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1
Contatto, Felipe. "Vortices, Painlevé integrability and projective geometry." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/275099.
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GaugThe first half of the thesis concerns Abelian vortices and Yang-Mills theory. It is proved that the 5 types of vortices recently proposed by Manton are actually symmetry reductions of (anti-)self-dual Yang-Mills equations with suitable gauge groups and symmetry groups acting as isometries in a 4-manifold. As a consequence, the twistor integrability results of such vortices can be derived. It is presented a natural definition of their kinetic energy and thus the metric of the moduli space was calculated by the Samols' localisation method. Then, a modified version of the Abelian–Higgs model is proposed in such a way that spontaneous symmetry breaking and the Bogomolny argument still hold. The Painlevé test, when applied to its soliton equations, reveals a complete list of its integrable cases. The corresponding solutions are given in terms of third Painlevé transcendents and can be interpreted as original vortices on surfaces with conical singularity. The last two chapters present the following results in projective differential geometry and Hamiltonians of hydrodynamic-type systems. It is shown that the projective structures defined by the Painlevé equations are not metrisable unless either the corresponding equations admit first integrals quadratic in first derivatives or they define projectively flat structures. The corresponding first integrals can be derived from Killing vectors associated to the metrics that solve the metrisability problem. Secondly, it is given a complete set of necessary and sufficient conditions for an arbitrary affine connection in 2D to admit, locally, 0, 1, 2 or 3 Killing forms. These conditions are tensorial and simpler than the ones in previous literature. By defining suitable affine connections, it is shown that the problem of existence of Killing forms is equivalent to the conditions of the existence of Hamiltonian structures for hydrodynamic-type systems of two components.
2
Zhang, Haiyu. "On the connection formulas of Painlevé transcendents /." access full-text access abstract and table of contents, 2009. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b23749441f.pdf.
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Thesis (Ph.D.)--City University of Hong Kong, 2009.<br>"Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [95]-100)
3
Lindblom, Ove. "Painlevé analysis and transformations for nonlinear partial differential equations /." Luleå, 2001. http://epubl.luth.se/1402-1544/2001/16/index.html.
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Wong, Wing-tak. "Bac̈klund transformations, the Painleve ̓property and some of their applications /." [Hong Kong : University of Hong Kong], 1987. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12350667.
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Dieng, Momar. "Distribution functions for edge eigenvalues in orthogonal and symplectic ensembles : Painlevé representations /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2005. http://uclibs.org/PID/11984.
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Fischer, Florian. "Behandlung des Painlevéschen Paradoxons in der modernen Mehrkörperdynamik /." Aachen : Shaker, 2009. http://d-nb.info/998740519/04.
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Morrison, Tegan Ann. "Asymptotics of higher-order Painlevé equations." Thesis, The University of Sydney, 2009. http://hdl.handle.net/2123/5140.
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We undertake an asymptotic study of a second Painlevé hierarchy based on the Jimbo-Miwa Lax pair in the limit as the independent variable approaches infinity. The hierarchy is defined by an infinite sequence of non-linear ordinary differential equations, indexed by order, with the classical second Painlevé equation as the first member. We investigate general and special asymptotic behaviours admitted by each equation in the hierarchy. We show that the general asymptotic behaviour is described by two related hyperelliptic functions, where the genus of the functions increases with each member of the hierarchy, and we prove that there exist special families of solutions which are represented by algebraic formal power series. For specific values of the constants which appear in the higher-order second Painlevé equations, exact solutions are also constructed. Particular attention is given to the fourth-order analogue of the classical second Painlevé equation. In this case, the general asymptotic behaviour is given to leading-order by two related genus-2 hyperelliptic functions. These functions are characterised by four complex parameters which depend on the independent variable through the perturbation terms of the leading-order equations, and we investigate how these parameters change with respect to this variable. We also show that the fourth-order equation admits two classes of algebraic formal power series and that there exist families of true solutions with these behaviours in specified sectors of the complex plane, as well as unique solutions in extended sectors. To complement our asymptotic study of higher-order Painlevé equations, we consider a new setting in which classical Painlevé equations arise. We study reaction-diffusion equations with quadratic and cubic source terms, with a spatio-temporal dependence included in those terms, and show that solutions of these equations are given by first and second Painlevé transcendents.
