bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the geometric form of free boundaries satisfying a bernoulli condition. II
Authors: Acker A. , Payne L. E. 
Published: March 2007

AbstractIn the x‐y plane, let Ω be an annular domain whose interior boundary Γ* is a known Jordan curve and whose exterior boundary Γ is a free boundary characterized by the condition that|ΔU| = 1 on Γ, where U is the capacity potential in Ω. We obtain a qualitative description of Γ involving such things as its inflection points and local maxima and minima relative to specified directions. We also extend these results to obtain qualitative properties of the free boundary when it is subjected to various geometric contraints. Our results generalize those in [1].
Generalized herglotz domains
Authors: Colton D. , Wimp J. , Hsiao G. C. 
Published: March 2007

AbstractLet F(θ k, α) be the far field pattern arising from the scattering of a time harmonic plane acoustic wave of wave number k and direction a by a sound‐soft cylinder of cross section D. Suppose F has the Fourier expansionmagnified imagewhere an = an(k, . Then if ϰ2 is a Dirichlet eigenvalue for D, sufficient conditions are given on D for the existence of a nontrivial sequence |bn| where the bn are independent of such that for all directions magnified imageDomains for which this is true are called generalized Herglotz domains. The conditions for a domain to be a generalized Herglotz domain are given either in terms of the Schwarz function for the analytic boundary ϱD or in terms of the Rayleigh hypothesis in acoustic scattering theory and examples are given showing the applicability of these conditions.
A free boundary problem and stability for the nonlinear beam
Authors: Miersemann E. , Mittelmann H. D. , Törnig W. 
Published: March 2007

AbstractThe stability bound for the classical nonlinear Euler beam is determined in the case that its deflection is limited by an obstacle parallel to the plane of the beam. Let a clamped or simply supported beam be axially compressed by a force P > P0, where P0 denotes the critical load. So far only a linear theory has been applied to analyze the stability of the solutions in contact with the obstacle and the jumping to a different state. Utilizing a free boundary problem formulation we analytically as well as numerically answer these questions for the nonlinear beam.
On the scattering frequencies of time‐dependent potentials
Authors: Cooper J. , Perla‐Menzala G. , Strauss W. , Werner P. 
Published: March 2007

AbstractThis paper discusses the scattering frequencies associated with the scalar wave equation and a time‐periodic, real, potential. It is shown that the scattering frequencies form a discrete set in the complex plane and depend continuously on the potential. Existence of the scattering frequencies is proved for periodic potentials which are perturbations of a time independent, nonnegative, potential.
Some algorithms of the projective‐Newton method for the finite element space
Authors: Hobot G. , Pokora T. , Mitchell A. R. 
Published: March 2007

AbstractThe paper presents the projective‐Newton method in the finite element space with curved finite elements along the boundary. The properties of this method are studied when the integrals are calculated by numerical quadrature. Some algorithms are derived when ω = {x ϵ R2: 0 < x1, x2 < 1}.
Finite time blow‐up and stability properties of materials with fading memory
Authors: Calderer M. C. , Hsiao G. 
Published: March 2007

AbstractA detailed analysis of the equations of nonlinear elasticity is carried out for a certain class of initial‐boundary value problems.In particular, I examine whether the presence in the differential equation of a mechanical mechanism of dissipation is able to prevent instabilities and ensure global existence in time of the solutions.
Stability of a layer of dipolar fluid heated from below
Authors: Straughan B. , Payne L. E. 
Published: March 2007

AbstractThe equations of Bleustein and Green [2] are formulated in a way suitable to describe the convective instability which occurs when a layer of dipolar fluid is heated from below. The linear instability boundary is shown to coincide with the nonlinear stability curve and the critical Rayleigh numbers describing this boundary are found; in particular, the non‐dimensional micro‐length is found to always stabilize.
On the geometric form of solutions of a free boundary problem involving galvanization
Authors: Acker A. , Payne L. E. 
Published: March 2007

