bluuebunny/crossref_metadata_2025 huggingface dataset:
Allocentric location cues and the visual guidance of walking towards seen targets
Authors: Herlihey Tracey A. , Cen Danlu , Vann Seralynne , Charron Cyril , Rushton Simon
Published: November 2019

We hypothesised allocentric location cues (information about the location of an observer relative to the surrounding environment) have a role in the on-line visual guidance of walking towards seen target objects. We used a standard technique for assessing the contribution of cues when walking to targets: we perturbed the perceived egocentric direction of the target, and measured the curvature of the resultant walking trajectories. By removing motion cues we were able to isolate allocentric location cues and quantify their utility. Enclosed, geometrically regular, environments contain rich allocentric location cues. In the first experiment participants walked through a large enclosed outdoor space; allocentric cues were isolated by synchronised eye closing and stepping. In the second experiment participants walked through a smaller enclosed indoor space; allocentric cues were isolated with stroboscopic lighting. Both experiments provided support for the hypothesis that, when they are available, allocentric location cues have a key role when walking to seen targets.
Validity and reliability of social anxiety disorder diagnoses in the Swedish National Patient Register
Authors: Vilaplana-Pérez Alba , Isung Josef , Krig Sonja Matu Marjatta , Vigerland Sarah , Jolstedt Maral , Bjureberg Johan , Högström Jens , Isomura Kayoko , Rautio Daniel , Serlachius Eva , Rück Christian , Mataix-Cols David , de la Cruz Lorena Fernández
Published: November 2019

BACKGROUND: Population-based administrative registers are often used for research purposes. However, their potential usefulness depends on the validity of the registered information. This study assessed the validity of the recorded codes for social anxiety disorder (SAD) in the Swedish National Patient Register (NPR). METHODS: The personal identification numbers of 300 randomly selected individuals with a diagnosis of SAD (also known as social phobia) recorded in the NPR were obtained from the Swedish National Board of Health and Welfare. The medical files of these individuals were then requested from clinics nationally. A total of 117 files were received and two independent raters reviewed each file to assess the presence or absence of SAD, according to the definition of the International Classification of Diseases, Tenth Edition (ICD-10) and the diagnostic criteria of the Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition, Text Revision (DSM-IV-TR). When disagreements between the two raters were found, a third rater reviewed the file to establish a best estimate diagnosis. Positive predictive values (PPV) and agreement between the two initial raters (using Cohen’s kappa) were calculated. Additionally, raters completed the Clinical Global Impression – Severity (CGI-S) and the Global Assessment of Functioning (GAF) rating scales for each file. Inter-rater agreement for the CGI-S and the GAF was assessed using intraclass correlation coefficients (ICC).RESULTS: After exclusion of files not comprising sufficient information, 95 files were included in the analyses. Of these, 77 files (81.05%) were considered to be ‘true positive’ cases. This resulted in a PPV of 0.81 (95% confidence interval, 0.72-0.88). Inter-rater agreement regarding the presence or absence of SAD was substantial (κ=0.72). CGI-S and GAF scores indicated that patients were in the moderate range of severity and functional impairment. Inter-rater agreement for the CGI-S and the GAF was moderate to good (ICC=0.72 and ICC=0.82, respectively). CONCLUSIONS: The ICD-10 codes for SAD in the Swedish NPR are generally valid and reliable, but we recommend sensitivity analyses in future register-based studies to minimise the impact of potential diagnostic misclassification. Most patients were moderately severe and impaired, suggesting that results from register-based studies of SAD may be generalizable.
The Keynesian-Monetarist Competition over Public Credibility
Authors: Gautier Morin Johanna
Published: November 2019

Mainstream economic theories went through an intellectual crisis during the recession that hit Western economies in the late 1970s. Academic debates extended to public media and mass culture, starting with the TV shows led by John Kenneth Galbraith ( The Age of Uncertainty) and Milton Friedman (Free to Choose). Such a translation of ideas and language had a spillover effect on the academic community. The simultaneous pursuit of honors in distinct fields raises the question of the role of economists in the public debate. By shifting the focal point beyond the notions of expertise and public opinion, this article explores the mechanisms of the conquest of the public sphere by experts and intellectuals, and its consequences on the field of economics.
De l’architecture en démocratie
Authors: Plagnol Hugo
Published: November 2019

L’effondrement de l’architecture depuis la seconde moitié du XXe siècle est indissociable de la crise de légitimité des architectes dans les pays occidentaux. Suivant un des grands paradigmes tocquevilliens, l’égalitarisme des sociétés démocratiques a conduit à la remise en cause des privilèges des architectes dont la position précaire, entre client et constructeur, nécessite des règles spécifiques. Au lieu des obligations de recours qui n’ont engendré que défiance et manœuvre de contournement, la principale réponse se trouve dans les concours. La difficulté ici découle de la spécificité des concours d’architecture qui sélectionnent le meilleur projet et non le meilleur architecte. L’article étudie l’échec du système des concours français instauré dans les années 1980 et aujourd’hui presque systématiquement contourné en le comparant au succès durable des concours finlandais, adaptés du système suédois avant même l’indépendance il y a plus de 130 ans, lui-même inspiré de la France des Lumières.
Le futur des nations
Authors: Cazeneuve Bernard
Published: November 2019