8
Morrison, Tegan Ann. "Asymptotics of higher-order Painlevé equations." University of Sydney, 2009. http://hdl.handle.net/2123/5140.
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Doctor of Philosophy (PhD)<br>We undertake an asymptotic study of a second Painlevé hierarchy based on the Jimbo-Miwa Lax pair in the limit as the independent variable approaches infinity. The hierarchy is defined by an infinite sequence of non-linear ordinary differential equations, indexed by order, with the classical second Painlevé equation as the first member. We investigate general and special asymptotic behaviours admitted by each equation in the hierarchy. We show that the general asymptotic behaviour is described by two related hyperelliptic functions, where the genus of the functions increases with each member of the hierarchy, and we prove that there exist special families of solutions which are represented by algebraic formal power series. For specific values of the constants which appear in the higher-order second Painlevé equations, exact solutions are also constructed. Particular attention is given to the fourth-order analogue of the classical second Painlevé equation. In this case, the general asymptotic behaviour is given to leading-order by two related genus-2 hyperelliptic functions. These functions are characterised by four complex parameters which depend on the independent variable through the perturbation terms of the leading-order equations, and we investigate how these parameters change with respect to this variable. We also show that the fourth-order equation admits two classes of algebraic formal power series and that there exist families of true solutions with these behaviours in specified sectors of the complex plane, as well as unique solutions in extended sectors. To complement our asymptotic study of higher-order Painlevé equations, we consider a new setting in which classical Painlevé equations arise. We study reaction-diffusion equations with quadratic and cubic source terms, with a spatio-temporal dependence included in those terms, and show that solutions of these equations are given by first and second Painlevé transcendents.
9
Smith, James. "Painleve equations and orthogonal polynomials." Thesis, University of Kent, 2016. https://kar.kent.ac.uk/54758/.
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In this thesis we classify all of the special function solutions to Painleve equations and all their associated equations produced using their Hamiltonian structures. We then use these special solutions to highlight the connection between the Painleve equations and the coefficients of some three-term recurrence relations for some specific orthogonal polynomials. The key idea of this newly developed method is the recognition of certain orthogonal polynomial moments as a particular special function. This means we can compare the matrix of moments with the Wronskian solutions, which the Painleve equations are famous for. Once this connection is found we can simply read o the all important recurrence coefficients in a closed form. In certain cases, we can even improve upon this as some of the weights allow a simplification of the recurrence coefficients to polynomials and with it, the new sequences orthogonal polynomials are simplified too.
10
Calvert, Guy. "Twistor theory, isomonodromy and the PainleveÌ equations." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427893.
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Alves, Victor César Costa. "Painlevé Integrability and mixed P_III-P_V system solutions /." São Paulo, 2017. http://hdl.handle.net/11449/149963.
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Orientador: Abraham Hirsz Zimerman<br>Abstract: The current work aims at applications of mathematical methods of Painlevé integrability in physics, on the other side it also approaches the integrable hierarchies formalism and the 2M-bose model where differential equations methods are used as well as a method for solutions using Padé approximants.<br>Resumo: O presente trabalho trata de um abordagem de aplicações em física dos métodos matemáticos de integrabilidade de Painlevé, por outro lado também aborda o formalismo de hierarquias integráveis e o modelo de 2M-bosons onde são usados métodos de equações diferenciais bem como um método para soluções usando aproximantes de Padé.<br>Mestre
12
Southall, Neil J. "Painlevé equations and applications." Thesis, Loughborough University, 2007. https://dspace.lboro.ac.uk/2134/34921.
