A frequency-independent boundary element method for scattering by two-dimensional screens and apertures

We propose and analyse a hybrid numerical–asymptotic hp boundary element method (BEM) for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of sound-soft two-dimensional screens. Our method uses an approximation space enriched with oscillatory basis functions, chosen to capture the high-frequency asymptotics of the solution. We provide a rigorous frequency-explicit error analysis which proves that the method converges exponentially as the number of degrees of freedom N increases, and that to achieve any desired accuracy it is sufficient to increase N in proportion to the square of the logarithm of the frequency as the frequency increases (standard BEMs require N to increase at least linearly with frequency to retain accuracy). Our numerical results suggest that fixed accuracy can in fact be achieved at arbitrarily high frequencies with a frequency-independent computational cost, when the oscillatory integrals required for implementation are computed using Filon quadrature. We also show how our method can be applied to the complementary ‘breakwater’ problem of propagation through an aperture in an infinite sound-hard screen.

A robust two-dimensional hydrogen-bonded network for the predictable assembly of ternary co-crystals of furosemide

Consideration of the geometrical features of the functional groups present in furosemide has enabled synthesis of a series of ternary co-crystals with predictable structural features, containing a robust asymmetric two-dimensional network.

The cleft ion fountain: a two-dimensional kinetic model

The transport of ionospheric ions from a source in the polar cleft ionosphere through the polar magnetosphere is investigated using a two-dimensional, kinetic, trajectory-based code. The transport model includes the effects of gravitation, longitudinal magnetic gradient force, convection electric fields, and parallel electric fields. Individual ion trajectories as well as distribution functions and resulting bulk parameters of density, parallel average energy, and parallel flux for a presumed cleft ionosphere source distribution are presented for various conditions to illustrate parametrically the dependences on source energies, convection electric field strengths, ion masses, and parallel electric field strengths. The essential features of the model are consistent with the concept of a cleft-based ion fountain supplying ionospheric ions to the polar magnetosphere, and the resulting plasma distributions and parameters are in general agreement with recent low-energy ion measurements from the DE 1 satellite.

Modelling the rheology of anisotropic particles adsorbed on a two-dimensional fluid interface

We present a general approach based on nonequilibrium thermodynamics for bridging the gap between a well-defined microscopic model and the macroscopic rheology of particle-stabilised interfaces. Our approach is illustrated by starting with a microscopic model of hard ellipsoids confined to a planar surface, which is intended to simply represent a particle-stabilised fluid–fluid interface. More complex microscopic models can be readily handled using the methods outlined in this paper. From the aforementioned microscopic starting point, we obtain the macroscopic, constitutive equations using a combination of systematic coarse-graining, computer experiments and Hamiltonian dynamics. Exemplary numerical solutions of the constitutive equations are given for a variety of experimentally relevant flow situations to explore the rheological behaviour of our model. In particular, we calculate the shear and dilatational moduli of the interface over a wide range of surface coverages, ranging from the dilute isotropic regime, to the concentrated nematic regime.

Bothrops insularis venomics: A proteomic analysis supported by transcriptomic-generated sequence data

A joint transcriptomic and proteomic approach employing two-dimensional electrophoresis, liquid chromatography and mass spectrometry was carried out to identify peptides and proteins expressed by the venom gland of the snake Bothrops insularis, an endemic species of Queimada Grande Island, Brazil. Four protein families were mainly represented in processed spots, namely metalloproteinase, serine proteinase, phospholipase A(2) and lectin. Other represented families were growth factors, the developmental protein G10, a disintegrin and putative novel bradykinin-potentiating peptides. The enzymes were present in several isoforms. Most of the experimental data agreed with predicted values for isoelectric point and M(r) of proteins found in the transcriptome of the venom gland. The results also support the existence of posttranslational modifications and of proteolytic processing of precursor molecules which could lead to diverse multifunctional proteins. This study provides a preliminary reference map for proteins and peptides present in Bothrops insularis whole venom establishing the basis for comparative studies of other venom proteomes which could help the search for new drugs and the improvement of venom therapeutics. Altogether, our data point to the influence of transcriptional and post-translational events on the final venom composition and stress the need for a multivariate approach to snake venomics studies. (c) 2009 Elsevier B.V. All rights reserved.

