bluuebunny/crossref_metadata_2025 huggingface dataset:
Some Generating Functions for the Generalized Bessel Polynomials
Authors: Chen Ming‐Po , Feng Chia‐Chin , Srivastava H. M.
Published: September 2015

The authors begin by presenting a systematic (historical) account of some linear generating functions for the generalized Bessel polynomials. It is then shown how these linear generating functions can be applied with a view to obtaining various new families of bilinear, bilateral, or mixed multilateral generating functions for the generalized Bessel polynomials. Some interesting generalizations of these classes of generating functions, involving hypergeometric functions, are also considered.
Painlevé Classification of a Class of Differential Equations of the Second Order and Second Degree
Authors: Cosgrove Christoper M. , Scoufis George
Published: September 2015

In this paper we construct all Painlevé‐type differential equations of the form (d2y/dx2)2 = F(x,y,dy/dx), where F is rational in y and y′=dy/dx, locally analytic in x, and not a perfect square. No further simplifying assumptions are made, but it is found that the absence of a term linear in y″ in the class of equations under investigation forces F to be a polynomial in y and y′. We find exactly six distinct classes of second‐degree Painlevé equations, denoted SD‐I,𠈆,SD‐VI, some of which further subdivide into canonical subcases. Only the first three classes (or at least equations transformable to the first three classes) and part of the sixth have appeared previously in the literature, especially the work of Chazy and Bureau. The fourth and fifth classes are new. The unified treatment of SD‐I, which we call the “master Painlevé equation,” is new. Complete solutions are given in terms of the classical Painlevé transcendents, elliptic functions, or solutions of linear equations. In an appendix, it is shown that a class of second‐degree equations generalizing the Appell equation can always be reduced to a second‐order linear equation.
On the Transient Behavior of the M/M/1 and M/M/1/M Queues
Authors: Xie Shisheng , Knessl Charles
Published: September 2015

This paper gives a transient analysis of the classic M/M/1 and M/M/1/K queues. Our results are asymptotic as time and queue length become simultaneously large for the infinite capacity queue, and as the system’s storage capacity K becomes large for the finite capacity queue. We give asymptotic expansions for pn(t), which is the probability that the system contains n customers at time t. We treat several cases of initial conditions and different traffic intensities. The results are based on (i) asymptotic expansion of an exact integral representation for pn(t) and (ii) applying the ray method to a scaled form of the forward Kolmogorov equation which describes the time evolution of pn(t).
Painlevé Classification of All Semi linear Partial Differential Equations of the Second Order. I. Hyperbolic Equations in Two Independent Variables
Authors: Cosgrove Christopher M.
Published: September 2015

In this paper we give a complete classification of all Painlevé‐type hyperbolic partial differential equations (PDE's) over the complex domain of the form uxy = F(x, y, u, ux, uy where F is rational in u, ux, and uy, and locally analytic in x and y. We find exactly 22 equivalence classes of equations (under coordinate changes and Mobius transformations in u), which we denote HS‐I, HS‐II,…, HS‐XXII. A canonical representative of each class is presented and solved by transforming it either to a well‐known soliton equation (sine‐Gordon, Bullough‐Dodd‐Mikhailov) or to a linear equation by means of a Bäcklund correspondence or simpler change of variables. (The parabolic case, in which 10 more canonical equations are obtained, and semilinear PDE's in three or more variables are treated in the accompanying paper II.) The proof that the list is complete involves investigating four sets of necessary conditions in turn, each of which has essentially new features peculiar to the PDE context, as well as familiar features analogous to the corresponding conditions for ordinary differential equations (ODE's) as discussed in the classical literature by Painleve, Gambier, Ince, Bureau, and others. In a setting sufficiently general to embrace ODE's, hyperbolic and parabolic PDE's, and higher dimensional semilinear PDE's, we classify 76 types of O/PDE's, denoted DE‐1,…, according to their Bureau symbols and resonance data, which satisfy those necessary conditions for the Painlevé property common to each of these four Painlevé classification problems.
Asymptotic Estimates of Stirling Numbers
Authors: Temme N. M.
Published: September 2015

New asymptotic estimates are given of the Stirling numbers and , of first and second kind, respectively, as n tends to infinity. The approximations are uniformly valid with respect to the second parameter m.
Two‐Wave Interactions for Hyperbolic Signaling Problems and the Application to Supersonic Gas Dynamics
Authors: He Yuanping , Moodie T. Bryant
Published: September 2015

The signaling problem for a system of conservation laws in a single space variable is treated through the deployment of a perturbation analysis. Our method of approach involves the direct use of two nonlinear phase variables making possible the study of weakly nonlinear interacting waves arising from a boundary disturbance consisting of two wave modes. As a result of our analysis, the asymptotic solution is derived, and the class of admissible boundary disturbances is distinguished as well. An application is then made to gas dynamics in one space dimension to investigate the propagation and interaction of two sound waves for which the base state is taken to be a steady supersonic flow.
Operator Identities and the Solution of Linear Matrix Difference and Differential Equations
Authors: Verde‐Star Luis
Published: September 2015

