Analytic Representation of The Dirac Equation

In this paper we construct an analytical separation (diagonalization) of the full (minimal coupling) Dirac equation into particle and antiparticle components. The diagonalization is analytic in that it is achieved without transforming the wave functions, as is done by the Foldy-Wouthuysen method, and reveals the nonlocal time behavior of the particle-antiparticle relationship. We interpret the zitterbewegung and the result that a velocity measurement (of a Dirac particle) at any instant in time is, as reflections of the fact that the Dirac equation makes a spatially extended particle appear as a point in the present by forcing it to oscillate between the past and future at speed c. From this we infer that, although the form of the Dirac equation serves to make space and time appear on an equal footing mathematically, it is clear that they are still not on an equal footing from a physical point of view. On the other hand, the Foldy-Wouthuysen transformation, which connects the Dirac and square root operator, is unitary. Reflection on these results suggests that a more refined notion (than that of unitary equivalence) may be required for physical systems

Electron correlation in Hooke’s law atom in the high-density limit

Closed-form expressions for the first three terms in the perturbation expansion of the exact energy and Hartree-Fock energy of the lowest singlet and triplet states of the Hooke's law atom are found. These yield elementary formulas for the exact correlation energies (-49.7028 and -5.807 65 mE(h)) of the two states in the high-density limit and lead to a pair of necessary conditions on the exact correlation kernel G(w) in Hartree-Fock-Wigner theory.The authors also thank Professor John D. Morgan III for advice concerning Eq. s1d and both EPSRC sGrant No. GR/R81121d and the Research School of Chemistry at ANU for funding

Investigating non-Fritzsch like texture specific quark mass matrices

A detailed investigation of all possible textures of Fritzsch-like and non-Fritzsch like, 144 for texture 6 zero and 432 for texture 5 zero mass matrices, have been carried out to ascertain their compatibility with the existing quark mixing data. It seems that all the texture 6 zero possibilities are completely ruled out whereas in the case of texture 5 zero mass matrices the only viable possibility looks to be that of Fritzsch-like.Comment: 13 pages, 4 figures, Accepted for publication in IJMP

The presence of valine at residue 129 in human prion protein accelerates amyloid formation

The polymorphism at residue 129 of the human PRNP gene modulates disease susceptibility and the clinicopathological phenotypes in human transmissible spongiform encephalopathies. The molecular mechanisms by which the effect of this polymorphism are mediated remain unclear. It has been shown that the folding, dynamics and stability of the physiological, alpha-helix-rich form of recombinant PrP are not affected by codon 129 polymorphism. Consistent with this, we have recently shown that the kinetics of amyloid formation do not differ between protein containing methionine at codon 129 and valine at codon 129 when the reaction is initiated from the a-monomeric PrPC-like state. In contrast, we have shown that the misfolding pathway leading to the formation of beta-sheet-rich, soluble oligomer waS favoured by the presence of methionine, compared with valine, at position 129. In the present work, we examine the effect of this polymorphism on the kinetics of an alternative misfolding pathway, that of amyloid formation using partially folded PrP allelomorphs. We show that the valine 129 allelomorph forms amyloids with a considerably shorter lag phase than the methionine 129 allelomorph both under spontaneous conditions and when seeded with pre-formed amyloid fibres. Taken together, our studies demonstrate that the effect of the codon 129 polymorphism depends on the specific misfolding pathway and on the initial conformation of the protein. The inverse propensities of the two allelomorphs to misfold in vitro through the alternative oligomeric and amyloidogenic pathways could explain some aspects of prion diseases linked to this polymorphism such as age at onset and disease incubation time. (c) 2005 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved

Estimation of Parameters in DNA Mixture Analysis

In Cowell et al. (2007), a Bayesian network for analysis of mixed traces of DNA was presented using gamma distributions for modelling peak sizes in the electropherogram. It was demonstrated that the analysis was sensitive to the choice of a variance factor and hence this should be adapted to any new trace analysed. In the present paper we discuss how the variance parameter can be estimated by maximum likelihood to achieve this. The unknown proportions of DNA from each contributor can similarly be estimated by maximum likelihood jointly with the variance parameter. Furthermore we discuss how to incorporate prior knowledge about the parameters in a Bayesian analysis. The proposed estimation methods are illustrated through a few examples of applications for calculating evidential value in casework and for mixture deconvolution

