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International Workshop Analytic and geometric theory of the Camassa-Holm equation and integrable systems (Bologna, 22-25 September 2004).
No full textThe workshop was held at CIRAM as part of the GNFM-INdAM research program "Onde nonlineari, struttura tau e geometria delle varietà invarianti: il caso della gerarchia di Camassa-Holm". The workshop was also partially supported by ESF research program MISGAM (Method of Integrable Systems, Geometry and Applied Mathematics). About 30 researchers presented their recent achievements in the theory of integrable systems with special attention to topics related to the CH hierarchy and its generalizations.
Scientific Committee: S. Abenda (Bologna), B. Dubrovin (SISSA), G. Falqui (SISSA), T. Grava (SISSA).
Organizing Committee: S. Abenda (Bologna), T. Grava (SISSA).
Invited speakers: R. Camassa (Chapel Hill), G. Carlet (Cambridge),
A. Constantin (Trinity College, Dublin), B. Dubrovin (SISSA), Yu. Fedorov (UPC-Spain), D. Holm (IC London), A. Hone (University of Kent at Canterbury), P. Lorenzoni (Milano Bicocca), F. Magri (Milano Bicocca), F. Musso (Rome III), M. Pedroni (Genova), J. Prada (University of Salamanca), O. Ragnisco (Rome III), V. Sokolov (Moscow), A. Shabat (Moscow and Roma III), Y. Zhang (Tsinghua U. Beijing)
Multibump solutions for Duffing-like systems
No full textSi studia il problema di esistenza di soluzioni omocline di un sistema
Hamiltoniano del secondo ordine asintoticamente periodico: trovare
tale che
dove si assume che l'origine è un massimo locale per il corrispondente
potenziale, uniformemente nel tempo, e dove V' è asintotico per
a delle funzioni periodiche e superquadratiche. Proviamo,
via metodi variazionali che se le varietà stabile e instabile associate
all'origine di uno dei problemi all'infinito hanno intersezione numerabile
allora il problema (HS) ha infinite soluzioni omocline di tipo multibump.We study the problem of existence of homoclinic solutions of a second
order asymptotically periodic Hamiltonian system: find
such that
where it is assumed that the origin is a local maximum for the corresponding
potential, uniformly in time, and that V' is asymptotic, as
to time periodic and superquadratic functions . We prove
via variational methods that if the stable and unstable manifolds
associated to the origin of one of the systems at infinity have countable
intersection then the problem (HS) has infinitely many homoclinic
solutions of multibump type
Onde nonlineari, struttura tau e geometria delle varietà invarianti: il caso della gerarchia di Camassa-Holm
No full textResponsabile del progetto: ABENDA Simonetta
Collaboratori: DUBROVIN Boris (SISSA), RAGNISCO Orlando (Roma III), PEDRONI Marco (Genova), FALQUI Gregorio (SISSA), GRAVA Tamara (SISSA), LORENZONI Paolo (Milano Bicocca), MUSSO Fabio (Roma III)
Descrizione:
Una motivazione di base per la ricerca di modelli alternativi di onde nonlineari dispersive è dovuta al fatto che i modelli matematici tradizionali, quali l'equazione di Korteweg-de Vries (KdV) per la descrizione di onde gravitazionali nell'acqua, falliscono nel rappresentare fenomeni fisici fondamentali quali l'onda estrema di Stokes. Con tale intento R. Camassa e D. Holm (1993) hanno proposto una nuova hamiltoniana, formalmente integrabile attraverso il metodo dello scattering inverso. L'equazione di Camassa-Holm si ottiene come equazione delle onde in acqua bassa con tensione superficiale in un'espansione asintotica di un'ordine superiore all'approssimazione Korteweg-de Vries. L'equazione fortemente nonlineare così ottenuta ammette anche soluzioni continue, analitiche a tratti (peakons). A partire dal 1993, si è sviluppata una cospicua letteratura sulla gerarchia integrabile bi-hamiltoniana di Camassa-Holm (CH), ma molti quesiti