We use operator identities in order to solve linear homogeneous matrix difference and differential equations and we obtain several explicit formulas for the exponential and for the powers of a matrix as an example of our methods. Using divided differences we find solutions of some scalar initial value problems and we show how the solution of matrix equations is related to polynomial interpolation.
Computation of Travelling Combustion Waves in a Porous Medium
Authors: Tam K. K. , Andonowati
Published: September 2015

Numerical solutions for travelling combustion waves in a porous medium are sought. The algorithm of computation is based on a shooting method used in an existence proof. The numerical result suggests that there is a limit for the inlet gas velocity below which no travelling wave solution can be constructed.
Convective Instabilities in Anisotropic Porous Media
Authors: Qin Y. , Kaloni P. N.
Published: September 2015

This paper addresses the problem of the onset of Rayleigh‐Bénard convection in a porous layer using Brinkman's equation and anisotropic permeability. The critical Rayleigh number and wave number at marginal stabilities are calculated for both free and rigid boundaries. In both cases, it is noted that there exist ranges for which the stability criteria is intermediate to the low porosity Darcy approximation and to high porosity single viscous fluid. The permeability anisotropy is found to select the mode of instability.
Nonlinear Development of Viscous Gertler Vortices in a Three‐Dimensional Boundary Layer
Authors: Otto S. R. , Bassom Andrew P.
Published: September 2015

In many practical situations where Görder vortices are known to arise, the underlying basic velocity profile is three‐dimensional. Only in recent years have studies been made of the stability of vortices in three‐dimensional flows, and it has been shown that only a small crossflow velocity component is required in order to stabilize the Görder mechanism completely. For large Görder number (G ≫ 1) flows, the most unstable linear vortex within a two‐dimensional boundary layer has a wavenumber of O(G⅕) and a corresponding growth rate of O(G⅗). Imposition of a crossflow component of size O(Re−½G⅗) (where Re is the Reynolds number of the flow) is sufficient to cause these higher wavenumber Gertler modes to decay. Indeed, for certain crossflow/vortex wavenumber combinations, the vortices can be made neutrally stable. A weakly nonlinear analysis of near neutral modes reveals that this slight nonlinearity is stabilizing and so can lead to finite amplitude equilibrium states. In the present work, we give a nonlinear account of the fate of the O(G⅕) wavenumber vortices as they evolve downstream. A study of the large wavenumber modes within a two‐dimensional boundary layer [5], has shown that the effect of this strong nonlinearity is destabilizing and leads to a finite distance breakdown in the flow structure. Here we include the influence of the crossflow component and demonstrate how the stabilizing effects of crossflow and the destabilizing nature of nonlinearity compete. Our calculations can also describe unsteadiness in the vortex structure and they allow us to speculate upon the relative likelihoods of observing various members of the nonlinear Görder modes in practice.
Singular Perturbations of Elliptic Problems on Domains with Small Holes
Authors: Haj‐Hariri Hossein , Weinitschke Hubertus J.
Published: September 2015

Singular perturbation techniques are used to study the solutions of nonlinear second order elliptic boundary value problems defined on arbitrary plane domains from which a finite number of small holes of radius ρi(ε) have been removed, in the limit ε → 0. Asymptotic outer and inner expansions are constructed to describe the behavior of solutions at simple bifurcation and limit points. Since bifurcation usually occurs a eigenvalues of a linearized problem, we study in detail the dependence of the eigenvalues and eigenfunctions on ε, for ε → 0. These results are applied to the vibration of a rectangular membrane with one or two circular holes. The asymptotic analysis predicts a remarkably large sensitivity of eigenvalues and limit points to the ε‐domain perturbation considered in this paper.
A Perturbation Analysis of an Interaction between Long and Short Surface Waves
Authors: Woodruff S. L. , Messiter A. F.
Published: September 2015

The interaction of finite‐amplitude long gravity waves with a small‐amplitude packet of short capillary waves is studied by a multiple‐scale method based on the invariance of the perturbation expansion under certain translations. The result of the analysis is a set of equations coupling the complex amplitude of the packet of short waves with the long‐wave velocity potential and surface elevation. The short wave is described by a Ginzburg‐Landau equation with coefficients that depend on properties of the long wave. The long‐wave potential and surface elevation satisfy the usual free‐surface conditions augmented by forcing terms representing effects of the short waves. The derivation removes some of the restrictions imposed in earlier studies.
Oblique Interactions between Internal Solitary Waves
Authors: Grimshaw R. , Zhu Y.
Published: September 2015

In this paper, we study the oblique interaction of weakly, nonlinear, long internal gravity waves in both shallow and deep fluids. The interaction is classified as weak when where Δ1=|cm/cn−cosδ|, Δ2=|cn/cm−cosδ|,cm,n, are the linear, long wave speeds for waves with mode numbers m, n, δ is the angle between the respective propagation directions, and α measures the wave amplitude. In this case, each wave is governed by its own Kortweg‐de Vries (KdV) equation for a shallow fluid, or intermediate long‐wave (ILW) equation for a deep fluid, and the main effect of the interaction is an 0(α) phase shift. A strong interaction (I) occurs when Δ1,2 are 0(α), and this case is governed by two coupled Kadomtsev‐Petviashvili (KP) equations for a shallow fluid, or two coupled two‐dimensional ILW equations for deep fluids. A strong interaction (II) occurs when Δ1 is 0(α), and (or vice versa), and in this case, each wave is governed by its own KdV equation for a shallow fluid, or ILW equation for a deep fluid. The main effect of the interaction is that the phase shift associated with Δ1 leads to a local distortion of the wave speed of the mode n. When the interacting waves belong to the same mode (i.e., m = n) the general results simplify and we show that for a weak interaction the phase shift for obliquely interacting waves is always negative (positive) for (1/2+cosδ)>0(<0), while the interaction term always has the same polarity as the interacting waves.
The Distributional Hankel Transform of Marcel Riesz's Ultrahyperbolic Kernel
Authors: Aguirre Téllez Manuel A.
Published: September 2015

In this article we give a sense to the distributional Hankel transform of Marcel Riesz's ultrahyperbolic kernel.