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The theme running throughout this thesis is the Painlevé equations, in their differential, discrete and ultra-discrete versions. The differential Painlevé equations have the Painlevé property. If all solutions of a differential equation are meromorphic functions then it necessarily has the Painlevé property. Any ODE with the Painlevé property is necessarily a reduction of an integrable PDE. Nevanlinna theory studies the value distribution and characterizes the growth of meromorphic functions, by using certain averaged properties on a disc of variable radius. We shall be interested in its well-known use as a tool for detecting integrability in difference equations—a difference equation may be integrable if it has sufficiently many finite-order solutions in the sense of Nevanlinna theory. This does not provide a sufficient test for integrability; additionally it must satisfy the well-known singularity confinement test.
13
Webster, Helen Nicola. "On the continuous and discrete third Painleve equations." Thesis, University of Kent, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.267390.
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Hicks, Andrew Christopher. "Theory and applications of the fourth Painleve equation." Thesis, University of Exeter, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.385779.
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Alrashdi, Huda Daefallh A. "q-discrete Painleve equations, their hierarchies and properties." Thesis, The University of Sydney, 2019. https://hdl.handle.net/2123/21311.
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The main objective of this thesis is to derive hierarchies of q-discrete Painelevé equations. Some of the important properties of these hierarchies will also be given, namely Lax pairs, Bäcklund transformations, solutions of their associated linear problems for special values of parameters and their symmetry groups. To construct these hierarchies, we apply a geometric reduction and a staircase method on a multi-parameteric generalized lattice modified Korteweg-de Vries equation. In addition, the property of consistency around the cube is used in order to find Bäcklund transformations. Starting with the base case of q-discrete second, third and fourth Painlevé equations on A_5 initial-values surface, new hierarchies of q-discrete third and fourth Painlevé equations are discovered, and we also rediscover the hierarchy of q-discrete second Painlevé equation. In this thesis, we provide the Lax pairs for each member in these hierarchies. Using the consistency around the cube, we also provide Bäcklund transformation for the entire hierarchy of q-discrete second and third Painlevé hierarchies. We generate a hierarchy of special solutions starting with seed solutions for q-discrete second and third Painlevé hierarchies. An assumption made is that particular parameter values would enable the ability to diagonalize the Lax pair. As a consequence, we found that the associated linear problem for the three hierarchies can be solved in terms of q-Gamma function. Furthermore, the hierarchy of q-discrete fourth Painlevé hierarchy can be reduced to one equation that can be linearlized to become Riccati equation which has hypergeometric special solutions. Finally, we investigated the affine Weyl group structure of the symmetry group for each hierarchy. In this thesis, we construct the explicit representation of the symmetry group for the first and second member of these hierarchies.
16
Fric, Jacques. "Painlevé et la relativité générale." Paris 7, 2013. http://www.theses.fr/2013PA070080.
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L'examen des contributions de Painlevé en 1921-1922, visant à comparer les théories de Newton et d'Einstein, révèle une incroyable richesse créative allant bien au-delà de la forme géniale orientée, la première dans l'histoire qui efface la singularité sur l'horizon, prouvant qu'on peut le traverser. Mais c'est sur ce concept essentiel d'orientation de l'espace-temps que les esprits, même les plus brillants, ont achoppé et le débat subséquent à l'Académie des Sciences, même s'il a produit des contributions magistrales, sombrera dans l'oubli. Sa formulation géométrique covariante spatiale de la solution newtonienne dévoile que le temps newtonien métaphysique est accessoire et que le paramètre dynamique physique est le temps propre, issu de la gravitation à travers la géométrie de son formalisme ! Si sa tentative d'extension à la relativité générale échouera, elle montrera tout de même que la structure causale qu'elle propose est la même que celle de la relativité générale. Ces avancées en rupture avec les concepts de temps et d'espace en vigueur nous conduiront à nous interroger sur les conditions de leurs émergences. Exhumée avec les honneurs dans des contributions récentes, nous montrerons, à travers les différentes descriptions