bluuebunny/crossref_metadata_2025 huggingface dataset:
Consonant clusters in child phonology and the directionality of syllable structure assignment
Authors: Lleó Conxita , Prinz Michael
Published: September 2008

The production of target consonant clusters at early stages of acquisition is analysed from a phonological representational perspective. The data stem from five normal monolingual German and four normal monolingual Spanish children at ages from 0;9 to 2;1, observed in naturalistic settings. At the beginning stages, target clusters are reduced to a single consonantal position, due to lack of branching of the syllabic constituents. This finding coincides with other results in the literature, which have in general been explained by means of universal principles. Nevertheless, there is an essential difference between the German and the Spanish data: German children tend to prefer the first consonant and Spanish children the second one. This difference can only be explained in terms of parameterization of syllabification, which in German takes place from left to right and in Spanish from right to left. At later stages, when clusters begin to be produced with two consonantal positions, they offer evidence for the beginning of branching of syllabic constituents, due to parameterization, and for the chronological order of the setting of the subsyllabic parameters. Our data offer evidence in favour of the following acquisitional hierarchy: CV > CVC > CVCC > CCVCC.
Eighteen-month-old children learn words in non-ostensive contexts
Authors: Tomasello Michael , Strosberg Randi , Akhtar Nameera
Published: September 2008

Previous studies have demonstrated that children aged 2;0 can learn new words in a variety of non-ostensive contexts. The current two studies were aimed at seeing if this was also true of children just beginning to learn words at 1;6. In the first study an adult interacted with 48 children. She used a nonce word to announce her intention to find an object (‘Let's find the gazzer’), picked up and rejected an object with obvious disappointment, and then gleefully found the target object (using no language). Children learned the new word as well in this condition as in a condition in which the adult found the object immediately. In the second study the adult first played several rounds of a finding game with each of 60 children, in which it was first established that one of several novel objects was always in a very distinctive hiding place (a toy barn). The adult then used a nonce word to announce her intention to find an object (‘Let's find the toma’) and then proceeded to the barn. In the key condition the barn was mysteriously ‘locked’; the child thus never saw the target object after the nonce word was introduced. Children learned the new word as well in this condition as in a condition in which the adult found the object immediately. The results of these two studies suggest that from very early in language acquisition children learn words not through passive, associative pro- cesses, but rather through active attempts to understand adult behaviour in a variety of action and discourse contexts.
Competition on the face: affect and language in ASL motherese
Authors: Reilly Judy Snitzer , Bellugi Ursula
Published: September 2008

Research on early mother-child interaction has documented the crucial role affect plays in the content and modulation of early interactions. For hearing mothers, voice quality is considered to be the single most informative channel for affective expression. For deaf caregivers who use American Sign Language (ASL), the vocal channel is unavailable, and facial expression is critically important. Not only do facial behaviours signal affective and communicative information, but specific facial behaviours also function as obligatory grammatical markers. This multifunctionality of facial expression presents a dilemma for deaf parents signing to their toddlers as these two systems potentially compete for expression on the face. This study addresses how affective facial expression interacts with the linguistic forms in ASL motherese. To address this issue, we present data from both cross-sectional and longitudinal videotaped interaction from a total of 15 deaf mothers signing with their deaf toddlers (ages 0;9–2;8). Using Ekman & Friesen's Facial Action Coding System (FACS) (1978) we analysed child-directed maternal wh- questions. Because they are frequent in early discourse, AND they require furrowed brows which also signal anger and puzzlement, wh- questions represent an ideal context to address the potential conflict of grammatical and affective facial expression in ASL motherese. Our studies indicate a shift from affect to grammar at about the child's second birthday. These findings shed new insight on the nature and possible role of input on the language acquisition process.
An outbreak of hepatitis A in recently vaccinated students from ice snacks made from contaminated well water
Authors: ZHANG L. J. , WANG X. J. , BAI J. M. , FANG G. , LIU L. G. , ZHANG Y. , FONTAINE R. E.
Published: September 2008

On 30 May 2006, township S in Sichuan Province, China, reported an outbreak of hepatitis A (HA) in students who had recently received HA vaccine. The concern was raised that the vaccine had caused the outbreak. We attempted to identify the source of infection and mode of transmission. A HA case was defined as onset of jaundice or anorexia since 1 April 2006 with a twofold elevation of alanine aminotransferase (ALT) and anti-HA virus-IgM in a resident of or visitor to the township. Exposures to vaccine and snacks of 90 case-students to those of 107 control-students were compared. Thirty-four per cent of cases ate ice slush compared to 4·7% of controls (OR 4·1), and 51% of cases ate snow cones compared to 17% of controls (OR 8·3). The ice snacks were made with well water. HA virus RNA was detected by reverse transcription–polymerase chain reaction from patients' blood and well water. Untreated well water poses important dangers to the public in areas where piped, potable water is available.
LargeSalmonellaEnteritidis outbreak with prolonged transmission attributed to an infected food handler, Texas, 2002
Authors: BEATTY M. E. , SHEVICK G. , SHUPE-RICKSECKER K. , BANNISTER E. , TULU A. , LANCASTER K. , ALEXANDER N. , ZELLNER D. E. , LYSZKOWICZ E. , BRADEN C. R.
Published: September 2008

