bluuebunny/crossref_metadata_2025 huggingface dataset:
Collectivism and Social Influence in the Buying Decision: A Four-Country Study of Inter- and Intra-National Differences
Authors: Kongsompong Kritika , Green Robert T. , Patterson Paul G.
Published: July 2009

Purpose

The paper reports the results of a four-nation study of the relationship between collectivism and social influence in the consumer buying decision, between and within countries. Hypotheses were investigated that revolve around the notion that the more collectivist the person's orientation, the more susceptible the person will be to social influence in the purchase decision.

Method

A cross-sectional survey employing a student sample was conducted across two Eastern and two Western countries (Thailand, Singapore, USA, and Australia).

Findings

The findings provide either whole or partial support for the hypotheses. In general, a higher collectivist orientation results in high levels of social influence, especially across nations. There are exceptions, however, which highlight the need to incorporate other factors into understanding the role that cultural orientation plays in purchasing decisions.

Managerial implications

When devising product, service, and communications strategies in collectivist countries, the findings suggest that the marketer from an individualist country should give overt consideration to, for instance, parental and sales related forces that could influence people's buying decisions. Parental influence in buying decisions is shown to be relatively low in individualist nations like the USA. In Thailand, however, parents exercise considerable influence over what their young adult children purchase. Similarly, the sales force at the retail level occupies elevated importance in collectivist societies. Provision of retailer support associated with sales force training should receive a higher priority in collectivist nations.
Für eine neue Balance von privater und gesetzlicher Krankenversicherung
Authors: Leienbach Volker
Published: July 2009

Einleitung

In Deutschland existieren zwar zwei Versicherungs-, nicht jedoch zwei Versorgungssysteme: Bisher steht allen Versicherten ein umfassendes Netz von Krankenhäusern und Ärzten offen. Dies ist nicht zuletzt ein Verdienst der Privatversicherten, die für viele medizinische Leistungen höhere Honorare zahlen. Ganz anders sieht es in Ländern aus, in denen zwar auf dem Papier nur eine Versicherungsform besteht, die Praxis aber von Rationierungen sowie parallelen Versorgungsstrukturen für Arm und Reich geprägt ist.
From Resurrection to Immortality: Theological and Political Implications in Modern Jewish Thought
Authors: Batnitzky Leora
Published: July 2009

Hans Jonas began his 1961 Ingersoll Lecture by acknowledging the “undeniable fact” “that the modern temper is uncongenial to the idea of immortality.”1 Jonas nonetheless concluded his lecture by affirming that “although the hereafter is not ours … we can have immortality … when in our brief span we serve our threatened mortal affairs and help the suffering immortal God.”2 While he may not have realized it, Jonas's words capture what I shall argue is the dominant view of immortality in modern Jewish thought. Underlying this view is an effort to refute materialist conceptions of human existence without committing to any particularly theological or traditionally metaphysical notion of immortality.
Friedrich Schleiermacher on the Old Testament
Authors: Capetz Paul E.
Published: July 2009

In the nineteenth century the unrestricted application of the historical-critical method posed an unprecedented challenge to inherited Christian notions about the Bible. While this challenge was eventually to be felt most acutely in the study of the New Testament (nt) once the distinction between the “Jesus of history” and the “Christ of faith” had firmly established itself, traditional viewpoints on the Old Testament (ot) were actually the first to be called into question. As a consequence of historical investigation, it became increasingly difficult for theologians to claim that the gospel is already taught in the ot. Regarding this matter, Friedrich Schleiermacher (1768–1834) made a bold proposal. He argued against the canonical standing of the ot on the grounds that it expresses Jewish, not Christian, religion. For him this conclusion was the unavoidable result of the advancing critical scholarship that was undermining the christological exegesis used to defend the church's claim to the ot against the synagogue's counter-claim to its sole rightful possession. Opposing such “christianizing” readings, Schleiermacher broke ranks from Christian theologians and championed the side of the Jews in this historic debate. His only predecessors in this regard were Marcion and the Socinians, although his proposal for relegating the ot to noncanonical status was later endorsed by Adolf von Harnack.
DISENTANGLING THE COMPLEX ASSOCIATION BETWEEN FEMALE GENITAL CUTTING AND HIV AMONG KENYAN WOMEN
Authors: MASLOVSKAYA OLGA , BROWN JAMES J. , PADMADAS SABU S.
Published: July 2009