formelles qu'on peut faire de cet espace-temps, comment la phénoménologie particulière que cette forme met en exergue, révèle mieux que toute autre, la physique sous-jacente et les implications épistémologiques associées à ces descriptions. L'analyse des propos de Painlevé sur le ds² montre qu'ils ne justifient pas l'ostracisme qui l'a frappé. La conclusion soulignera la convergence des approches historiques, épistémologiques et scientifiques<br>The study of the Painlevé papers, published in 1921-1922, analyzing differences between the Newtonian theory and the general relativity, reveals an incredible creativity even beyond the still inspired oriented formalism described in his first paper which was the first in the history erasing the singularity on the horizon allowing it to be inwards crossed over by an observer. This spacetime incredible character baffled even the most brilliant minds and the subsequent debate at the "Académie des Sciences" whether it produced masterful contributions, sank into oblivion. Painlevé proposed also a space covariant geometrical formalism for deriving the equations of geodesic motion in the Newtonian theory. This does not longer involve the absolute time of the classical mechanics but thakes the proper time, affine parameter of this geodesic, as dynamical parameter. Whether the extension of this space formalism to general relativity will not fully succeed it still will yield a correct result for describing the conformal spacetime structure of the Schwarzschild problem in general relativity. One might wonder how, a scientist, not familiar with the general relativity, as Painlevé was able to set up such breaking concepts of time and space in his work. Brought to light with honors in recent papers, we will show how, by using various formal descriptions suitable for this spacetime, the Painlevé formalism reveals better than any other the underlying physics and its epistemological involvements. The controversial Painlevé's claims about the ds² did not deserve to be struck by such ostracism. At the end, we will stress convergence of historical, epistemological and scientific approaches
17
Finch, M. R. "The Painleve-Gambier equation and the relativistic static fluid sphere." Thesis, University of Sussex, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.380529.
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Larson, Jay Walter. "Painleve singularity analysis applied to charged particle dynamics during reconnection." W&M ScholarWorks, 1992. https://scholarworks.wm.edu/etd/1539623818.
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For a plasma in the collisionless regime, test-particle modelling can lend some insight into the macroscopic behavior of the plasma, e.g conductivity and heating. A common example for which this technique is used is a system with electric and magnetic fields given by B = {dollar}\delta y{dollar}cx x + xcx y + {dollar}\gamma{dollar}cx z and E = {dollar}\epsilon{dollar}cx z, where {dollar}\delta{dollar}, {dollar}\gamma{dollar}, and {dollar}\epsilon{dollar} are constant parameters. This model can be used to model plasma behavior near neutral lines, ({dollar}\gamma{dollar} = 0), as well as current sheets ({dollar}\gamma{dollar} = 0, {dollar}\delta{dollar} = 0). The integrability properties of the particle motion in such fields might affect the plasma's macroscopic behavior, and we have asked the question "For what values of {dollar}\delta{dollar}, {dollar}\gamma{dollar}, and {dollar}\epsilon{dollar} is the system integrable?" to answer this question, we have employed Painleve singularity analysis, which is an examination of the singularity properties of a test particle's equations of motion in the complex time plane. This analysis has identified two field geometries for which the system's particle dynamics are integrable in terms of the second Painleve transcendent: the circular O-line case and the case of the neutral sheet configuration. These geometries yield particle dynamics that are integrable in the Liouville sense (i.e. there exist the proper number of integrals in involution) in an extended phase space which includes the time as a canonical coordinate, and this property is also true for nonzero {dollar}\gamma{dollar}. The singularity property tests also identified a large, dense set of X-line and O-line field geometries that yield dynamics that may possess the weak Painleve property. In the case of the X-line geometries, this result shows little relevance to the physical nature of the system, but the existence of a dense set of elliptical O-line geometries with this property may be related to the fact that for {dollar}\epsilon{dollar} positive, one can construct asymptotic solutions in the limit {dollar}t \to \infty{dollar}.
19
Chakraborty, Susanto. "Solutions of some nonlinear field equations, painleve` properties and Chaos." Thesis, University of North Bengal, 2006. http://hdl.handle.net/123456789/610.