In March 2002, an outbreak ofSalmonellaEnteritidis (SE) infections occurred at a convention centre in Dallas, Texas and continued for 6 weeks. We conducted epidemiological studies, obtained clinical and environmental cultures, and interviewed employees to identify risk factors for infection. From 17 March–25 April 2002, the implicated hotel kitchen catered 41 multi-day conferences attended by 9790 persons. We received 617 illness reports from residents of 46 states. Sauces or items served with sauces were implicated in three cohort studies. SE phage-type 8 was identified as the agent. Eleven food service employees, including one who prepared sauces and salsa, had stool cultures that yielded SE. Although the original source was not determined, prolonged transmission resulted in the largest food handler-associated outbreak reported to date, affecting persons from 46 US states. Transmission ended with implementation of policies to screen food handlers and exclude those whose stool cultures yielded salmonellas.
A free boundary problem involving a cusp Part I: Global analysis
Authors: Alt H. W. , van Duijn C. J.
Published: September 2008

We consider the behaviour of the interface (free boundary) between fresh and salt water in a porous medium (a reservoir). The salt water is below the interface (with respect to the direction of gravity) and is stagnant. The fresh water is above the interface and moves towards the wells which are present in the reservoir. We give a description of the corresponding flow problem leading to a weak variational formulation involving a parameter Q which is related to the strength of the wells. We show that Q is a critical parameter in the following sense: there exists Qcr > 0 such that for Q < Qcr a smooth interface exists which is monotone with respect to Q. For Q = Qcr, a free boundary with one or more singularities (cusps) will occur at a positive distance from the wells. The global analysis for the problem (existence, uniqueness, monotonicity) is given here for two and three dimensional flow situations. The local cusp analysis is two-dimensional, and will be discussed in Part II.
A selfsimilar solution to the focusing problem for the porous medium equation
Authors: Aronson D. G. , Graveleau J.
Published: September 2008

In the focusing problem we seek a solution to the porous medium equation whose initial distribution is in the exterior of some compact set (e.g. a ball). At a finite time T the gas will reach all points of the initially empty region R. We construct a selfsimilar solution of the radially symmetric focusing problem. This solution is an example of a selfsimilar solution of the second kind, i.e. one in which the similarity variable cannot be determined a priori from dimensional considerations. Our solution also shows that in more than one space dimension, the velocity of the gas is infinite at the centre of R at the focusing time T.
Laminates and microstructure
Authors: Pedregal Pablo
Published: September 2008

This paper deals with the mathematical characterization of microstructure in elastic solids. We formulate our ideas in terms of rank-one convexity and identify the set of probability measures for which Jensen's inequality for this type of functions holds. This is the set of laminates. We also introduce generalized convex hulls of sets of matrices and investigate their structure.
A one-dimensional quasi-static contact problem in linear thermoelasticity
Authors: Copetti M. I. M. , Elliott C. M.
Published: September 2008

The existence, uniqueness and regularity of the solution to a one-dimensional linear thermoelastic problem with unilateral contact of the Signorini type are established. A finite element approximation is described, and an error bound is derived. It is shown that if the time step is O(h2), then the error in L2 in the temperature and in L∞ in the displacement is O(h). Some numerical experiments are presented.
Boundary integral equations for contact problems of plane quasi-steady viscous flows
Authors: Antanovskii Leonid K.
Published: September 2008

Plane, quasi-steady, free-boundary flows of an incompressible viscous fluid with surface tension in a container are considered. The mathematical problem is decomposed into an auxiliary elliptic problem for the Stokes system in a fixed flow domain, whose solution leads to the Cauchy problem for the free boundary with the so-called ‘normal velocity’ operator. By introducing the complex stress-stream function and applying time-dependent conformal mapping, the auxiliary problem is reduced to a boundary integral equation via consideration of two Hilbert problems for analytic functions in a unit disc. As an application, plane capillary flow with moving contact points is investigated asymptotically for small capillary numbers. We prove that in the case when a dynamic contact angle is equal to π, this problem is well-posed for a filling regime, and ill-posed for a drying one.
A generalized Danckwerts transformation
Authors: McNabb A.
Published: September 2008