Two-dimensional electron states bound to an off-plane donor in a magnetic field

The states of an electron confined in a two-dimensional (2D) plane and bound to an off-plane donor impurity center, in the presence of a magnetic field, are investigated. The energy levels of the ground state and the first three excited states are calculated variationally. The binding energy and the mean orbital radius of these states are obtained as a function of the donor center position and the magnetic field strength. The limiting cases are discussed for an in-plane donor impurity (i.e. a 2D hydrogen atom) as well as for the donor center far away from the 2D plane in strong magnetic fields, which corresponds to a 2D harmonic oscillator.

STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

Exploratory semiparametric analysis of two-dimensional diffusions in finance

We examine bivariate extensions of Aït-Sahalia’s approach to the estimation of univariate diffusions. Our message is that extending his idea to a bivariate setting is not straightforward. In higher dimensions, as opposed to the univariate case, the elements of the Itô and Fokker-Planck representations do not coincide; and, even imposing sensible assumptions on the marginal drifts and volatilities is not sufficient to obtain direct generalisations. We develop exploratory estimation and testing procedures, by parametrizing the drifts of both component processes and setting restrictions on the terms of either the Itô or the Fokker-Planck covariance matrices. This may lead to highly nonlinear ordinary differential equations, where the definition of boundary conditions is crucial. For the methods developed, the Fokker-Planck representation seems more tractable than the Itô’s. Questions for further research include the design of regularity conditions on the time series dependence in the data, the kernels actually used and the bandwidths, to obtain asymptotic properties for the estimators proposed. A particular case seems promising: “causal bivariate models” in which only one of the diffusions contributes to the volatility of the other. Hedging strategies which estimate separately the univariate diffusions at stake may thus be improved.

Structure-function relationship of new crotamine isoform from the Crotalus durissus cascavella

In this work we isolated a novel crotamine like protein from the Crotalus durissus cascavella venom by combination of molecular exclusion and analytical reverse phase HPLC. Its primary structure was:YKRCHKKGGHCFPKEKICLPPSSDLGKMDCRWKRK-CCKKGS GK. This protein showed a molecular mass of 4892.89 da that was determined by Matrix Assisted Laser Desorption Ionization Time-of-flight (MALDI-TOF) mass spectrometry. The approximately pI value of this protein was determined in 9.9 by two-dimensional electrophoresis. This crotamine-like protein isolated here and that named as Cro 2 produced skeletal muscle spasm and spastic paralysis in mice similarly to other crotamines like proteins. Cro 2 did not modify the insulin secretion at low glucose concentration (2.8 and 5.6 mM), but at high glucose concentration (16.7 mM) we observed an insulin secretion increasing of 2.7-3.0-fold than to control. The Na+ channel antagonist tetrodoxin (6 mM) decreased glucose and Cro 2-induced insulin secretion. These results suggested that Na+ channel are involved in the insulin secretion. In this article, we also purified some peptide fragment from the treatment of reduced and carboxymethylated Cro 2 (RC-Cro 2) with cyanogen bromide and protease V8 from Staphylococcus aureus. The isolated pancreatic beta-cells were then treated with peptides only at high glucose concentration (16.7 mM), in this condition only two peptides induced insulin secretion. The amino acid sequence homology analysis of the whole crotamine as well as the biologically-active peptide allowed determining the consensus region of the biologically-active crotamine responsible for insulin secretion was KGGHCFPKE and DCRWKWKCCKKGSG.

Effect of umbelliferone (7-hydroxycoumarin, 7-HOC) on the enzymatic, edematogenic and necrotic activities of secretory phospholipase A2 (sPLA2) isolated from Crotalus durissus collilineatus venom

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