On assiste au retour des nations, communautés de destin dont la nécessité apparaît renforcée par la progression des inégalités sociales et territoriales et une mondialisation entraînant une concurrence parfois déloyale entre les États. Dans cet article Bernard Cazeneuve analyse l’évolution historique qui a conduit après la chute de l’Urss en 1991 à considérer la démocratie libérale comme la fin de l’histoire ou un horizon indépassable. Malgré les attentats de 2001, l’Europe s’est construite sur l’idée d’abolitions des nations et a privilégié l’extension vers l’Est, avant que ne soit remise en cause cette disqualification de la nation. Depuis une dizaine d’années on redécouvre la vertu protectrice pour les peuples des nations, qui sont le niveau le plus adéquat d’une délibération à distance des particularismes régionaux mais respectueuse des héritages historiques. Ce retour des nations doit beaucoup à la concurrence des instances internationales et des grandes entreprises qui semblent mettre en péril la capacité des hommes à choisir leur destin ; il doit aussi beaucoup en Europe de l’Est à une intégration peut être trop rapide des petites nations dont la nationalité écrasée par le communisme n’a pas eu le temps de se reconstruire. Face à ce sentiment du « à quoi bon », au désenchantement né de l’insuffisante attention portée par l’Europe aux réalités nationales, Bernard Cazeneuve rappelle le mot de Jaurès dans l’Armée nouvelle (1911) : « Un peu d’internationalisme éloigne de la patrie ; beaucoup d’internationalisme y ramène »6 pour en tirer un programme d’action pour l’Europe et pour la France.
Development of pulmonary endovascular metastases following vertebroplasty: case report
Authors: Mercer Joel , Lam Andrew C. L. , Smith Roger , Fallah-Rad Nazanin , Kavanagh John
Published: November 2019

A 69-year-old man developed pulmonary metastases following vertebroplasties for pathological fractures of vertebrae T12–L4. The fractures developed due to spinal metastases from castrate-resistant prostate cancer. A CT scan performed 1 month prior indicated no evidence of pulmonary malignancy. However, CT scans performed 2 months after the vertebroplasties demonstrated intravascular pulmonary metastases distributed similarly to embolized polymethylmethacrylate. Vertebroplasty is a well-established procedure for symptomatic management of vertebral compression fractures. However, studies have demonstrated an increase in circulating tumor cells following vertebroplasties, theoretically increasing the risk of distant metastases. In this case, the chronicity and radiological findings suggest that the pulmonary intravascular metastases may have resulted from the vertebroplasties.
Gambaran Kadar Kolesterol pada Akseptor Kontrasepsi Suntik
Authors: Wulandari Pupung Cahya , Surati Surati
Published: November 2019

Berdasarkan data hasil sensus penduduk yang tercatat 2016 lebih dari 258 juta jiwa dan diproyeksikan bahwa jumlah ini akan terus bertambah. Program keluarga berencana untuk perencanaan jumlah keluarga dan pembatasan dengan peggunaan alat kontrasepsi. Jumlah Pasangan Usia Subur (PUS) Provinsi Jawa Tengah tahun 2016 sebanyak 6.727.894 dari seluruh PUS sebesar 78.6% peserta KB aktif. Kontrasepsi yang paling banyak digunakan kontrasepsi  suntik 3 bulan (DMPA). Di Kota Semarang, Kecamatan Pedurungan jumlah PUS paling banyak. Kelurahan yang paling banyak akseptor kontrasepsi suntik adalah Kelurahan Telogosari Kulon. Kontrasepsi suntik menyebabkan perubahan metabolisme lemak melalui perubahan kadar kolesterol adanya pengaruh hormon progesteron. Rancangan penelitian yang digunakan adalah penelitian jenis deskriptif dengan pendekatan cross-sectional. Sampel penelitian sebanyak 25 akseptor kontrasepsi suntik 3 bulan. Hasil penelitian menunjukkan rata-rata kadar kolesterol 209.5 mg/dl, sebanyak 12 akseptor kotrasepsi suntik memiliki kadar kolesterol normal (48%) dan 13 akseptor memiliki kadar kolesterol diatas normal (52%). Kontrasepsi suntik 3 bulan dapat meningkatkan kadar kolesterol.
Digital methods for process development in manufacturing and their relevance to value driven design
Authors: Butterfield J. , McEwan W. , Han P. , Price M. , Soban D. , Murphy A.
Published: November 2019

This paper examines the applicability of a digital manufacturing framework to the implementation of a Value Driven Design (VDD) approach for the development of a stiffened composite panel. It presents a means by which environmental considerations can be integrated with conventional product and process design drivers within a customized, digital environment. A composite forming process is used as an exemplar for the work which creates a collaborative environment for the integration of more traditional design drivers with parameters related to manufacturability as well as more sustainable processes and products. The environmental stakeholder is introduced to the VDD process through a customized product/process/resource (PPR) environment where application specific power consumption and material waste data has been measured and characterised in the process design interface. This allows the manufacturing planner to consider power consumption as a concurrent design driver and the inclusion of energy as a parameter in a VDD approach to the development of efficiently manufactured, sustainable transport systems.
The elephant in the mist: What we don't know about the design, development, test and management of complex systems
Authors: Felder Wilson N. , Collopy Paul
Published: November 2019