Linear Fredholm operators (J, k) of the form u(x, t) = (J, k) v (x, t) ≡ J(t) v (x, t)+ k(t, s) v (x, s)ds can be found which map solutions v of the linear matrix system of n partial differential equations ∂u/∂t = DLv + Bv, into solutions u of the like system ∂u/∂t = DLu + Au, when the diagonal matrix D with positive elements and the matrices A and B commute with the linear, scalar operator L. For solution sets in appropriate function spaces, this mapping (J, k) is unique, independent of L, and 1–1 onto if it preserves initial values so that u(x, 0) = v(x, 0). When the set of solutions is restricted to those with zero initial values, this uniqueness aspect of (j, k) breaks down, and there are many linear maps of this Fredholm form which preserve the zero initial conditions and map all such solutions of the first equation in the appropriate function space into solutions of the second. When L is an unbounded operator like the Laplacian ∇2, the initial value problems have many solutions depending on the values of u and u on the boundaries of the region of the solutions, as well as their values in the region at time t = 0. Danckwerts introduced the concept of a ‘constant preserving’ map of Volterra form mapping solutions of the scalar diffusion equation ∂u/∂t = D∇2u, which are initially zero, onto solutions of a scalar diffusion equation ∂u/∂t = D∇2u + Au, with a linear, homogeneous, constant coefficient source term. This concept of a ‘constant preserving’ map extends to the nth order matrix Fredholm maps described. A map (J, k∗) is said to be constant preserving if for all constant n x n matrices C, (J, k∗)C = C, and hence J(t) + k∗(t, s)ds = I, where I is the unit matrix. In the restricted solution spaces where u(x, 0) and v(x, 0) are zero, there is a unique 1–1 onto Danckwerts map of this type transforming solutions of the v equation into solutions of the u equation. In the cases where the coupling matrix A is constant and B is zero, the kernel k∗ of the Danckwerts map can be expressed in terms of the kernel k for the more general Fredholm map associated with the same equations, but mapping the larger solution sets containing elements which need not vanish at time zero. The Danckwerts mapping is used to establish a generalized Ussing flux-ratio theorem for some coupled diffusion problems involving several chemically interacting components.
Slowly varying filtration combustion waves
Authors: Booty M. R. , Matkowsky B. J.
Published: September 2008

We describe the slow evolution of the wave speed and reaction temperature in a model of filtration combustion. In the counterflow configuration of the process, a porous solid matrix is converted to a porous solid product by injecting an oxidizing gas at high pressure into one end of a fresh sample of the solid while igniting it at the other end. The solid and gas react exothermically at high activation energy and, under favourable conditions, a self-sustaining combustion wave travels along the sample, converting reactants to product. Since the reaction rate depends on the gas pressure p in the pores, small gradients in p cause variations in the conditions of combustion, which, in turn, cause inhomogeneities in the physical properties of the product. We determine the slow evolution of the wave speed, the reaction temperature, and the mass flux of the gas downstream of the reaction zone. In the absence of a pressure gradient, there is a branch of steadily propagating solutions which has a fold. For planar disturbances on the slow time scale, we show that the middle part of the branch is unstable, with the change of stability occurring at the turning points of the branch. When the pressure gradient is nonzero, there are no steadily propagating solutions and the wave continually evolves. Conditions on the state of the gas at the inlet are described such that the variation in the wave speed and reaction temperature throughout the process can be minimized.
Cardiac magnetic resonance imaging by retrospective gating: mathematical modelling and reconstruction algorithms
Authors: Roerdink J. B. T. M. , Zwaan M.
Published: September 2008

This paper is concerned with some mathematical aspects of magnetic resonance imaging (MRI) of the beating human heart. In particular, we investigate the so-called retrospective gating technique which is a non-triggered technique for data acquisition and reconstruction of (approximately) periodically changing organs like the heart. We formulate the reconstruction problem as a moment problem in a Hilbert space and give the solution method. The stability of the solution is investigated and various error estimates are given. The reconstruction method consists of temporal interpolation followed by spatial Fourier inversion. Different choices for the Hilbert space ℋ of interpolating functions are possible. In particular, we study the case where ℋ is (i) the space of bandlimited functions, or (ii) the space of spline functions of odd degree. The theory is applied to reconstructions from synthetic data as well as real MRI data.
Decay estimates of solutions for a hybrid system of flexible structures
Authors: Rao Bopeng
Published: September 2008

We consider a hybrid system consisting of a cable linked at its end to a rigid body. It is proved that such a hybrid system can be asymptotically stabilized by means of dissipative boundary feedbacks. Uniform decay estimates of energy are also established.
Optimal design of periodic antireflective structures for the Helmholtz equation
Authors: Dobson David C.
Published: September 2008

We study the problem of designing a periodic interface between two homogeneous materials with different impedance properties, in such a way that time-harmonic waves incident on the interface over a given range of angles have minimal total reflected energy. It is shown that the problem can be ‘relaxed’ to include continuously varying profiles. A simple gradient descent minimization scheme is proposed and examples from several numerical calculations are given.
Initiation of shape instabilities of free boundaries in planar Cauchy–Stefan problems
Authors: Zhu Qiang , Peirce Anthony , Chadam John
Published: September 2008

