Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Integrative functional genomics analysis of sustained polyploidy phenotypes in breast cancer cells identifies an oncogenic profile for GINS2

Aneuploidy is among the most obvious differences between normal and cancer cells. However, mechanisms contributing to development and maintenance of aneuploid cell growth are diverse and incompletely understood. Functional genomics analyses have shown that aneuploidy in cancer cells is correlated with diffuse gene expression signatures and that aneuploidy can arise by a variety of mechanisms, including cytokinesis failures, DNA endoreplication and possibly through polyploid intermediate states. Here, we used a novel cell spot microarray technique to identify genes with a loss-of-function effect inducing polyploidy and/or allowing maintenance of polyploid cell growth of breast cancer cells. Integrative genomics profiling of candidate genes highlighted GINS2 as a potential oncogene frequently overexpressed in clinical breast cancers as well as in several other cancer types. Multivariate analysis indicated GINS2 to be an independent prognostic factor for breast cancer outcome (p = 0.001). Suppression of GINS2 expression effectively inhibited breast cancer cell growth and induced polyploidy. In addition, protein level detection of nuclear GINS2 accurately distinguished actively proliferating cancer cells suggesting potential use as an operational biomarker.

Comparative study of some constitutive equations characterising non-Newtonian fluids

This paper compares, in a general way, the predictions of the constitutive equations given by Rivlin and Ericksen, Oldroyd, and Walters. Whether we consider the rotational problems in cylindrical co-ordinates or in spherical polar co-ordinates, the effect of the non-Newtonicity on the secondary flows is collected in a single parameterα which can be explicitly expressed in terms of the non-Newtonian parameters that occur in each of the above-mentioned constitutive equations. Thus, for a given value ofα, all the three fluids will have identical secondary flows. It is only through the study of appropriate normal stresses that a Rivlin-Ericksen fluid can be distinguished from the other two fluids which are indistinguishable as long as this non-Newtonian parameter has the same value.

Functional role of the Mso1p-Sec1p complex in membrane fusion regulation

Sec1/Munc18 (SM) protein family members are evolutionary conserved proteins. They perform an essential, albeit poorly understood function in SNARE complex formation in membrane fusion. In addition to the SNARE complex components, only a few SM protein binding proteins are known. Typically, their binding modes to SM proteins and their contribution to the membrane fusion regulation is poorly characterised. We identified Mso1p as a novel Sec1p interacting partner. It was shown that Mso1p and Sec1p interact at sites of polarised secretion and that this localisation is dependent on the Rab GTPase Sec4p and its GEF Sec2p. Using targeted mutagenesis and N- and C-terminal deletants, it was discovered that the interaction between an N-terminal peptide of Mso1p and the putative Syntaxin N-peptide binding area in Sec1p domain 1 is important for membrane fusion regulation. The yeast Syntaxin homologues Sso1p and Sso2p lack the N-terminal peptide. Our results show that in addition to binding to the putative N-peptide binding area in Sec1p, Mso1p can interact with Sso1p and Sso2p. This result suggests that Mso1p can mimic the N-peptide binding to facilitate membrane fusion. In addition to Mso1p, a novel role in membrane fusion regulation was revealed for the Sec1p C-terminal tail, which is missing in its mammalian homologues. Deletion of the Sec1p-tail results in temperature sensitive growth and reduced sporulation. Using in vivo and in vitro experiments, it was shown that the Sec1p-tail mediates SNARE complex binding and assembly. These results propose a regulatory role for the Sec1p-tail in SNARE complex formation. Furthermore, two novel interaction partners for Mso1p, the Rab GTPase Sec4p and plasma membrane phospholipids, were identified. The Sec4p link was identified using Bimolecular Fluorescence Complementation assays with Mso1p and the non-SNARE binding Sec1p(1-657). The assay revealed that Mso1p can target Sec1p(1-657) to sites of secretion. This effect is mediated via the Mso1p C-terminus, which previously has been genetically linked to Sec4p. These results and in vitro binding experiments suggest that Mso1p acts in cooperation with the GTP-bound form of Sec4p on vesicle-like structures prior to membrane fusion. Mso1p shares homology with the PIP2 binding domain of the mammalian Munc18 binding Mint proteins. It was shown both in vivo and in vitro that Mso1p is a phospholipid inserting protein and that this insertion is mediated by the conserved Mso1p amino terminus. In vivo, the Mso1p phospholipid binding is needed for sporulation and Mso1p-Sec1p localisation at the sites of secretion at the plasma membrane. The results reveal a novel layer of membrane fusion regulation in exocytosis and propose a coordinating role for Mso1p in connection with membrane lipids, Sec1p, Sec4p and SNARE complexes in this process.

Numerical procedure for second order non-linear ordinary differential equations and application to heat transfer problem

In this paper, we have first given a numerical procedure for the solution of second order non-linear ordinary differential equations of the type y″ = f (x;y, y′) with given initial conditions. The method is based on geometrical interpretation of the equation, which suggests a simple geometrical construction of the integral curve. We then translate this geometrical method to the numerical procedure adaptable to desk calculators and digital computers. We have studied the efficacy of this method with the help of an illustrative example with known exact solution. We have also compared it with Runge-Kutta method. We have then applied this method to a physical problem, namely, the study of the temperature distribution in a semi-infinite solid homogeneous medium for temperature-dependent conductivity coefficient.

Lattice density-functional theory on graphene

A density-functional approach on the hexagonal graphene lattice is developed using an exact numerical solution to the Hubbard model as the reference system. Both nearest-neighbour and up to third nearest-neighbour hoppings are considered and exchange-correlation potentials within the local density approximation are parameterized for both variants. The method is used to calculate the ground-state energy and density of graphene flakes and infinite graphene sheet. The results are found to agree with exact diagonalization for small systems, also if local impurities are present. In addition, correct ground-state spin is found in the case of large triangular and bowtie flakes out of the scope of exact diagonalization methods.

Coherent quantum Boltzmann equations from cQPA

We reformulate and extend our recently introduced quantum kinetic theory for interacting fermion and scalar fields. Our formalism is based on the coherent quasiparticle approximation (cQPA) where nonlocal coherence information is encoded in new spectral solutions at off-shell momenta. We derive explicit forms for the cQPA propagators in the homogeneous background and show that the collision integrals involving the new coherence propagators need to be resummed to all orders in gradient expansion. We perform this resummation and derive generalized momentum space Feynman rules including coherent propagators and modified vertex rules for a Yukawa interaction. As a result we are able to set up self-consistent quantum Boltzmann equations for both fermion and scalar fields. We present several examples of diagrammatic calculations and numerical applications including a simple toy model for coherent baryogenesis.

Use of Abel integral equations in water wave scattering by two surface-piercing barriers

In this paper the classical problem of water wave scattering by two partially immersed plane vertical barriers submerged in deep water up to the same depth is investigated. This problem has an exact but complicated solution and an approximate solution in the literature of linearised theory of water waves. Using the Havelock expansion for the water wave potential, the problem is reduced here to solving Abel integral equations having exact solutions. Utilising these solutions,two sets of expressions for the reflection and transmission coefficients are obtained in closed forms in terms of computable integrals in contrast to the results given in the literature which,involved six complicated integrals in terms of elliptic functions. The two different expressions for each coefficient produce almost the same numerical results although it has not been possible to prove their equivalence analytically. The reflection coefficient is depicted against the wave number in a number of figures which almost coincide with the figures available in the literature wherein the problem was solved approximately by employing complementary approximations. (C) 2009 Elsevier B.V. All rights reserved.