The authors survey the literature on complex systems to develop a fundamental critique of the systems engineering methods that value-driven design will attempt to replace. The current approach to systems engineering applies industrial revolution methods to information revolution problems. Not only the flowdown of requirements, but also the ability to verify and validate large engineered systems is brought into question.
A novel method to enable trade-offs across the whole product life of an aircraft using value driven design
Authors: Price M. , Soban D. , Mullan C. , Butterfield J. , Murphy A.
Published: November 2019

The increasing need to understand complex products and systems with long life spans, presents a significant challenge to designers who increasingly require a broader understanding of the operational aspects of the system. This demands an evolution in current design practice, as designers are often constrained to provide a subsystem solution without full knowledge of the global system operation. Recently there has been a push to consider value centric approaches which should facilitate better or more rapid convergence to design solutions with predictable completion schedules. Value Driven Design is one such approach, in which value is used as the system top level objective function. This provides a broader view of the system and enables all sub-systems and components to be designed with a view to the effect on project value. It also has the capacity to include value expressions for more qualitative aspects, such as environmental impact. However, application of the method to date has been restricted to comparing value in a programme where the lifespan is fixed and known a priori. This paper takes a novel view of value driven design through the surplus value objective function, and shows how it can be used to identify key sensitivities to guide designers in design trade-off decisions. By considering a new time based approach it can be used to identify optimum programme life-span and hence allow trade-offs over the whole product life.
Designing for shared cognition in air traffic management
Authors: van Paassen M.M. (René) , Borst Clark , Klomp Rolf , Mulder Max , van Leeuwen Pim , Mooij Martijn
Published: November 2019

It is to be expected that the task of an air traffic controller will change with the introduction of four-dimensional (space and time) trajectories for aircraft, as can be seen in ongoing developments in ATM systems in Europe (SESAR) and the US (NextGen). It is clear that higher levels of automation will need to be developed to support the management of four-dimensional trajectories, but a definite concept on a distribution of the roles of automation and human users has not yet been well defined. This paper presents one approach to the design of a shared representation for 4D trajectory management. The design is based on the Cognitive Systems Engineering framework and by using a formative approach in the analysis of the work domain, a step-wise refinement in the planning and execution of 4D trajectories is proposed. The design is described in three Abstraction Hierarchies, one for each phase in the refinement. The ultimate goal is to design a shared representation that underlies both the design of the human-machine interface and the rationale that guides the automation. It is foreseen that such a shared representation will greatly benefit the shared cognition in ATM and allows shifting back and forth across various levels of automation. A preliminary version of a joint cognitive system for 4D trajectory management has been developed and will be introduced in this paper. Further work will focus on the refinement of the shared representation by means of human-in-the-loop experiments.
Adverse weather diversion model DIVMET
Authors: Hauf Thomas , Sakiew Ludmila , Sauer Manuela
Published: November 2019

Concept and first results are presented of a model development DIVMET for providing guidance for two-dimensional, horizontal navigation of an aircraft on an arbitrary prescribed flight level around or through adverse weather. In this paper we focus on thunderstorms but a later model development will allow for other weather hazards such as icing or volcanic ash. Adverse weather is represented as impermeable polygons on vertically staggered horizontal planes. The model concept maps the joint decision making process of pilot and air traffic controller into an algorithm, which encompasses (1) the recognition of thunderstorms within the pilot's field of view. The latter may consist either of the typical on-board weather radar display of varying range, or of the visible range determined by atmospheric conditions, or of the spatially unlimited “full view”. DIVMET then (2), in accordance with international flight rules, applies a minimum safety distance to any recognized adverse weather object, and (3) determines a reasonably short route not only around a single weather object but also through a whole field of them. Finally (4), DIVMET moves the aircraft purely kinematic along the previously determined diverted route ignoring so far any potential aircraft-aircraft conflicts. That movement may also be achieved by an externally coupled air traffic model which then also avoids the latter conflicts, accounts for aircraft performance and thus enables to study the combined effect of weather and traffic. Here we present the concept of the path finding through a storm field from a meteorological perspective and outline its potential applications.
Some considerations related to flight in dusty conditions
Authors: Lekas Th. I. , Kushta J. , Solomos S. , Kallos G.
Published: November 2019

Volcanic ash eruptions and mineral dust injection into the atmosphere are of particular importance to the aviation industry. Ash and dust affect almost any aspect of air operations, from airport facilities to cruise flight. This paper is focused on the advantage of using dust forecasting tools and the potential benefit for Air Traffic Management (ATM), flight safety and aircraft performance. It is suggested that state of the art Chemical Weather Prediction (CWP) model coupled with accurate dust cycle module could be a useful operational tool for more efficient Air Traffic Management and aircraft exploitation.
Contributions of advanced taxi time calculation to airport operations efficiency
Authors: Günther Thomas , Hildebrandt Matthias , Fricke Hartmut , Strasser Moritz
Published: November 2019

