On a class of three-phase checkerboards with unusual effective properties

We examine the band spectrum, and associated Floquet-Bloch eigensolutions, arising in a class of three-phase periodic checkerboards. On a periodic cell $[-1,1[^2$, the refractive index is defined by $n^2= 1+ g_1(x_1)+g_2(x_2)$ with $g_i(x_i)= r^2\quad {\rm for} \quad 0\leq x_i-1$ the lowest frequency branch goes through origin with linear behaviour, which leads to effective properties encountered in most periodic structures. However, the case whereby $r^2=-1$ is very unusual, as the frequency $\lambda$ behaves like $\sqrt{k}$ near the origin, where $k$ is the wavenumber. Finally, when $r^2<-1$, the lowest branch does not pass through the origin and a zero-frequency band gap opens up. In the last two cases, effective medium theory breaks down even in the quasi-static limit, while the high-frequency homogenization [Craster et al., Proc. Roy. Soc. Lond. A 466, 2341-2362, 2010] neatly captures the detailed features of band diagrams

A Solvent Model for Simulations of Peptides in Bilayers. I. Membrane-Promoting α-Helix Formation

AbstractWe describe an efficient solvation model for proteins. In this model atomic solvation parameters imitating the hydrocarbon core of a membrane, water, and weak polar solvent (octanol) were developed. An optimal number of solvation parameters was chosen based on analysis of atomic hydrophobicities and fitting experimental free energies of gas-cyclohexane, gas-water, and octanol-water transfer for amino acids. The solvation energy term incorporated into the ECEPP/2 potential energy function was tested in Monte Carlo simulations of a number of small peptides with known energies of bilayer-water and octanol-water transfer. The calculated properties were shown to agree reasonably well with the experimental data. Furthermore, the solvation model was used to assess membrane-promoting α-helix formation. To accomplish this, all-atom models of 20-residue homopolypeptides—poly-Leu, poly-Val, poly-Ile, and poly-Gly in initial random coil conformation—were subjected to nonrestrained Monte Carlo conformational search in vacuo and with the solvation terms mimicking the water and hydrophobic parts of the bilayer. All the peptides demonstrated their largest helix-forming tendencies in a nonpolar environment, where the lowest-energy conformers of poly-Leu, Val, Ile revealed 100, 95, and 80% of α-helical content, respectively. Energetic and conformational properties of Gly in all environments were shown to be different from those observed for residues with hydrophobic side chains. Applications of the solvation model to simulations of peptides and proteins in the presence of membrane, along with limitations of the approach, are discussed

A Solvent Model for Simulations of Peptides in Bilayers. II. Membrane-Spanning α-Helices

AbstractWe describe application of the implicit solvation model (see the first paper of this series), to Monte Carlo simulations of several peptides in bilayer- and water-mimetic environments, and in vacuum. The membrane-bound peptides chosen were transmembrane segments A and B of bacteriorhodopsin, the hydrophobic segment of surfactant lipoprotein, and magainin2. Their conformations in membrane-like media are known from the experiments. Also, molecular dynamics study of surfactant lipoprotein with different explicit solvents has been reported (Kovacs, H., A. E. Mark, J. Johansson, and W. F. van Gunsteren. 1995. J. Mol. Biol. 247:808–822). The principal goal of this work is to compare the results obtained in the framework of our solvation model with available experimental and computational data. The findings could be summarized as follows: 1) structural and energetic properties of studied molecules strongly depend on the solvent; membrane-mimetic media significantly promote formation of α-helices capable of traversing the bilayer, whereas a polar environment destabilizes α-helical conformation via reduction of solvent-exposed surface area and packing; 2) the structures calculated in a membrane-like environment agree with the experimental ones; 3) noticeable differences in conformation of surfactant lipoprotein assessed via Monte Carlo simulation with implicit solvent (this work) and molecular dynamics in explicit solvent were observed; 4) in vacuo simulations do not correctly reproduce protein-membrane interactions, and hence should be avoided in modeling membrane proteins

