Studies in the geometry of the discrete plane

This thesis is an attempt to initiate the development of a discrete geometry of the discrete plane H = {(qmxo,qnyo); m,n e Z - the set of integers}, where q s (0,1) is fixed and (xO,yO) is a fixed point in the first quadrant of the complex plane, xo,y0 ¢ 0. The discrete plane was first considered by Harman in 1972, to evolve a discrete analytic function theory for geometric difference functions. We shall mention briefly, through various sections, the principle of discretization, an outline of discrete a alytic function theory, the concept of geometry of space and also summary of work done in this thesis

Importance of the embedding environment on the strain within small rings in siliceous materials

The effect of the local environment on the energetic strain within small (SiO)N rings (with N=2,3) in silica materials is investigated via periodic model systems employing density functional calculations. Through comparison of the energies of various nonterminated systems containing small rings in strained and relatively unstrained environments, with alpha quartz, we demonstrate how small ring strain is affected by the nature of the embedding environment. We compare our findings with numerous previously reported calculations, often predicting significantly different small-ring strain energies, leading to a critical assessment of methods of calculating accurate localized ring energies. The results have relevance for estimates of the strain-induced response (e.g., chemical, photo, and radio) of small silica rings, and the propensity for them to form in bulk glasses, thin films, and nanoclusters.

Strain induced anomalous red shift in mesoscopic iron oxide prepared by a novel technique

Nano magnetic oxides are promising candidates for high density magnetic storage and other applications. Nonspherical mesoscopic iron oxide particles are also candidate materials for studying the shape, size and strain induced modifications of various physical properties viz. optical, magnetic and structural. Spherical and nonspherical iron oxides having an aspect ratio, ~2, are synthesized by employing starch and ethylene glycol and starch and water, respectively by a novel technique. Their optical, structural, thermal and magnetic properties are evaluated. A red shift of 0⋅24 eV is observed in the case of nonspherical particles when compared to spherical ones. The red shift is attributed to strain induced changes in internal pressure inside the elongated iron oxide particles. Pressure induced effects are due to the increased overlap of wave functions. Magnetic measurements reveal that particles are superparamagnetic. The marked increase in coercivity in the case of elongated particles is a clear evidence for shape induced anisotropy. The decreased specific saturation magnetization of the samples is explained on the basis of weight percentage of starch, a nonmagnetic component and is verified by TGA and FTIR studies. This technique can be modified for tailoring the aspect ratio and these particles are promising candidates for drug delivery and contrast enhancement agents in magnetic resonance imaging

"A Sequence in Subdomain 2 of DBL1a of Plasmodium falciparum Erythrocyte Membrane Protein 1 Induces Strain Transcending Antibodies"

Immunity to severe malaria is the first level of immunity acquired to Plasmodium falciparum. Antibodies to the variant antigen PfEMP1 (P. falciparum erythrocyte membrane protein 1) present at the surface of the parasitized red blood cell (pRBC) confer protection by blocking microvascular sequestration. Here we have generated antibodies to peptide sequences of subdomain 2 of PfEMP1-DBL1a previously identified to be associated with severe or mild malaria. A set of sera generated to the amino acid sequence KLQTLTLHQVREYWWALNRKEVWKA, containing the motif ALNRKE, stained the live pRBC. 50% of parasites tested (7/14) were positive both in flow cytometry and immunofluorescence assays with live pRBCs including both laboratory strains and in vitro adapted clinical isolates. Antibodies that reacted selectively with the sequence REYWWALNRKEVWKA in a 15-mer peptide array of DBL1a-domains were also found to react with the pRBC surface. By utilizing a peptide array to map the binding properties of the elicited anti-DBL1a antibodies, the amino acids WxxNRx were found essential for antibody binding. Complementary experiments using 135 degenerate RDSM peptide sequences obtained from 93 Ugandan patient-isolates showed that antibody binding occurred when the amino acids WxLNRKE/D were present in the peptide. The data suggests that the ALNRKE sequence motif, associated with severe malaria, induces strain-transcending antibodies that react with the pRBC surface

A sequence in subdomain 2 of DBL1 alpha of plasmodium falciparum erythrocyte membrane protein 1 induces strain transcending antibodies

Immunity to severe malaria is the first level of immunity acquired to Plasmodium falciparum. Antibodies to the variant antigen PfEMP1 (P. falciparum erythrocyte membrane protein 1) present at the surface of the parasitized red blood cell (pRBC) confer protection by blocking microvascular sequestration. Here we have generated antibodies to peptide sequences of subdomain 2 of PfEMP1-DBL1 alpha previously identified to be associated with severe or mild malaria. A set of sera generated to the amino acid sequence KLQTLTLHQVREYWWALNRKEVWKA, containing the motif ALNRKE, stained the live pRBC. 50% of parasites tested (7/14) were positive both in flow cytometry and immunofluorescence assays with live pRBCs including both laboratory strains and in vitro adapted clinical isolates. Antibodies that reacted selectively with the sequence REYWWALNRKEVWKA in a 15-mer peptide array of DBL1 alpha-domains were also found to react with the pRBC surface. By utilizing a peptide array to map the binding properties of the elicited anti-DBL1 alpha antibodies, the amino acids WxxNRx were found essential for antibody binding. Complementary experiments using 135 degenerate RDSM peptide sequences obtained from 93 Ugandan patient-isolates showed that antibody binding occurred when the amino acids WxLNRKE/D were present in the peptide. The data suggests that the ALNRKE sequence motif, associated with severe malaria, induces strain-transcending antibodies that react with the pRBC surface.