The linearized shape stability of melting and solidifying fronts with surface tension is discussed in this paper by using asymptotic analysis. We show that the melting problem is always linearly stable regardless of the presence of surface tension, and that the solidification problem is linearly unstable without surface tension, but with surface tension it is linearly stable for those modes whose wave numbers lie outside a certain finite interval determined by the parameters of the problem. We also show that if the perturbed initial data is zero in the vicinity of the front, but otherwise quite general, it does not affect the stability. The present results complement those in Chadam & Ortoleva [4] which are only valid asymptotically for large time or equivalently for slow-moving interfaces. The theoretical results are verified numerically.
Asymptotic stability for nonlinear PDEs with hysteresis
Authors: Kenmochi Nobuyuki , Visintin Augusto
Published: September 2008

Nonlinear evolution equations including hysteresis functionals are studied. It is the purpose of this paper to investigate the asymptotic stability of the solution as time t → + ∞. In the case when the forcing term of the equation tends to a time-independent function as t → + ∞, we shall show that the solution stabilizes at + ∞ and the system is asymptotically stable (equilibrium stability). In the case when the forcing term is periodic in time, we shall show that there is at least one periodic solution and that in some restricted cases the periodic solution is unique.
Global solutions of Maxwell's equations in an electromagnetic field with a temperature-dependent electrical conductivity
Authors: Yin Hong-Ming
Published: September 2008

This paper deals with Maxwell's equations in a quasi-stationary electromagnetic field subject to the effects of temperature. This model is encountered in the penetration of a magnetic field in substances where the electrical conductivity depends on the temperature. Similar phenomena also occur in some industrial problems such as the thermistor. Taking the effect of Joule heating into the consideration, we obtain a strongly coupled nonlinear system. Global solvability is established for this system.
Reducing parabolic partial differential equations to canonical form
Authors: Harper J. F.
Published: September 2008

A simple method of reducing a parabolic partial differential equation to canonical form if it has only one term involving second derivatives is the following: find the general solution of the first-order equation obtained by ignoring that term and then seek a solution of the original equation which is a function of one more independent variable. Special cases of the method have been given before, but are not well known. Applications occur in fluid mechanics and the theory of finance, where the Black-Scholes equation yields to the method, and where the variable corresponding to time appears to run backwards, but there is an information-theoretic reason why it should.
Propagation of frontal polymerization—crystallization waves
Authors: Volpert Vit. , Volpert Vl.
Published: September 2008

We consider polymerization–crystallization waves in a cylindrical reactor, in which monomer is converted to polymer in a planar front. The polymer is subsequently crystallized in a wider zone behind the front. Specifically, we study uniformly propagating polymerization–crystallization waves, and determine profiles of temperature, and concentrations of polymer and crystallized polymer, as well as the propagation velocity. A linear stability analysis of the travelling wave solutions indicates the possibility of Hopf bifurcation, which describes the transition to the experimentally observed spinning mode of propagation, in which a hot spot is observed to propagate along a helical path on the surface of the cylinder. Since conditions at the time of conversion determine the nature of the polymer produced, spiral hollows, which trace out a helical path, appear on the surface of the crystallized polymer product.
Travelling wave solutions of a reaction—infiltration problem and a related free boundary problem
Authors: Chadam John , Chen Xinfu , Comparini Elena , Ricci Riccardo
Published: September 2008

We consider travelling wave solutions of a reaction–diffusion system arising in a model for infiltration with changing porosity due to reaction. We show that the travelling wave solution exists, and is unique modulo translations. A small parameter ε appears in this problem. The formal limit as ε → 0 is a free boundary problem. We show that the solution for ε > 0 tends, in a suitable norm, to the solution of the formal limit.
Effective constitutive algorithms in elastoplasticity and elastoviscoplasticity
Authors: Nemat-Nasser Sia , Ni Luqun
Published: September 2008

The basic constitutive relations for elastoplasticity and elastoviscoplasticity are shown to form a typical boundary layer-type stiff system of ordinary differential equations. Three numerical algorithms are discussed: (i) The singular perturbation method (O'Malley, 1971a, b; Hoppensteadt, 1971; Miranker, 1981; Smith, 1985), which yields accurate results for both the rate-independent and rate-dependent cases, where in the former case, the algorithm is explicit, whereas in the latter case, it is implicit and requires the solution of a nonlinear equation; therefore it is impractical as a constitutive algorithm for large-scale finite-element applications, where the constitutive algorithm is used a great number of times at each finite-element node. (ii) The new constitutive algorithm (Nemat-Nasser, 1991; Nemat-Nasser & Chung, 1989, 1992) which is explicit and accurate for both the rate-independent and rate-dependent cases; the underlying mathematical feature of this new method is investigated, and it is shown that it can be classified as a simplified perturbation method; computable error bounds for this algorithm are obtained, and when the flow rule is given by the commonly used power law, it is shown that the errors are very small, (iii) A modified outer-solution method, which combines the above two techniques, and is simple, explicit, and accurate.
Nonstationary filtration in partially saturated porous media
Authors: Chen Xinfu , Friedman Avner , Kimura Tsuyoshi
Published: September 2008

