Parcel theory in three dimensions and the calculation of SCAPE

Slantwise convective available potential energy (SCAPE) is a measure of the degree to which the atmosphere is unstable to conditional symmetric instability (CSI). It has, until now, been defined by parcel theory in which the atmosphere is assumed to be nonevolving and balanced, that is, two-dimensional. When applying this two-dimensional theory to three-dimensional evolving flows, these assumptions can be interpreted as an implicit assumption that a timescale separation exists between a relatively rapid timescale for slantwise ascent and a slower timescale for the development of the system. An approximate extension of parcel theory to three dimensions is derived and it is shown that calculations of SCAPE based on the assumption of relatively rapid slantwise ascent can be qualitatively in error. For a case study example of a developing extratropical cyclone, SCAPE calculated along trajectories determined without assuming the existence of the timescale separation show large SCAPE values for parcels ascending from the warm sector and along the warm front. These parcels ascend into the cloud head within which there is some evidence consistent with the release of CSI from observational and model cross sections. This region of high SCAPE was not found for calculations along the relatively rapidly ascending trajectories determined by assuming the existence of the timescale separation.

Arctic oscillation or North Atlantic oscillation?

The definition and interpretation of the Arctic oscillation (AO) are examined and compared with those of the North Atlantic oscillation (NAO). It is shown that the NAO reflects the correlations between the surface pressure variability at its centers of action, whereas this is not the case for the AO. The NAO pattern can be identified in a physically consistent way in principal component analysis applied to various fields in the Euro-Atlantic region. A similar identification is found in the Pacific region for the Pacific–North American (PNA) pattern, but no such identification is found here for the AO. The AO does reflect the tendency for the zonal winds at 35° and 55°N to anticorrelate in both the Atlantic and Pacific regions associated with the NAO and PNA. Because climatological features in the two ocean basins are at different latitudes, the zonally symmetric nature of the AO does not mean that it represents a simple modulation of the circumpolar flow. An increase in the AO or NAO implies strong, separated tropospheric jets in the Atlantic but a weakened Pacific jet. The PNA has strong related variability in the Pacific jet exit, but elsewhere the zonal wind is similar to that related to the NAO. The NAO-related zonal winds link strongly through to the stratosphere in the Atlantic sector. The PNA-related winds do so in the Pacific, but to a lesser extent. The results suggest that the NAO paradigm may be more physically relevant and robust for Northern Hemisphere variability than is the AO paradigm. However, this does not disqualify many of the physical mechanisms associated with annular modes for explaining the existence of the NAO.

Threshold effects in price transmission: The case of Brazilian wheat, maize, and soya prices

Recent studies into price transmission have recognized the important role played by transport and transaction costs. Threshold models are one approach to accommodate such costs. We develop a generalized Threshold Error Correction Model to test for the presence and form of threshold behavior in price transmission that is symmetric around equilibrium. We use monthly wheat, maize, and soya prices from the United States, Argentina, and Brazil to demonstrate this model. Classical estimation of these generalized models can present challenges but Bayesian techniques avoid many of these problems. Evidence for thresholds is found in three of the five commodity price pairs investigated.

Buddenbrockia is a Cnidarian worm

A major evolutionary divide occurs in the animal kingdom between the so-called radially symmetric animals, which includes the cnidarians, and the bilaterally symmetric animals, which includes all worm phyla. Buddenbrockia plumatellae is an active, muscular, parasitic worm that belongs to the phylum Myxozoa, a group of morphologically simplified microscopic endoparasites that has proved difficult to place phylogenetically. Phylogenetic analyses of multiple protein-coding genes demonstrate that Buddenbrockia is a cnidarian. This active muscular worm increases the known diversity in cnidarian body plans and demonstrates that a muscular, wormlike form can evolve in the absence of overt bilateral symmetry.