AbstractIn [6], T. I. Vogel studied a free boundary problem originating in the galvanization process. He showed that if the given boundary Γ* is starlike or convex, then so is the free boundary solution Γ. Our purpose is to generalize Vogel's second result by showing (under certain assumptions) that Γ cannot have more (local) maxima or minima (relative to a given direction) than Γ*; also that Γ cannot have more inflection points or greater total curvature than Γ*. The author has already proven analogous results for the Bernoulli free boundary problem in [1], [2] and [3].
On a class of probability distributions
Authors: Lehnigk S. H. , Roach G. F. 
Published: March 2007

AbstractThe application of a three parameter class of one‐sided probability distributions is being discussed. For specific parameter values, this class contains as special cases a number of well‐known distributions of statistics and statistical physics, namely, Gauss, Weibull, exponential, Rayleigh, Gamma, chi‐square, Maxwell, and Wien (limiting case of Planck's distribution). One of the three parameters represents scale; the other two represent initial and terminal shape of the associated probability density function. A fourth parameter, shift, may be introduced. The distribution class discussed in this paper was introduced by L. Amoroso [2] in 1924. It is closely connected with a family of linear Fokker‐Planck equations (generalized Feller equation). In fact, the class of probability density functions associated with the distribution class considered here is a special case of the set of all delta function initial condition solutions of the generalized Feller equation for a fixed value of the time variable. It will be shown that, as a function of the logarithm of the independent variable, the logarithm of the cumulative distribution function is asymptotically linear as the independent variable approaches zero from above. This fact leads to a general criterion for the applicability of the presented distribution family relative to given empirical data. The applicability criterion can be used to determine approximate values for the two shape parameters. They can subsequently be used as initial values in any of the established parameter estimation techniques.
Study of an elliptic problem with nonlinear boundary conditions
Authors: Caussignac Ph. , Descloux J. , Rappaz J. , Rappaz J. , Nedelec J. C. 
Published: March 2007

AbstractWe consider the problem of finding on a trapezium a harmonic function u the normal derivative of which is equal on one side to λ exp(u). We prove the existence of a solution branch (λ,u(λ)) with a turning point and, for the case of the square, the presence of bifurcations. The “inverse power” algorithm converges on a part of the branch.
Motion of a vibrating string in the presence of a convex obstacle: A free boundary problem
Authors: Cabannes H. , Neunzert H. 
Published: March 2007

AbstractHere we study the motion of a vibrating string in the presence of an arbitrary obstacle. We show that if the string always rebounds on the concave parts of the obstacle, it can either rebound or roll on the convex parts. The latter is the case if the velocity of the string is null at the contact point just before contact, or if the contact point propagates at a characteristic speed. Four examples are given. The three first correspond to the same obstacle, a sinusoidal arc, but with different initial conditions. In the first case, the string rebounds on the whole of the obstacle and the motion is explicitly determined when it is periodic. In the second case, the string rolls on the convex part of the obstacle up to the inflexion point and then rebounds on the concave part and unwinds on the convex part. In the third case, the string is initially at rest on the obstacle; then it instantaneously leaves the concave part while it unwinds progressively on the convex part. The fourth case is similar to the third but with a different obstacle; the motion, which is periodic, is determined explicitly.
The electrostatic potential of spherical polyelectrolytes in aqueous solution
Authors: Ohlenbusch H.‐D. , Freeden W. , Törnig W. 
Published: March 2007

AbstractThe electrostatic potential in systems of spherical polyelectrolytes is determined by superposition of spherically symmetric solutions of the linearized Poisson‐Boltzmann equation. The case of constant surface potential is investigated in detail. Higher‐order approximations are given by use of a generalization of the addition theorem for modified Bessel functions.
On the initial layer and the existence theorem for the nonlinear Boltzmann equation
Authors: Lachowicz M. , Neunzert H. 
Published: March 2007

AbstractThe truncated Hilbert expansion including the initial layer terms is considered. This enables us to replace the singulary perturbed Boltzmann equation by a weakly nonlinear equation. In this way the existence of a strong solution of the Boltzmann equation is obtained for initial data close enough to a local Maxwellian. The solution exists in the physically significant time interval on which smooth solutions to the Euler equations exist.
On approximation to convective diffusion equation
Authors: Nigam K. D. P. , Srivastava V. K. , Haque M. W. , Lvov V. 
Published: March 2007