Nonstationary two-dimensional filtration in a porous medium is considered, whereby part of the medium is saturated, another part is unsaturated but wet, and the remaining part is dry. The saturated/unsaturated and unsaturated/dry interfaces are free boundaries. It is shown that there exists a unique solution, and that the saturation function is continuous in the wet portion of the medium; this implies that the two interfaces are separated. Under some monotonicity-type conditions on the initial and boundary data it is shown that the free boundaries are continuous.
Nucleation of superconductivity in decreasing fields. I
Authors: Chapman S. J.
Published: September 2008

The bifurcation from a normally conducting to a superconducting state as an external magnetic field is lowered is examined using the Ginzburg-Landau theory. The results for three specific examples are reviewed, extended and unified in the framework of a systematic perturbation theory introduced in [1].
A mathematical model for washing a tow of fibres: Part 1
Authors: Terrill E. L. , Byatt-Smith J. G.
Published: September 2008

A mathematical model is presented for the washing of a band, or tow, of fibres which is pulled past a submerged obstacle. A lubrication flow between the obstacle and the tow is coupled to a flow through the tow, which is modelled as a porous medium. Coupled first-order ordinary differential equations for the fluid pressure and volume flux are solved numerically and the results are analysed. The washing of the tow induced by the reversal of the viscous boundary layers lying above and below the tow is discussed briefly. In Part 2, the model is extending to allow for fibre bending. The numerical solution of the resulting differential equation shows that at a critical value of the tow porosity, the tow touches the obstacle. An existence proof for a family of touching solutions is obtained. Using the existence of these solutions, a method for constructing a solution with a rubbing region, where the gap width is zero, is outlined. The numerical solutions for these solutions are also given.
The evolution of turbulent bursts: theb—ε model
Authors: Bertsch M. , Dal Passo R. , Kersner R.
Published: September 2008

We study the semi-empiricalb—ε model which describes the time evolution of turbulent spots in the case of equal diffusivity of the turbulent energy densityband the energy dissipation rate ε. We prove that the system of two partial differential equations possesses a solution, and that after some time this solution exhibits self-similar behaviour, provided that the system has self-similar solutions. The existence of such self-similar solutions depends upon the value of a parameter of the model.
Thermal runaway in a non-local problem modelling Ohmic heating: Part I: Model derivation and some special cases
Authors: Lacey A. A.
Published: September 2008

We consider the non-local problem

which models the temperature when an electric current flows through a material with temperature dependent electrical resistivity f(u) > 0, subject to a fixed potential difference. It is found that for some special cases where f is decreasing and

so the problem can be scaled to make

then:(a) for λ < 8 there is a unique steady state which is globally asymptotically stable: (b) for λ = 8 there is no steady state and u is unbounded; (c) for λ > 8 there is no steady state and u blows up for all x, – 1 < x < 1.
On nonclassical invertible transformations of hyperbolic equations
Authors: Sokolov V. V. , Svinolupov S. I.
Published: September 2008

The main result of this paper is a complete description of local invertible transformations

relating one equation of the form uxy = F(x, y, u, ux, uy) to another equation of the form υxy = G(x, y, υ, υx, υy).
Exceptional hyperbolic systems of Hamiltonian form
Authors: Carbonaro P.
Published: September 2008

Some years ago, Bluman [1] gave the ‘integrability conditions’ for a linear second-order hyperbolic Equation, i.e. the conditions under which it can be mapped invertibly to a constant coefficient wave equation. Considering that a second-order hyperbolic equation in two dimensions can be regarded as the hodograph representation of a 2x2 quasi-linear homogeneous system, one may wonder how the fulfilment of the above-mentioned integrability conditions is reflected in the structure of the quasi-linear system. The question is especially interesting if the quasi-linear system derives from a Hamiltonian density.
Thermal runaway in a non-local problem modelling Ohmic heating. Part II: General proof of blow-up and asymptotics of runaway
Authors: Lacey A. A.
Published: September 2008

We consider the non-local problem

It is found that for the case of decreasingfthen: (i) for

there is a unique steady state which is globally asymptotically stable; (ii) for

then the problem can be scaled so that

in which case: (a) for λ < 8 there is a unique steady state which is globally asymptotically stable; (b) for λ = 8 there is no steady state anduis unbounded; (c) for λ > 8 there is no steady state andublows up for allx, −1 <x, < 1. Some formal asymptotic estimates for the local behaviour ofuas it blows up are obtained.
Travelling waves in bubbly liquid with continuous bubble-size distribution
Authors: Gavrilyuk S. L.
Published: September 2008

An existence and uniqueness theorem for travelling waves in a bubbly liquid with a continuous bubble-size distribution is proved.
B-determining equations: applications to nonlinear partial differential equations
Authors: Kaptsov O. V.
Published: September 2008

We introduce the concept of B-determining equations of a system of partial differential equations that generalize the defining equations of the symmetry groups. We show how this concept may be applied to obtain exact solutions of partial differential equations. The exposition is reasonable self-contained, and supplemented by examples of direct physical importance, chosen from fluid mechanics.
Diffusion-driven instability in oscillating environments
Authors: Sherratt Jonathan A.
Published: September 2008

