bluuebunny/crossref_metadata_2025 huggingface dataset:
Addressee co-operation and request reformulation in young children
Authors: Marcos Haydée , Bernicot Josie
Published: September 2008

The purpose of the present study was to show that children under age 3;0 are capable of reformulating requests in different ways depending on how their addressee responds to the request. This adaptive ability is considered to be an indication of the use of both communicative and conversational skills. Children from French-speaking families were observed at two developmental thresholds: the end of the prelinguistic period (1;6) and the start of the linguistic period (2;6). The verbal and nonverbal outputs of the two groups of 12 children (1;6 and 2;6) were compared in three object request situations: the adult immediately complies with the request (satisfaction), the adult asks a clarification question (clarification), and the adult refuses to comply with the request (refusal). The ways in which the children adapted to each situation were found to be similar at the two ages considered. In the clarification situation, vocal productions and their repairs were more numerous, whereas in the refusal situation, non-reformulations and gazes to and from the requested object and addressee predominated. The discussion deals with the significance of these results in the development of communicative and conversational skills in children.
A developmental study of the acquisition of colour terms in Setswana
Authors: Davies Ian , Corbett Greville , McGurk Harry , Jerrett David
Published: September 2008

We report a study of the acquisition of colour terms by speakers of Setswana, the language of Botswana in Southern Africa. This was carried out as a test of Berlin & Kay's theory of colour term universals, on a language with less than the maximum complement of eleven basic colour terms, and in order to document changes in Setswana under the impact of economic development. Seventy-seven five- to nine-year-olds were studied on two colour tasks: elicited lists and colour naming. In general the data were consistent with Berlin & Kay's theory: the rank order of frequency of correct use of colour terms was similar to the order of the Berlin & Kay hierarchy; and primary colour terms were offered more frequently and were more likely to be used correctly than secondary colour terms. The use of English colour terms was prevalent, especially amongst the younger groups, but they functioned as substitutes for Setswana terms, rather than as a means to fill the vacant basic colour term slots.
Children's songs to infant siblings: parallels with speech
Authors: Trehub Sandra E. , Unyk Anna M. , Henderson Joanna L.
Published: September 2008

Children aged 2;11 to 8;3 sang informally, once in the presence of their infant sibling and once when the infant was out of view. Paired excerpts from 22 children were presented to adult listeners, who were required to identify the infant-directed excerpt in each pair. Listeners' accuracy was above chance levels but below what would be expected for mothers' singing in comparable contexts. Children altered their singing style in the infant's presence by singing at a higher pitch level and with a different vocal quality.
Production as a source of input for analysis: evidence from the developmental course of a word-blend
Authors: Elbers Loekie
Published: September 2008

Theoretical arguments for considering production as a source of input for analysis (the OUTPUT-AS-INPUT hypothesis) are reviewed, and empirical evidence supporting this hypothesis is presented. The evidence consists of a longitudinal study of the developmental course of a self-created form, produced by one Dutch child. This form is the product of blending two words,watandiets, to yield unitarywat-iets. In Dutch, independentwatandietsmay each mean ‘some’ and/or ‘something’. Thoughwat-ietsis not permitted by the language, and so does not occur in environmental input, the form stays in the child's repertoire for about 10 months (between 3;8 and 4;7) and is apparently subjected to processes of generalization: first the child treatswat-ietsas a two-word frame that may be regularized, later as a unitary word that may be semantically extended. After the extension ofwat-iets, independent synonymouswatandietsappear for the first time in the child's speech. It is argued that the child actually analysed his own creation.
The effect of conversational setting on topic continuation in mother–child dyads
Authors: Kertoy Marilyn K. , Vetter Dolores Kluppel
Published: September 2008

Twelve children (five boys and seven girls, mean age 4;1) interacted with their mothers in two conversational settings: playing with a favourite toy and helping to prepare lunch or muffins. The percentage of two topic continuation processes – topic incorporation and collaboration – used by mothers and children was analysed. It was hypothesized that the help setting with a predetermined structure would elicit a greater percentage of topic incorporation by the dyads than the play setting. In fact, the play setting elicited a greater percentage of topic incorporation from mothers than the help setting. Children did not differ significantly in the percentage of use of topic incorporation between the two settings, but appeared to be equally proficient in incorporating topics in settings with and without a predetermined structure. The play setting also elicited more topic collaboration from the children than the help setting. While the help setting appeared to support collaborative action, the play setting permitted the dyads to be informative about the toys as well as related topics. Therefore, the two settings provided different opportunities for the dyads to continue topics.
How shall a deceptive thing be called?
Authors: Merriman William E. , Jarvis Lorna H. , Marazita John M.
Published: September 2008