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Luu, Steven. "Exponential asymptotics for discrete Painlevé equations." Thesis, The University of Sydney, 2018. http://hdl.handle.net/2123/18284.
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In this thesis we study Stokes phenomena behaviour present in the solutions of both additive and multiplicative difference equations. Specifically, we undertake an asymptotic study of the second discrete Painlevé equation (dPII) as the independent variable approaches infinity, and consider the asymptotic behaviour of solutions of the q-Airy equation and the first q-Painlevé equation in the limits q□(→┴ ) 1 and n□(→┴ ) ∞. Exponential asymptotic methods are used to investigate Stokes phenomena and obtain uniform asymptotic expansions of solutions of these equations. In the first part of this thesis, we obtain two types of asymptotic expansions which describe vanishing and non-vanishing type solution behaviour of dPII. In particular, we show that both types of solution behaviour can be expressed as the sum of an optimally-truncated asymptotic series and an exponentially subdominant correction term. We then determine the Stokes structure and investigate Stokes behaviour present in these solutions. From this information we show that the asymptotic expansions contain one free parameter hidden beyond-all-orders and determine regions of the complex plane in which these asymptotic descriptions are valid. Furthermore, we deduce special asymptotic solutions which are valid in extended regions and draw parallels between these asymptotic solutions to the tronquée and tri-tronquée solutions of the second Painlevé equation. In the second part of this thesis, we then extend the exponential asymptotic method to q-difference equations. In our analysis of both the q-Airy and first q-Painlevé equations, we find that the Stokes structure is described by curves referred to as q-spirals. As a consequence, we discover that the Stokes structure for solutions of q-difference equations separate the complex plane into sectorial regions bounded by arcs of spirals rather than traditional rays.
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Wong, Wing-tak, and 黃永德. "Ba¨cklund transformations, the Painleve̓ property and some of their applications." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1987. http://hub.hku.hk/bib/B31231408.
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Liu, Qing. "Elliptic Asymptotic Behaviours of Continuous and Discrete Painlevé Equations." Thesis, The University of Sydney, 2018. http://hdl.handle.net/2123/18883.
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This thesis investigates the asymptotic behaviours of both continuous and discrete Painlevé equations as their independent variables approach complex infinity. We focus on the third to the fifth Painlevé equations and three discrete Painlevé equations referred to as d-PI, q-PI and q-PIII in the literature. In each case, the generic asymptotic behaviours are found to be given by elliptic functions. We deduce the properties of the respective elliptic functions in terms of energy-like parameters which are Hamiltonians and invariants of the corresponding autonomous continuous and discrete Painlevé equations. By using the method of averaging, we show that the Hamiltonians and invariants vary slowly across a local period parallelogram of the leading-order behaviour. For the continuous Painlevé equations we show the surprising result that all the equations PI-PV share the same modulation to the first two orders. We also show that the Hamiltonians are bounded on a path to infinity at any fixed angle. The Picard-Fuchs equations are derived for the related elliptic integrals. We solve the Picard-Fuchs equation at its regular singular points to find expansions of the approximate-periods at their degenerate points. The method of averaging is extended to discrete Painlevé equations to show that the invariants are also slowly varying. We also find the singular points of the invariant curves. The Picard-Fuchs equation is derived for q-PIII for its periods. The expansion of the periods at their degenerate points are also given. The main new results of this thesis are summarised in Theorems 1 and 2.1-2.3.
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Yurdusen, Ismet. "Prolongation Structures, Backlund Transformations And Painleve Analysis Of Nonlinear Evolution Equations." Phd thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12605633/index.pdf.
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The Wahlquist-Estabrook prolongation
technique and the Painleve analysis, used for testing
the integrability
of nonlinear evolution equations, are
considered and
applied both to the Drinfel'<br>d-Sokolov system of
equations, indeed known to be one of the coupled
Korteweg-de Vries (KdV)
systems, and Kersten-Krasil'<br>shchik coupled KdV-mKdV equations. Some new Backlund
transformations for the Drinfel'<br>d-Sokolov system of equations are also found.