First we evaluate Rα(u) in α = −2k and α = 2k for the cases μ even and ν odd, μ even and ν even, and μ odd and ν odd, μ odd and ν even, where
urn:x-wiley:00222526:media:sapm1994932133:sapm1994932133-math-0001
and
urn:x-wiley:00222526:media:sapm1994932133:sapm1994932133-math-0002
Finally in Section 4 we obtain the distributional Hankel transform of Marcel Riesz's ultrahyperbolic kernel.
On Short‐Scale Oscillatory Tails of Long‐Wave Disturbances
Authors: Akylas T. R. , Yang T.‐S.
Published: September 2015

Using the forced Korteweg‐de Vries equation as a simple model, a perturbation procedure is presented for calculating the amplitude of short‐scale oscillatory tails induced by steady long‐wave disturbances. In the limit of weak dispersion, these tails have exponentially small amplitude that lies beyond all orders of the usual long‐wave expansion. It is demonstrated that by working in the wavenumber domain, the tail amplitude can be determined quite simply, without the need for asymptotic matching in the complex plane. The induced short‐wave tail is sensitive to the details of the long‐wave profile. The proposed technique is applicable to nonlocal solitary waves and to other problems that require the use of exponential asymptotics.
Nonclassical Symmetries for Nonlinear Diffusion and Absorption
Authors: Arrigo D. J. , Hill J. M.
Published: September 2015

Nonclassical symmetry methods are used to study the nonlinear diffusion equation with a nonlinear source. In particular, exponential and power law diffusivities are examined and we obtain mathematical forms of the source term which permit nonclassical symmetry reductions. In addition to the known source terms obtained by classical symmetry methods, we find new source terms which admit symmetry reductions. We also deduce a class of nonclassical symmetries which are valid for arbitrary diffusivity and deduce corresponding new solution types. This is an important result since previously only traveling wave solutions were known to exist for arbitrary diffusivity. A number of examples are considered and new exact solutions are constructed.
Optimal Disturbance Growth in Watertable Flow
Authors: Olsson P. J. , Henningson D. S.
Published: September 2015

The linear stability of a liquid flow down an inclined plane is investigated. The equations governing the evolution of the disturbance are written in vector form where the dependent variables are the normal velocity and the normal vorticity. Similar to other shear flows, it is shown that there can be transient growth in the energy of a disturbance followed by an exponential decay although all eigenvalues predict decay only. Parameter studies reveal that the maximum amplification occur for waves with no streamwise dependence and with a spanwise wavenumber of (1). The mechanism involved in this growth is analyzed. A free surface parameter (S) can be identified that is related to the extent gravity and surface tension influence the free surface. A scaling of the equations is studied which revealed that the maximum transient growth scales with the Reynolds number as Re2 if k2 S Re2 is kept constant, where k is the absolute value of the wavenumber vector. For small values of S exponential growth of free‐surface modes also exists. In general, however, we have found that for moderate times the transient growth dominates over the exponential growth and that its characteristics are similar to the transient growth found in other shear flows, e.g., plane Poiseuille flow.
Quasisolutions as Group‐Invariant Solutions for Partial Differential Equations
Authors: Pucci Edvige , Giuseppe Giuseppe
Published: September 2015

The group theoretical explanation is given of the quasisolution method for partial differential equations recently introduced by Rubel. The examples show that the group approach is simpler from the computational point of view.
Double‐Diffusive Convection in a Porous Medium, Nonlinear Stability, and the Brinkman Effect
Authors: Guo Jianlin , Kaloni P. N.
Published: September 2015

This paper establishes a nonlinear energy stability theory for the double‐diffusive convection in a porous medium when both viscosity and thermal expansion coefficient are allowed to vary with temperature. After presenting a nonlinear stability theorem, a variational problem is formulated and the numerical solutions via the compoound matrix method are carried out. It is noted that higher values of the thermal coefficient and higher values of the viscosity ratio have the effect of delaying the onset of convection.
On the Existence of Solutions and the Convergence of Approximations to Scalar Conservation Laws
Authors: Fernández‐Cara E. , González‐Burgos M.
Published: September 2015

This paper deals with a new proof of the existence of weak solutions to scalar conservation laws. Our approach relies on the use of a particular finite difference scheme for time discretization which introduces a viscous term. The approximate solutions can be computed explicitly by solving a set of linear ordinary differential problems. We prove that they converge towards a weak solution which is, in a certain sense, unique and stable.
Bäcklund Transformations and Solution Hierarchies for the Fourth Painlevé Equation
Authors: Bassom Andrew P. , Clarkson Peter A. , Hicks Andrew C.
Published: September 2015