Thirty-six three-, four- and five-year-olds were asked to select labels for deceptive stimuli (e.g. for an eraser that looked like a pencil). Three types of labelling were investigated –simple (e.g. ‘is an eraser’); appearance-predicated (e.g. ‘looks like an eraser’); and reality-predicated (e.g. ‘is really and truly an eraser’). An age-related appearance-reality shift was observed in simple labelling (e.g. older children were more likely than younger ones to accepteraserand rejectpencilas simple names for the pencil-eraser). This trend was robust over method and semantic domain, though weaker with object than with colour labels. As in previous research, older children were more likely than younger ones to map different appearance- than reality-predicated labels onto an item (e.g. to accept that the pencil-eraser looks like a pencil, but is really and truly an eraser); however, all age groups were reluctant to extend more than one name to a stimulus via a common predicate (e.g. to accept two reality-predicated labels for the same object). This one-label-per-predicate pattern was observed more frequently within reality than within appearance predicates; more frequently with colour than with object names, and with questions blocked by predicate than by name. It is argued that younger children maintained this pattern because of inflexible encoding, but that older ones did so because of better understanding of the appearance-reality distinction, greater reality dominance, and a Mutual Exclusivity bias.
Cross-language synonyms in the lexicons of bilingual infants: one language or two?
Authors: Pearson Barbara Zurer , Fernández Sylvia , Oller D. K.
Published: September 2008

This study tests the widely-cited claim from Volterra & Taeschner (1978), which is reinforced by Clark's Principle Of Contrast (1987), that young simultaneous bilingual children reject cross-language synonyms in their earliest lexicons. The rejection of translation equivalents is taken by Volterra & Taeschner as support for the idea that the bilingual child possesses a single-language system which includes elements from both languages. We examine first the accuracy of the empirical claim and then its adequacy as support for the argument that bilingual children do not have independent lexical systems in each language. The vocabularies of 27 developing bilinguals were recorded at varying intervals between ages 0;8 and 2;6, using the MacArthur GDI, a standardized parent report form in English and Spanish. The two single-language vocabularies of each bilingual child were compared to determine how many pairs of translation equivalents (TEs) were reported for each child at different stages of development. TEs were observed for all children but one, with an average of 30% of all words coded in the two languages, both at early stages (in vocabularies of 2–12 words) and later (up to 500 words). Thus, Volterra & Taeschner's empirical claim was not upheld. Further, the number of TEs in the bilinguals' two lexicons was shown to be similar to the number of lexical items which co-occurred in the monolingual lexicons of two different children, as observed in 34 random pairings for between-child comparisons. It remains to be shown, therefore, that the bilinguals' lexicons are not composed of two independent systems at a very early age. Furthermore, the results appear to rule out the operation of a strong principle of contrast across languages in early bilingualism.
The bilingual lexicon: implications for studies of language choice
Authors: Quay Suzanne
Published: September 2008

Lexical gaps in vocabulary development have been acknowledged as a reason for language mixing in young bilingual children. In spite of this, most studies do not take into account whether young bilinguals have the lexical resources to make a choice between their two languages. Inferences are nevertheless still being made about whether or not young bilinguals differentiate between their two languages based on language choice. It is widely believed, however, that young bilinguals do not have the resources to make lexical choices at a pre-syntactic stage of development before age two. A bilingual case study of an infant acquiring Spanish and English from birth to age 1;10 is used to address this issue. Daily diary records and weekly video recordings in the two language contexts are used to construct the child's lexicon and to establish that translation equivalents that make possible language choice are available from the beginning of speech. The results are used to discuss the importance of translation equivalents in the bilingual lexicon for viable interpretations of language choice.
The use of props in a syntactic awareness task
Authors: Blackmore Amanda Marie , Pratt Chris , Dewsbury Alison
Published: September 2008

The study investigated the effects of using props to illustrate the meaning of sentences in a syntactic awareness task in which subjects were required to correct ungrammatical sentences. Forty preschool children (aged 4;11 to 5;11) were asked to correct 20 sentences, 10 of which were illustrated using props, and 10 of which were not. Children scored significantly higher in the props condition though the proportion of meaning-changing errors to total errors was not significantly lower in this condition. It is argued that the use of props, by providing contextual support, reduces the processing capacity required to complete the task.
Early lexical acquisition and the vocabulary spurt: a response to Goldfield & Reznick
Authors: Mervis Carolyn B. , Bertrand Jacquelyn
Published: September 2008

Vocabulary development of three children (aged 1;6–1;8 at the start of the study) who had not begun to evidence a vocabulary spurt even though their productive vocabularies already included well over 50 words was followed to determine if these children eventually would have a vocabulary spurt. All three children evidenced a spurt, beginning at a mean productive vocabulary size of 112 words. The vocabulary spurt occurred at about the same time as the children first demonstrated the ability to sort objects exhaustively and to fast map new object names. Results are discussed in the context of Goldfield & Reznick's (1990; Reznick & Goldfield, 1992) argument that a substantial proportion of children never evidence a vocabulary spurt.
The acquisition of phonology by Cantonese-speaking children
Authors: So Lydia K. H. , Dodd Barbara J.
Published: September 2008

