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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 25 (1974), S. 209-228 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Résumé On considère le problème de la détermination par approximation du champ électromagnétique produit par deux dipôles électriques placés au centre d'une cavité sphérique au milieu d'un plasma non linéaire, dans le cas stationnaire. En particulier, on décrit les phénomènes non linéaires de ‘cross-modulation’ des deux dipôles, par l'emploi de la méthode ‘quasi-hydrodynamique’ qui relie les équations de Maxwell aux équations d'Euler des fluides parfaits. On obtient ainsi une solution analytique approchée, à l'aide d'une méthode itérative interrompue au deuxième ordre, de même que de nombreux résultats numériques en correspondance de valeurs paramétriques d'importance pour la propagation des ondes radiophoniques dans la ionosphère. Le résultat principal de ce travail est la prédiction d'un champ observable d'interaction en deuxième approximation.
    Notes: Abstract We consider the problem of the approximate determination of the electromagnetic field generated by two oscillating electric dipoles in the center of a spherical cavity imbedded in a nonlinear plasma. The influence of the nonlinearities of the plasma upon the field are investigated by means of a perturbative solution of the relevant equations, deduced from the ‘quasi-hydrodynamic’ approach. Analytical and numerical results, which illustrate several nonlinear effects, as well as the influence of the rarefaction and ionization of the gas, are included. The main result of the paper is the prediction of an observable second harmonic field.
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 20 (1969), S. 781-784 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Résumé On considère le problème non-linéaire de l'écoulement plan d'un fluide en présence d'un coin symétrique avec cavitation, à l'aide d'un modèle à ≪cavité ouverte≫. On en donne la solution analytique par l'application de la théorie des transformations conformes et des techniques de Riemann-Hilbert.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 27 (1976), S. 815-831 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Sommario Si presenta una trattazione analitica e numerica modificata, relativa al ‘problema di Graffi-Cesari’ in Ottica Non Lineare, studiato in [1] e [12]. Si dimostra un teorema di esistenza, unicità e dipendenza continua (dall' onda laser incidente) per il campo elettromagnetico entro la lamina di cristallo, seguendo, come in [1], lo schema teorico elaborato da L. Cesari in [8–12]. Il presente metodo fornisce valori numerici per lo spessore ammissibile della lamina di cristallo (di quarzo) dell' ordine di 2 mm, in buon accordo con valori dello spessore delle lamine (di quarzo) usate negli esperimenti.
    Notes: Summary A modified analytical and numerical method is presented for a preliminary study of the ‘problem of Graffi-Cesari’ in Nonlinear Optics [1, 12]. This problem concerns electromagnetic laser wave propagation in a nonlinear (quartz) crystal slab embedded between two linear media, and is a suitably simplified version of the experimental situation of Franken, Ward and co-workers (1961). A new version of an existence and uniqueness theorem is proved in a functional class which is chosen following Cesari's works on quasilinear hyperbolic systems in the Schauder canonic form, under a set of restrictions upon the admissible slab widtha of the crystal. The present method consists essentially in centering the relevant functional ball at the linear solution, and yields numerical values fora of the order of 2 mm, with a good agreement with values of quartz crystal widths used in experiments.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 39 (1988), S. 455-467 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Sunto Si costruisce un modello di flusso con scia e vortici a doppia spirale alla Tulin per un ostacolo poligonale arbitrario. Il flusso risulta univalente per un' ampia classe di geometrie. Inoltre viene proposto un criterio per correlare il parametro del modello al numero di Reynolds del corrispondente flusso viscoso, combinando la soluzione di Stokes per la diffusione di uno strato di vortici con la teoria di Tulin e Hsu (1980).
    Notes: Summary A free-streamline flow model for flow past a polygonal obstacle with a near-wake terminating in Tulin's double spiral vortices is constructed. The flows are univalent for a large class of geometries. In addition a criterion is given for determining the underpressure as function of the Reynolds number using the Stokes solution for diffusion of a vortex sheet, and an extension of Tulin and Hsu's matching theory to transitional flows.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 44 (1993), S. 695-706 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Sommario Si propone un metodo di calcolo della pressione lungo un profile alare in regime di flusso stazionario in prossimitã dello stallo. II metodo combina le equazioni dello strato limite con un modello di flusso a linee di corrente libere e scia separata. I risultati numerici richiedono un minimo dispendio di tempo di calcolo e sono in buon accordo con gli esperimenti e con una soluzione viscosa.