Female genital cutting (FGC) is a widespread cultural practice in Africa and the Middle East, with a number of potential adverse health consequences for women. It was hypothesized by Kun (1997) that FGC increases the risk of HIV transmission through a number of different mechanisms. Using the 2003 data from the Kenyan Demographic and Health Survey (KDHS), this study investigates the potential association between FGC and HIV. The 2003 KDHS provides a unique opportunity to link the HIV test results with a large number of demographic, social, economic and behavioural characteristics of women, including women's FGC status. It is hypothesized that FGC increases the risk of HIV infection if HIV/AIDS is present in the community. A multilevel binary logistic regression technique is used to model the HIV status of women, controlling for selected individual characteristics of women and interaction effects. The results demonstrate evidence of a statistically significant association between FGC and HIV, after controlling for the hierarchical structure of the data, potential confounding factors and interaction effects. The results show that women who had had FGC and a younger or the same-age first-union partner have higher odds of being HIV positive than women with a younger or same-age first-union partner but without FGC; whereas women who had had FGC and an older first-union partner have lower odds of being HIV positive than women with an older first-union partner but without FGC. The findings suggest the behavioural pathway of association between FGC and HIV as well as an underlying complex interplay of bio-behavioural and social variables being important in disentangling the association between FGC and HIV.
Milk yield, udder health and reproductive performance in Swedish organic and conventional dairy herds
Authors: Fall Nils , Emanuelson Ulf
Published: July 2009

Organic dairy farming is an expanding segment of the dairy sector where cow management differs from the conventional model in many respects. Thus, a comparative evaluation of disease and welfare status in organically and conventionally managed dairy cows is required. Assessment of milk yield, udder health and reproductive performance (RP) was done in 20 organically and 20 conventionally managed Swedish dairy herds. In accordance with earlier findings we confirmed lower milk yield in organic cows. Udder health and RP were chosen as indicators of animal health in view of their clinical relevance and the availability of appropriate data bases providing good background knowledge for further animal health assessment. No obvious differences were found in the investigations of somatic cell count (SCC) profiles or time to veterinary-treated cases of mastitis between organically and conventional managed cows. Pregnancy success at first insemination, an appropriate measurement of RP with biological interpretation and background, did not reveal any difference between management types, whereas the hazard rate-ratio (HR) of having a calving-interval was significantly lower (HR=0·71) in organically managed cows. The calving-interval is an important financial determinator in dairy production, but it is not considered an optimal indicator of biologic relevance as it partially reflects farmer decisions. In conclusion, the organically managed cows in this study did not differ from conventionally managed cows in udder health or RP, with the exception of calving interval.
Use of botulinum toxin in voice restoration after laryngectomy
Authors: Khemani S , Govender R , Arora A , O'Flynn P E , Vaz F M
Published: July 2009

Background:

Following laryngectomy, a distinct population of patients fails to achieve successful tracheoesophageal voice. These patients' voices range from strained and effortful to none at all. Such patients may present with severe hypertonicity or spasm of the pharyngoesophageal segment. Botulinum toxin has been used to chemically denervate the pharyngeal musculature, and is an alternative to invasive surgical procedures. The aim of this article is to review the evidence for using botulinum toxin to achieve an improvement in post-laryngectomy voice.

Methods:

A Medline literature review (1966 to January 2009) and a search of the Cochrane database were performed. Foreign language articles and those not pertaining to post-laryngectomy voice restoration were excluded.

Results:

Nine articles reporting a total of 134 patients were identified. Although there were differences in the outcome measures used, objective improvement in voice production occurred in between 70 and 100 per cent of cases.

Conclusion:

Botulinum toxin can be used as a safe and cost-effective treatment in patients with confirmed pharyngoesophageal segment hypertonicity and/or spasm following laryngectomy, to obtain an improvement in voice quality.
Bell's palsy before Bell: Evert Jan Thomassen à Thuessink and idiopathic peripheral facial paralysis
Authors: van de Graaf R C , IJpma F F A , Nicolai J-P A , Werker P M N
Published: July 2009

Bell's palsy is the eponym for idiopathic peripheral facial paralysis. It is named after Sir Charles Bell (1774–1842), who, in the first half of the nineteenth century, discovered the function of the facial nerve and attracted the attention of the medical world to facial paralysis. Our knowledge of this condition before Bell's landmark publications is very limited and is based on just a few documents. In 1804 and 1805, Evert Jan Thomassen à Thuessink (1762–1832) published what appears to be the first known extensive study on idiopathic peripheral facial paralysis. His description of this condition was quite accurate. He located several other early descriptions and concluded from this literature that, previously, the condition had usually been confused with other afflictions (such as ‘spasmus cynicus’, central facial paralysis and trigeminal neuralgia). According to Thomassen à Thuessink, idiopathic peripheral facial paralysis and trigeminal neuralgia were related, being different expressions of the same condition. Thomassen à Thuessink believed that idiopathic peripheral facial paralysis was caused by ‘rheumatism’ or exposure to cold. Many aetiological theories have since been proposed. Despite this, the cold hypothesis persists even today.
Paradoxical long-term enhancement of distortion product otoacoustic emission amplitude after repeated exposure to moderate level, wide band noise in awake guinea pigs
Authors: Mei L , Huang Z-W , Tao Z-Z
Published: July 2009

Objective:

Hearing sensitivity usually diminishes with noise exposure. In the present study, we examined the effect of 93 dB(A) wide band noise on cochlear micromechanical sensitivity in awake guinea pigs.

Methods:

Animals were randomly assigned to groups receiving either single or repeated noise exposure. Distortion product otoacoustic emission amplitudes were recorded before, during and after noise exposure.