Non-adiabatic Effects in the Dissociation of Oxygen Molecules at the Al(111) Surface

The measured low initial sticking probability of oxygen molecules at the Al(111) surface that had puzzled the field for many years was recently explained in a non-adiabatic picture invoking spin-selection rules [J. Behler et al., Phys. Rev. Lett. 94, 036104 (2005)]. These selection rules tend to conserve the initial spin-triplet character of the free O2 molecule during the molecule's approach to the surface. A new locally-constrained density-functional theory approach gave access to the corresponding potential-energy surface (PES) seen by such an impinging spin-triplet molecule and indicated barriers to dissociation which reduce the sticking probability. Here, we further substantiate this non-adiabatic picture by providing a detailed account of the employed approach. Building on the previous work, we focus in particular on inaccuracies in present-day exchange-correlation functionals. Our analysis shows that small quantitative differences in the spin-triplet constrained PES obtained with different gradient-corrected functionals have a noticeable effect on the lowest kinetic energy part of the resulting sticking curve.Comment: 17 pages including 11 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm

Studies on Macronutrient Fertilization in Pomegranate under Sub-Tropical Plains

An investigation was carried out to study the influence of different levels of NPK fertilizers on plant growth, fruit yield and quality, and leaf NPK content in pomegranate cv. Kandhari under sub-tropical conditions. Graded doses of nitrogen (0-300g/plant), phosphorus (0-150g/plant) and potassium (0-300g/plant) fertilizers were applied through soil, in addition to a basal dose of FYM. Control plants were fed FYM only. Maximum increase in plant growth and fruit yield was recorded in plants receiving NPK @ 300:50:100g/plant, while Control plants registered least growth and yield. Potassium levels improved fruit weight over the Control. Higher dose of potassium also improved fruit colour and enhanced peel thickness and grain weight. Maximum TSS:acid ratio was seen with NPK @ 200:50:100g/plant. Reducing sugars were not affected by any treatment. Leaf N, P and K content increased with application of the respective nutrient

Why is timing of bird migration advancing when individuals are not?

Recent advances in spring arrival dates have been reported in many migratory species but the mechanism driving these advances is unknown. As population declines are most widely reported in species that are not advancing migration, there is an urgent need to identify the mechanisms facilitating and constraining these advances. Individual plasticity in timing of migration in response to changing climatic conditions is commonly proposed to drive these advances but plasticity in individual migratory timings is rarely observed. For a shorebird population that has significantly advanced migration in recent decades, we show that individual arrival dates are highly consistent between years, but that the arrival dates of new recruits to the population are significantly earlier now than in previous years. Several mechanisms could drive advances in recruit arrival, none of which require individual plasticity or rapid evolution of migration timings. In particular, advances in nest-laying dates could result in advanced recruit arrival, if benefits of early hatching facilitate early subsequent spring migration. This mechanism could also explain why arrival dates of short-distance migrants, which generally return to breeding sites earlier and have greater scope for advance laying, are advancing more rapidly than long-distance migrants

Exploring the parameter space of texture 4 zero quark mass matrices

We have attempted to extend the parameter space of the elements of the texture 4 zero Hermitian quark mass matrices, to include the case of `weak hierarchy' amongst them along with the usually considered `strong hierarchy' case. This has been carried out by giving wide variation to the hierarchy defining parameters D_U and D_D, having implications for the structural features of the mass matrices. We find that not only the weakly hierarchical mass matrices are able to reproduce the strongly hierarchical mixing angles but also both the phases having their origin in the mass matrices have to be non zero to achieve compatibility of these matrices with recent quark mixing data. Further noting the difference between the exclusive and inclusive values of V_ub, we have carried out separate analyses corresponding to these.Comment: 13 pages, 4 figures, version accepted for publication in Journal Of Physics

Computation of molecular Hartree–Fock Wigner intracules

The computation of molecular Wigner intracules from Hartree–Fock wave functions using Gaussian basis functions is described. The Wigner intracule is a new type of intracule that contains information about both the relative position and momentum of the electrons. Two methods for evaluating the required integrals are presented. The first approach uses quadrature while the second requires summation of an infinite series.This research was partly supported by the Engineering and Physical Sciences Research Council through a project studentship (GR/R81121) to D.P.O. and an Advanced Research Fellowship (GR/R77636) to N.A.B