The current paper stresses the high priority of accurate taxi time calculation and suitable pre-departure management strategies in the context of Airport Collaborative Decision Making (Airport CDM) and contributes to an improved overall understanding of the associated requirements. Based on data analysis performed at Frankfurt Airport this paper compares results of static and advanced taxi time calculation. Contrarily to static calculations, where look-up tables for stand-runway-relations are used, advanced taxi time calculation takes into account the current traffic situation and calculates taxi times dynamically. The paper shows that the taxi time uncertainties when using static data lead to only 42% of flights within the accuracy of ± 2 minutes according to the requirements of the Airport CDM Implementation Manual for short term predictions (maximum 30 minutes before off-block). The application of advanced taxi time calculation leads to significant improvements with 66% of flights within the accuracy of ± 2 minutes at the moment when the aircraft leaves the stand. Hence, app. 50% more predictions are compliant with the Airport CDM requirements compared to static data. Based on these results, the paper assesses the effects of improved taxi time predictability onto airport operation efficiency with particular focus set to taxi time reductions due to minimized queuing at the departure runway. It is shown that advanced taxi time calculation contributes to a reduction of delays, fuel burn, CO2 emissions and costs for airspace users compared to the use of static look-up tables. However, it is also emphasized that the shifting of delays from the runway holding positions to the stand does not necessarily contribute to efficiency improvements. It is recommended that the pre-departure sequencing strategy must be chosen cautiously in dependence on the fuel and time costs for airlines as well the amount of departure delay that has to be absorbed.
The Laplace operator on the nth tensor power of a line bundle: eigenvalues which are uniformly bounded in n
Authors: Guillemin V. , Uribe A.
Published: November 2019

The ground-state eigenvalues of the Laplace operator on the nth tensor power of a line bundle are shown to have a simple asymptotic distribution as n tends to infinity provided the connection on the bundle is sufficiently twisted.
On the meromorphic equivalence of standard matrix differential equations
Authors: Jurkat W.B. , Zwiesler H.J.
Published: November 2019

In this paper we address the problem of determining all the meromorphic differential equations that are meromorphically equivalent to a given equation; and we also discuss how one can effectively check whether two given equations are equivalent.

In the case of equations of block size 1, which is a generalization of the case of distinct eigenvalues, we provide solutions to these problems which involve only algebraic processes. This allows a detailed description of the structure of the involved transformations. Our discussion is based on the concept of direct transformations which we define and study thoroughly.
Stabilité et convergence dans les problèmes de perturbation singulière
Authors: Huet Denise
Published: November 2019

It is shown that Sobolev spaces with two indices Hsε(X), s=(s1,s2)∈R2 are proper approximations of usual Sobolev spaces HS1(X). It is also stated that, under natural conditions, an estimate of the form ‖u‖Hε≤C{‖Aεu‖Fε+‖u‖Eε} for an operator Aε from a space Hε to a space Fε can be sharpened and can lead to the inverse stability of Aε. Under minimal assumptions on the data, these results can be used for establishing convergence results for solutions of classical or Wiener–Hopf coercive singularly perturbed problems investigated by Frank and Wendt [10,11,12,37,38] and for solutions of boundary value problems in Lp-spaces.
Bounds for the eigenfunctions of multiparameter Sturm–Liouville systems
Authors: Schäfke Reinhard , Volkmer Hans
Published: November 2019

We derive bounds for the values of L2-normalized eigenfunctions of Sturm–Liouville systems containing k spectral parameters λ1,…,λk. In the case of continuous coefficients this bound is of order O(|λ|k/4 as |λ|→∞, where λ=(λ1,…,λk) is the corresponding eigenvalue and |λ|=max|λi|. If the coefficients are continuously differentiable then we obtain a better bound of order O(|λ|(k−1)/6). The latter result generalizes a bound of order O(|λ|1/6) given by Faierman (1980) in the two-parameter case k = 2 under the assumption of analytic coefficients. We show by examples that the powers ¼k and ⅙(k−1) of |λ| in the above bounds are optimal.
Homogenization of the stokes flow in a connected porous medium
Authors: Allaire Grégoire
Published: November 2019

In this paper we prove the convergence of the homogenization process of the Stokes equations with Dirichlet boundary condition in a periodic porous medium. We consider here the case where the solid part of the porous medium is connected, and we generalize to this case the results obtained by Tartar (1980).
Existence and characterization of higher-order terms in an asymptotic expansion method for linearized elastic beams
Authors: Trabucho L. , Viaño J.M.
Published: November 2019

This work is a continuation of an earlier work by Bermudez and Viaño (1984) on the same subject. In fact, using the same asymptotic expansion in linear elastic beams we give a complete characterization of displacements, bending moments and shear forces of orders 0, 1 and 2. These results include a characterization of the stress field of order 0 and of the axial and shear stresses of order 1. An appropriate physical interpretation of these results, which is considered elsewhere, will allow us to derive and to justify, from a mathematical point of view, the most well-known classical extension, bending and torsion theories for linear elastic beams, including the Bernoulli-Navier, Saint Venant, Timoshenko and Vlasov models.
The relaxation of functionals with surface energies
Authors: Kinderlehrer David , Vergara-Caffarelli Giorgio
Published: November 2019

The relaxation of a variational principle is determined when a superficial term is present. Lower semicontinuity of the functional may fail even when both integrands are convex. Generalized solutions, in terms of parametrized measures or Young measures, are introduced and analyzed. Several examples are given.
A partial regularity theorem for harmonic maps at a free boundary
Authors: Duzaar Frank , Steffen Klaus
Published: November 2019

For a Riemannian manifold M with boundary, a Riemannian manifold N, an open subset Σ≠∅ of ∂M and a submanifold S of N, we prove that every map u:M→N of class H1,2 which is energy minimizing with respect to the free boundary condition u(Σ)⊂S is regular on an open subset Reg(u) of M∪Σ whose complement Sing(u)=(M∪Σ)\Reg(u) has vanishing m−2 dimensional measure. The result is new for the singular set Σ∩Sing(u) contained in the free boundary Σ. There are no restrictions on the image of u in N and no dimensional restrictions on M, N and S.