Results:

Ninety-three decibel(A) wide band noise reduced the distortion product otoacoustic emission amplitudes at all tested frequencies. The distortion product otoacoustic emission amplitudes for higher frequencies showed a permanent reduction, whereas those for lower frequencies showed a temporary reduction. Distortion product otoacoustic emission amplitudes for middle frequencies showed prolonged enhancement after repeated noise exposure.

Conclusion:

Our results suggest that (1) it is likely that there are intermediate stages between permanent threshold shift and temporary threshold shift, and (2) long-term enhancement of distortion product otoacoustic emission amplitudes may be an indication of tinnitus generation.
Single stage, transmastoid approach for otogenic intracranial abscess
Authors: Morwani K P , Jayashankar N
Published: July 2009

Objective:

To evaluate the treatment of intracranial abscess of otogenic origin, and to study the outcome measures of single stage treatment of the otogenic focus and drainage of intracranial abscess via a transmastoid approach.

Study design:

Retrospective case review.

Setting:

Dr Balabhai Nanavati Hospital and Medical Research Centre, Mumbai, India, an academic tertiary referral centre, and Shri H Bhagwati Municipal General Hospital, Mumbai, India, an academic secondary referral centre.

Patients:

Seventy-three patients with intracranial abscess secondary to otogenic pathology, confirmed by computed tomographic scanning.

Intervention:

Single stage treatment of the ear pathology and drainage of intracranial abscess via a transmastoid approach, performed by the senior author (KPM).

Results:

Of the 73 patients, 12 were lost to follow up and were excluded from the study. Outcomes for the remaining 61 patients were known, and these patients were followed up for at least two years. Adults were more commonly affected by otogenic intracranial abscess than children, with a male preponderance. Otogenic intracranial abscess was associated with both cholesteatomatous (41 per cent) and non-cholesteatomatous ears (59 per cent). All cases were treated with transmastoid drainage of the intracranial abscess and canal wall up or down tympanomastoidectomy, depending on the ear pathology. Two cases developed post-operative cerebrospinal fluid leakage (3 per cent), and another two cases developed meningitis (3 per cent). Five patients had recurrent abscess; two of these patients (3 per cent) died but were included in the study. Three patients had residual abscess, improved with additional management.

Conclusion:

In this series, the low morbidity and mortality rate, combined with a shorter hospital stay, suggest that single stage, transmastoid drainage of intracranial abscess and concurrent treatment of the otogenic pathology is an effective treatment for otogenic intracranial abscess.
Evaluation of 18fluoro-2-deoxyglucose positron emission tomography in iodine scan negative, differentiated thyroid cancer recurrence
Authors: Chisholm E J , Tolley N S
Published: July 2009

Background:

Follow up of patients with differentiated thyroid cancer is based upon anatomical imaging, thyroglobulin assay and functional imaging in the form of iodine uptake scanning. A significant cohort of such patients have rising thyroglobulin levels but negative iodine scans. In this group, 18fluoro-2-deoxyglucose positron emission tomography scans have been commonly employed. The aim of this study was to assess the usefulness of such investigation.

Methods:

The sensitivity of 18fluoro-2-deoxyglucose positron emission tomography for detecting recurrence of differentiated thyroid cancer was calculated from a retrospective review of scan results from patients with iodine scan negative recurrence.

Results:

Eighteen patients with rising thyroglobulin levels underwent 18fluoro-2-deoxyglucose positron emission tomography scanning. Fourteen patients had negative (and four equivocal) whole body iodine scintigraphy scans. Of these 14, six patients had a positive 18fluoro-2-deoxyglucose positron emission tomography scan, giving a sensitivity of 42.9 per cent.

Conclusions:

When assessed in the clinical setting and restricted to patients with negative iodine scans, the sensitivity of 18fluoro-2-deoxyglucose positron emission tomography was found to be lower than in previous case series.
Stability analysis of a closed thermosyphon
Authors: Herrero M. A. , Velazquez J. J. L.
Published: July 2009

This paper deals with the motion of a fluid in a closed loop under the effect of natural convection and a given external heat flux. More precisely, we show that the stationary solutions of a system describing the intermediate asymptotics of the previous problem are structurally linearly unstable.
Productivity enhancement in hydrofractured oil reservoirs
Authors: Hagan Patrick S. , Cox Robert W.
Published: July 2009

Low permeability formations are often hydrofractured to increase the production rate of oil and gas. This process creates a thin, but highly permeable, fracture which provides an easy path for oil and gas to flow through the reservoir to the borehole. Here we examine the payoff of hydrofracturing by determining the increased production rate of a hydrofractured well. We find explicit formulas for the steady production rate in the three regimes of small, intermediate, and large (dimensionless) fracture conductivities. Previously, only the formula for the large fracture conductivity case was known.