In this paper our concern is with solutionsw(z;α,β) of the fourth Painlevé equation (PIV), whereαandβare arbitrary real parameters. It is known that PIV admits a variety of solution types and here we classify and characterise these. Using Backlund transformations we describe a novel method for efficiently generating new solutions of PIV from known ones. Almost all the established Bäcklund transformations involve differentiation of solutions and since all but a very few solutions of PIV are given by extremely complicated formulae, those transformations which require differentiation in this way are very awkward to implement in practice. Depending on the values of the parametersαandβ, PIV can admit solutions which may either be expressed as the ratio of two polynomials inz, or can be related to the complementary error or parabolic cylinder functions; in fact, all exact solutions of PIV are thought to fall in one of these three hierarchies. We show how, given a few initial solutions, it is possible to use the structures of the hierarchies to obtain many other solutions. In our approach we derive a nonlinear superposition formula which relates three solutions of PIV; the principal attraction is that the process involves only algebraic manipulations so that, in particular, no differentiation is required. We investigate the properties of our computed solutions and illustrate that they have a large number of physical applications.
Approximate Analytical and Numerical Solutions of the Stationary Ostrovsky Equation
Authors: Gilman O. A. , Grimshaw R. , Stepanyants Yu. A.
Published: September 2015

Approximate stationary solutions of the Ostrovsky equation describing long weakly nonlinear waves in a rotating liquid are constructed. These solutions may be regarded as a periodic sequence of arcs of parabolas containing Korteweg‐de Vries solitons at the junctures. Results of numerical computations of the dynamics of the approximate solutions obtained from the nonstationary Ostrovsky equation are presented. It is found that, in the presence of negative dispersion, the shape of a stationary wave is well predicted by the approximate theory, whereas the calculated wave velocity differs slightly from the theoretical value. The stationary solutions in media with positive dispersion are evidently unstable (at least for sufficiently strong rotation), and numerical computations demonstrate a complicated picture of nonstationary destruction.
Hydrodynamic Stability and Turbulence: Beyond Transients to a Self‐Sustaining Process
Authors: Waleffe Fabian
Published: September 2015

Transition from laminar to turbulent flows has generally been studied by considering the linear and weakly nonlinear evolution of small disturbances to the laminar flow. That approach has been fruitless for many shear flows, and a last hope for its success has been the existence of transient growth phenomena. The physical origin of those linear transient effects is elucidated, revealing serious limitations both of previous analyses and of the phenomena themselves, which preclude them from causing direct transition. Nonetheless, some transient effects are symptomatic of one element of a nonlinear process that becomes self‐sustaining at a small enough dissipation. The process is identified, and its description requires a departure from the traditional focus on the laminar flow. A theory is outlined in which the mean flow has an intrinsic spanwise variation. Evidence indicates this is also the central mechanism in the near wall‐region of fully turbulent shear flows.
Plethystic Exponential Polynomials and Plethystic Stirling Numbers
Authors: Méndez Miguel
Published: September 2015

In this article we introduce a plethystic generalization of the exponential polynomials and their umbral inverses. We obtain recursive formulas for both families of polynomials, and use them to get recursions for the plethystic Stirling numbers of the first and second kind and for the plethystic Bell numbers. Finally, we apply Bergeron's S‐species to obtain a Dobinsky formula for the plethystic exponential polynomials and a close formula for the plethystic Stirling numbers of the second kind.
Nonlinear Convective Stability in a Porous Medium with Temperature‐Dependent Viscosity and Inertial Drag
Authors: Qin Y. , Chadam J.
Published: September 2015

A nonlinear stability analysis of convection in a fluid‐saturated porous medium with temperature‐dependent viscosity and inertia drag is presented. It is shown that the quadratic drag term is mathematically important and physically significant in ensuring conditional stability.
Enumeration of Full Graphs: Onset of the Asymptotic Region
Authors: Cowen L. J. , Kleitman D. J. , Lasaga F. , Sussman D. E.
Published: September 2015

A full graph on n vertices, as defined by Fulkerson, is a representation of the intersection and containment relations among a system of n sets. It has an undirected edge between vertices representing intersecting sets and a directed edge from a to b if the corresponding set A contains B;. Kleitman, Lasaga, and Cowen gave a unified argument to show that asymptotically, almost all full graphs can be obtained by taking an arbitrary undirected graph on the n vertices, distinguishing a clique in this graph, which need not be maximal, and then adding directed edges going out from each vertex in the clique to all vertices to which there is not already an existing undirected edge. Call graphs of this type members of the dominant class. This article obtains the first upper and lower bounds on how large n has to be, so that the asymptotic behavior is indeed observed. It is shown that when n > 170, the dominant class predominates, while when n < 17, the full graphs in the dominant class compose less than half of the total number of realizable full graphs on n vertices.
Coherent Structures in Weakly Birefringent Nonlinear Optical Fibers
Authors: Yang Jianke
Published: September 2015