Diffusion-driven instability in systems of reaction-diffusion equations is a commonly used model for pattern formation in both embryology and ecology. In ecological applications, model parameters tend to oscillate in time, because of either daily or seasonal fluctuations in the environment. I investigate the effects of such fluctuations on diffusion-driven instability by considering analytically the possibility of Turing bifurcations when the parameter values (diffusion coefficients and kinetic parameters) oscillate in time between two sets of constant values, with a period that is either very short or very long compared to the time scale of the growth and predation kinetics. I show that oscillations in the kinetics can have quite different effects from oscillations in the dispersal terms. I also discuss the comparison between the solution forms predicted by linear theory and the numerical solutions of a simple nonlinear predator-prey model.
Approximation of the elastic deformation of a thin cylinder
Authors: Baldo Sisto
Published: September 2008

The elastic displacement of a thin cylinder subject to given forces is approximated by means of a function constructed from the solutions of certain one-dimensional problems. Estimates are given for the error in terms of a decreasing function of the radius of the cylinder.
Estimates for critical Mach number under isoperimetric constraints
Authors: Avkhadiev F. G. , Elizarov A. M. , Fokin D. A.
Published: September 2008

The problem of maximization of the critical Mach number in a subsonic flow of an ideal gas is considered. The Chaplygin gas approximation and the integral representation of the solution of the inverse boundary-value problem of aerohydrodynamics are used to reduce the problem to a special minimax one. The exact solution of the latter is obtained on the basis of the Lindelöf principle. An upper estimate for the critical Mach number is obtained. The results are generalized for the case of airfoil cascades. Some open problems are described.
Development of singularities in some moving boundary problems
Authors: King J. R.
Published: September 2008

We investigate the local behaviour at the boundary singularity for the following moving boundary problems: (i) Hele-Shaw flows in which the interface is initially non-analytic; (ii) power-law Hele-Shaw flows in which the interface contains a corner; (iii) Stefan problems in which the interface contains a corner. Both well-posed (‘injection’) and ill-posed (‘suction’) problems are considered. Related results for corner development in the presence of an impermeable boundary are also noted.
On the existence of solutions in plane quasistationary Stokes flow driven by surface tension
Authors: Prokert G.
Published: September 2008

Recently, the free boundary problem of quasistationary Stokes flow of a mass of viscous liquid under the action of surface tension forces has been considered by R. W. Hopper, L. K. Antanovskii, and others. The solution of the Stokes equations is represented by analytic functions, and a time dependent conformal mapping onto the flow domain is applied for the transformation of the problem to the unit disk. Two coupled Hilbert problems have to be solved there, which leads to a Fredholm boundary integral equation. The solution of this equation determines the time evolution of the conformal mapping. The question of the existence of a solution to this evolution problem for arbitrary (smooth) initial data has not yet been answered completely. In this paper, local existence in time is proved using a theorem of Ovsiannikov on Cauchy problems in an appropriate scale of Banach spaces. The necessary estimates are obtained in a way that is oriented at the a priori estimates for the solution given by Antanovskii. In the case of small deviations from the stationary solution represented by a circle, these a priori estimates, together with the local results, are used to prove even global existence of the solution in time.
Asymptotics of slow flow of very small exponent power-law shear-thinning fluids in a wedge
Authors: Brewster M. E. , Chapman S. J. , Fitt A. D. , Please C. P.
Published: September 2008

The incompressible slow viscous flow of a power-law shear-thinning fluid in a wedge-shaped region is considered in the specific instance where the stress is a very small power of the strain rate. Asymptotic analysis is used to determine the structure of similarity solutions. The flow is shown to possess an outer region with boundary layers at the walls. The boundary layers have an intricate structure consisting of a transition layer 0(ɛ) adjoining an inner layer O(ɛlnɛ), which further adjoins an inner-inner layer 0(ɛ) next to the wall. Explicit solutions are found in all the regions and the existence of ‘dead zones’ in the flow is discussed.
On boundary value problems in fracture of elastic Composites
Authors: Mishuris Gennady S. , Olesiak Zbigniew S.
Published: September 2008

We present a method of solution of a class of fracture problems in the theory of elasticity. The method can be applied to any problem reducible to Poisson's equation, e.g. heat conduction and mass diffusion in solids, theory of consolidation and the like. The novelty of the paper is that we address regions of layered composites with notches, or, in a particular case, with a crack. Within the framework of classical analysis, we apply Fourier and Mellin transforms, 'fit' them together, and reduce the problem to solving a singular integral equation with fixed singularities on a semi-axis. We show the existence and uniqueness of solutions of the equations under consideration, and justify the asymptotics necessary for applications. We show the practical usefulness of the method on the examples of an antiplane problem of fracture mechanics. From our solution, we are able to find the stress intensity factor in the case when a crack tip penetrates a layered composite consisting of 60 layers, and show the limits of applicability of the anisotropic model of such composites.
Fluid flow in a medium distorted by a quasiconformal map can produce fractal boundaries
Authors: Martio Olli , Øksendal Bernt
Published: September 2008