We assume that Darcy flow pertains throughout the reservoir. Then, the steady fluid flow through the reservoir is governed by Laplace's equation with a second-order boundary condition along the fracture. We first analyze this boundary value problem for the case of small fracture conductivities. An explicit formula for the production rate is obtained for this case, essentially by combining singular perturbation methods with spectral methods in a function space which places the second-order boundary condition on the same footing as Laplace's equation. Next, we re-cast Laplace's equation as a variational principle which has the second-order boundary condition as its natural boundary condition. This allows us to use simple trial functions to derive accurate estimates of the production rate in the intermediate conductivity case. Then, an asymptotic analysis is used to find the production rate for the large fracture conductivity case. Finally, the asymptotic and variationally-derived production rate formulasare compared to exact values of the production rate, which have been obtained numerically.

It may be feasible to create more than a single fracture about a borehole. So we also develop similar asymptotic and variational formulas for the production rate of a well with multiple fractures.
On the computation of blow-up
Authors: Stuart A. M. , Floater M. S.
Published: July 2009

Numerical methods for initial-value problems which develop singularities in finite time are analyzed. The objective is to determine simple strategies which produce the correct asymptotic behaviour and give an accurate approximation of the blow-up time. Fixed step methods for scalar ordinary differential equations are studied first and it is shown that there is a natural embedding of the discrete process in a continuous one. This shows clearly how and why the fixed-step strategy fails. A class of time-stepping strategies that correspond to a time- continuous re-scaling of the underlying differential equation is then proposed; this class is analyzed and criteria established to determine suitable choices for the re-scaling. Finally the ideas are applied to a partial differential equation arising from the study of a fluid with temperature-dependent viscosity. The numerical method involves re-formulating the equationas a moving boundary problem for the peak value and applying the ODE time-steppingstrategies based on this peak value.
Nonlinear analysis of condensed-phase surface combustion
Authors: Garbey Marc , Kaper Hans G. , Leaf Gary K. , Matkowsky Bernard J.
Published: July 2009

This article is concerned with the structure and stability properties of a combustion front that propagates in the axial direction along the surface of a cylindrical solid fuel element. The fuel consists of a mixture of two finely ground metallic powders, which combine upon ignition in a one-step chemical reaction. The reaction is accompanied by a melting process, which in turn enhances the reaction rate. The combustion products are in the solid state. The reaction zone, inside which the melting occurs, is modelled as a front that propagates along the surface of the cylinder. The different modes of propagation that have been observed experimentally (such as single- and multiheaded spin combustion and multiple-point combustion) are explained as the results of bifurcations from a uniformly propagating plane circular front. The stability properties of the various modes are discussed.
A nonlinear system for irreversible phase changes
Authors: Blanchard Dominique , Ghidouche Hamid
Published: July 2009

This paper is concerned with the mathematical study of a nonlinear system modelling an irreversible phase change problem. Uniqueness of the solution is proved using the accretivity of the system in (L1)2. Expressing one of the two unknowns as an explicit functional of the other reduces the system to a single nonlinear evolution equation and ultimately leads to an existence theorem.

In this paper the existence and uniqueness of the solution of a nonlinear system modelling some irreversible phase changes is established.
Hyperelasticity for crystals
Authors: Chipot Michel
Published: July 2009

The goal of this note is to explain the process of computing the lowest energy level achieved by an elastic crystal subject to homogeneous boundary deformation. This analysis follows mainly the lines of Chipot and Kinderlehrer or Fonesca but we expect that it will lead to some new results for some other energy functional having different invariance properties. The mathematical interest of the result also lies in the fact that the lowest energy level computed this way coincides with the relaxed energy functional (see Fonesca). This relaxed energy is determined by a known thermodynamic quantity, Ericksen' subenergy. Within this review we will also analyse some of the mathematical and physical aspects of these highly oscillatory problems.
Appearance of mushy regions in a symmetrical Stefan problem with vanishing heat capacity
Authors: Marangunic Pedro R. , Stampella Mirta B.
Published: July 2009

We prove that in the Stefan problem with planar, cylindrical or spherical symmetry, with vanishing heat capacity and constant boundary temperature, no mushy region can appear, even in the presence of constant volumetric heat sources, if the initial data are consistent with the presence of just two pure phases. If the boundary temperature is not constant, a mushy region may or may not appear; we find some general conditions ensuring one case or the other and we give a specific example illustrating the appearance of a mushy region.
Symmetry-based algorithms to relate partial differential equations: I. Local symmetries
Authors: Bluman G. W. , Kumei S.
Published: July 2009

Simple and systematic algorithms for relating differential equations are given. They are based on comparing the local symmetries admitted by the equations. Comparisons of the infinitesimal generators and their Lie algebras of given and target equations lead to necessary conditions for the existence of mappings which relate them. Necessary and sufficient conditions are presented for the existence of invertible mappings from a given nonlinear system of partial differential equations to some linear system of equations with examples including the hodograph and Legendre transformations, and the linearizations of a nonlinear telegraph equation, a nonlinear diffusion equation, and nonlinear fluid flow equations. Necessary and sufficient conditions are also given for the existence of an invertible point transformation which maps a linear partial differential equation with variable coefficients to a linear equation with constant coefficients. Other types of mappings are also considered including the Miura transformation and the invertible mapping which relates the cylindrical KdV and the KdV equations.
Nonlinear effects of variable conductivities in thermistor-related problems: an explicit example
Authors: Young J. H. , Tenti G.
Published: July 2009