This article studies two coupled nonlinear Schrodinger equations that govern the pulse propagation in weakly birefringent nonlinear optical fibers. The coherent structures for these equations, such as vector solitons and localized oscillating solutions, are studied analytically and numerically. Three types of localized oscillating structures are identified and their functional forms determined by perturbation methods. In some of these structures, infinite oscillating tails are present. The implications of these tails are also discussed.
Wavenumber Selection for Small‐Wavelength Gertler Vörtices in Curved Channel Flows
Authors: Dando Andrew , Hall Philip
Published: September 2015

We consider the problem of wavenumber selection for fully nonlinear, small‐wavelength Görtler vortices in a curved channel flow. These type of Görtler vortices were first considered by Hall and Lakin [1] for an external boundary layer flow. They proved particularly amenable to asymptotic description, it was possible to consider vortices large enough that the mean flow correction driven by them is as large as the basic state, and this prompted us to consider them in a curved channel flow as an initial application of the phase‐equation approach to Görtler vortices. This involves the assumption that the phase variable of these Görtler vortices varies on slow spanwise and time scales, then an analysis of both inside and outside the core region, to which vortex activity is restricted, leads to a system of partial differential equations, which we can solve numerically for the wavenumber. We consider in particular the effect on the wavenumber of the outer channel wall varying on the same slow spanwise scale as the phase variable.
The Structure of Internal Layers for Unstable Nonlinear Diffusion Equations
Authors: Witelski Thomas P.
Published: September 2015

We study the structure of diffusive layers in solutions of unstable nonlinear diffusion equations. These equations are regularizations of the forward‐backward heat equation and have diffusion coefficients that become negative. Such models include the Cahn‐Hilliard equation and the pseudoparabolic viscous diffusion equation. Using singular perturbation methods we show that the balance between diffusion and higher‐order regularization terms uniquely determines the interface structure in these equations. It is shown that the well‐known “equal area” rule for the Cahn‐Hilliard equation is a special case of a more general rule for shock construction in the viscous Cahn‐Hilliard equation.
Non local Models for Envelope Waves in a Stratified Fluid
Authors: Pelinovsky Dmitry E. , Grimshaw Roger H. J.
Published: September 2015

A new, nonlocal evolution equation similar to the nonlinear Schrödinger equation is derived for envelope waves in a continuously stratified fluid by means of a multiscale perturbation technique. This new equation governs propagation of quasi‐harmonic wave packets having length scales much longer than the depth of the density variations and much shorter than the total depth of fluid. Generalizations of the nonlocal evolution equation for a description of two‐dimensional wave modulations are also presented. The modulational stability of small‐amplitude waves is then investigated in the framework of the derived equations. It is shown that quasi‐harmonic waves with the scales under consideration are unstable with respect to oblique perturbations at certain angles.
Characteristics of morphology, structure and composition of titanium surface under its modification by electrochemical polarization in phosphate‐alkaline solutions
Authors: Akimov Vladlen Vladimirovich , Tyukhai Elena Anatolievna , Tauson Vladimir Lvovich , Safronov Alexander Yurievich , Kashevskii Alexey Valerievich , Pushkarev Boris Georgievich , Nikiforov Sergey Borisovich , Voloshin Evgeny Viktorovich
Published: September 2015

The modification of titanium surface under electrochemical polarization (EP) in the phosphate‐alkaline solutions has been studied using the methods of X‐ray diffraction, electron probe microanalysis, atomic force microscopy, X‐ray photoelectron spectroscopy (XPS), cyclic voltammetry and spectroscopic ellipsometry. It is shown that the morphological parameters of the surface, e.g. roughness and stringiness, as well as its structural‐chemical characteristics, e.g. preferred orientation, size and habit of crystallites, titanium chemical forms, thickness and phase composition of oxide film are generally dependent on the polarization potential. The characteristics of titanium surface modified at low anodic potentials 500, 750 and 1000 mV and 10‐min polarization time have been measured. The processes of Ti surface dissolution and etching along grain boundaries are found to be most intensive at 750 mV. Under 500 mV, these processes are poorly developed yet, while at 1000 mV, the surface passivating film formation limits the previous processes. Despite relatively low polarization potentials (1 V), the surficial oxide films have sufficient thickness (up to ~20 nm) and a specific multilayer structure of variable composition and oxidation state of titanium. The data obtained allow to assert that EP represents an effective tool for morphological and a structural chemical modification of a titanium surface. Copyright © 2015 John Wiley & Sons, Ltd.
Microstructural origin of localized corrosion in anodized AA2099‐T8 aluminium–lithium alloy
Authors: Ma Yanlong , Chen Xiaoli , Zhou Xiaorong , Yi Yanan , Liao Yi , Huang Weijiu
Published: September 2015

The microstructural origin of localized corrosion in AA2099‐T8 aluminium–lithium alloy after tartaric‐sulfuric acid anodizing and sulfuric acid anodizing has been investigated. It is suggested that the high‐copper‐containing constituent Al–Fe–Mn–Cu particles are responsible for the initiation of localized corrosion in the anodized alloy. Once the anodic film at the defects associated with the high‐copper‐containing particles has been penetrated by the corrosive media, localized corrosion may further propagate in the alloy substrate, and the propagation is controlled by the alloy microstructure immediately beneath the anodic film at the initiation site. Copyright © 2015 John Wiley & Sons, Ltd.
Mechanical polishing, surface roughness, near‐surface deformation, and electrochemical corrosion of Alloy 690TT
Authors: Arjmand Farzin , Zhang Lefu
Published: September 2015