Cascade dicopper architectures of a dibenzodioxatetraazamacrocycle

The dibenzodioxatetraazamacrocycle [26]pbz(2)N(4)O(2) was characterised by single crystal X-ray diffraction and the protonation constants of this compound and the stability constants of its copper(II) and lead(II) complexes were determined by potentiometry in water at 298.2 K in 0.10 mol dm(-3) in KNO3. Mono- and dinuclear complexes were found for both metal ions, the dinuclear complexes being the main species in the 5-7.5 pH range for copper(II) and 7.5-8.5 for lead(II). As expected the values of the stability constants for the copper(II) complexes are lower than those for related macrocycles containing only nitrogen atoms. The presence of mono- and dinuclear copper complexes was also confirmed by electrospray ionization mass spectrometry. These results suggest that the symmetric macrocyclic cavity of [26]pbZ(2)N(4)O(2) has enough space for the coordination of two metal ions. Additionally, NMR spectroscopy showed that the dinuclear complex of lead(II) has high symmetry. The equilibrium constants of the dinuclear copper(II) complexes and dicarboxylate anions (oxalate, malonate and succinate) were also determined in 0.10 mol dm-3 aqueous KNO3 solution. Only species containing one anion, Cu(2)H(h)LA((2+h)), were found, strongly suggesting that the anion bridges the two copper(II) ions. The binding constants of the cascade species formed by [Cu-2[26]pbZ(2)N(4)O(2)(H2O)(4+) with dicarboxylate anions decrease with the increase in length of the alkyl chain of the anion, a fact which was attributed to a higher conformational energy necessary for the rearrangement of the macrocycle to accommodate the larger anions bridging the two copper(II) centres. The variation of the magnetic susceptibility with temperature Of [Cu-2(H-2[26]pbz(2)N(4)O(2))(oxa)(3)]-4H(2)O and [Cu-2([26]pbz(2)N(4)O(2))(suc)Cl-2] were measured and the two complexes showed different behaviour. (c) 2007 Elsevier Ltd. All rights reserved.

Ordering in thin films of block copolymers: fundamentals to potential applications

The ordering of block copolymers in thin films is reviewed, starting, from the fundamental principles and extending to recent promising developments as templates for nanolithography which may find important applications in the semiconductor industry. Ordering in supported thin films of symmetric and asymmetric AB diblock and ABA triblock copolymers is discussed, along with that of more complex materials such as ABC triblocks and liquid crystalline block copolymers Techniques to prepare thin films, and to characterise ordering within them, are summarized. Several methods to align Hock copolymer nanostructures, important in several applications are outlined A number of potential applications in nanolithography, production of porous materials, templating. and patterning of organic and inorganic materials are then presented. The influence of crystallization on the morphology of a block copolymer film is briefly discussed, as are structures in grafted block copolymer films. (C) 2009 Elsevier Ltd All rights reserved.

Bidentates versus monodentates in asymmetric hydrogenation catalysis: synergic effects on rate and allosteric effects on enantioselectivity

C-1-Symmetric phosphino/phosphonite ligands are prepared by the reactions of Ph2P(CH2)(2)P(NMe2)(2) with (S)-1,11'-bi-2-naphthol (to give L-A) or (S)-10,10'-bi-9-phenanthrol (to give L-B). Racemic 10,10'-bi-9-phenanthrol is synthesized in three steps from phenanthrene in 44% overall yield. The complexes [PdCl2(L-A,L-B)] (1a,b), [PtCl2(L-A,L-B)] (2a,b), [Rh(cod)(L-A,L-B)]BF4 (3a,b) and [Rh(L-A,L-B)(2)]BF4 (4a,b) are reported and the crystal structure of la has been determined. A P-31 NMR study shows that M, a 1:1 mixture of the monodentates, PMePh2 and methyl monophosphonite L-1a (based on (S)-1,11'-bi-2-naphthol), reacts with 1 equiv of [Rh(cod)(2)]BF4 to give the heteroligand complex [Rh(cod)(PMePh2)(L-1a)]BF4 (5) and homoligand complexes [Rh(cod)(PMePh2)(2)]BF4 (6) and [Rh(cod)(L-1a)(2)]BF4 (7) in the ratio 2:1:1. The same mixture of 5-7 is obtained upon mixing the isolated homoligand complexes 6 and 7 although the equilibrium is only established rapidly in the presence of an excess of PMePh2. The predominant species 5 is a monodentate ligand complex analogue of the chelate 3a. When the mixture of 5-7 is exposed to 5 atm H-2 for 1 h (the conditions used for catalyst preactivation in the asymmetric hydrogenation studies), the products are identified as the solvento species [Rh(PMePh2)(L-1a)(S)(2)]BF4 (5'), [Rh(S)(2)(PMePh2)(2)]BF4 (6') and [Rh(S)(2)(L-1a)(2)]BF4 (7') and are formed in the same 2:1:1 ratio. The reaction of M with 0.5 equiv of [Rh(cod)(2)]BF4 gives exclusively the heteroligand complex cis-[Rh(PMePh2)(2)(L-1a)(2)]BF4 (8), an analogue of 4a. The asymmetric hydrogenation of dehydroamino acid derivatives catalyzed by 3a,b is reported, and the enantioselectivities are compared with those obtained with (a) chelate catalysts derived from analogous diphosphonite ligands L-2a and L-2b, (b) catalysts based on methyl monophosphonites L-1a and L-1b, and (c) catalysts derived from mixture M. For the cinnamate and acrylate substrates studied, the catalysts derived from the phosphino/phosphonite bidentates L-A,L-B generally give superior enantioselectivities to the analogous diphosphonites L-2a and L-2b; these results are rationalized in terms of delta/lambda-chelate conformations and allosteric effects of the substrates. The rate of hydrogenation of acrylate substrate A with heterochelate 3a is significantly faster than with the homochelate analogues [Rh(L-2a)(cod)]BF4 and [Rh(dppe)(cod)]BF4. A synergic effect on the rate is also observed with the monodentate analogues: the rate of hydrogenation with the mixture containing predominantly heteroligand complex 5 is faster than with the monophosphine complex 6 or monophosphonite complex 7. Thus the hydrogenation catalysis carried out with M and [Rh(cod)(2)]BF4 is controlled by the dominant and most efficient heteroligand complex 5. In this study, the heterodiphos chelate 3a is shown to be more efficient and gives the opposite sense of optical induction t the heteromonophos analogue