The coupled nonlinear partial differential equations obeyed by the electrical potential and temperature distribution for a medium undergoing steady state electrical heating are applied to a one-dimensional rod having its surface temperature held constant as current is conducted along its length due to a potential difference maintained between its ends. Extension is given to the previously discussed class of solutions by the inclusion of a thermal conductivity which varies linearly with temperature. The resulting electrical current and resistance are found to be significantly influenced by the thermal conductivity of the medium. Molybdenum is identified as a material exemplifying such a thermal conductivity and the general effects are then numerically illustrated.
New exact solutions of the Boussinesq equation
Authors: Clarkson Peter A.
Published: July 2009

In this paper new exact solutions are derived for the physically and mathematically significant Boussinesq equation. These are obtained in two different ways: first, by generating exact solutions to the ordinary differential equations which arise from (classical and nonclassical) similarity reductions of the Boussinesq equation (these ordinary differential equations are solvable in terms of the first, second and fourth Painlevé equations); and second, by deriving new space-independent similarity reductions of the Boussinesq equation. Extensive sets of exact solutions for both the second and fourth Painlevé equations are also generated. The symbolic manipulation language MACSYMA is employed to facilitate the calculations involved.
Disappearance of phase in the Stefan problem: one space dimension
Authors: Aronson D. G. , Kamin S.
Published: July 2009

We consider the two-phase one-dimensional Stefan problem in a finite interval, with initial and boundary conditions such that the solid phase vanishes at a finite time T and at a single point. We show that the temperature in the solid phase decreases to zero and is bounded by c exp (α/(t − T)) as extinction approaches (C, α > 0) and that phase boundaries at extinction have finite speeds.
A non-local diffusion equation arising in terminally attached polymer chains
Authors: Chen Xinfu , Friedman Avner
Published: July 2009

We consider a polymer melt in a domain Ω whereby each polymer chain is attached at one endpoint to a fixed surface S contained in ∂Ω. Denote by G(x, t;y) the normalized number density of all subchains from x to y of length t. Then, according to the selfconsistent mean field theory, G satisfies, for each y: Gt - Δ2G + σϕG = 0, where σ is a real parameter, and ϕ is a functional of G(·, ·; ·) both non-local and nonlinear. We establish the existence of G and C∞ regularity of ϕ, as a function of x.
Existence and uniqueness of solutions to a concentrated capacity problem with change of phase
Authors: Andreucci Daniele
Published: July 2009

A concentrated capacity problem is posed for the heat equation in a multidimensional domain. In the concentrated capacity (i.e. in a portion of the boundary of the domain) a change of phase takes place, and a Stefan-like problem is posed. This scheme has been introduced in the literature as the formal limiting case of a certain class of diffusion problems.

Our main result is a theorem of continuous dependence of the solution on the data. It is also used to prove the existence of the solution (in a weak sense), assuming only integrability of the data. The solution is found as the limit of the solutions of the approximating problems.
Uniqueness and stability of the solution to a thermoelastic contact problem
Authors: Shi Peter , Shillor Meir
Published: July 2009

Uniqueness and continuous dependence on the initial temperature are proved for a onedimensional, quasistatic and frictionless contact problem in linear thermoelasticity. First the problem is reformulated in such a way that it decouples. The resulting problem for the temperature is a nonlinear integro-differential equation. Once the temperature is known the displacement is recovered from an appropriate variational inequality. Uniqueness is proved by considering an integral transform of the temperature. The steady solution is obtained and the asymptotic stability is shown. It turns out that the asymptotic behaviour and the steady state are determined by a relation between the coupling constant a and the initial gap.
On the stability of some solutions of the Stefan problem
Authors: Ricci Riccardo , Weiqing Xie
Published: July 2009

We investigate the stability of travelling wave solutions of the one-dimensional under-cooled Stefan problem. We find a necessary and sufficient condition on the initial datum under which the free boundary is asymptotic to a travelling wave front. The method applies also to other types of solutions.
Modes of burning in filtration combustion
Authors: Booty M. R. , Matkowsky B. J.
Published: July 2009

We describe and analyze a model of filtration combustion, in which a gas is forced at high pressure into a porous solid matrix so that after ignition and under favourable conditions a combustion wave can propagate through the medium. We consider the case of counter flow, where the gas is forced into the reaction zone through the unreacted part of the porous solid. Relations are derived for the steady state propagation of a planar combustion wave or front in the limit of high-activation energy, from which the propagation speed, reaction temperature, and reacted mass fraction of the solid product can be found in terms of the mass flux of the injected gas, the gas pressure and mass flux on exit from the front, and other physico-chemical parameters describing the system. Two distinct modes of combustion are discussed, corresponding to the reaction being driven to completion by exhaustion of either the gaseous or the solid component, these being referred to as the gas-deficient and solid-deficient modes of burning respectively. For both homogeneous and heterogeneous forms of the reaction rate we find that there is a critical inlet mass flux for the incoming gas below which steady state solutions no longer exist and that there are parameter values for which multiple steady states occur.
A uniqueness result for the thermistor problem
Authors: Chipot M. , Cimatti G.
Published: July 2009