AbstractA closed‐form analytical solution for the problem of homogeneous and heterogeneous reactions in a isothermal non‐Newtonian laminar flow tubular reactor is presented. A technique is evolved where Galerkin method is applied in Laplace‐transformed domain.
Evolution systems in semiconductor device modeling: A cyclic uncoupled line analysis for the gummel map
Authors: Jerome Joseph W. , Brosowski B. 
Published: March 2007

AbstractThe initial/boundary‐value problem for isothermal, lattice, semiconductor device modeling is described and analyzed. This nonlinear elliptic/parabolic system of reaction/diffusion/convection type is determined by a Maxwell equation, relating space/charge and the electric field, and by two continuity equations for the free electron and hole carrier concentrations. The Einstein relations for Brownian motion are not assumed in this analysis, so that the electrostatic potential, u, and the carrier concentrations, n and p, are the fundamental dependent variables of the system. The boundary conditions are Dirichlet conditions for dependent variable values on the contact portions of the device, and homogeneous Neumann conditions, expressing insulation, on the complement. Complicating the analysis are the transition singularity points between the mixed boundary conditions, and the field dependence of the mobility and diffusion coefficients. By means of a physically motivated analysis of the convective current component, we are able to uncouple the system by a cyclic horizontal line analysis, without an unreasonable time step restriction. The corresponding linear equations are solved by a contractive inner iteration. The outer iteration is shown to converge to a unique solution of the system, under singularity classification at the transition points. The definition of this outer iteration follows the steady‐state Gummel iteration at discrete time steps. An existence theory is a by‐product of the analysis, and is separated from uniqueness theory.
The Galerkin‐averaging method for nonlinear, undamped continuous systems
Authors: Stroucken A. C. J. , Verhulst F. , Eckhaus W. 
Published: March 2007

AbstractThe analysis of initial‐boundary value problems for nonlinear evolution equations with a small parameter is carried out by projection and averaging. The complications of the extension to a second order approximation is discussed and subsequently demonstrated for the perturbed Klein‐Gordon equation. The difference between the case of resonance and nonresonance at first order is emphasized.
An integral equation of the first kind for a free boundary value problem of the stationary Stokes' equations
Authors: Hebeker F. K. , Nedelec J. C. 
Published: March 2007

AbstractWe investigate a free boundary value problem of the stationary Stokes' equations. In a previous paper adapted hydrodynamical potentials have been constructed and their jump relations have been discussed. Here we study a direct method to obtain an equivalent boundary integral equations' system of the first kind. Its solution properties are investigated in the framework of strongly elliptic pseudodifferential operators. For numerical purposes a suitable representation formula for the variational equation is given in terms of integro‐differential operators which avoids the evaluation of hypersingular integrals.
Plane potential flow past a cylinder with porous surface
Authors: Wegert E. , Wolfersdorf L. V. , Meister E. 
Published: March 2007

AbstractIn the paper two models for the potential flow past a cylinder with porous or perforated surface are reduced to nonlinear Riemann‐Hilbert problems for the complex velocity function and general existence and uniqueness theorems for the solution of the problems are derived. Further the problems are reduced to nonlinear singular integral equations of Hilbert type whose solvability is investigated by means of the Schauder and Banach fixed point theorem.
Approximation dans un Problème de Viscoélasticité Périodique
Authors: Teniou D. , Nedelec J. C. 
Published: March 2007

AbstractWe are concerned with equations which derive from a quasistatic periodic problem of viscoelasticity. We give a condition which yields to existence and uniqueness of a periodic solution. Then we prove a finite element method based on equilibrium elements for the space approximation and on the explicit Euler scheme for the time approximation.
Energy properties preserving schemes for Burgers' equation
Authors: Anguelov R. , Djoko J.K. , Lubuma J.M.‐S. 
Published: March 2007

