Numerical solution of the PTT constitutive equation for unsteady three-dimensional free surface flows

This work deals with the development of a numerical technique for simulating three-dimensional viscoelastic free surface flows using the PTT (Phan-Thien-Tanner) nonlinear constitutive equation. In particular, we are interested in flows possessing moving free surfaces. The equations describing the numerical technique are solved by the finite difference method on a staggered grid. The fluid is modelled by a Marker-and-Cell type method and an accurate representation of the fluid surface is employed. The full free surface stress conditions are considered. The PTT equation is solved by a high order method, which requires the calculation of the extra-stress tensor on the mesh contours. To validate the numerical technique developed in this work flow predictions for fully developed pipe flow are compared with an analytic solution from the literature. Then, results of complex free surface flows using the FIT equation such as the transient extrudate swell problem and a jet flowing onto a rigid plate are presented. An investigation of the effects of the parameters epsilon and xi on the extrudate swell and jet buckling problems is reported. (C) 2010 Elsevier B.V. All rights reserved.

A simplified description of the evolution of organic aerosol composition in the atmosphere

Organic aerosol (OA) in the atmosphere consists of a multitude of organic species which are either directly emitted or the products of a variety of chemical reactions. This complexity challenges our ability to explicitly characterize the chemical composition of these particles. We find that the bulk composition of OA from a variety of environments (laboratory and field) occupies a narrow range in the space of a Van Krevelen diagram (H: C versus O:C), characterized by a slope of similar to-1. The data show that atmospheric aging, involving processes such as volatilization, oxidation, mixing of air masses or condensation of further products, is consistent with movement along this line, producing a more oxidized aerosol. This finding has implications for our understanding of the evolution of atmospheric OA and representation of these processes in models. Citation: Heald, C. L., J. H. Kroll, J. L. Jimenez, K. S. Docherty, P. F. DeCarlo, A. C. Aiken, Q. Chen, S. T. Martin, D. K. Farmer, and P. Artaxo (2010), A simplified description of the evolution of organic aerosol composition in the atmosphere, Geophys. Res. Lett., 37, L08803, doi: 10.1029/2010GL042737.

Nonlinear Schrodinger equation with chaotic, random, and nonperiodic nonlinearity

In this Letter we deal with a nonlinear Schrodinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time coordinates and to check its robustness under these conditions. Here we show that the chaotic perturbation is more effective in destroying the soliton behavior, when compared with random or nonperiodic perturbation. For a real system, the perturbation can be related to, e.g., impurities in crystalline structures, or coupling to a thermal reservoir which, on the average, enhances the nonlinearity. We also discuss the relevance of such random perturbations to the dynamics of Bose-Einstein condensates and their collective excitations and transport. (C) 2010 Elsevier B.V. All rights reserved.

Dirac equation in noncommutative space for hydrogen atom

We consider the energy levels of a hydrogen-like atom in the framework of theta-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels 2S(1/2), 2P(1/2) and 2P(3/2) is lifted completely, such that new transition channels are allowed. (C) 2009 Elsevier B.V. All rights reserved.

A Direct Numerov Sixth-order Numerical Scheme to Accurately Solve the Unidimensional Poisson Equation with Dirichlet Boundary Conditions

In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with Dirichlet boundary conditions. Our results should improve numerical codes used mainly in self-consistent calculations in solid state physics.

A multivariate ultrastructural errors-in-variables model with equation error

This paper deals with asymptotic results on a multivariate ultrastructural errors-in-variables regression model with equation errors Sufficient conditions for attaining consistent estimators for model parameters are presented Asymptotic distributions for the line regression estimators are derived Applications to the elliptical class of distributions with two error assumptions are presented The model generalizes previous results aimed at univariate scenarios (C) 2010 Elsevier Inc All rights reserved

A DISCRETIZATION SCHEME FOR AN ONE-DIMENSIONAL REACTION-DIFFUSION EQUATION WITH DELAY AND ITS DYNAMICS

The goal of this paper is to present an approximation scheme for a reaction-diffusion equation with finite delay, which has been used as a model to study the evolution of a population with density distribution u, in such a way that the resulting finite dimensional ordinary differential system contains the same asymptotic dynamics as the reaction-diffusion equation.

On the Hamilton-Jacobi equation in the framework of generalized functions

In this work we study, in the framework of Colombeau`s generalized functions, the Hamilton-Jacobi equation with a given initial condition. We have obtained theorems on existence of solutions and in some cases uniqueness. Our technique is adapted from the classical method of characteristics with a wide use of generalized functions. We were led also to obtain some general results on invertibility and also on ordinary differential equations of such generalized functions. (C) 2011 Elsevier Inc. All rights reserved.

Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

In [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the delta-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186-196.] Colombeau and Langlais prove that these equations have a unique solution even if the delta-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais` result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371-399.]. (C) 2009 Elsevier Ltd. All rights reserved.

Stability of periodic travelling shallow-water waves determined by Newton`s equation

We study the existence and stability of periodic travelling-wave solutions for generalized Benjamin-Bona-Mahony and Camassa-Holm equations. To prove orbital stability, we use the abstract results of Grillakis-Shatah-Strauss and the Floquet theory for periodic eigenvalue problems.

Fluctuations of the Stokes and anti-Stokes surface-enhanced resonance Raman scattering intensities in an electrochemical environment

Stokes and anti-Stokes SERRS intensity fluctuations were observed from a roughened silver electrode immersed in diluted solutions of Brilliant Green (BG), a behaviour linked to single-molecule events. The distributions of the anti-Stokes to Stokes ratios were obtained and their shape showed a strong dependence on the applied potential.

Simplified follow-up after medical abortion using a low-sensitivity urinary pregnancy test and a pictorial instruction sheet in Rajasthan, India : study protocol and intervention adaptation of a randomised control trial

The World Health Organisation suggests that simplification of the medical abortion regime will contribute to an increased acceptability of medical abortion, among women as well as providers. It is expected that a home-based follow-up after a medical abortion will increase the willingness to opt for medical abortion as well as decrease the workload and service costs in the clinic. Trial design The study is a randomised, controlled, non-superiority trial . Methods Women screened to participate in the study are those with unwanted pregnancies and gestational ages equal to or less than nine weeks. Eligible women randomised to the home-based assessment group will use a low-sensitivity pregnancy test and a pictorial instruction sheet at home, while the women in the clinic follow-up group will return to the clinic for routine follow-up carried out by a doctor. The primary objective of the study is to evaluate the effectiveness of home-based assessment using a low-sensitivity pregnancy test and a pictorial instruction sheet 10-14 days after an early medical abortion. Providers or research assistants will not be blinded during outcome assessment. To ensure feasibility of the self-assessment intervention an adaption phase took place at the selected study sites before study initiation. This was to optimise and tailor-make the intervention and the study procedures and resulted in the development of the pictorial instruction sheet for how to use the low-sensitivity pregnancy test and the danger signs after a medical abortion. Discussion In this paper, we will describe the study protocol for a randomised control trial investigating the efficacy of simplified follow-up in terms of home-based assessment, 10-14 days after a medical abortion. Moreover, a description of the adaptation phase is included for a better understanding of the implementation of the intervention in a setting where literacy is low and the road-connections are poor. Trial registration: Clinicaltrials.gov NCT01827995. Registered 04 May 2013