    Notes: Abstract We propose a model which combines boundary layer computations with a free streamline potential flow for obtaining pressure distributions on an airfoil section in steady flow near stall conditions. The model is conceptually simple and uses elements which can be computed rapidly and efficiently. The solution is essentially analytical and can be used naturally in the larger context of matching asymptotic expansions to get information about three dimensional flows.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Meccanica 31 (1996), S. 433-440 
    ISSN: 1572-9648
    Keywords: Irrotational flow ; Surface tension flow ; Naval hydromechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Si risolve, nell' ambito di una formulazione integrale al contorno, il problema linearizzato delle onde di gravità irrotazionali generate da un dipolo di Havelock in presenza di tensione superficiale. Si hanno due distinti regimi di flusso separati da una velocità critica. Il regime transcritico, in cui si ha un fenomeno di risonanza, viene descritto tenendo conto della presenza di uno strato limite viscoso sulla frontiera libera.
    Notes: Abstract The prototype problem of the linearized irrotational gravity-capillarity water waves due to a Havelock doublet in a uniform planar stream is solved via a layer ansatz and a boundary integral formulation. As an effect of surface tension, two distinct flow regimes arise, separated by a critical speed where a resonance occurs. The transcirtical flow is described by including the viscous vorticity diffusion at the free boundary.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 18 (1967), S. 915-917 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Résumé On considère le problème d'une source ponctuelle placée dans un milieu aléatoire borné avec de fortes fluctuations de l'indice de réfraction. On dérive une expression pour l'énergie diffuse dans la zone de Fraunhofer, dans le cas où le milieu aléatoire est sphérique. Pour un milieu aléatoire quelconque la méthode proposée ici permit d'obtenir la valeur moyenne de l'énergie diffuse.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 27 (1976), S. 409-422 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Summary Analytical and numerical results are given for the ‘problem of Graffi’, recently proposed by D. Graffi in order to give a rigorous mathematical theory of the experiments carried out by Franken, Ward and coworkers (1961) in Nonlinear Optics, following the theoretical scheme developed by L. Cesari in some recent papers concerning boundary value problems for quasilinear hyperbolic systems in the Schauder canonic forms. Numerical results refer to the estimate by defect of the maximal slab widtha of the nonlinear medium (a quartz crystal slab), under which the relevant existence and uniqueness theorem holds, in a suitable functional class which is chosen following Cesari's works and is well-suited for applications to Mathematical Physics.
    Notes: Riassunto Si presentano risultati analitici e numerici relativi al ‘problema di Graffi’, recentemente proposto da D. Graffi per una teoria matematica degli esperimenti di Franken, Ward et al. (1961) in Ottica Non Lineare, seguendo lo schema teorico elaborato da L. Cesari in alcuni recentissimi lavori su certi problemi ai limiti per sistemi iperbolici quasi lineari nella forma canonica di Schauder. I risultati numerici si riferiscono alla stima per difetto del massimo spessore del mezzo non lineare (lamina di cristallo di quarzo) per cui restano validi teoremi di esistenza, unicità e dipendenza continua dall'onda (laser) incidente, in una opportuna classe funzionale, scelta seguendo i lavori citati di Cesari.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 37 (1986), S. 849-858 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Sunto Si studiano gli effetti dovuti ad un campo di gravità uniforme trasversale sul flusso con scia attorno ad un profilo sottile con spoiler usando un modello proposto nel precedente lavoro (I). Si dimostra l'esistenza, unicità, e la convergenza di un procedimento iterativo sulle linee di corrente libere, per grandi numeri di Froude, mediante il principio di contrazione in spazi di Banach.
    Notes: Summary The effects of transverse gravity on steady flow past a split plate are investigated, by adopting the wake model proposed in the preceding paper (I). The existence and uniqueness of the solution as well as the convergence of an iteration process involving the free streamlines are proved for large Froude numbers by means of the Banach contraction mapping principle using Lipschitz norms.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 35 (1984), S. 658-670 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Sunto Si studia un semplice modello a scia finita per l'analisi teorica di spoiler e split flap. Si risolve analiticamente un problema inverso mediante tecniche alla Riemann-Hilbert, e si confrontano i risultati numerici per la resistenza e la portanza con dati sperimentali e teorici dovuti a Elcrat & Wentz (1983). Viene messa in luce la presenza di scie con resistenza nulla e con sovrapressione.
    Notes: Summary A simple finite wake model for free streamline flow past a split plate is considered. An inverse problem is solved analytically by Riemann-Hilbert techniques. Numerical results for drag/lift are compared with experimental data for spoilers and split flaps and with theoretical results by Elcrat & Wentz (1983). Wakes of zero drag and wake overpressure are discussed.
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