fondamentali sono tuttora irrisolti. La difficoltà principale nello studio diretto della gerarchia è dovuto al fatto che le leggi di conservazione e le simmetrie sono non-locali mentre le equazioni associate alla gerarchia sono integro-differenziali. Inoltre, la gerarchia di CH non rientra nella classificazione assiomatica di Dubrovin-Zhang dei sistemi integrabili basata sulle varieta` di Frobenius. Uno dei principali problemi aperti è, infatti, se sia possibile trovare un modo di modificare uno degli assiomi di base della classificazione di Dubrovin e Zhang, per potervi includere la gerarchia CH. Tale assioma, cui qui ci riferiremo come "assioma tau", richiede l'esistenza di una funzione speciale (la funzione tau), che genera le densita` conservate del sistema, e che tale funzione soddisfi un opportuno sistema di vincoli, detti vincoli di Virasoro. La ragione della non esistenza di una struttura di tipo funzione tau per la gerarchia CH, dimostrata da Dubrovin e Zhang, puo' essere facilmente motivata studiando le proprietà analitiche delle soluzioni quasi-periodiche (algebro-geometriche). Tali soluzioni sono state classificate in una serie di lavori (ad esempio A. Constantin e H.P.McKean (1999) e M.S. Alber, R. Camassa, Yu.N. Fedorov, D. Holm e J.E. Marsden (2001)). Come nel caso KdV, le soluzioni quasiperiodiche sono esprimibili usando le funzioni theta iperellittiche. Tuttavia, a differenza del caso KdV, la dipendenza dalla variabile x nell'argomento è non lineare. Un fenomeno simile si riscontra nei sistemi finito dimensionali algebricamente integrabili con deficienza studiati per la prima volta da S. Abenda e Yu. N. Fedorov (2000). Piu' specificamente, si intende investigare i seguenti problemi:
1) Nel quadro del problema dell'assioma tau, si intende studiare la
modulazione di soluzioni periodiche dell'equazione di Camassa-Holm e classificare le corrispondenti equazioni Whitham. In particolare, si intendono costruire gli invarianti di Riemann con il metodo WKB nonlineare e verificare l'esistenza o meno di un fascio di metriche piatte sulla varieta` R di tali invarianti di Riemann che, tramite un risultato ben noto di Dubrovin e Novikov, fornirebbero un fascio di strutture di Poisson locali sullo spazio del lacci a valori in R. Tale ricerca è strettamente legata alla verifica che le varietà invarianti associate a tale sistema integrabile siano di Frobenius. Ci si aspetta che questa verifica fornisca importanti indicazioni sulla conseguente modifica dell'assioma tau.
2) Studiare le proprietà dei flussi negativi associati alla gerarchia di Camassa-Holm. Nel lavoro originale di Camassa-Holm sono state determinate un numero bi-infinito di leggi di conservazione, ma solo quelle legate ai cosiddetti flussi positivi sono state studiate in l..
3D Modeling of a Bipolar Smart Optical Sensor Fabricated in CMOS Technology
No full textThis paper presents the electro-optical characteristics of a CMOS-Compatible PNP bipolar phototransistor fabricated using the VLSI fabrication process developed at IRST. The study has been performed by using the three-dimensional version of the device simulator HFIELDS. A good agreement has been found between the simulated characteristics and the results of the measurements
Conference on Riemann-Hilbert Problems, Integrability and Asymptotics
No full textA Conference on Riemann-Hilbert Problems, Integrability and Asymptotics is being organized at SISSA within the activities of the Marie Curie FP6 RTN ENIGMA (European Network In Geometry, Mathematical Physics and Applications), the ESF Research Programme MISGAM (Methods of Integrable Systems in Geometry and Applied Mathematics), in collaboration with the Italian MIUR 2004 research project Geometrical Methods in the Theory of Nonlinear Waves and Applications, run by the SISSA Mathematical Physics Sector.