The proof is based on a method introduced by R. Schoen and K. Uhlenbeck in the interior partial regularity theory for harmonic mappings, a novel partial reflection construction ũ extending u and a precise control of the local averages ur,a, ũr,a on balls Br,a with radius r>0 and center a∈Σ in terms of the small normalized energy ε of u on Br,a. The crucial estim ate is dist(ur,a,S) $\lesssim$ ε1/2 and dist(ũr,a,S) $\lesssim$ ε2/3 as ε↓0.
On quasilinear parabolic equations involving measure data
Authors: Gmira Abdelilah
Published: November 2019

In this paper we prove that a nontrivial solution of the quasilinear parabolic ut=div(|∇|p−2∇u)−uq in RN×(0,T),u(x,0)=0 for x≠0, p>2 exists if and only if 0<q<p−1+p/N.
Homogénéisation d'un modèle d'écoulements miscibles en milieu poreux
Authors: Amirat Youcef , Hamdache Kamel , Ziani Abdelhamid
Published: November 2019

We consider a 1-D model for incompressible miscible displacements in porous media without any dispersion term. Existence and uniqueness results for nonsmooth data are proved. We study the homogenization of the model. The limit problem is of the same type. The result is obtained thanks to compactness properties of the corresponding characteristic curves.
Lp-Lq-estimates for solutions to the equations of linear thermoelasticity in exterior domains
Authors: Racke Reinhard
Published: November 2019

Lp-Lq decay estimates are proved for the solution of an initial boundary value problem in linear thermoelasticity. A method using generalized eigenfunction expansions is presented.
Asymptotic analysis of boundary value problems for quasi-linear monotone operators
Authors: Defranceschi Anneliese
Published: November 2019

By means of the notion of G-convergence introduced in [4] we deal with the limit behaviour, as h→+∞, of the solutions uh to Neumann boundary value problems for quasi-linear monotone operators of the form Ahu=−div(ah(x,Duh)), and we also include in our analysis more general linear boundary conditions. Furthermore, we extend the homogenization result obtained in [6] to this case and the corresponding correctors studied in [7]. Finally, we deal with the asymptotic behaviour, as h→+∞, of the solutions uh to quasi-linear equations −div(ah(x,Duh))=f on perforated domains Ωh⊆Ω of Rn with homogeneous Neumann boundary conditions on the holes, when the regularity assumptions on ah required in [5] are dropped.
Diffusion through thin layers with high specific heat
Authors: Colli Pierluigi , Rodrigues José-Francisco
Published: November 2019

We study the asymptotic behaviour of the diffusion-transmission problem in a fixed domain surrounded by a layer whose thickness of order δ goes to zero and where the specific heat σ goes to infinity. We characterize essentially three limit cases according to the limit α of the product δσ: if α=0 or α=∞, we have a Neumann or a Dirichlet boundary condition respectively, while if 0<α<∞, we obtain a mixed boundary condition involving the trace of the time derivative. We also extend this result to a class of unilateral problems of Signorini type.
Uniform estimates for some degenerating quasilinear elliptic equations and a bound on the Harnack constant for linear equations
Authors: Bardi Martino , Perthame Benoît
Published: November 2019

Let u be any smooth solution of −εaijuxixj+aijuxiuxj+biuxi=εc in B1={x:|x|<1}, where ε is a small parameter. We prove some uniform estimates on u in W1,q under weak assumptions on the coefficients aij, bi and c. This is motivated by the study of exponential behaviors for solutions of linear elliptic equations −εaijvxixj+bivxi+cv=0, as ε goes to 0. For this equation, our result provides an estimate of Harnack type sup Brv≤Cinf Brv, with C=e−krα/ε for some α≤1.
Estimations semi-classiques pour l'opérateur de Schrödinger à potentiel de type coulombien et avec champ magnétique
Authors: Mohamed Abderemane
Published: November 2019

We give a BKW method in the semiclassical analysis of a Schrödinger operator in a magnetic field, with an electrical potential having singularities of Coulombian type. As applications, we obtain sharp estimates for the splitting in the double wells problem and for the first band in the periodic problem.
Taylor expansions and bounds for the effective conductivity and the effective elastic moduli of multicomponent composites and polycrystals
Authors: Bruno Oscar P.
Published: November 2019

We describe a construction, based on variational inequalities, which gives a hierarchy of upper and lower bounds (of odd orders 2k+1), on the various effective moduli of random multiphase materials and polycrystals. The bounds of order 2k+1 on a given effective modulus can be explicitly evaluated if a truncated Taylor expansion of the given modulus is known to order 2k+1. Our approach is motivated by prior investigations of Beran and other authors. Our calculations do not involve Green functions or n-point correlation functions, and they are very simple. We thus rederive known and obtain new sequences of bounds on the different effective moduli. We also describe a method that, for cell materials (i.e. materials in which cells of smaller and smaller length scales cover all space, with material properties assigned at random), permits one to calculate the truncated Taylor expansions that are needed for the explicit evaluation of the bounds. In connection with this, we show that the first coefficient in the low volume fraction expansion of any effective modulus of a cell material, coincides with the corresponding low volume fraction coefficient for an array of cells randomly distributed in a matrix.
Correctors for the homogenization of almost periodic monotone operators
Authors: Braides Andrea
Published: November 2019

In a previous paper (Braides et al., 1990) it has been proven, under very mild almost periodicity conditions, that we have weak convergence in H1,p(Ω) of the solutions uε of boundary problems in an open set Ω related to the quasi-linear monotone operator −div(a(x/ε,Duε)), to a function u, which solves an analogous problem related to a homogenized operator −div(b(Du)).