The thermistor problem is a system of equations modelling the electric heating of a conducting material. We prove uniqueness of a solution to this system.
Global instability of viscous fingering in a Hele–Shaw cell: formation of oscillatory fingers
Authors: Xu Jian-Jun
Published: July 2009

This work deals with the global instability mechanism of viscous fingering in a Hele–Shaw cell with the inclusion of surface tension. We investigate the interaction and propagation of travelling waves in the system, and obtain two discrete sets of global wave modes: symmetrical modes and anti-symmetrical modes. We call the instability mechanism determined by these global modes the global trapped wave (GTW) instability. A unique global, neutrally stable state of the system is found; it explains the formation of the narrow, oscillatory fingers discovered by Couder el al. (1986) and by Kopf-Sill & Homsy (1987).
On the existence of homoclinic and heteroclinic orbits for differential equations with a small parameter
Authors: Byatt-Smith John G.
Published: July 2009

Low order differential equations typically have solutions which represent homoclinic or heteroclinic orbits between singular points in the phase plane. These orbits occur when the stable manifold of one singular point intersects or coincides with its unstable manifold, or the unstable manifold of another singular point. This paper investigates the persistence of these orbits when small dispersion is added to the system. In the perturbed system the stable manifold of a singular point passes through an exponentially small neighbourhood of a singular point and careful analysis is required to determine whether a homoclinic or heteroclinic connection is achieved.
Diffusivity determination in nonlinear diffusion
Authors: Cortázar Carmen , Elgueta Manuel , Vázquez Juan Luis
Published: July 2009

We are concerned with the problem of determining the diffusivity D of a diffusion process governed by the equation ut = (Dux)x', under the assumption that D depends on u. The main point consists in the observation that there exist solutions of travelling-wave type and that the dependence D = D(u) can be explicitly found in terms of the profile of such solutions. The property of finite propagation speed is required for this method to work. We propose two concrete implementations of the inverse problem, and give a rigorous mathematical proof of our statements. We also describe the application of the travelling-wave method to another interesting class of nonlinear parabolic equations.
Three-dimensional solutions of nonlinear degenerate diffusion-convection processes
Authors: Gagneux Gérard , Madaune-Tort Monique
Published: July 2009

The main objective of this work is to present, for practical use, some original results about several qualitative properties of the solutions of a large class of degenerate diffusion-convection equations arising from fluid mechanics. Current interest in models of the simultaneous motion of two immiscible incompressible liquids results from its significance for many applied fields such as, for instance, the theoretical modelling of oil reservoirs where the pores of a threedimensional porous medium contain some hydrocarbon component (oil). In secondary recovery, a second inexpensive fluid (water) is injected into the porous medium in order to push the oil towards the producing wells.
Experimental and theoretical investigation of an equation of dendritic crystal growth
Authors: Dewynne J. N. , Robinson F. N. H.
Published: July 2009

An experimental study using an analogue electronic model of the equation x‴ + x′ = є sin x, modified by the addition of small terms ax″ and βx with 0 < β < α ≫ є shows that these dissipative terms have a profound effect on the solutions for large time. If ∈ is not too large, experimental solutions tend to a simple periodic form, unlike the case α=β = 0. The existence of this limiting periodic form suggests the possibility of a simple analytic treatment using the method of harmonic balance, and this treatment leads to excellent agreement with the experimental results for a wide range of initial conditions and values of the parameters. The approach towards attracting limiting periodic solutions is analysed by using the method of multiple scales.
Matched asymptotics for a generalisation of a model equation for optical tunnelling
Authors: Liu Jinsong , Wood Alastair
Published: July 2009

We apply the method of matched asymptotic expansions to link the outgoing wave solution at infinity of the differential equation y″(x)+(lgr;+єxn)y(x) = 0, x∈(0, ∞),λ∈Cє>0, n∈N across the turning point x = (—λ/є)1/n nearest to the positive real axis to a linear homogeneous boundary condition at the origin. The equation with n = 1 models the leakage of energy from the core of a bent fibre optic waveguide, the rate of leakage corresponding to Im λ, which was shown to be exponentially small like O(exp[— 1/є]) by Paris & Wood (1989). The extension n = 2 by Brazel et al. (1990) obtained Im λ = O(exp[— 1/є1/2]). Both these papers involve delicate analysis of the asymptotics of special functions near to Stokes' lines. When n > 2 no special functions are available, and completely different methods must be employed to obtain the result Im λ = O(exp[— 1/є1/n]).
Finding abstract Lie symmetry algebras of differential equations without integrating determining equations
Authors: Reid Gregory J.
Published: July 2009

