Effects of a temperature dependent viscosity in surface nonlinear waves propagating in a shallow fluid heated from below

The effects of a temperature dependent viscosity in surface nonlinear waves propagating in a shallow fluid heated from below are investigated. It is shown that the (2+1)-dimensional Burgers equation may appear as the equation governing the upper free surface perturbations of a Bénard system, even when the viscosity is assumed to depend on temperature. The critical Rayleigh number for the appearance of waves governed by the Kadomtsev-Petviashvili equation, however, will be smaller than R=30, which is the critical number obtained for a constant viscosity. © 1992.

On the integrable perturbations of the Camassa-Holm equation

We present an investigation of the nonlinear partial differential equations (PDE) which are asymptotically representable as a linear combination of the equations from the Camassa-Holm hierarchy. For this purpose we use the infinitesimal transformations of dependent and independent variables of the original PDE. This approach is helpful for the analysis of the systems of the PDE which can be asymptotically represented as the evolution equations of polynomial structure. © 2000 American Institute of Physics.

Exact solvability of potentials with spatially dependent effective masses

We discuss the relationship between exact solvability of the Schroedinger equation, due to a spatially dependent mass, and the ordering ambiguity. Some examples show that, even in this case, one can find exact solutions. Furthermore, it is demonstrated that operators with linear dependence on the momentum are nonambiguous. (C) 2000 Elsevier Science B.V.

Amphiphilic planar membranes in ionic equilibrium: a study of pH position-dependent values

The pH values near a planar dissociating membrane are studied under a mean field approximation using the Poisson-Boltzmann equation and its linear form. The equations are solved in planar symmetry with the consideration that the charge density on the dissociating membrane surface results from an equilibrium process with the neighboring electrolyte. Results for the membrane dissociation degree are presented as a function of the electrolyte ionic strength and membrane surface charge density. Our calculations indicate that pH values have an appreciable variation within 2 nm from the membrane. It is shown that the dissociation process is enhanced due to the presence of bivalent ions and that pH values acquire better stability than in an electrolyte containing univalent ions.

Potenciais singulares na equação de Schrodinger unidimensional via transformada de Laplace

The present work has as its goal to treat well known and interesting unidimensional cases from quantum mechanics through an unusual approach within this eld of physics. The operational method of Laplace transform, in spite of its use by Erwin Schrödinger in 1926 when treating the radial equation for the hydrogen atom, turned out to be forgotten for decades. However, the method has gained attention again for its use as a powerful tool from mathematical physics applied to the quantum mechanics, appearing in recent works. The method is specially suitable to the approach of cases where we have potential functions with even parity, because this implies in eigenfunctions with de ned parity, and since the domain of this transform ranges from 0 to ∞, it su ces that we nd the eigenfunction in the positive semi axis and, with the boundary conditions imposed over the eigenfunction at the origin plus the continuity (discontinuity) of the eigenfunction and its derivative, we make the odd, even or both parity extensions so we can get the eigenfunction along all the axis. Factoring the eigenfunction behavior at in nity and origin, we take the due care with the points that might bring us problems in the later steps of the solving process, thus we can manipulate the Schrödinger's Equation regardless of time, so that way we make it convenient to the application of Laplace transform. The Chapter 3 shows the methodology that must be followed in order to search for the solutions to each problem

Application of the log-conformation tensor to three-dimensional time-dependent free surface flows

The numerical simulation of flows of highly elastic fluids has been the subject of intense research over the past decades with important industrial applications. Therefore, many efforts have been made to improve the convergence capabilities of the numerical methods employed to simulate viscoelastic fluid flows. An important contribution for the solution of the High-Weissenberg Number Problem has been presented by Fattal and Kupferman [J. Non-Newton. Fluid. Mech. 123 (2004) 281-285] who developed the matrix-logarithm of the conformation tensor technique, henceforth called log-conformation tensor. Its advantage is a better approximation of the large growth of the stress tensor that occur in some regions of the flow and it is doubly beneficial in that it ensures physically correct stress fields, allowing converged computations at high Weissenberg number flows. In this work we investigate the application of the log-conformation tensor to three-dimensional unsteady free surface flows. The log-conformation tensor formulation was applied to solve the Upper-Convected Maxwell (UCM) constitutive equation while the momentum equation was solved using a finite difference Marker-and-Cell type method. The resulting developed code is validated by comparing the log-conformation results with the analytic solution for fully developed pipe flows. To illustrate the stability of the log-conformation tensor approach in solving three-dimensional free surface flows, results from the simulation of the extrudate swell and jet buckling phenomena of UCM fluids at high Weissenberg numbers are presented. (C) 2012 Elsevier B.V. All rights reserved.

Hirota method for oblique solitons in two-dimensional supersonic nonlinear Schrodinger flow

In a previous work El et al. (2006) [1] exact stable oblique soliton solutions were revealed in two-dimensional nonlinear Schrodinger flow. In this work we show that single soliton solution can be expressed within the Hirota bilinear formalism. An attempt to build two-soliton solutions shows that the system is "close" to integrability provided that the angle between the solitons is small and/or we are in the hypersonic limit. (C) 2012 Elsevier B.V. All rights reserved.

EXISTENCE OF SOLUTIONS FOR A FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATION WITH UNBOUNDED DELAY

In this article, we study the existence of mild solutions for fractional neutral integro-differential equations with infinite delay.