In general we do not have strong convergence of Duε, to Du in (Lp(Ω))n, even in the linear periodic case.

It is possible however (Theorems 2.1 and 4.2) to express Duε in terms of Du, up to a rest converging strongly to 0 in (Lp(Ω))n, applying correctors built up exploiting only the geometric properties of a.

In the last section, we use the correctors result to obtain a homogenization theorem for quasi-linear equations with natural growth terms.
On the diffusion approximation of a transport process without time scaling
Authors: Ringeisen E. , Sentis R.
Published: November 2019

We are concerned with the asymptotic behaviour of the linear transport equation ∂tu+ω▿u+(1/ε)Qu=0, u|t=0=f, when ε→0. We prove that this process is equivalent up to order 1 to the viscosity perturbation of a hyperbolic process, provided that the conservative collision operator Q(x) has a 1-dimensional null-space. This can be considered as a justification of the diffusion approximation the classical scaling of the t or x variable.
Asymptotics for semilinear elliptic equations with supercritical nonlinearities in annular domains
Authors: Budd C.J. , Peletier L.A.
Published: November 2019

We study radially symmetric solutions of the equation Δu+up=0 in annular domains {a<|x|<1} in R3. In particular we are interested in the behaviour of solutions when the power p tends to the critical Sobolev exponent 5 in R3 and simultaneously, the inner radius shrinks to zero. When p $\searrow$ 5, two forms of behaviour are observed, depending on whether (p−5)2«a or a«(p−5)2.
On the convergence of splitting algorithms for some kinetic equations
Authors: Desvillettes Laurent
Published: November 2019

We study the convergence of splitting algorithms for the radiative transfer equation and for the Vlasov–Maxwell system of equations.
Exponentially stable positive solutions to a forced semilinear parabolic equation
Authors: Haraux A.
Published: November 2019

Let Ω be a bounded connected open subset of RN with a Lipschitz continuous boundary and f:R→R a locally Lipschitz continuous function such that f(0)=0, f is strictly convex on [0,+∞) and f′d(0)<−λ1(Ω) where λ1(Ω) is the smallest eigenvalue of (−Δ) in H10(Ω), and f(s)→+∞ as s→+∞. For any h∈L∞(R×Ω) with h(t,x)≥0, a.e. on R×Ω, the semilinear parabolic problem ut−Δu+f(u)=h(t,x) in R×Ω; u=0 on R×∂Ω has one and only one nonnegative global solution ω∈CB(R;H10(Ω)∩L∞(Ω)) such that w(t,·) does not tend to 0 as t→−∞. In addition, if h is T-periodic, then ω is T-periodic. If h:R→L∞(Ω) is continuous and almost-periodic, then ω:R→H01(Ω)∩L∞(Ω) is almost-periodic. Finally assuming either that u0≥0 is not identically 0 or that h(t,x)>0 on a subset of positive measure of R+×Ω, the unique solution u of ut−Δu+f(u)=h(t,x) in R+×Ω; u=0 on R+×∂Ω such that u(0)=u0 satisfies ‖u(t,·)−ω(t,·)‖∞≤C(u0)exp (−γt), for all t≥0, with γ>0 independent of u0 and h.
Vibrations of viscous compressible fluid in bounded domains: spectral properties and asymptotics
Authors: Levitin Michael R.
Published: November 2019

In this paper we consider the equations of small (acoustic) vibrations of a viscous compressible barotropic fluid in a bounded smooth domain under different boundary conditions. The structure of the spectrum is investigated; the estimates of the norm of the resolvent operator of the forced vibration problems are presented; the infinite asymptotic expansions of eigenfrequencies and eigenfunctions in series in a vanishing viscosity coefficient are obtained; the leading terms of these expansions are determined analytically.
Homogenization of the Neumann problem with nonisolated holes
Authors: Allaire Grégoire , Murat François
Published: November 2019

We consider the homogenization of second-order elliptic equations with a Neumann boundary condition in open sets periodically perforated with holes of the size of the period. When the holes are isolated, Cioranescu and Saint Jean Paulin (1979) proved the convergence of the homogenization process. One of their main tool was the construction of an extension of the solution, which is uniformly bounded. In the present paper, we give a new proof of the convergence, which avoids the use of such an extension. The main advantage of our approach is that it generalizes the result of Cioranescu and Saint Jean Paulin to the general case of periodic holes which may be not isolated (including, for example in three dimensions, the case of a domain perforated by interconnected cylinders).
On the asymptotic behaviour as t→∞ of the solutions of the equation ut=uxxx+F[u]
Authors: Sukhanov V.V.
Published: November 2019

A study is made of the asymptotic behaviour of the solutions of the nonlinear nonintegrable equations of KdV type. The formal solutions in three regions: x/t>0, x/t<0, x/t1/3=O(1) are constructed. As a result of the the investigation of the rearrangement of those solutions formulas connecting the parameters of asymptotics in different regions are obtained. The final formula corresponds the relation connecting the amplitude of the solutions which is exponentially decreasing as x→−∞ and the amplitude of the solution of the dispersion type for the KdV equation. All constructions are carried out within the context of formal solutions.
Local uniqueness of a boundary value problem in the complex plane
Authors: Tabara Tatsuhiko J.
Published: November 2019