There are symbolic programs based on heuristics that sometimes, but not always, explicitly integrate the determining equations for the infinitesimal Lie symmetries admitted by systems of differential equations. We present a heuristic-free algorithm ‘Structure constant’, which can always determine whether the Lie symmetry group of a given system of PDEs is finite- or infinite-dimensional. If the group is finite-dimensional then ‘Structure constant’ can determine the dimension and structure constants of its associated Lie algebra without the heuristics of integration involved in other methods. If the group is infinite-dimensional, then ‘Structure constant’ computes the number of arbitrary functions which determine the infinite-dimensional component of its Lie symmetry algebra and also calculates the dimension and structure of its associated finite-dimensional subalgebra. ‘Structure constant’ employs the algorithms ‘Standard form’ and ‘Taylor’, described elsewhere. ‘Standard form’ is a heuristic-free algorithm which brings any system of determining equations to a standard form by including all integrability conditions in the system. ‘Taylor’ uses the standard form of a system of differential equations to calculate its Taylor series solution. These algorithms have been implemented in the symbolic language MAPLE. ‘Structure constant’ can also automatically determine the dimension and structure constants of the Lie symmetry algebras of entire classes of differential equations dependent on variable coefficients. In particular, we obtain new group classification results for some physically interesting classes of nonlinear telegraph equations depending on two variable coefficients, one representing a nonlinear wave speed and the other representing a nonlinear dispersion.
Asymptotic and numerical study of Brusselator chaos
Authors: Deller Klaus , Erneux Thomas , Bayliss Alvin
Published: July 2009

We investigate the Brusselator reaction–diffusion equations with periodic boundary conditions. We consider the range of values of the parameters used by Kuramoto in his study of chaotic concentration waves. We determine numerically the bifurcation diagram of the long-time travelling and standing wave solutions using a highly accurate Fourier pseudo-spectral method. For moderate values of the bifurcation parameter, we have found a sequence of instabilities leading either to periodic and quasiperiodic standing waves, or to chaotic regimes. However, for large values of the control parameter, we have found only uniform time-periodic solutions or time-periodic travelling wave solutions. Our numerical study motivates a new asymptotic analysis of the Brusselator equations for large values of the control parameter and small diffusion coefficients. This analysis explains the numerical predictions. The chaotic regime is limited to moderate values of the control parameter and periodic solutions are the only solutions for large values of the control parameter. We identify the stabilizing mechanism as the relaxation oscillations which appear when the control parameter is large. Our asymptotic result on the stability of periodic solutions is then generalized to a class of two-variable reaction-diffusion equations.
Laminar channel flow driven by accelerating walls
Authors: Watson P. , Banks W. H. H. , Zaturska M. B. , Drazin P. G.
Published: July 2009

The two-dimensional flow of a viscous incompressible fluid in a channel with accelerating walls is analysed by use of Hiemenz's similarity solution. Steady flows and their instabilities are calculated, and unsteady flows are computed by solving the initial-value problem for the governing partial-differential system. Thereby, these exact solutions of the Navier–Stokes equations are found to exhibit turning points, pitchfork bifurcations, Hopf bifurcations and Takens–Bogdanov bifurcations along the route to chaos. The substantial physical result is that the chaos previously found for flows with symmetrically accelerating walls is easily destroyed by a little asymmetry.
Surface-concentration-dependent nonlinear diffusion
Authors: King J. R.
Published: July 2009

We discuss a nonlinear diffusion equation in which the diffusivity has a non-local dependence on the surface concentration. Exact results are obtained for some special cases by means of similarity methods and non-local transformations. We indicate some of the implications the analysis has for more general cases.
Integral characteristics of elastic inclusions and cavities in the two-dimensional theory of elasticity
Authors: Movchan A. B.
Published: July 2009

Integral characteristics, such as elastic polarization matrices of elastic inclusions and cavities, are described. The matrix of elastic polarization of a finite cavity is constructed in the case of the two-dimensional Lamé operator under the assumption that the geometry of the domain occupied by the cavity is defined by a conformal mapping from the unit disk. Examples and applications of these integral characteristics in the theory of cracks are considered.
Multiple Fourier analysis for bang-bang controls with memory
Authors: Sternberg Robert L.
Published: July 2009

Bennett functions , (h, k), defined below and elsewhere, have been used extensively in Fourier analysing the output of certain devices such as rectifiers, limiters and other instantaneous modulators responding to a two-frequency input for which the output at time t depends only on the device input–output characteristic Y = Y(X) and the input at time t. Here, with the aid of a new set of modified Bennett functions , (h, k), these methods are extended to solve the same problems for non-instantaneous bang-bang controls with multivalued input–output characteristics Y = Y(X) and hence having memory.
On the computation of modified Bennett functions
Authors: Hood M. J.
Published: July 2009

A simple computational procedure is described for the evaluation of the modified Bennett functions, which arise in the multiple Fourier analysis for bang-bang controls with memory.
Homoclinic orbits in the dynamic phase-space analogy of an elastic strut
Authors: Amick C. J. , Toland J. F.
Published: July 2009