The effects of mechanical grinding/polishing, surface roughness, and near‐surface deformation on the electrochemical corrosion behavior of thermally treated (TT) Alloy 690 were studied in a sodium chloride solution. The X‐ray photoelectron spectroscopy and transmission electron microscopy analyses revealed that mechanical grinding/polishing can change the ratio of the elements at the surface of the as‐received Alloy 690TT specimen by removing its Cr‐rich outer layer and causing deformation at the near‐surface microstructure, something which has a direct impact on the rate of the oxygen reduction reaction (ORR), the pitting potential (Epit), and the corrosion potential (Ecorr) of Alloy 690TT. It was observed that the ratio of Cr in the surface is a significant factor that controls the rate of the ORR and the corrosion parameters such as Ecorr. Higher amounts of Cr at the surface accelerate the ORR. The near‐surface deformation shifts the Epit values towards less positive potentials. It was also found that due to the different near‐surface chemical composition of the as‐received Alloy 690TT specimen compared with the ground and the polished specimens, the surface roughness parameters do not have a regular correlation with the rate of the ORR and the values of the Ecorr and the Epit. Only the passive current density increases when the surface roughness is increased. Copyright © 2015 John Wiley & Sons, Ltd.
Influence of the grain boundary chemistry on the intergranular corrosion mechanisms of a high‐strength Al‐Mg‐Si alloy
Authors: Schnatterer Christian , Zander Daniela
Published: September 2015

The influence of solution annealing (T4) and artificial aging (T6) on the corrosion properties of a technical Al‐Mg‐Si alloy was investigated. In the T4 condition, the material was not susceptible to intergranular corrosion; however, pitting was identified to occur. Subsequent artificial aging of the solution annealed and quenched alloys introduced susceptibility to intergranular corrosion. This phenomenon was attributed to two microgalvanic coupling situations: one that occurred between the noble Cu‐phases located on the grain boundary and the anodic adjacent area and one between a Mg‐ and Si‐depleted zone along the grain boundaries and the adjacent area. Pitting corrosion was proposed to occur as a result of the absence of these microgalvanic coupling situations, and therefore with the absence of a distinct, preexisting corrosion path in the solution annealed condition. Copyright © 2015 John Wiley & Sons, Ltd.
Electrochemical characterization of anodized AA 2139 friction stir‐welded butt joint for aeronautical applications
Authors: Astarita Antonello , Marzocchi Vincenza , Squillace Antonino , Bellucci Francesco
Published: September 2015

In the present work, AA2139 rolled sheets were friction stir welded in butt joint configuration and anodized in sulfo‐tartaric acid solution. Both the microstructure and the corrosion behavior of the joints were studied. Electrochemical spectroscopy measurements were carried out in aggressive solution (NaCl 0.6 N with 5 mV amplitude sine wave), and the mechanism of formation and degradation of the surface oxide was discussed. Micro‐polarization tests were carried out to show the electrochemical behavior of the different metallurgical zones produced by the welding process. Exfoliation tests were also carried out. Different microstructures were observed; such a result is in agreement with the available literature on friction stir welding. The Electrochemical Impedance Spectroscopy (EIS) measurements showed the occurrence of corrosion phenomena and pointed out the need for a different sealing treatment; moreover, the exfoliation test proved that the weld bead behaves as a cathode with respect to the base material. Copyright © 2015 John Wiley & Sons, Ltd.
The Importance of Developing a Foundation for Naive Category Theory
Authors: Cabbolet Marcoen J.T.F. ,   Philosophy Documentation Center
Published: September 2015

Recently Feferman (Rev. Symb. Logic 6: 6–15, 2013) has outlined a program for the development of a foundation for naive category theory. While Ernst (ibid. 8: 306–327, 2015) has shown that the resulting axiomatic system is still inconsistent, the purpose of this note is to show that nevertheless some foundation has to be developed before naive category theory can replace axiomatic set theory as a foundational theory for mathematics. It is argued that in naive category theory currently a ‘cookbook recipe’ is used for constructing categories, and it is explicitly shown with a formalized argument that this “foundationless” naive category theory therefore contains a paradox similar to the Russell paradox of naive set theory.
A method for mapping the turbulence intensity and excess energy available to building mounted wind turbines over a UK City
Authors: Emejeamara F. C. , Tomlin A. S.
Published: September 2015

Assessing the potential of proposed urban wind installations is hindered by insufficient assessments of both urban wind resource, and the effectiveness of commercial gust control solutions within built up areas. Evaluating the potential performance of wind turbines within the urban environment requires an estimation of the total energy that would be available to them were effective control systems to be used. This paper presents a methodology for estimating the excess energy content (EEC) present in the gusty urban wind, which is usually under represented when using assessments based only on mean wind speeds. The method is developed using high temporal resolution wind measurements from eight potential turbine sites within the urban and suburban environment. By assessing the relationship between turbulence intensities and the EEC, an analytical methodology for predicting the total wind energy available at a potential turbine site is proposed. Sensitivity analysis with respect to temporal data resolution on the predicted EEC is also demonstrated. The methodology is then integrated with an analytical methodology that was initially developed to predict mean wind speeds at different heights within a UK city based on detailed mapping of its aerodynamic characteristics. Additional estimates of turbulence intensities and EEC based on the current methodology allow a more complete assessment of the wind resource available. The methodology is applied to the UK city of Leeds as a case study and the potential to map turbulence intensities and the total kinetic energy available at different heights within a typical urban city is demonstrated. Copyright © 2015 John Wiley & Sons, Ltd.
Assembly and Function of the Precursor B-Cell Receptor
Authors: Übelhart Rudolf , Werner Markus , Jumaa Hassan
Published: September 2015