The impact of deformation strain on the formation of banded clouds in idealized modeling experiments

Experiments are performed using an idealized version of an operational forecast model to determine the impact on banded frontal clouds of the strength of deformational forcing, low-level baroclinicity, and model representation of convection. Line convection is initiated along the front, and slantwise bands extend from the top of the line-convection elements into the cold air. This banding is attributed primarily to M adjustment. The cross-frontal spreading of the cold pool generated by the line convection leads to further triggering of upright convection in the cold air that feeds into these slantwise bands. Secondary low-level bands form later in the simulations; these are attributed to the release of conditional symmetric instability. Enhanced deformation strain leads to earlier onset of convection and more coherent line convection. A stronger cold pool is generated, but its speed is reduced relative to that seen in experiments with weaker deformational strain, because of inhibition by the strain field. Enhanced low-level baroclinicity leads to the generation of more inertial instability by line convection (for a given capping height of convection), and consequently greater strength of the slantwise circulations formed by M adjustment. These conclusions are based on experiments without a convective-parametrization scheme. Experiments using the standard or a modified scheme for this model demonstrate known problems with the use of this scheme at the awkward 4 km grid length used in these simulations. Copyright © 2008 Royal Meteorological Society

Microscopic Mechanisms of Strain Hardening in Glassy Polymers

The mechanisms underlying the increase in stress for large mechanical strains of a polymer glass, quantified by the strain-hardening modulus, are still poorly understood. In the present paper we aim to elucidate this matter and present new mechanisms. Molecular-dynamics simulations of two polymers with very different strain-hardening moduli (polycarbonate and polystyrene) have been carried out. Nonaffine displacements occur because of steric hindrances and connectivity constraints. We argue that it is not necessary to introduce the concept of entanglements to understand strain hardening, but that hardening is rather coupled with the increase in the rate of nonaffine particle displacements. This rate increases faster for polycarbonate, which has the higher strain-hardening modulus. Also more nonaffine chain stretching is present for polycarbonate. It is shown that the inner distances of such a nonaffinely deformed chain can be well described by the inner distances of the worm-like chain, but with an effective stiffness length (equal to the Kuhn length for an infinite worm-like chain) that increases during deformation. It originates from the finite extensibility of the chain. In this way the increase in nonaffine particle displacement can be understood as resulting from an increase in the effective stiffness length of the perturbed chain during deformation, so that at larger strains a higher rate of plastic events in terms of nonaffine displacement is necessary, causing in turn the observed strain hardening in polymer glasses.

The elliptic sine-Gordon equation in a half plane

We consider boundary value problems for the elliptic sine-Gordon equation posed in the half plane y > 0. This problem was considered in Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) using the classical inverse scattering transform approach. Given the limitations of this approach, the results obtained rely on a nonlinear constraint on the spectral data derived heuristically by analogy with the linearized case. We revisit the analysis of such problems using a recent generalization of the inverse scattering transform known as the Fokas method, and show that the nonlinear constraint of Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) is a consequence of the so-called global relation. We also show that this relation implies a stronger constraint on the spectral data, and in particular that no choice of boundary conditions can be associated with a decaying (possibly mod 2π) solution analogous to the pure soliton solutions of the usual, time-dependent sine-Gordon equation. We also briefly indicate how, in contrast to the evolutionary case, the elliptic sine-Gordon equation posed in the half plane does not admit linearisable boundary conditions.

Spectral analysis of the elliptic sine-Gordon equation in the quarter plane

We study the elliptic sine-Gordon equation in the quarter plane using a spectral transform approach. We determine the Riemann-Hilbert problem associated with well-posed boundary value problems in this domain and use it to derive a formal representation of the solution. Our analysis is based on a generalization of the usual inverse scattering transform recently introduced by Fokas for studying linear elliptic problems.