An asymptotic higher-order theory for rectangular beams

A direct asymptotic integration of the full threedimensional problem of elasticity is employed to derive a consistent governing equation for a beam with the rectangular cross-section. The governing equation is consistent in the sense that it has the same long-wave low-frequency behaviour as the exact solution of the original three-dimensional problem. Performance of the new beam equation is illustrated by comparing its predictions against the results of direct finite element computations. Limiting behaviours for beams with large (and small) aspect ratios, which can be established using classic plate theories, are recovered from the new governing equation to illustrate its consistency and also to illustrate the importance of using plate theories with the correctly refined boundary conditions. The implications for the correct choice of the shear correction factor in Timoshenko’s beam theory are also discusse

Composite wave models for elastic plates

© 2018 The Author(s). The long-term challenge of formulating an asymptotically motivated wave theory for elastic plates is addressed. Composite two-dimensional models merging the leading or higher-order parabolic equations for plate bending and the hyperbolic equation for the Rayleigh surface wave are constructed. Analysis of numerical examples shows that the proposed approach is robust not only at low- and high-frequency limits but also over the intermediate frequency range.Scientific Projects of Anadolu Universit

Explicit asymptotic modelling of transient Love waves propagated along a thin coating

The official published version can be obtained from the link below.An explicit asymptotic model for transient Love waves is derived from the exact equations of anti-plane elasticity. The perturbation procedure relies upon the slow decay of low-frequency Love waves to approximate the displacement field in the substrate by a power series in the depth coordinate. When appropriate decay conditions are imposed on the series, one obtains a model equation governing the displacement at the interface between the coating and the substrate. Unusually, the model equation contains a term with a pseudo-differential operator. This result is confirmed and interpreted by analysing the exact solution obtained by integral transforms. The performance of the derived model is illustrated by numerical examples.This work is sponsored by the grant from Higher Education of Pakistan and by the Brunel University’s “BRIEF” research award

Impact of system factors on the water saving efficiency of household grey water recycling

Copyright © 2010 Taylor & Francis. This is an Author's Accepted Manuscript of an article published in Desalination and Water Treatment Volume 24, Issue 1-3 (2010), available online at: http://www.tandfonline.com/10.5004/dwt.2010.1542A general concern when considering the implementation of domestic grey water recycling is to understand the impacts of system factors on water saving efficiency. Key factors include household occupancy, storage volumes, treatment capacity and operating mode. Earlier investigations of the impacts of these key factors were based on a one-tank system only. This paper presents the results of an investigation into the effect of these factors on the performance of a more realistic ‘two tank’ system with treatment using an object based household water cycle model. A Monte-Carlo simulation technique was adopted to generate domestic water appliance usage data which allows long-term prediction of the system's performance to be made. Model results reveal the constraints of treatment capacity, storage tank sizes and operating mode on percentage of potable water saved. A treatment capacity threshold has been discovered at which water saving efficiency is maximised for a given pair of grey and treated grey water tank. Results from the analysis suggest that the previous one-tank model significantly underestimates the tank volumes required for a given target water saving efficiency

Lack of association between proton pump inhibitor use and brain aging: a cross-sectional study

PURPOSE Due to conflicting scientific evidence for an increased risk of dementia by intake of proton pump inhibitors (PPIs), this study investigates associations between PPI use and brain volumes, estimated brain age, and cognitive function in the general population. METHODS Two surveys of the population-based Study of Health in Pomerania (SHIP) conducted in Northeast Germany were used. In total, 2653 participants underwent brain magnetic resonance imaging (MRI) and were included in the primary analysis. They were divided into two groups according to their PPI intake and compared with regard to their brain volumes (gray matter, white matter, total brain, and hippocampus) and estimated brain age. Multiple regression was used to adjust for confounding factors. Cognitive function was evaluated by the Verbal Learning and Memory Test (VLMT) and the Nuremberg Age Inventory (NAI) and put in relation to PPI use. RESULTS No association was found between PPI use and brain volumes or the estimated brain age. The VLMT score was 1.11 lower (95% confidence interval: - 2.06 to - 0.16) in immediate recall, and 0.72 lower (95% CI: - 1.22 to - 0.22) in delayed recall in PPI users than in non-users. PPI use was unrelated to the NAI score. CONCLUSIONS The present study does not support a relationship between PPI use and brain aging