Little is known about the acquisition of phonology by children learning Cantonese as their first language. This paper describes the phoneme repertoires and phonological error patterns used by 268 Cantonese-speaking children aged 2;0 to 6;0, as well as a longitudinal study of tone acquisition by four children aged 1;2 to 2;0. Children had mastered the contrastive use of tones and vowels by two years. While the order of acquisition of consonants was similar to that reported for English, the rate of acquisition was more rapid. The developmental error patterns used by more than 10% of children are also reported as common in other languages. However, specific rules associated with Cantonese phonology were also identified. Few phonological errors were made after age four. The results are consistent with the hypothesis that the ambient language influences the implementation of universal tendencies in phonological acquisition.
Early acquisition of verbs in Korean: a cross-linguistic study
Authors: Choi Soonja , Gopnik Alison
Published: September 2008

This cross-linguistic study investigates children's early lexical development in English and Korean, and compares caregivers' linguistic input in the two languages. In Study 1, the lexical development of nine Korean children was followed from 1;2 to 1;10 by monthly visits and maternal reports. These Korean data were compared to previously collected English longitudinal data. We find that: (1) Korean children as young as 1;3 use verbs productively with appropriate inflections. (2) Seven of the nine children show a verb spurt at around 1;7; for six of these children the verb spurt occurs before the noun spurt. No such early verb spurt is found in the English data. Unlike in English, both verbs and nouns in Korean are dominant categories from the single-word stage. (3) Korean children express language-specific distinctions of locative actions with verbs. Study 2, a crosslinguistic study of caregivers' input in English and Korean, shows that Korean mothers provide more action verbs but fewer object nouns than American mothers. Also, Korean mothers engage in activity-oriented discourse significantly more than American mothers. Our study suggests that verbs are accessible to children from the beginning, and that they may be acquired early in children who are encouraged to do so by their language-specific grammar and input.
Reference states and reversals: undoing actions with verbs
Authors: Clark Eve V. , Carpenter Kathie L. , Deutsch Werner
Published: September 2008

The purpose of these studies is to characterize children's conception of reversal and its relation to a reference state. A reversal is the move from one state to some prior state of affairs. For example, shoes that have been TIED can be UNTIED, parcels WRAPPED then UNWRAPPED, and dishes COVERED then UNCOVERED. The present studies were designed to find out how children (aged 1;0 to 5;0) describe reversals of action that restore objects to a prior, less constrained, state. In English, the prefix un- offers the most productive device for this, but, initially, children rely on a verb like open, on general purpose undo, and on particles like out and off, As they acquire un-, English-speaking children must learn that this prefix applies primarily to verbs for change-of-state, often for enclosing, covering and attaching. In German, there is no reversal prefix, but there are productive particles. German-speaking children also begin with a verb like open and then turn to verb particles on a course similar to that in English to express reversals.
An examination of similarity neighbourhoods in young children's receptive vocabularies
Authors: Charles-Luce Jan , Luce Paul A.
Published: September 2008

Based on an analysis of similarity neighbourhoods of words in children's lexicons, Dollaghan (1994) argues that because of the degree of phonological overlap among lexical items in memory, children must perform detailed acoustic-phonetic analyses in order to recognize spoken words. This is in contradiction to Charles-Luce & Luce (1990), who reported that the similarity neighbourhoods in younger children's expressive lexicons are sparse relative to older children's and adult lexicons and that young children may be able to use more global word recognition strategies. The current investigation re-examined these issues. Similarity neighbourhoods of young children's RECEPTIVE vocabularies were analysed for three-phoneme, four-phoneme and five-phoneme words. The pattern of the original results from Charles-Luce & Luce (1990) was replicated.
Context-sensitive underspecification and the acquisition of phonemic contrasts
Authors: Dinnsen Daniel A.
Published: September 2008

Several competing proposals for the (under)specification of phonological representations are evaluated against the facts of phonemic acquisition. Longitudinal evidence relating to the emergence of a voice contrast in the well-documented study of Amahl (from age 2;2 to 3;11) is reconsidered. Neither contrastive specification nor context-free radical underspecification is capable of accounting for the facts. The problem is in the characterization of the change in the status of a feature from being noncontrastive and conditioned by context at one stage to being contrastive with phonetic effects that diffuse gradually through the lexicon. Both frameworks must treat as accidental the persistence of the early substitution pattern and require the postulation of wholesale changes in underlying representations, where these changes do not accord well with the observed phonetic changes or with the facts available to the learner. Context-sensitive radical underspecification provides a plausible account of each stage and the transition between stages with minimal grammar change.
The development of syntactic subjects in Portuguese-speaking children
Authors: Valian Virginia , Eisenberg Zena
Published: September 2008