During early stages of development, precursor B lymphocytes express a characteristic type of antigen receptor known as the pre-B-cell receptor (pre-BCR). This receptor differs from conventional BCRs in that it possesses a germ line-encoded surrogate light chain (SLC), which is associated with the signal transduction machinery via heavy chain (HC) proteins that have been generated by productive rearrangement of the immunoglobulin HC genes. The pre-BCR marks a key step of B-cell commitment, as it activates the B-cell-specific signaling cascade and mediates the selection, expansion, and differentiation of cells expressing a productively rearranged HC protein. Another difference between the pre-BCR and conventional BCR might be the initial event that triggers receptor activation, as the pre-BCR is activated in the absence of external ligands, while conventional BCRs require antigen for activation. Nonetheless, the pre-BCR downstream signaling cascade is largely similar to that of the BCR suggesting that the characteristic LC of the pre-BCR mediates important receptor interactions thereby providing distinctive, germ line-encoded features to the pre-BCR. In fact, the SLC enables the pre-BCR to act as a surrogate autoreactive receptor. Here, we outline the structure and function of the pre-BCR and how the autonomous signaling capacity might be a direct consequence of pre-BCR assembly. In addition to its role in early B-cell development, we discuss how the ordered activation of downstream signaling cascades enables the pre-BCR to activate seemingly opposing cellular programs such as proliferation and differentiation.
The FAST-EU trial: 12-month clinical outcomes of women after intrauterine sonography-guided transcervical radiofrequency ablation of uterine fibroids
Authors: Brölmann Hans , Bongers Marlies , Garza-Leal José Gerardo , Gupta Janesh , Veersema Sebastiaan , Quartero Rik , Toub David
Published: September 2015

The FAST-EU Trial was designed to establish the effectiveness and confirm the safety of transcervical intrauterine sonography-guided radiofrequency ablation with the VizAblate™ System in the treatment of symptomatic uterine fibroids. This was a multicenter, prospective, single-arm trial involving academic and community hospitals in the United Kingdom, the Netherlands, and Mexico. Women with qualifying uterine fibroids and heavy menstrual bleeding underwent intrauterine sonography-guided transcervical radiofrequency ablation (RFA) with the VizAblate System; anesthesia was individualized. Patients were required to have up to five fibroids from 1 to 5 cm in diameter. The primary trial endpoint was the percentage change in perfused fibroid volume, as assessed by contrast-enhanced MRI at 3 months by an independent core laboratory. Secondary endpoints, evaluated at 6 and 12 months, included safety, percentage reductions in the Menstrual Pictogram (MP) score, and the Symptom Severity Score (SSS) subscale of the Uterine Fibroid Symptom-Quality of Life (UFS-QOL) questionnaire, along with the rate of surgical reintervention for abnormal uterine bleeding and the mean number of days to return to normal activity. Additional assessments included the Health-Related Quality of Life (HRQOL) subscale of the UFS-QOL, nonsurgical reintervention for abnormal uterine bleeding, anesthesia regimen, patient satisfaction, and pain during the recovery period. An additional MRI study was performed at 12 months on a subgroup of patients. Fifty patients (89 fibroids) underwent transcervical radiofrequency ablation with the VizAblate System. At 3 and 12 months, perfused fibroid volumes were reduced from baseline by an average of 68.1 ± 28.6 and 67.4 ± 31.9 %, respectively, while total fibroid volumes were reduced from baseline by an average of 54.7 ± 37.4 and 66.6 ± 32.1 %, respectively (all P < .001 compared with baseline; Wilcoxon signed-rank test). At 12 months, mean MP score and SSS decreased by 53.8 ± 50.5 and 55.1 ± 41.0 %, respectively; the mean HRQOL score increased by 277 ± 483 %. There were four surgical reinterventions (8 %) within 12 months. This is the first report of the 12-month follow-up for patients in the FAST-EU Trial. In concert with previously reported 3- and 6-month endpoint data, the 12-month results of the FAST-EU Trial suggest that in addition to substantially reducing the perfused and total volume of targeted uterine fibroids, the VizAblate System is safe and effective through 12 months in providing relief of abnormal uterine bleeding associated with submucous, intramural, and transmural fibroids.
How Ecotheological Beliefs Vary among Australian Churchgoers and Consequences for Environmental Attitudes and Behaviors
Authors: Pepper Miriam , Leonard Rosemary
Published: September 2015