The long-term stability of self-esteem: Its time-dependent decay and nonzero asymptote

How stable are individual differences in self-esteem? We examined the time-dependent decay of rank-order stability of self-esteem and tested whether stability asymptotically approaches zero or a nonzero value across long test–retest intervals. Analyses were based on 6 assessments across a 29-year period of a sample of 3,180 individuals aged 14 to 102 years. The results indicated that, as test–retest intervals increased, stability exponentially decayed and asymptotically approached a nonzero value (estimated as .43). The exponential decay function explained a large proportion of variance in observed stability coefficients, provided a better fit than alternative functions, and held across gender and for all age groups from adolescence to old age. Moreover, structural equation modeling of the individual-level data suggested that a perfectly stable trait component underlies stability of self-esteem. The findings suggest that the stability of self-esteem is relatively large, even across very long periods, and that self-esteem is a trait-like characteristic.

Impedance of foundations using the Boundary Integral Equation Method

Dynamic soil-structure interaction has been for a long time one of the most fascinating areas for the engineering profession. The building of large alternating machines and their effects on surrounding structures as well as on their own functional behavior, provided the initial impetus; a large amount of experimental research was done,and the results of the Russian and German groups were especially worthwhile. Analytical results by Reissner and Sehkter were reexamined by Quinlan, Sung, et. al., and finally Veletsos presented the first set of reliable results. Since then, the modeling of the homogeneous, elastic halfspace as a equivalent set of springs and dashpots has become an everyday tool in soil engineering practice, especially after the appearance of the fast Fourier transportation algorithm, which makes possible the treatment of the frequency-dependent characteristics of the equivalent elements in a unified fashion with the general method of analysis of the structure. Extensions to the viscoelastic case, as well as to embedded foundations and complicated geometries, have been presented by various authors. In general, they used the finite element method with the well known problems of geometric truncations and the subsequent use of absorbing boundaries. The properties of boundary integral equation methods are, in our opinion, specially well suited to this problem, and several of the previous results have confirmed our opinion. In what follows we present the general features related to steady-state elastodynamics and a series of results showing the splendid results that the BIEM provided. Especially interesting are the outputs obtained through the use of the so-called singular elements, whose description is incorporated at the end of the paper. The reduction in time spent by the computer and the small number of elements needed to simulate realistically the global properties of the halfspace make this procedure one of the most interesting applications of the BIEM.

Photosystem II single crystals studied by EPR spectroscopy at 94 GHz: The tyrosine radical Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{D}^{{\bullet}}}}\end{equation*}\end{document}

Electron paramagnetic resonance (EPR) spectroscopy at 94 GHz is used to study the dark-stable tyrosine radical Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{D}^{{\bullet}}}}\end{equation*}\end{document} in single crystals of photosystem II core complexes (cc) isolated from the thermophilic cyanobacterium Synechococcus elongatus. These complexes contain at least 17 subunits, including the water-oxidizing complex (WOC), and 32 chlorophyll a molecules/PS II; they are active in light-induced electron transfer and water oxidation. The crystals belong to the orthorhombic space group P212121, with four PS II dimers per unit cell. High-frequency EPR is used for enhancing the sensitivity of experiments performed on small single crystals as well as for increasing the spectral resolution of the g tensor components and of the different crystal sites. Magnitude and orientation of the g tensor of Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{D}^{{\bullet}}}}\end{equation*}\end{document} and related information on several proton hyperfine tensors are deduced from analysis of angular-dependent EPR spectra. The precise orientation of tyrosine Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{D}^{{\bullet}}}}\end{equation*}\end{document} in PS II is obtained as a first step in the EPR characterization of paramagnetic species in these single crystals.

Redox-dependent activation of CO dehydrogenase from Rhodospirillum rubrum

Studies of initial activities of carbon monoxide dehydrogenase (CODH) from Rhodospirillum rubrum show that CODH is mostly inactive at redox potentials higher than −300 mV. Initial activities measured at a wide range of redox potentials (0–500 mV) fit a function corresponding to the Nernst equation with a midpoint potential of −316 mV. Previously, extensive EPR studies of CODH have suggested that CODH has three distinct redox states: (i) a spin-coupled state at −60 to −300 mV that gives rise to an EPR signal termed Cred1; (ii) uncoupled states at <−320 mV in the absence of CO2 referred to as Cunc; and (iii) another spin-coupled state at <−320 mV in the presence of CO2 that gives rise to an EPR signal termed Cred2B. Because there is no initial CODH activity at potentials that give rise to Cred1, the state (Cred1) is not involved in the catalytic mechanism of this enzyme. At potentials more positive than −380 mV, CODH recovers its full activity over time when incubated with CO. This reductant-dependent conversion of CODH from an inactive to an active form is referred to hereafter as “autocatalysis.” Analyses of the autocatalytic activation process of CODH suggest that the autocatalysis is initiated by a small fraction of activated CODH; the small fraction of active CODH catalyzes CO oxidation and consequently lowers the redox potential of the assay system. This process is accelerated with time because of accumulation of the active enzyme.

A procedure for determining a spacewise dependent heat source and the initial temperature

The inverse problem of determining a spacewise dependent heat source, together with the initial temperature for the parabolic heat equation, using the usual conditions of the direct problem and information from two supplementary temperature measurements at different instants of time is studied. These spacewise dependent temperature measurements ensure that this inverse problem has a unique solution, despite the solution being unstable, hence the problem is ill-posed. We propose an iterative algorithm for the stable reconstruction of both the initial data and the source based on a sequence of well-posed direct problems for the parabolic heat equation, which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for a typical benchmark test example, which has the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure gives accurate numerical approximations in relatively few iterations.