AbstractThe Burgers' equation, a simplification of the Navier–Stokes equations, is one of the fundamental model equations in gas dynamics, hydrodynamics, and acoustics that illustrates the coupling between convection/advection and diffusion. The kinetic energy enjoys boundedness and monotone decreasing properties that are useful in the study of the asymptotic behavior of the solution. We construct a family of non‐standard finite difference schemes, which replicate the energy equality and the properties of the kinetic energy. Our approach is based on Mickens' rule [Nonstandard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994.] of nonlocal approximation of nonlinear terms. More precisely, we propose a systematic nonlocal way of generating approximations that ensure that the trilinear form is identically zero for repeated arguments. We provide numerical experiments that support the theory and demonstrate the power of the non‐standard schemes over the classical ones. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007
Superconvergence analysis of the Galerkin FEM for a singularly perturbed convection–diffusion problem with characteristic layers
Authors: Franz Sebastian , Linß Torsten 
Published: March 2007

AbstractWe analyze the superconvergence property of the Galerkin finite element method (FEM) for elliptic convection–diffusion problems with characteristic layers. This method on Shishkin meshes is known to be almost first‐order accurate (up to a logarithmic factor) in the energy norm induced by the bilinear form of the weak formulation, uniformly in the perturbation parameter. In the present paper the method is shown to be almost second‐order superconvergent in this energy norm for the difference between the FEM solution and the bilinear interpolant of the exact solution. This supercloseness property is used to improve the accuracy to almost second order by means of a postprocessing procedure. Numerical experiments confirm these results. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007
A new development in polyesters derived from terephthalic acid: A polyether ester based on polyethylene terephthalate
Authors: Ijzermans A. B. , Pluijm F. J. , Huntjens F. J. , Repin J. F. 
Published: March 2007

AbstractAn exploratory investigation has been carried out into a segmented polyether ester which consists of amorphous soft segments of polytertramethylene ether glycol and crystalline short chain hard segments of polyethylene terephthalate. The properties of this block copolymer have been compared with those of polyethylene terephthalate and polytetramethylene terephthalate (PTMT) and with those of the block copolymer based on PTMT. After a description of the preparation and the structure of the polyether ester, the thermal properties are discussed by means of DTA thermograms. From the stress‐strain behaviour, compared with that of the homopolymers, the elastomeric properties of the block copolymers stand out clearly. Processing characteristics are discussed on the basis of the crystallisation behaviour and the relationship between melt viscosity and shear rate. Finally, data about u.v., oxidative and hydrolytic stability are given.
The thermal degradation of perfluoroalkylene‐linked organosiloxane polymers
Authors: Cotter John L. , Knight Graham J. , Wright Walter W. 
Published: March 2007

AbstractTwo perfluoroalkylene‐linked organosiloxane polymers have been studied by thermogravimetry, pyrolysis–gas chromatography–mass spectrometry and fluoride ion analysis. Fluorine transfer processes play an important part in the thermal breakdown.
Electroinitiated emulsion polymerisation of vinyl acetate. II. Characteristics of the emulsion polymerisation
Authors: Tidswell Bryan M. , Train Andrew W. 
Published: March 2007

AbstractThe characteristics of the propagation process for the electroinitiated emulsion polymerisation of vinyl acetate are described when current is varied by a factor of 36 and emulsifier concentration by 128. The order with respect to current is 0.8, whilst with emulsifier concentration, two definite ranges are observed with exponents 0.26 and 1.12 at low and high concentrations respectively. A similar two range effect is observed using particle size measurements. Behaviour at low emulsifier concentration is similar to that described previously for vinyl acetate, involving particle formation mainly by precipitation from solution. At high emulsifier concentrations micelle formation appears to be of increased importance.
Polymerisation reactions initiated by high electric fields. Kinetic applications in the field of free cationic polymerisations
Authors: Brendle Marcel C. C. , Ilvoas Anne‐Marie 
Published: March 2007

AbstractFree cationic polymerisations were initiated in bulk by field ionisation with a positive tip. Dilatometric measurements obtained with ‘dry’ and ‘ultra‐dry’ styrene, a‐methylstyrene and isobutylvinylether were in agreement with kinetic equations derived by assuming that in the absence of deactivating impurities the space charge is built up only by growing macromolecules.Determination of the space charge by independent physical methods suggests that the kp values of the literature need to be re‐evaluated. It was also shown that charge injection enhances the degree of dryness (measurable by this process) and is therefore useful in ultimate purification of monomers.
Liquid‐liquid phase separation in multicomponent polymer systems. XIII quasi‐binary phase diagrams with three‐liquid‐phase separation
Authors: Kleintjens L. A. , Schoffeleers H. M. , Domingo L. 
Published: March 2007