We will consider the following boundary value problem for a second-order linear differential equation with polynomial coefficients in the complex plane: is there a differential equation of the specific type with linearly independent solutions y1(x) and y2(x) such that the ratio y1(x)/y2(x) can be prescribed both at the origin and at infinity? We shall derive uniqueness conditions for the problem.
Asymptotic invertibility of Bergman and Bargmann space Toeplitz operators
Authors: Böttcher Albrecht , Wolf Hartmut
Published: November 2019

We establish a criterion for the asymptotic invertibility of Toeplitz operators with continuous symbols on weighted Bergman spaces of the polydisk and their formal limit, the multi-dimensional Bargmann space.
Solution formelle Gevrey d'une équation singulièrement perturbée
Authors: Canalis-Durand M.
Published: November 2019

Nous nous intéressons à un problème d'équations différentielles singulièrement perturbées. Après avoir précisé la notion d'équation élémentaire sur C, nous étudions les solutions formelles de telles équations possédant certaines propriétés de régularité. Nous prouvons, par des majorations directes, le caractère Gevrey 1 de ces séries formelles. Nous obtenons alors par des techniques de sommation de séries divergentes, une nouvelle preuve de l'existence des solutions surstables d'une équation élémentaire. Ce texte est le développement de la note aux C. R. Acad. Sci. qui porte le titre: “Caractère Gevrey des solutions canard de l'équation de Van der Pol”.
Weak limits of solutions to the steady incompressible two-dimensional Euler equation in a bounded domain
Authors: Bethuel Fabrice , Ghidaglia Jean-Michel
Published: November 2019

In this work we show that any sequence uε of smooth solutions to the steady incompressible two-dimensional Euler equation in a bounded domain Ω, which converges weakly in L2(Ω) as ε goes to zero, converges to a weak solution of this equation provided curl uε remains bounded in L1(Ω).
Limiting sets of eigenvalues and singular values of Toeplitz matrices
Authors: Roch Steffen , Silbermann Bernd
Published: November 2019

The paper is devoted to the asymptotic behavior of the eigenvalues and singular values of Toeplitz and Hankel matrices with piecewise continuous generating functions. The central result is a norm stability theorem for sequences of matrices belonging to a Banach algebra of Toeplitz operators. This theorem applies to derive a complete description of the partial and the uniform limiting set of the eigenvalues and the singular values of the matrices under consideration.
On the Laplace formula for the capillary tube
Authors: Miersemann Erich
Published: November 2019

The asymptotic correctness is shown of a formal expansion given by Laplace in 1806 of the rise height of a fluid in a circular capillary tube. The proof is completely based on the comparison principle of Concus and Finn. The first two non-constant terms in the expansion are calculated. It is of special interest that the expansion is uniform with respect to the boundary contact angle although the governing quasilinear elliptic equation becomes singular on the boundary if the contact angle tends to zero.
Justification of the asymptotic analysis of elastic plates, II. The non-linear case
Authors: Miara B.
Published: November 2019

In the first part of this study, where the linear case was considered, the appropriate scalings of the components of the displacement and the appropriate assumptions on the data (Lamé constants and applied forces) that are an essential step for deriving Kirchhoff-Love plate models by an asymptotic analysis, were justified up to a multiplicative factor. The study of the nonlinear case undertaken here, provides a full justification of this asymptotic analysis by “freezing” this dangling factor.
Proof of the Landau–Zener formula
Authors: Joye Alain
Published: November 2019

We consider the time dependent Schrodinger equation in the adiabatic limit when the Hamiltonian is an analytic unbounded operator. It is assumed that the Hamiltonian possesses for any time two instantaneous non-degenerate eigenvalues which display an avoided crossing of finite minimum gap. We prove that the probability of a quantum transition between these two non-degenerate eigenvalues is given in the adiabatic limit by the well-known Landau–Zener formula.
On the differential equation y″+exp (ym−t)=0
Authors: Volkmer Hans
Published: November 2019

It is shown that the zero T(a) of the solution y(·,a) of y″+exp (ym−t)=0, y(t,a)→a as t→∞, satisfies

T(a)=(1−(m/2))am+(m−1)log a+log (m/2)+3/2(m−1)+Ol((log 3a)/(am))  as a→∞

if 1≤m<2. This asymptotic expansion of T(a) is related to a result of Atkinson and Peletier (1986). Moreover, if m=2 then

T(a)=log a+s0+O((log 3a)/(am))  as a→∞

where s0=s=1.6853749… is the solution of the transcendental equation

s−1.5=exp (−s).
Shocks and free boundaries: the local behaviour
Authors: Kersner R. , Natalini R. , Tesei A.
Published: November 2019

We study the Cauchy problem both for a non-linear diffusion-convection equation and for a first order hyperbolic conservation law. The latter can be regarded as the zero diffusion limit of the former, which is of degenerate parabolic type. Concerning support properties, the behaviour of solutions of both problems exhibits striking analogies when the effect of convection is stronger than diffusion. Hence previously reported phenomena concerning the parabolic problem can be interpreted as being of hyperbolic type.
Weakly non-linear geometric optics for hyperbolic systems of conservation laws with shock waves
Authors: Corli Andrea
Published: November 2019

