarization magic-angle spinning nuclear magnetic resonance (29Si CP/MAS NMR) spectroscopy, attenuated total reflection Fourier transform infrared (ATR FTIR) spectroscopy, and infrared emission spectroscopy (IES). The ribbon shaped crystallites with a “rodlike” aggregation were observed through transmission electron microscopy (TEM) images. The aggregation was explained by the T2 and T3 types of linkage between adjacent silane molecules as indicated in the 29Si NMR spectrum. In addition, the silylated products show high thermal stability by maintained Si related bands even when the temperature was increased to 1000 °C as observed in IES spectra.

Robust estimation of tear film surface quality in lateral shearing interferometry

Interferometry is a sensitive technique for recording tear film surface irregularities in a noninvasive manner. At the same time, the technique is hindered by natural eye movements resulting in measurement noise. Estimating tear film surface quality from interferograms can be reduced to a spatial-average-localized weighted estimate of the first harmonic of the interference fringes. However, previously reported estimation techniques proved to perform poorly in cases where the pattern fringes were significantly disturbed. This can occur in cases of measuring tear film surface quality on a contact lens on the eye or in a dry eye. We present a new estimation technique for extracting the first harmonic from the interference fringes that combines the traditional spectral estimation techniques with morphological image processing techniques. The proposed technique proves to be more robust to changes in interference fringes caused by natural eye movements and the degree of dryness of the contact lens and corneal surfaces than its predecessors, resulting in tear film surface quality estimates that are less noisy

Modeling multivariate autoregressive conditional heteroskedasticity with the double smooth transition conditional correlation GARCH Model

In this paper, we propose a multivariate GARCH model with a time-varying conditional correlation structure. The new double smooth transition conditional correlation (DSTCC) GARCH model extends the smooth transition conditional correlation (STCC) GARCH model of Silvennoinen and Teräsvirta (2005) by including another variable according to which the correlations change smoothly between states of constant correlations. A Lagrange multiplier test is derived to test the constancy of correlations against the DSTCC-GARCH model, and another one to test for another transition in the STCC-GARCH framework. In addition, other specification tests, with the aim of aiding the model building procedure, are considered. Analytical expressions for the test statistics and the required derivatives are provided. Applying the model to the stock and bond futures data, we discover that the correlation pattern between them has dramatically changed around the turn of the century. The model is also applied to a selection of world stock indices, and we find evidence for an increasing degree of integration in the capital markets.

The doctrine of double effect

• The doctrine of double effect is an exception to the general rule that taking active steps that end life is unlawful. • The essence of the doctrine at common law is intention. • Hastening a patient’s death through palliative care will be lawful provided the primary intention is to relieve pain, and not cause death, even if that death is foreseen. • Some States have enacted legislative excuses that deal with the provision of palliative care. • These statutory excuses tend to be stricter than the common law as they impose other requirements in addition to having an appropriate intent, such as adherence to some level of recognised medical practice.