Physical experiments indicate that when an expanding fluid flows through a porous rock then the boundary between the wet and the dry region can be very irregular (e.g. see [OMBAFJ] and the references therein). In fact, it has been conjectured that this boundary is a fractal with Hausdorff dimension about 2.5. The (one-phase) fluid flow in a porous medium can be modelled mathematically by a system of partial differential equations, which, under some simplifying assumptions, can be reduced to a family of semi-elliptic boundary value problems involving the (unknown) pressure p(x) of the fluid (at the point x and at t) and the (unknown) wet region Ut at time t. (See equations (1.5)–(1.7) below). This set of equations, called the moving boundary problem involves the permeability matrix K(x) of the medium at x. A question which has been debated is whether this relatively simple mathematical model can explain such a complicated fractal nature of ∂Ut. More precisely, does there exist a symmetric non-negative definite matrix K(x) such that the solution Ut of the corresponding (expanding) moving boundary problem has a fractal boundary? The purpose of this paper is to prove that this is indeed the case. More precisely, we show that a porous medium which produce fractal wet boundaries can be obtained by distorting a completely homogeneous medium by means of a quasiconformal map.
Asymptotic behaviour of functional-differential equations with proportional time delays
Authors: Liu Yunkang
Published: September 2008

This paper discusses the initial value problem

whereA, BiandCiared × dcomplex matrices,pi,qi∈ (0, 1),i= 1, 2, …, andy0is a column vector in ℂd. By using ideas from the theory of ordinary differential equations and the theory of functional equations, we give a comprehensive analysis of the asymptotic behaviour of analytic solutions of this initial value problem.
Non-equilibrium imbibition of a porous block
Authors: Gilman Arkady
Published: September 2008

We consider a phenomenological model proposed by Barenblatt [1] for non-equilibrium two-phase flow in porous media. In the case of zero total flow it reduces to a pair of equations:

where Φ(σ) is a non-decreasing (not necessarily increasing) smooth function defined in the interval 0 ≤ σ ≤ 1. We consider initial-boundary problems for this system in which the initial data are given only for s, and the boundary data only for ς (which corresponds to the physical sense of the model). The degenerate character of the system allows us to apply simple topological methods. We show that the boundary problem is well-posed, in the sense that there exits a unique (weak) solution which satisfies the maximum principle and depends continuously on the initial data. The solution is no less smooth than the initial and boundary data.
Existence of solutions for elastohydrodynamic piezoviscous lubrication problems with a new model of cavitation
Authors: Bayada G. , Talibi M. El Alaoui , Vázquez C.
Published: September 2008

The purpose of this paper is to study a mathematical model of lubricating flow between elastic surfaces obeying the linear Hertzian theory when cavitation takes place. Cavitation is a free boundary phenomenon that is described in this paper by the New Elrod–Adams model. This model introduces the concentration of fluid as well as the pressure as unknown functions and is suggested in preference to the classical variational inequality due to its ability to describe inflow and outflow. This leads to a nonlinear variational and nonlocal equation. Herein, an existence theorem is proved by means of two different techniques.
A note on the classical solution of a two-dimensional superconductor free boundary problem
Authors: Yi Fahuai
Published: September 2008

In this paper we consider a superconductor free boundary problem. Under isothermal conditions, a superconductor material (of ‘type I’) will develop two phases separated by a sharp interface Γ(t). In the ‘normal’ conducting phase the magnetic field is divergence free and satisfies the heat equation, whereas on the interface Γ(t), curl , where n is the normal and Vn is the velocity of Γ(t) in the direction of n; further, (constant) on Γ(t). Existence and uniqueness of a classical solution locally in time are established by Newton's iteration method under assumptions which enable us to reduce the 3-dimensional problem to a problem depending on essentially two space variables.
Variational model of sandpile growth
Authors: Prigozhin Leonid
Published: September 2008

A model describing the evolving shape of a growing pile is considered, and is shown to be equivalent to an evolutionary quasi-variational inequality. If the support surface has no steep slopes, the inequality becomes a variational one. For this case existence and uniqueness of the solution are proved.
Spherically symmetric Stefan problem with the Gibbs–Thomson law at the moving boundary
Authors: Götz I. G. , Primicerio M.
Published: September 2008

This paper deals with the spherically symmetric Stefan problem in three space dimensions. The melting temperature satisfies the Gibbs–Thomson law. The solution is obtained as a limit of solutions of similar problems containing a small additional kinetic term in the melting temperature. Under some structural assumptions we show that the phase-change boundary has at most one discontinuity point t = T0 (see the corresponding result for the planar Stefan problem in Götz & Zaltzman (1995)). In the one-phase problem the discontinuity point always exists. At the time T0 the whole solid phase melts instantaneously. We study also the asymptotical stability (t → ∞) of stationary solutions satisfying boundary conditions of thermostat type.
Self-similarity in the post-focussing regime in porous medium flows
Authors: Angenent S. B. , Aronson D. G.
Published: September 2008