Instability of surface-temperature filaments in strain and shear

The effects of uniform straining and shearing on the stability of a surface quasi-geostrophic temperature filament are investigated. Straining is shown to stabilize perturbations for wide filaments but only for a finite time until the filament thins to a critical width, after which some perturbations can grow. No filament can be stabilized in practice, since there are perturbations that can grow large for any strain rate. The optimally growing perturbations, defined as solutions that reach a certain threshold amplitude first, are found numerically for a wide range of parameter values. The radii of the vortices formed through nonlinear roll-up are found to be proportional to θ/s, where θ is the temperature anomaly of the filament and s the strain rate, and are not dependent on the initial size of the filament. Shearing is shown to reduce the normal-mode growth rates, but it cannot stabilize them completely when there are temperature discontinuities in the basic state; smooth filaments can be stabilized completely by shearing and a simple scaling argument provides the shear rate required. Copyright © 2010 Royal Meteorological Society

Forward modelling to determine the observational signatures of white-light imaging and interplanetary scintillation for the propagation of an interplanetary shock in the ecliptic plane

Recent coordinated observations of interplanetary scintillation (IPS) from the EISCAT, MERLIN, and STELab, and stereoscopic white-light imaging from the two heliospheric imagers (HIs) onboard the twin STEREO spacecraft are significant to continuously track the propagation and evolution of solar eruptions throughout interplanetary space. In order to obtain a better understanding of the observational signatures in these two remote-sensing techniques, the magnetohydrodynamics of the macro-scale interplanetary disturbance and the radio-wave scattering of the micro-scale electron-density fluctuation are coupled and investigated using a newly constructed multi-scale numerical model. This model is then applied to a case of an interplanetary shock propagation within the ecliptic plane. The shock could be nearly invisible to an HI, once entering the Thomson-scattering sphere of the HI. The asymmetry in the optical images between the western and eastern HIs suggests the shock propagation off the Sun–Earth line. Meanwhile, an IPS signal, strongly dependent on the local electron density, is insensitive to the density cavity far downstream of the shock front. When this cavity (or the shock nose) is cut through by an IPS ray-path, a single speed component at the flank (or the nose) of the shock can be recorded; when an IPS ray-path penetrates the sheath between the shock nose and this cavity, two speed components at the sheath and flank can be detected. Moreover, once a shock front touches an IPS ray-path, the derived position and speed at the irregularity source of this IPS signal, together with an assumption of a radial and constant propagation of the shock, can be used to estimate the later appearance of the shock front in the elongation of the HI field of view. The results of synthetic measurements from forward modelling are helpful in inferring the in-situ properties of coronal mass ejection from real observational data via an inverse approach.

Mutations in the NS2B and NS3 genes affect mouse neuroinvasiveness of a Western European field strain of tick-borne encephalitis virus

An attenuated strain (263) of the tick-borne encephalitis virus, isolated from field ticks, was either serially subcultured, 5 times in mice, or at 40 degrees C in PS cells, producing 2 independent strains, 263-m5 and 263-TR with identical genomes; both strains exhibited increased plaque size, neuroinvasiveness and temperature-resistance. Sequencing revealed two unique amino acid substitutions, one mapping close to the catalytic site of the viral protease. These observations imply that virus adaptation from ticks to mammals occurs by selection of pre-existing virulent variants from the quasispecies population rather than by the emergence of new random mutations. The significance of these observations is discussed. (c) 2008 Elsevier Inc. All rights reserved.

Thiamine is synthesized by a salvage pathway in Rhizobium leguminosarum bv. viciae strain 3841

In the absence of added thiamine, Rhizobium leguminosarum bv. viciae strain 3841 does not grow in liquid medium and forms only "pin" colonies on agar plates, which contrasts with the good growth of Sinorhizobium meliloti 1021, Mesorhizobium loti 303099, and Rhizobium etli CFN42. These last three organisms have thiCOGE genes, which are essential for de novo thiamine synthesis. While R. leguminosarum bv. viciae 3841 lacks thiCOGE, it does have thiMED. Mutation of thiM prevented formation of pin colonies on agar plates lacking added thiamine, suggesting thiamine intermediates are normally present. The putative functions of ThiM, ThiE, and ThiD are 4-methyl-5-(beta-hydroxyethyl) thiazole (THZ) kinase, thiamine phosphate pyrophosphorylase, and 4-amino-5-hydroxymethyl-2-methyl pyrimidine (HMP) kinase, respectively. This suggests that a salvage pathway operates in R. leguminosarum, and addition of HMP and THZ enabled growth at the same rate as that enabled by thiamine in strain 3841 but elicited no growth in the thiM mutant (RU2459). There is a putative thi box sequence immediately upstream of the thiM, and a gfp-mut3.1 fusion to it revealed the presence of a promoter that is strongly repressed by thiamine. Using fluorescent microscopy and quantitative reverse transcription-PCR, it was shown that thiM is expressed in the rhizosphere of vetch and pea plants, indicating limitation for thiamine. Pea plants infected by RU2459 were not impaired in nodulation or nitrogen fixation. However, colonization of the pea rhizosphere by the thiM mutant was impaired relative to that of the wild type. Overall, the results show that a thiamine salvage pathway operates to enable growth of Rhizobium leguminosarum in the rhizosphere, allowing its survival when thiamine is limiting.