In order to separate competence and performance factors in acquisition of knowledge of syntactic subjects, we audiotaped and analysed the spontaneous speech of 20 Portuguese-speaking two-year-olds in natural conversation with Portuguese-speaking adults. We separated the children into three groups based on Mean Length of Utterance in Words: 1·5–1·99; 2·0–2·99; 3·0–4·99. Our cross-sectional data demonstrated that Portuguese-speaking children increased their use of subjects from 28% in the lowest-MLUW group to 57% in the highest-MLUW group. The children in the highest-MLUW group almost perfectly matched the adult speakers in the study on every measure. The increase in children's use of subjects was primarily due to an increase in the use of pronominal subjects. A comparison between Portuguese- and English-speaking children suggests that adult competence about the status of subjects is present at the onset of combinatorial speech, as shown by differential production of subjects. Each group also experiences performance limitations, as shown by the increase in subject use as development proceeds.
Early passive acquisition in Inuktitut
Authors: Allen Shanley E. M. , Crago Martha B.
Published: September 2008

Passive structures are typically assumed to be one of the later acquired constructions in child language. English-speaking children have been shown to produce and comprehend their first simple passive structures productively by about age four and to master more complex structures by about age nine. Recent crosslinguistic data have shown that this pattern may not hold across languages of varying structures. This paper presents data from four Inuit children aged 2;0 to 3;6 that shows relatively early acquisition of both simple and complex forms of the passive. Within this age range children are productively producing truncated, full, action and experiential passives. Some possible reasons for this precociousness are explored including adult input and language structure.
Colour term knowledge in two-year-olds: evidence for early competence
Authors: Shatz Marilyn , Behrend Douglas , Gelman Susan A. , Ebeling Karen S.
Published: September 2008

It is commonly believed that colour terms are acquired unusually slowly. However, several recent studies suggest that preschoolers have more colour term knowledge than previously believed. In two studies, we investigated the colour term knowledge of 49 two-year-olds and the influence of schooling on their colour term acquisition. Both studies revealed considerable knowledge in such young children. A longitudinal comparison of children with and without school experience in Study 2 indicated that the higher performance of the school group could not be accounted for by differences predating that group's experience. In reviewing the evidence from the children's performance, we conclude that contemporary children's early and frequent experience with colour terms may account for this cohort's improved performance over previous generations of children.
Developmental changes in the incidence and likelihood of simultaneous talk during the first two years: a question of function
Authors: Elias Gordon , Broerse Jack
Published: September 2008

Global tendencies for the relative absence of covocalization (simul- taneous talk) have been identified in both conversations between adult partners and conversations between mothers and their infants; in each case, the alternating mode in which one partner speaks at a time is predominant. The present investigation examined the timing of the partners' talk in mother-infant engagements over infant age to determine whether: (a) variations occur in the incidence of the alternating mode; and (b) variations occur in the extent to which the alternating mode predominates. Conversations involving a total of 48 mothers and their infants aged from 0;3 to 2;0 were investigated at each of eight infant ages (0;3, 0;6, 0;9, 1;0, 153, 1;6, 1;9 and 2;0). The results indicated that, within a global tendency for the relative absence of covocalization, there was: (a) a curvilinear tendency for the incidence of covocalization to decrease over the first 18 months, and then to increase; and (b) a linear tendency for the extent to which the alternating mode predominates to increase over age. These changes are interpreted as reflecting the facilitative effects of covocalization in the case of young preverbal infants, and the need for the alternating, turn-taking pattern to predominate as mutual comprehension becomes possible in conversations between mothers and their older infants.
On the generalized pantograph functional-differential equation
Authors: Iserles A.
Published: September 2008

The generalized pantograph equation y′(t) = Ay(t) + By(qt) + Cy′(qt), y(0) = y0, where q ∈ (0, 1), has numerous applications, as well as being a useful paradigm for more general functional-differential equations with monotone delay. Although many special cases have been already investigated extensively, a general theory for this equation is lacking–its development and exposition is the purpose of the present paper. After deducing conditions on A, B, C ∈ ℂd×d that are equivalent to well-posedness, we investigate the expansion of y in Dirichlet series. This provides a very fruitful form for the investigation of asymptotic behaviour, and we duly derive conditions for limt⋅→∞y(t) = 0. The behaviour on the stability boundary possesses no comprehensive explanation, but we are able to prove that, along an important portion of that boundary, y is almost periodic and, provided that q is rational, it is almost rotationally symmetric. The paper also addresses itself to a detailed analysis of the scalar equation y′(t) = by(qt), y(0) = 1, to high-order pantograph equations, to a phenomenon, similar to resonance, that occurs for specific configurations of eigenvalues of A, and to the equation Y′(t) = AY(t) + Y(qt) B, Y(0) = Y0.
Remarks on the Reynolds problem of elastohydrodynamic lubrication
Authors: Rodrigues José-Francisco
Published: September 2008