Nanostructure formation in poly(gamma-benzyl-L-glutamate)-poly(ethylene glycol)-poly(gamma-benzyl-L-glutamate) triblock copolymers in the solid state

The morphology in the solid state of a series of triblock copolymers comprising a poly(ethylene glycol) (PEG) midblock and symmetric poly(gamma-benzyl-L-glutamate) (PBLG) end blocks has been studied using X-ray scattering and microscopy techniques. Transmission electron microscopy (TEM) on samples selectively stained with uranyl acetate provided clear assignment of morphologies for as-cast and annealed samples. The thickness of both PEG and PBLG domains was in good agreement with calculations based on the conformations of the respective chains, allowing for the crystal or amorphous state of PEG and the a-helical or P-sheet structure of the PBLG. Atomic force microscopy provided complementary information on surface morphology for several samples that was in good agreement with the structure observed by TEM. A morphology diagram was constructed. Cylindrical structures were observed for ordered samples with low f(PBLG), whereas at higher f(PLBG) there was evidence for broken lamellar and "hockey puck" nanostructures. Regular lamellae were observed for intermediate compositions.

Grey-box radial basis function modelling: the art of incorporating prior knowledge

A basic principle in data modelling is to incorporate available a priori information regarding the underlying data generating mechanism into the modelling process. We adopt this principle and consider grey-box radial basis function (RBF) modelling capable of incorporating prior knowledge. Specifically, we show how to explicitly incorporate the two types of prior knowledge: the underlying data generating mechanism exhibits known symmetric property and the underlying process obeys a set of given boundary value constraints. The class of orthogonal least squares regression algorithms can readily be applied to construct parsimonious grey-box RBF models with enhanced generalisation capability.

A new solution of the rendering equation with stratified Monte Carlo approach

This paper is turned to the advanced Monte Carlo methods for realistic image creation. It offers a new stratified approach for solving the rendering equation. We consider the numerical solution of the rendering equation by separation of integration domain. The hemispherical integration domain is symmetrically separated into 16 parts. First 9 sub-domains are equal size of orthogonal spherical triangles. They are symmetric each to other and grouped with a common vertex around the normal vector to the surface. The hemispherical integration domain is completed with more 8 sub-domains of equal size spherical quadrangles, also symmetric each to other. All sub-domains have fixed vertices and computable parameters. The bijections of unit square into an orthogonal spherical triangle and into a spherical quadrangle are derived and used to generate sampling points. Then, the symmetric sampling scheme is applied to generate the sampling points distributed over the hemispherical integration domain. The necessary transformations are made and the stratified Monte Carlo estimator is presented. The rate of convergence is obtained and one can see that the algorithm is of super-convergent type.

Robustness and applicability of Markov chain Monte Carlo algorithms for eigenvalue problems

In this paper we analyse applicability and robustness of Markov chain Monte Carlo algorithms for eigenvalue problems. We restrict our consideration to real symmetric matrices. Almost Optimal Monte Carlo (MAO) algorithms for solving eigenvalue problems are formulated. Results for the structure of both - systematic and probability error are presented. It is shown that the values of both errors can be controlled independently by different algorithmic parameters. The results present how the systematic error depends on the matrix spectrum. The analysis of the probability error is presented. It shows that the close (in some sense) the matrix under consideration is to the stochastic matrix the smaller is this error. Sufficient conditions for constructing robust and interpolation Monte Carlo algorithms are obtained. For stochastic matrices an interpolation Monte Carlo algorithm is constructed. A number of numerical tests for large symmetric dense matrices are performed in order to study experimentally the dependence of the systematic error from the structure of matrix spectrum. We also study how the probability error depends on the balancing of the matrix. (c) 2007 Elsevier Inc. All rights reserved.