Riemann Hilbert problems and asymptotic expansions lie at the crossroads of the three main research areas of the ENIGMA network and of the MISGAM project: Geometry, Integrable Systems, and Applications. The aim of the Trieste Conference is to establish the state of the art in this interdisciplinary, historically deeply rooted but still extremely lively subject, as well as point out new directions of research.
Participants: J. Arnlind (Stokholm), O. Babelon (Paris), A. Bobenko (Berlin), G. Carlet (Cambridge), A. Cattaneo (Zürich), Y. Chen (London), T. Claeys (Leuwen), D. Crowdy (London), E. Daems (Leuwen), M. Duits (Leuwen), M. Dunajski (Cambridge), P. Elbau (Zürich), Y. Fedorov (Barcelona), E. Ferapontov (Loughborough), T. Fokas (Cambridge), P. Garcia-Estevez (Salamanca), J. Gibbons (IC, London), M. Hallnas (Stocholm), C. Hertling (Mannheim), I. Hitzazis (Patra), A. Hone (Kent), J. Hoppe (Stockolm), T. Ikeda (Okayama), S. Kamvissis (Greece), V. Kazakov (Paris), G. Khimshiashvili (Tbilisi), C. Klein (Leipzig). B. Konopelchenko (Lecce), A. Kuijlaars (Leuwen), R. Ivanov (Dublin), P. Lorenzoni (Milano), E. Loubet (Zurich), M. Manas (Madrid), J. Marshall (London), L. Martinez-Alonso (Madrid), L. Mason (Oxford), M. Mazzocco (Manchester), P. van Moerbeke (Louvain), Y. Morita (Kiryu), A. Moro (Lecce), F. Musso (Roma), S.P. Novikov (Maryland), V. Novokshenov (Ufa), A. Panasyuk (Warsaw), J. Prada (Salamanca), O. Ragnisco (Roma), M. Saito (Kobe), L. Samaj (Bratislava), P. Santini (Rome), V. Shramchenko (Bonn), F. Smirnov (Paris), V. Spiridonov (Dubna), I. Strachan (Glasgow), Y. Suris (Munich), K. Takasaki (Kyoto), K. Takemura (Yokohama), K. Toda (Toyama), C. Tracy (Davis), M. Vanlessen (Leuwen), A. Veselov (Loughborough), S. West (Cambridge), J-B. Zuber (Paris).
Organizing Committee: S. Abenda, B. Dubrovin, G. Falqui, T. Grava.
Sponsors: ESF programme MISGAM, European RTN network ENIGMA, SISSA - Scuola Internazionale Superiore di Studi Avanzati and Italian MIUR Research Project "Geometrical Methods in the theory of Nonlinear Waves and Applications".
Registration and Financial Support: Please register for the conference with the online registration form. Limited partial financial support is available. Priority will be given to young researchers working in Europe. Deadline for application for financial support: 5th of June 2005.
The day of arrival will be September 19th (Monday), and the day of departure September 25th (Sunday). The working days of the Workshop are September 20th through 24th
Numerical solution of the small dispersion limit of the Camassa-Holm equation and Whitham equations and Multiscale expansion
No full textThe small dispersion limit of solutions to the Camassa-Holm (CH) equation is characterized by the appearance of a zone of rapid modulated oscillations. An asymptotic description of these oscillations is given, for short times, by the one-phase solution to the CH equation, where the branch points of the corresponding elliptic curve depend on the physical coordinates via the Whitham equations. We present a conjecture for the phase of the asymptotic solution. A numerical study of this limit for smooth hump-like initial data provides strong evidence for the validity of this conjecture. We present a quantitative numerical comparison between the CH and the asymptotic solution. The dependence on the small dispersion parameter ϵ is studied in the interior and at the boundaries of the Whitham zone. In the interior of the zone, the difference between CH and asymptotic solution is of the order ϵ, at the trailing edge of the order ϵ√ and at the leading edge of the order ϵ1/3. For the latter we present a multiscale expansion which describes the amplitude of the oscillations in terms of the Hastings-McLeod solution of the Painlev\'e II equation. We show numerically that this multiscale solution provides an enhanced asymptotic description near the leading edge
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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