The mathematical model of the flow of a viscous lubricant between elastic bearings leads to the study of a highly non-linear and non-local elliptic variational inequality. We discuss the existence of a solution by using an a prioriL∞-estimate. This method allows us to solve a large class of problems, including those arising from the linear Hertzian theory, and yields new existence results for the cases of a pressure-dependent viscosity or the inclusion of a load constraint. For small data the uniqueness of the solution holds, and we show that in the cylindrical journal bearing problem with small eccentricity ratio, the free boundary is given by two disjoint differentiable arcs close to the free boundary of the first-order approximate solution.
Hele–Shaw flows with a free boundary produced by multipoles
Authors: Entov Vladimir M. , Etingof Pavel I. , Kleinbock Dmitry Ya.
Published: September 2008

We study Hele–Shaw flows with a moving boundary and multipole singularities. We find that such flows can be defined only on a finite time interval. Using a complex variable approach, we construct a family of explicit solutions for a single multipole. These solutions turn out to have the maximal possible lifetime in a certain class of solutions.

We also discuss the generalized Hele-Shaw model in which surface tension at the moving boundary is considered, and develop a method of finding steady shapes. This method yields new one-parameter families of stationary solutions. In the Appendix we discuss a connection between these solutions and a variational problem of potential theory.
A mathematical model of damage accumulation taking into account microstructural effects
Authors: Barenblatt G. I. , Prostokishin V. M.
Published: September 2008

It is shown that the influence of microstructure in the damage accumulation process leads to a nonlinear diffusion effect, with a strongly stress-dependent diffusion coefficient. A nonlinear parabolic equation with a source term is obtained for the damage parameter. This equation is relevant to blow-up and quenching problems well known to mathematicians with rupture corresponding to blow-up or quenching. However, the damage accumulation equation possesses an additional nonlinearity due to the non-healing of damage. Depending on the value of a dimensionless constant parameter (the ratio of a properly defined microstructural length-size to a characteristic length-size of the initial damage distribution), two essentially different types of damage accumulation process appear to be possible for a given initial damage distribution over the bar length. In processes of the first type, the damage accumulation remains non-homogeneous over the length of the bar, so that the lifetime for the whole specimen is determined by the maximal initial damage within the bar. For processes of the second type the damage distribution over the specimen at first becomes homogeneous (at least in a considerable part of specimen), and then the damage accumulation proceeds uniformly over all or part of the specimen. The lifetime for processes of the second type is essentially longer than the first. Results of a numerical experiment based on the proposed model are presented. In particular, the origin and development of damage propagation waves is demonstrated. Also, it is demonstrated that when there is substantial damage transfer, the ultimate value of the damage parameter in the life-time calculation is of no significance.
Asymptotic evaluation of oscillatory sums
Authors: Keller Joseph B. , Knessl Charles
Published: September 2008

A stationary phase method is developed for the asymptotic evaluation, as R → ∞, of oscillatory sums of the form

It is extended to multidimensional sums. Numerical comparisons demonstrate the accuracy of the asymptotic approximations. The results are applied to the practical estimation of the number of lattice points in large domains in ℝ2.
Some mathematical results in the pricing of American options
Authors: Dewynne J. N. , Howison S. D. , Rupf I. , Wilmott P.
Published: September 2008

We examine the Black–Scholes partial differential equation for the pricing of a traded option (an American call option on an asset paying a continuous dividend) and make comparisons with other well known free boundary diffusion problems, such as the oxygen consumption problem. The pricing of American options can be viewed as a free boundary problem and is, therefore, inherently nonlinear. We consider the short and long time behaviour of the free boundary, present analytic results for the option value in such limits, and consider the formulation of the problem as a variational inequality, and its numerical solution.
The Stefan problem with surface tension in the three dimensional case with spherical symmetry: nonexistence of the classical solution
Authors: Meirmanov A. M.
Published: September 2008

The Stefan problem with surface tension in the three-dimensional case with spherical symmetry is considered. We first establish the existence and uniqueness of the classical solution with surface tension and kinetic undercooling effects for all time, and then pass to the limit as the kinetic undercooling tends to zero. The limiting solution is the global-in-time weak solution and the local-in-time classical solution for the Stefan problem with surface tension. This solution cannot be the global-in-time classical solution. If S(t) is the radius of a solid ball in a supercooled liquid, then (1) there exists at least one point t* of discontinuity of the function S(t):

or (2) the continuous function S(t) cannot be absolutely continuous, and it maps some zero-measure set of (t*, T*) onto some set of Ω with a strictly positive measure.
Mullins–Sekerka stability analysis for melting-freezing waves in helium
Authors: Fehribach Joseph D.
Published: September 2008

This paper considers the stability of melt-solid interfaces to eigenfunction perturbations for a system of equations which describe the melting and freezing of helium. The analysis is carried out in both planar and spherical geometries. The principal results are that when the melt is freezing, under certain far-field conditions, the interface is stable in the sense of Mullins and Sekerka. On the other hand, when the solid is melting (at least when the melting is sufficiently fast), the interface is unstable. In some circumstances these instabilities are oscillatory, with amplitude and growth rate increasing with surface tension and frequency. The last section considers the original problem of Mullins and Sekerka in the present notation.
On roll, square and hexagonal cellular flames
Authors: Kuske R. , Matkowsky B.J.
Published: September 2008