Ocean acoustic models for low frequency propagation in 2D and 3D environments

In this paper we are mainly concerned with the development of efficient computer models capable of accurately predicting the propagation of low-to-middle frequency sound in the sea, in axially symmetric (2D) and in fully 3D environments. The major physical features of the problem, i.e. a variable bottom topography, elastic properties of the subbottom structure, volume attenuation and other range inhomogeneities are efficiently treated. The computer models presented are based on normal mode solutions of the Helmholtz equation on the one hand, and on various types of numerical schemes for parabolic approximations of the Helmholtz equation on the other. A new coupled mode code is introduced to model sound propagation in range-dependent ocean environments with variable bottom topography, where the effects of an elastic bottom, of volume attenuation, surface and bottom roughness are taken into account. New computer models based on finite difference and finite element techniques for the numerical solution of parabolic approximations are also presented. They include an efficient modeling of the bottom influence via impedance boundary conditions, they cover wide angle propagation, elastic bottom effects, variable bottom topography and reverberation effects. All the models are validated on several benchmark problems and versus experimental data. Results thus obtained were compared with analogous results from standard codes in the literature.

On the spectra of certain integro-differential-delay problems with applications in neurodynamics

We investigate the spectrum of certain integro-differential-delay equations (IDDEs) which arise naturally within spatially distributed, nonlocal, pattern formation problems. Our approach is based on the reformulation of the relevant dispersion relations with the use of the Lambert function. As a particular application of this approach, we consider the case of the Amari delay neural field equation which describes the local activity of a population of neurons taking into consideration the finite propagation speed of the electric signal. We show that if the kernel appearing in this equation is symmetric around some point a= 0 or consists of a sum of such terms, then the relevant dispersion relation yields spectra with an infinite number of branches, as opposed to finite sets of eigenvalues considered in previous works. Also, in earlier works the focus has been on the most rightward part of the spectrum and the possibility of an instability driven pattern formation. Here, we numerically survey the structure of the entire spectra and argue that a detailed knowledge of this structure is important within neurodynamical applications. Indeed, the Amari IDDE acts as a filter with the ability to recognise and respond whenever it is excited in such a way so as to resonate with one of its rightward modes, thereby amplifying such inputs and dampening others. Finally, we discuss how these results can be generalised to the case of systems of IDDEs.

Droplets of structured fluid on a flat substrate

We study the equilibrium morphology of droplets of symmetric AB diblock copolymer on a flat substrate. Using self-consistent field theory (SCFT), we provide the first predictions for the equilibrium droplet shape and its internal structure. When the sustrate affinity for the A component, $\eta_A$, is small, the droplet adopts a nearly spherical shape much like that of simple fluids. Inside the spherical droplet, however, concentric circular lamellar layers stack on top of each other; hence the thickness of the droplet is effectively quantized by a half-integer or integer number of layers. At larger $\eta_A$ and smaller contact angle, the area of the upper-most layer becomes relatively large, resulting in a nearly flat, faceted top surface, followed by a semi-spherical slope. This geometry is remarkably reminiscent of the droplet shapes observed with smetic liquid crystals.

Acoustic trapped modes in a three-dimensional waveguide of slowly varying cross section

In this paper we develop an asymptotic scheme to approximate the trapped mode solutions to the time harmonic wave equation in a three-dimensional waveguide with a smooth but otherwise arbitrarily shaped cross section and a single, slowly varying `bulge', symmetric in the longitudinal direction. Extending the work in Biggs (2012), we first employ a WKBJ-type ansatz to identify the possible quasi-mode solutions which propagate only in the thicker region, and hence find a finite cut-on region of oscillatory behaviour and asymptotic decay elsewhere. The WKBJ expansions are used to identify a turning point between the cut-on and cut-on regions. We note that the expansions are nonuniform in an interior layer centred on this point, and we use the method of matched asymptotic expansions to connect the cut-on and cut-on regions within this layer. The behaviour of the expansions within the interior layer then motivates the construction of a uniformly valid asymptotic expansion. Finally, we use this expansion and the symmetry of the waveguide around the longitudinal centre, x = 0, to extract trapped mode wavenumbers, which are compared with those found using a numerical scheme and seen to be extremely accurate, even to relatively large values of the small parameter.