We consider in this paper a strictly hyperbolic system of conservation laws, in one space dimension. We suppose that a shock wave solution to this system is given and superimpose to it small amplitude fast oscillations. These oscillations are described by sets of phase functions, and resonances are taken into account. We justify the asymptotic expansions given by the weakly non-linear geometric optics: the oscillating part of the perturbed solution is approximated by an almost periodic function (a profile) which is solution to a non-linear integro-differential mixed problem. We give at the same time an asymptotics to the shock front.
Justification of a hyperbolic approach to phase changes in materials with memory
Authors: Colli Pierluigi , Grasselli Maurizio
Published: November 2019

This paper is concerned with phase transition problems in materials with memory. Two different sets of constitutive assumptions are considered for the internal energy and the heat flux, one leading to a parabolic integro-differential equation and the other giving rise to a hyperbolic one. Both of them are coupled with phase change laws and suitable initial and boundary conditions. While the first class of resulting problems corresponds to a well-established and widely investigated approach, the second model could be partly arguable from a constitutive point of view. Here, it is shown that actually the hyperbolic phase change problems are nothing but singular perturbations of the parabolic ones. By performing a rigorous asymptotic analysis, we prove convergence results and deduce error estimates.
Asymptotic approximation of an elastic beam with a rotating cross section
Authors: Veiga M.F.
Published: November 2019

In the framework of linearized elasticity, the asymptotic expansion method is used to obtain an approximation of the displacement field of a beam with a variable cross section (in the sense that the section rotates along the longitudinal axis of the beam, keeping its form). We give a complete characterization of the equations governing the bending, stretching and torsion components, generalizing, in this way, previous results for straight beams.
Existence of exceptional growing-up solutions for a class of non-linear second order ordinary differential equations
Authors: Souplet Philippe
Published: November 2019

We establish the existence of nontrivial global solutions for the ordinary differential equation u″+f(u)=g(u′), when f is at most linear and g is superlinear. We then provide a result of global uniqueness in certain classes of power-like functions for general autonomous second order ordinary differential equations. This result allows us to show the exceptional character of the global solutions for a class of equations including u″+u=|u′|p−1u′, for p>1.
Travelling wave analysis and jump relations for Euler–Poisson model in the quasineutral limit
Authors: Cordier Stéphane , Degond Pierre , Markowich Peter , Schmeiser Christian
Published: November 2019

This paper is devoted to the travelling wave analysis of the Euler–Poisson model for a plasma consisting of electrons and ions. When the Debye length tends to 0, this system leads to a non-linear hyperbolic system in a non-conservative form called quasineutral Euler system. Our aim is to determine the admissible jump relations and shock solutions for the quasineutral Euler system as limits of travelling wave solutions for the Euler–Poisson system. We show that only one of the three types of travelling wave solutions converges to admissible shock solutions of the quasineutral Euler system.
Spectral asymptotics of periodic discrete Schrödinger operators, I
Authors: van Mouche P.
Published: November 2019

Asymptotics, for coupling constant A tending to zero and to infinity, for the bands and gaps of the Schrödinger operator (HAg)(n)=g(n+1)+Abng(n)+g(n−1) on l2(Z) with periodic potential b are studied. In this context special attention is paid to ‘asymptotic spectral powers’. Three different perturbation techniques are used to obtain results. In this first paper the emphasis lies on results that can be obtained by a first-order degenerate or arbitrary-order non-degenerate Rayleigh–Schrödinger perturbation calculus.
Asymptotic analysis of linearly elastic shells
Authors: Miara B. , Sanchez-Palencia E.
Published: November 2019

Using the formal approach of asymptotic expansions we identify the two-dimensional limit membrane and bending models in the theory of linearly elastic shells. In this fashion, we retrieve the two asymptotic behaviors already announced in a short communication based on a multiple-scale technique.
Local behavior for the solutions of a second order nonlinear differential equation
Authors: Salvatori M.C. , Vitillaro E.
Published: November 2019

In this paper we study the local behavior near zero for the solutions of a class of second order differential equations which include, as a particular case, the radial version of the partial nonlinear differential equation, involving the m-Laplacian operator,

div(|∇u|m−2∇u)+f(|x|,u)=0, x∈Rn\{0},

where n>m>1. Some important examples of f are given by

f(t,u)=Ctνu|u|q−2  and  f(u)=C1u|u|p−2+C2u|u|q−2.

As an application of our general results to the first case we extend to m>1 and ν>−m some estimates given in the literature for the Laplacian case m=2 or for ν=0.
Justification de l'optique géométrique faiblement non linéaire pour le problème mixte: Cas des concentrations
Authors: Sablè-Tougeron Monique
Published: November 2019

We suggest a justification for all time of the formal development of geometric optics, for a conservative, genuinely nonlinear, initial-boundary value problem, in case of BV data with compact support and function of slow variables.
Exponential attractors for non-dissipative systems modeling convection in porous media
Authors: Fabrie Pierre , Nicolaenko Basil
Published: November 2019

We consider a system of equations for natural convection in an porous medium, with Darcy's law for the momentum equation. Such a system is only partially dissipative; we establish the existence of an exponential attractor (inertial set) and we obtain estimates for its fractal dimension. The main difficulty lies in the lack of compactness of the corresponding semi group. We show strong continuity of the exponential attractors for a singular limit of the convection model.