We consider the behaviour of a premixed flame anchored on a flat burner. For Lewis numbers L < L* < 1, stationary spatially periodic solutions corresponding to stationary cellular flames bifurcate from the basic solution which corresponds to a steady planar flame. We study the existence and stability of two-dimensional patterns which correspond to certain imposed symmetries by considering the evolution of N pairs of wave vectors, each of which is separated from the next by angle π/N. In the neighbourhood of the critical Lewis number L*, we derive evolution equations for the amplitudes corresponding to N = 2, which corresponds to square patterns, and N = 3, which corresponds to triangular or hexagonal patterns. We determine existence and stability results in terms of m∈(0, 1), the flow rate of the fuel, and K > 2/e, the scaled heat loss to the burner. Square patterns exist for L < L* and are stable for values of m and K above a stability boundary in the m−K plane, which has a maximum at K = K* ∼ 4.77, so that for K > K* square patterns are stable for all m. The stability of the square patterns does not vary with L. Hexagonal patterns exist for L < LH, where 1 > LH > L*. The size of the stability region increases with decreasing L < L*. For a range of values of L there is bistability, that is, for given parameter values rolls and hexagons are simultaneously stable, each with its own domain of attraction.
Hele–Shaw flows with time-dependent free boundaries in which the fluid occupies a multiply-connected region
Authors: Richardson S.
Published: September 2008

We consider the classical Hele-Shaw situation with two parallel planes separated by a narrow gap. A blob of Newtonian fluid is sandwiched between the planes, and we suppose its plan-view to occupy a bounded, multiply-connected domain; physically, we have a viscous fluid with the holes giving rise to the multiple connectivity occupied by relatively inviscid air. The relevant free boundary condition is taken to be one of constant pressure, but we allow different pressures to act within the different holes, and at the outer boundary. The motion is driven either by injection of further fluid into the blob at certain points, or by injection of air into the holes to change their area, or by a combination of these; suction, instead of injection, is also contemplated. A general mathematical theory of the above class of problems is developed, and applied to the particular situation that arises when fluid is injected into an initially empty gap bounded by two straight, semi-infinite barriers meeting at right-angles: injection into a quarterplane. For a range of positions of the injection point, air is trapped in the corner and, invoking images, the problem is equivalent to one involving a doubly-connected blob. When there is an air vent in the corner, so that the pressure is the same on the two free boundaries in these circumstances, the air hole rapidly disappears, as might be expected. If, however, there is no air vent and we suppose the air to be incompressible, so that the area of the region occupied by the air in the plan-view remains constant, we find there to be no solution within the framework of our model. Other scenarios within this same geometry, involving both suction and injection of fluid at the injection point, and air at the corner, are also examined.
Mathematical model and method for spontaneous potential well-logging
Authors: Tatsien Li , Yongji Tan , Yuejun Peng
Published: September 2008

Spontaneous potential well-logging is an important technique in petroleum exploitation. To make the corresponding log interpretation chart, it is supposed that the geometrical structure of the formation, the resistivity in each subdomain, and the spontaneous potential difference on each interface are all known; then in the direct problem, the spontaneous potential u = u(r, z) satisfies an elliptic boundary value problem with jump conditions on interfaces. At the joint points A and B of the interfaces (figure 2), the jumps of the spontaneous potential do not, in general, satisfy the compatibility condition. It turns out that it is impossible to find a piecewise H1 solution to the problem, and the standard finite element method cannot be applied to get an approximate solution. In this paper, by means of a method of removing the singularities at A and B, it is proved that the problem admits a unique weak solution that is piecewise W1,p for any fixed p with 1 ≤ p <2. Moreover, based on this method a numerical scheme is suggested, and some numerical examples and some conclusions of practical interest are given. The techniques used in this paper will find a wider applicability in other problems.
Exact solution to a class of functional difference equations with application to a moving contact line flow
Authors: Lawrie J. B. , King A. C.
Published: September 2008

A new integral representation for the Barnes double gamma function is derived. This is canonical in the sense that solutions to a class of functional difference equations of first order with trigonometrical coefficients can be expressed in terms of the Barnes function. The integral representation given here makes these solutions very simple to compute. Several well-known difference equations are solved by this method, and a treatment of the linear theory for moving contact line flow in an inviscid fluid wedge is given.
The anomalous exponent of the Barenblatt equation
Authors: Peletier L. A.
Published: September 2008

The self-similar source solution of the Barenblatt equation for elasto-plastic filtration through porous rock is known to be of the second kind. We determine the behaviour of the associated anomalous exponent and the profile of the solution in the limit of large compressibility and small elastic recovery of the rock.
Mathematical modelling of active parameters for transmission line equations
Authors: Kadish A.
Published: September 2008