In the focussing problem for the porous medium equation, one considers an initial distribution of material outside some compact set K. As time progresses material flows into K, and at some finite time T first covers all of K. For radially symmetric flows, with K a ball centred at the origin, it is known that the intermediate asymptotics of this focussing process is described by a family of self-similar solutions to the porous medium equation. Here we study the postfocussing regime and show that its onset is also described by self-similar solutions, even for nonsymmetric flows.
Models for thin viscous sheets
Authors: Howell P. D.
Published: September 2008

Leading-order equations governing the dynamics of a two-dimensional thin viscous sheet are derived. The inclusion of inertia effects is found to result in an ill-posed model when the sheet is compressed, and the resulting paradox is resolved by rescaling the equations over new length-and timescales which depend on the Reynolds number of the flow and the aspect ratio of the sheet. Physically this implies a dominant lengthscale for transverse displacements during viscous buckling. The theory is generalized to give new models for fully three-dimensional sheets.
Explicit solutions for LBIC signals in semiconductors by asymptotic method
Authors: Cumberbatch Ellis , Fang Weifu
Published: September 2008

A non-destructive testing technique to obtain information on the electrical structure in semiconductor materials involves traversing the material surface with a laser beam, and measuring induced currents generated by the beam's interaction with the electrical field. A mathematical model has been established, and the inverse problem of reconstructing the electrical structure from the current image has been studied. Here we obtain explicit solutions for simple structures (p–n and p–n–p junctions) in the asymptotic limit of strong doping. Comparison with numerical results show that the asymptotic solutions are quite accurate. These solutions may provide a quick way to identify the doping profile by matching actual current signals to a class of simple functions.
Asymptotic profiles of a decaying contaminant in transport through a porous medium
Authors: Escobedo M. , Grundy R. E.
Published: September 2008

In this paper we construct formal large-time solutions of a model equation, with initial data possessing bounded support, describing transport of a reacting and decaying contaminant in a porous medium. This we do in one, two and three space dimensions where, depending on the reaction model used, the solution may or may not have bounded support for all time. In the former case, working with what we call the reduced equation, we prove convergence, in one space dimension, to an outer limit as t → ∞. The outer solution has to be supplemented by inner solutions valid near the edges of the support. These inner solutions take the form of decaying travelling waves which we analyse using phase plane methods. Using the travelling waves as sub- and super-solutions, we establish the large-time behaviour of the interfaces which we refine using asymptotic matching. These ideas can be formally extended to higher space dimensions where we deduce the shape of the support of the large-time profiles which turns out to be ellipsoidal. For reaction models where the support is unbounded we prove convergence of the solution of the reduced equation to a travelling and decaying fundamental solution of the linear heat equation with convection and absorption. Finally, we indicate how the results for the reduced equations can be formally embedded in an asymptotic analysis of the original model equation.
An analysis of phase transition models
Authors: Fasano A. , Primicerio M.
Published: September 2008

We consider phase transition processes in which the thermodynamic variables are the temperature and an order parameter. Various classes are identified and many specific examples are illustrated. In this framework the question of the range of applicability of the so-called ‘additivity rules’ is investigated, showing that they apply only to a very special type of processes.
Maximal viscosity solutions of the modified porous medium equation and their asymptotic behaviour
Authors: Hulshof Josephus , Vazquez Juan Luis
Published: September 2008

We construct a theory for maximal viscosity solutions of the Cauchy problem for the modified porous medium equation ut + γ|ut| = Δ(um) with γ∈(−1, 1) and m > 1. We investigate the existence, uniqueness, finite propagation speed and optimal regularity of these solutions. As a second main theme, we prove that the asymptotic behaviour is given by a certain family of self-similar solutions of the so-called second kind with anomalous similarity exponents.
On a Signorini problem for inclusions in shells
Authors: Khludnev A. M.
Published: September 2008

We consider an equilibrium problem for a thin inclusion in a shell. The faces of the inclusion are assumed to satisfy a non-penetration condition, which is an inequality imposed on the tangential shell displacements. The properties of the solution are studied, in particular, the smoothness of the stress field in the vicinity of the inclusion. The tangential displacements are proved to belong to the space H2 near the internal points of the inclusion. The character of the contact between the inclusion faces is described in terms of a suitable non-negative measure. The stability of the solution is investigated for small perturbations to the inclusion geometry.
Reduction of systems of nonlinear partial differential equations to simplified involutive forms
Authors: Reid Gregory J. , Wittkopf Allan D. , Boulton Alan
Published: September 2008

We describe an algorithm which uses a finite number of differentiations and algebraic operations to simplify a given analytic nonlinear system of partial differential equations to a form which includes all its integrability conditions. This form can be used to test whether a given differential expression vanishes as a consequence of such a system and may be more amenable to numerical or analytical solution techniques than the original system. It is also useful for determining consistent initial conditions for such a system. A computer implementable version of our algorithm is given for polynomially nonlinear systems of partial differential equations. This version uses Grobner basis techniques for constructing the radical of the polynomial ideal generated by the equations of such systems.