AbstractUsing the Gibbs free energy of mixing relation of Flory and Huggins with a concentration‐dependent interaction parameter one can calculate quasi‐binary phase diagrams for solvent‐polymer systems. If the polymer has a very asymmetric molecular weight distribution, separation into three‐liquid‐phases occurs which may result in a cloud‐point curve without stable critical point. In the latter case the spinodal does not touch the stable branches of the cloud‐point curve and the coexistence curves show marked bends and kinks. These phenomena could be qualitatively verified by experiments on the system cyclohexane‐polystyrene. The phase‐volume ratio method for the determination of consolute states itself clearly indicates when situations prevail precluding its applicability.
Electric birefringence of cellulose trinitrate in acetone
Authors: Isles M. , Jennings Barry R. 
Published: March 2007

AbstractElectric birefringence studies have been made on a sample of high molecular weight cellulose trinitrate in acetone. The molecule is shown to have only a permanent dipole moment and no significant anisotropic polarisability in this solvent. Both the rotary relaxation times obtained from transient time dependent effects and the amplitudes of the observed birefringence have been analysed in terms of theories for rigid rods, weakly bending rods, worm‐like chains and both flexible and stiff random coils. The study indicates that (a) electric birefringence data are sensitive to molecular flexibility and (b) that in this solvent, nitrocellulose of 12% nitrogen content appears to be a stiff, non free draining coil with a dipole moment of the order of a few debye (i.e. ⋍ 10−29 C m) per monomer unit.
Thermally initiated oxidation and ignition of flexible polyurethane foams
Authors: Eaves D. E. , Keen C. V. 
Published: March 2007

AbstractOxidation and ignition of flexible polyurethane foams have been investigated by observing the effects of internal and external heating. External temperatures of some 190°C are required to induce combustion. Internal temperatures of 250 −350°C initiate a self‐propagating internal reaction which results in foam ignition when the reaction reaches the foam surface. The stability of a polyurethane foam to such heating increases with the age of the foam.
Diffusion of some dyes in aqueous polymer solutions
Authors: Farag Ahmed A. , Sedahmed G. H. , Farag H. A. , Nagawi A. F. 
Published: March 2007

AbstractThe diffusion of both Direct Blue 76 and acid orange dyes in aqueous dilute polymer solutions was studied using the capillary method. The polymer systems studied included dilute solutions of carboxymethyl cellulose, polyethylene oxide and polyacrylamide. It was found that the diffusion coefficients of the two dyestuffs in carboxymethyl cellulose solutions are higher than that in pure water, while in polyacrylamide solutions the values of the coefficients are lower than that in pure water. In case of polyethylene oxide solutions, the diffusion coefficient of Direct Blue 76 was found to be lower than that in pure water, whereas that of acid orange was found to be higher than that in pure water.The diffusion coefficients of both dyes were found to decrease with increasing polymer concentration in the case of polyethylene oxide and polyacrylamide, whereas in the case of carboxymethyl cellulose the diffusion coefficients increased with polymer concentration.With change of temperature, the diffusion coefficients of both dyes in the three polymer solutions were found to obey the Arrhenius equation. The activation energy for diffusion of the two dyes was calculated in pure water, as well as in the different polymer solutions.
Effect of natural ageing on the dielectric properties of some synthetic rubber mixtures
Authors: Hakim Itedal K. , Hanna Faika F. 
Published: March 2007

AbstractThe dielectric constant ε′ and dielectric loss ε″ have been investigated for SBR samples loaded with some white fillers and for perbunan rubber loaded with silica and carbon black in the frequency range from 60 to 107 Hz at room temperature. The samples were exposed to normal weathering conditions for about five years. The results are compared with those obtained five years before and the differences are interpreted.