The relationship between mathematical models of active parameters for transmission lines is studied. Treating transmission lines as a series of differential lumped circuits, we show that pairs of line parameters for inductance and capacitance per unit length must satisfy one of two constraints. One of these is a symmetry condition, which is satisfied by passive (i.e. constant) parameters. If a parameter pair satisfies either of these constraints, the energy per unit length and power loss in the line may be written as integrals of known functions, no matter what the pair's dependence on line current and voltage may be. Potential applications of these results to other subject areas are discussed.
Finite amplitude convection between stress-free boundaries; Ginzburg–Landau equations and modulation theory
Authors: Bernoff Andrew J.
Published: September 2008

The stability theory for rolls in stress-free convection at finite Prandtl number is affected by coupling with low wavenumber two-dimensional mean-flow modes. In this work, a set of modified Ginzburg–Landau equations describing the onset of convection is derived which accounts for these additional modes. These equations can be used to extend the modulation equations of Zippelius & Siggia describing the breakup of rolls, bringing their stability theory into agreement with the results of Busse & Bolton.
Subsonic flow around the leading edge of a thin aerofoil with a parabolic nose
Authors: Rusak Z.
Published: September 2008

Subsonic potential flow around the leading edge of a thin two-dimensional general aerofoil with a parabolic nose at small angles of attack is analysed. Asymptotic expansions of the velocity potential function are constructed at a fixed Mach number in terms of the thickness ratio of the aerofoil in an outer region around the aerofoil and in an inner region near the nose. These expansions are matched asymptotically. The outer expansion consists of linearized aerofoil theory and its second-order problem, where the leading-edge singularity appears. The inner expansion accounts for the flow around the nose, where a stagnation point exists. A boundary-value problem is formulated in the inner region for the solution of a compressible uniform flow with the same Mach number, past a semi-infinite two-dimensional parabola. The analysis shows that the drag of any general aerofoil with a round nose is zero for every subsonic Mach number below the critical Mach number, where the drag component that is calculated by the integration of the outer pressure distribution over the aerofoil is cancelled exactly by the drag of the parabolic nose. The numerical solution of the flow field in the inner region results in the pressure distribution on the parabolic nose. The stagnation point tends to shift toward the leading edge due to the compressibility effects as the Mach number is increased at a fixed angle of attack and camber of the aerofoil. Good agreement is found in the leading edge region between the present asymptotic solution and numerical solutions of the Euler equations. Using the outer linearized solution and the nose solution a uniformly valid pressure distribution on the entire aerofoil surface in a subsonic flow is derived.
Asymptotic results for nonlinear outdiffusion
Authors: King J.R.
Published: September 2008

Asymptotic methods are applied to the outdiffusion of a diffusant whose behaviour is governed by a power-law diffusivity. Both semi-infinite and finite domain problems are considered. The ‘fast’ diffusion (negative power-law) case is of particular interest, and the results are significantly different from those for the corresponding indiffusion problem.
Zeros of a complex Ginzburg–Landau order parameter with applications to superconductivity
Authors: Elliott C. M. , Matano H. , Qi Tang
Published: September 2008

We consider the minimizers of the Gibbs free energy which couples a complex Ginzburg–Landau order parameter with a magnetic potential. It is established that the set on which the complex order parameter equals zero consists only of isolated points. Some estimates concerning the set on which the absolute value of the order parameter is small are also given. Numerical simulations are presented for the problem without a magnetic potential.
Existence and uniqueness of radially symmetric stationary points within the gradient theory of phase transitions
Authors: Niethammer Barbara S.
Published: September 2008

We study radially symmetric stationary points of the functional

whereudenotes the density of a fluid confined to a containerΩ, W(u)is the course-grain free energy and ε accounts for surface energy. Under the further assumption of small energy, that is

for small ε, we prove existence of precisely two solutions for the corresponding Euler-Lagrange equation. Each of these solutions is monotone in the radial direction and converges as ε→0 to one of two possible radially symmetric single interface minimizers ofE0. Our main tool is the method of matched asymptotic expansions from which we construct exact solutions.
A non-local thermistor problem
Authors: Allegretto W. , Xie H.
Published: September 2008

We consider the question of the existence/non-existence of solutions for the non-local nonlinear elliptic system which models a thermistor driven by a current source. Specifically, we show that for small input current there exists a solution, while this will not in general be the case for a sufficiently large current. A feature of our estimates is that the conditions for non-existence are determined by local criteria on the domain and the coefficients. Our basic tools for existence involve truncation, L2.μ estimates and fixed point arguments. Non-existence is obtained by averaging procedures and an application of Barta's Inequality.
A Ginzburg–Landau type model of superconducting/normal junctions including Josephson junctions
Authors: Chapman S. Jonathan , Du Qiang , Gunzburger Max D.
Published: September 2008