The equation

is a possible dimensionless version of a model for the configuration of a very long strut resting on a nonlinear elastic foundation with axial loading P. By seeking to establish the existence of homoclinic orbits connecting the zero equilibrium of (*), now regarded as defining a four dimensional dynamical system, to itself one is pursuing the so-called ‘dynamical phase-space analogy’ for the spatial configuration suggested by the form of the equation. The existence of homoclinic solutions is then interpreted as indicating the presence of spatially localized buckling of the deformed strut.
Diffraction of sound by a surface inhomogeneity at a fluid-solid interface
Authors: Tew R. H.
Published: July 2009

The diffraction of a plane sound wave in a fluid by an adjacent elastic solid containing a surface flaw is analysed using ray techniques. By solving the eikonal equation with suitable boundary data, the pattern of the rays leaving the boundary and propagating into the fluid and solid respectively is established, with the corresponding amplitudes being furnished by the appropriate system of transport equations. For the acoustic and elastic cylindrical bulk waves that emanate from the flaw itself, the amplitude directivities cannot be found from this ray analysis alone.
The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part II: Numerical analysis
Authors: Blowey J. F. , Elliott C. M.
Published: July 2009

In this paper we consider the numerical analysis of a parabolic variational inequality arising from a deep quench limit of a model for phase separation in a binary mixture due to Cahn and Hilliard. Stability, convergence and error bounds for a finite element approximation are proven. Numerical simulations in one and two space dimensions are presented.
On the correctness of a phenomenological model of equilibrium phase transitions in a deformable elastic medium
Authors: Meirmanov A. M. , Shemetov N. V.
Published: July 2009

In this paper we investigate the mathematical model of the equilibrium of a finite volume in ℝn (n = 1,2, 3) of a two-phase continuous medium, under the assumption that each pure phase is an isotropic elastic solid. The main results in this paper are:

(i) the existence and uniqueness of a solution of this mathematical model;

(ii) a discussion of the stress-strain law associated with the free energy of this two-phase continuous medium, which is multiple-valued due to the non-smoothness of the Gibbs potential (complementary energy);

(iii) a description of the structure of solutions in plane strain.
Complex variable methods in Hele–Shaw moving boundary problems
Authors: Howison S. D.
Published: July 2009

We discuss the one-phase Hele–Shaw problem in two space dimensions. We review exact solutions in the zero-surface-tension case, giving a unified account of the Schwarz function and conformal mapping approaches. We discuss the extension of the former method to the cases in which surface tension or ‘kinetic undercooling’ terms apply on the moving boundary, and we give some conjectures on the resulting singularity structure. Finally, we give a new interpretation of the linear stability analysis of the zero-surface-tension problem, and we suggest a possible regularization of ill-posed problems by the imposition of a unilateral constraint on the moving boundary.
Scale-invariant initial value problems in one-dimensional dynamic elastoplasticity, with consequences for multidimensional nonassociative plasticity
Authors: Schaeffer David G. , Shearer Michael
Published: July 2009

This paper solves a class of one-dimensional, dynamic elastoplasticity problems for equations which describe the longitudinal motion of a rod. The initial conditionsU(x, 0)are continuous and piecewise linear, the derivative ∂U/∂x(x, 0) having just one jump atx= 0. Both the equations and the initial data are invariant under the scalingŨ(x, t) = α−1U(αx, αt), where α > 0; hence the termscale-invariant. Both in underlying motivation and in solution, this problem is highly analogous to the Riemann problem from gas dynamics. These ideas are applied to the Sandler–Rubin example of non-unique solutions in dynamic plasticity with a nonassociative flow rule. We introduce an entropy condition that re-establishes uniqueness, but we also exhibit problems regarding existence.
On the identifiability of steel reinforcement bars in concrete from magnetostatic measurements
Authors: Engl Heinz W. , Isakov Victor
Published: July 2009

We describe a specific measurement process that works well in practice for locating steel reinforcement bars in concrete. For the case that the total volume of these bars is small, we derive an approximate linear, but sufficiently accurate, mathematical model for which we can prove a uniqueness result.
The propagation of turbulent bursts
Authors: Kamin Shoshana , Vazquez Juan Luis
Published: July 2009

We consider the equation of turbulent burst propagation

with m > 1 and k ≥ 0, or, in an equivalent formulation

We consider initial data u(x, 0) which are radially symmetric and have compact support; x = l(t) = r(T) describes the interface of the solution.
Bifurcations in a class of complex differential equations
Authors: Moroz Irene M.
Published: July 2009

In this paper we introduce a class of nonlinear complex ordinary differential equations that arises in the removal of channel distortion in digital telecommunication signals. Techniques from dynamical systems theory show that Hopf bifurcations are possible in the simplest of these systems. Numerical integrations, however, show that such bifurcations are degenerate. When attempts are made to follow the periodic orbits, both the period of oscillation and the principal bifurcation parameter remain fixed at their values at bifurcation. The periodic orbits exist as a family at discrete parameter values, i.e. we have a nonlinear centre. A stability régime diagram is presented