Worldviews play an important part in shaping and driving people's more specific environmental attitudes and behaviors. In a religious context, attention to eco(theo)logical worldviews, defined as foundational beliefs about the relationships between God, the Earth and humanity, helps researchers and environmental practitioners alike to better understand the religious frameworks which may foster or impede environmental action. This study draws on data from the 2011 Australian National Church Life Survey to examine churchgoers’ beliefs about the presence of God in nature and human dominion over the environment. Australian churchgoers strongly affirmed the presence of God in the natural world, but were less affirming of dominion theology. Dominion varied between church traditions, but beliefs about the presence of God did not. The beliefs predicted a range of measures of environmental attitudes and behaviors. The results regarding dominion are consistent with findings from other countries, and the research extends previous limited work on the sanctification of nature to a concept of the presence of God in the natural world.
Collective motion in a suspension of micro-swimmers that run-and-tumble and rotary diffuse
Authors: Krishnamurthy Deepak , Subramanian Ganesh
Published: September 2015

Recent experiments have shown that suspensions of swimming micro-organisms are characterized by complex dynamics involving enhanced swimming speeds, large-scale correlated motions and enhanced diffusivities of embedded tracer particles. Understanding this dynamics is of fundamental interest and also has relevance to biological systems. The observed collective dynamics has been interpreted as the onset of a hydrodynamic instability, of the quiescent isotropic state of pushers, swimmers with extensile force dipoles, above a critical threshold proportional to the swimmer concentration. In this work, we develop a particle-based model to simulate a suspension of hydrodynamically interacting rod-like swimmers to estimate this threshold. Unlike earlier simulations, the velocity disturbance field due to each swimmer is specified in terms of the intrinsic swimmer stress alone, as per viscous slender-body theory. This allows for a computationally efficient kinematic simulation where the interaction law between swimmers is knowna priori. The neglect of induced stresses is of secondary importance since the aforementioned instability arises solely due to the intrinsic swimmer force dipoles.

Our kinematic simulations include, for the first time, intrinsic decorrelation mechanisms found in bacteria, such as tumbling and rotary diffusion. To begin with, we simulate so-called straight swimmers that lack intrinsic orientation decorrelation mechanisms, and a comparison with earlier results serves as a proof of principle. Next, we simulate suspensions of swimmers that tumble and undergo rotary diffusion, as a function of the swimmer number density$(n)$, and the intrinsic decorrelation time (the average duration between tumbles,${\it\tau}$, for tumblers, and the inverse of the rotary diffusivity,$D_{r}^{-1}$, for rotary diffusers). The simulations, as a function of the decorrelation time, are carried out with hydrodynamic interactions (between swimmers) turned off and on, and for both pushers and pullers (swimmers with contractile force dipoles). The ‘interactions-off’ simulations allow for a validation based on analytical expressions for the tracer diffusivity in the stable regime, and reveal a non-trivial box size dependence that arises with varying strength of the hydrodynamic interactions. The ‘interactions-on’ simulations lead us to our main finding: the existence of a box-size-independent parameter that characterizes the onset of instability in a pusher suspension, and is given by$nUL^{2}{\it\tau}$for tumblers and$nUL^{2}/D_{r}$for rotary diffusers; here,$U$and$L$are the swimming speed and swimmer length, respectively. The instability manifests as a bifurcation of the tracer diffusivity curves, in pusher and puller suspensions, for values of the above dimensionless parameters exceeding a critical threshold.
Self-sustained states at Kolmogorov microscale
Authors: Deguchi Kengo
Published: September 2015

It is shown theoretically how the scaling of coherent structures in shear flows changes their asymptotic development at large Reynolds number. Based on the theory a family of nonlinear self-sustained states at Kolmogorov microscale is numerically identified on the laminar–turbulent boundary of shear flows. Theoretically and numerically the states connect to known asymptotic states existing at larger scale. The asymptotically very small amplitude of the new states may explain why strongly sheared, linearly stable laminar flows can cause a turbulent transition by small disturbances. The numerically obtained Kolmogorov-scale solutions can be used to describe the theoretically minimal self-sustained structures appearing in various shear flows.
Oscillatory behaviour in an emptying–filling box
Authors: Vauquelin O.
Published: September 2015

The emptying–filling box problem is examined theoretically in a general non-Boussinesq case. The steady solutions are first reviewed and expressed both as a function of a pure geometrical parameter and as a function of a dimensionless number ${\it\Theta}$ that characterizes the strength of the buoyant source relative to the box height. A linearization of the conservation equations is performed around the steady state and a second-order differential equation is derived that facilitates consideration of the existence of underdamped oscillations in the emptying–filling process. These oscillations are quantified in terms of frequency, damping ratio and phase shift, which constitutes the major outcome of this study. It is shown that oscillations can exist whatever the strength of the buoyancy source, even if their amplitude remains extremely weak for ‘small plumes’.
No longer take a tree for the forest: A cross-level learning-related perspective on individual innovative behavior
Authors: Yang Fu , Qian Jing , Tang Le , Zhang Lihua
Published: September 2015

Using trait activation theory as a framework, this study developed and tested a cross-level model of individual innovative behavior. Data from a sample of 334 employees within 75 work teams were used to examine the hypothesized model. Results showed that employee learning goal orientation was positively related to innovative behavior only when the team structure was more organic. Additionally, the relationship between employee learning goal orientation and innovative behavior would be strongest when both the team structure was more organic and team mean learning goal orientation was higher.