A model for superconductors co-existing with normal materials is presented. The model, which applies to such situations as superconductors containing normal impurities and superconductor/normal material junctions, is based on a generalization of the Ginsburg–Landau model for superconductivity. After presenting the model, it is shown that it reduces to well-known models due to de Gennes for certain superconducting/normal interfaces, and in particular, for Josephson junctions. A provident feature of the modified model is that it can, by itself, account for all of these as well as other physical situations. The results of some preliminary computational experiments using the model are then provided; these include flux pinning by normal impurities and a superconductor/normal/superconductor junction. A side benefit of the modified model is that, through its use, these computational simulations are more easily obtained.
Vortex annihilation in nonlinear heat flow for Ginzburg–Landau systems
Authors: Bauman Patricia , Chen Chao-Nien , Phillips Daniel , Sternberg Peter
Published: September 2008

We consider the Cauchy problem for the system

where . Let e ∈ ℝ2 with |e| = 1. If u(x, 0) is smooth, bounded and

we prove u → e uniformly in x as t → ∞. Of particular interest is the motion of the zeros (vortices) of u. In this case, all zeros disappear after a finite time.
Non-uniqueness for flame propagation when the Lewis number is less than 1
Authors: Bonnet Alexis
Published: September 2008

We discuss the question of uniqueness of planar flames for a simple one-step chemical reaction. We show that when the Lewis number is less than unity (i.e. species diffusion is larger than heat diffusion) uniqueness cannot be generally assumed. An example with three flames, two of them being stable, is exhibited. Other related questions, such as sufficient conditions for uniqueness to hold and high activation energy limits, are discussed.
The damping of flexural and acoustic waves by a bias-flow perforated elastic plate
Authors: Howe M. S.
Published: September 2008

An analysis is made of the damping of sound and structural vibrations by vorticity production in the apertures of a bias flow, perforated elastic plate. Unsteady motion causes vorticity to be generated at the aperture edges; the vorticity and its energy are swept away by the bias flow and result in a net loss of acoustic and vibrational energy. In this paper we investigate the interaction of an arbitrary fluid-structure disturbance with a small circular aperture in the presence of a high Reynolds number, low Mach number bias flow. By considering the limit in which the aperture is small compared to the length scale of the impinging disturbance, it is shown that the effect of the interaction can be represented by a concentrated source in the plate bending wave equation consisting of a delta function and two of its axisymmetric derivatives. A generalized bending wave equation is then formulated for a plate perforated with an homogeneous distribution of small, bias flow circular apertures. This equation is used to predict the attenuation of sound and resonant bending waves by vorticity production. Acoustic damping is found to be significant provided the fluid loading is sufficiently small for the plate to be regarded as rigid (e.g. for an aluminium plate in air when the frequency is not too small). On the other hand, a bending wave is effectively damped only when the fluid loading is large enough for the wave to produce a substantial pressure drop across the plate; when this occurs the predicted attenuations are comparable with those usually achieved by the application of elastomeric damping materials. Numerical predictions are presented for steel and aluminium plates in air and water.
The reducibility of partially invariant solutions of systems of partial differential equations
Authors: Ondich Jeffrey
Published: September 2008

Ovsiannikov's partially invariant solutions of differential equations generalize Lie's group invariant solutions. A partially invariant solution is only interesting if it cannot be discovered more readily as an invariant solution. Roughly, a partially invariant solution that can be discovered more directly by Lie's method is said to be reducible. In this paper, I develop conditions under which a partially invariant solution or a class of such solutions must be reducible, and use these conditions both to obtain non-reducible solutions to a system of hyperbolic conservation laws, and to demonstrate that some systems have no non-reducible solutions. I also demonstrate that certain elliptic systems have no non-reducible solutions.
On nonlinear interface dynamics in Hele-Shaw flows
Authors: Entov V. M. , Etingof P. I. , Kleinbock D. Ya.
Published: September 2008

Flows with free boundaries in a Hele-Shaw cell provide a unique opportunity to study non-linear boundary dynamics using rigorous analytic approaches. While of limited direct ‘practical value’, these studies give rise to a plethora of new phenomena and insights which may serve as beacons in the turbulent ocean of moving free boundaries and pattern forming. This paper gives a brief summary of the authors' studies of Hele-Shaw flows with free boundaries and some related problems based upon Richardson's approach. Some promising directions of further research are also discussed.
On classical solvability for the Hele-Shaw moving boundary problems with kinetic undercooling regularization
Authors: Hohlov Yu. E. , Reissig M.
Published: September 2008

In this paper, Hele-Shaw moving boundary problems with kinetic undercooling regularization are studied. By application of the nonlinear abstract Cauchy–Kovalevskaya theorem the local existence of analytic solutions is shown. Therefore we have to study the behaviour of the gradient of harmonic functions up to the boundary of the domain.