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Lu, Yixia. "Painleve Analysis, Lie Symmetries and Integrability of Nonlinear Ordinary Differential Equations." Diss., Tucson, Arizona : University of Arizona, 2005. http://etd.library.arizona.edu/etd/GetFileServlet?file=file:///data1/pdf/etd/azu%5Fetd%5F1103%5F1%5Fm.pdf&type=application/pdf.
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Mabb, C. J. "A problem in differential equations connected with the third Painleve transcendant." Thesis, University of Oxford, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.233552.
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Iwaki, Kohei. "On WKB theoretic transformations for Painleve transcendents on degenerate Stokes segments." 京都大学 (Kyoto University), 2014. http://hdl.handle.net/2433/188457.
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Camacho, César, and B. Scárdua. "Generalización de un teorema de P. Painlevé." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/95335.
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Roussillon, Julien. "Fonctions de Painlevé et blocs conformes irréguliers." Thesis, Tours, 2019. http://www.theses.fr/2019TOUR4006/document.
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Cette thèse a pour but de résoudre certains problèmes de connexion et de décrire diverses propriétés asymptotiques des fonctions de Painlevé V et I. Dans le cas de l’équation de Painlevé V, nous approchons ces problèmes en développant une nouvelle approche basée sur la théorie conforme des champs bidimensionelle. Nous proposons de calculer les blocs conformes irréguliers de première et seconde espèce par confluence des blocs conformes réguliers de Virasoro. Une conséquence de cette construction est la solution du problème de connexion de l’équation de Painlevé V entre 0 et +i∞. Les formules pour les normalisations relatives (constantes de connexion) de la fonction tau de Painlevé V entre 0, +∞, et +i∞ sont également proposées. Enfin, le développement asymptotique complet de la fonction tau à courte distance pour des données de monodromie génériques est prouvé. Ce résultat est obtenu en construisant une représentation de la fonction tau en termes d’un déterminant de Fredholm. Dans le cas de l’équation de Painlevé I, nous présentons les constantes de connexion relatant les asymptotiques de la fonction tau sur les cinq raies canoniques à l’infini. Ce résultat est obtenu en construisant une extension de la forme différentielle de Jimbo-Miwa-Ueno à l’espace des données de monodromie. Ces constantes de connexion sont exprimées en termes de dilogarithmes de coordonnées de type cluster dans l’espace des données de Stokes<br>The aim of this thesis is to solve several connection problems and describe asymptotic properties of Painlevé V and I functions. In the case of Painlevé V equation, we approach these problems by developing a new toolbox based on two dimensional conformal field theory. We propose to compute irregular conformal blocks of the first and second kind by confluence of regular Virasoro conformal blocks. One consequence of this construction is the solution of the connection problem for Painlevé V equation between 0 and +i∞. Formulas for the relative normalizations (connection constants) of Painlevé V tau function between 0, +∞, and +i∞ are also proposed. Finally, the full asymptotic expansion of the tau function at short distances for generic monodromy data is proved. This result is obtained by constructing a Fredholm determinant representation for the tau function. In the case of Painlevé I equation, we present connection constants relating asymptotics of the tau function on the five canonical rays at infinity. This result is obtained by extending the definition of the Jimbo-Miwa-Ueno differential to the space of monodromy data. These connection constants are expressed in terms of dilogarithms of cluster type coordinates on the space of Stokes data
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Frostic, Maria Tucker. "Coloring science outside the lines: the poetry and passion of Jean Painleve." Thesis, Montana State University, 2007. http://etd.lib.montana.edu/etd/2007/frostic/FrosticM0507.pdf.
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The majority of current science films for popular audiences follow a formula that can best be described as conventional journalism. Artistic science films are rare, and historically they have generated outrage and distrust by the scientific community. In this paper, I explore the possibility that artful science films are a valid method of conveying the wonders of science to an audience. Underwater French filmmaker Jean Painleve made films that strike a clever balance between art and science, and this unique fusion of divergent parts results in moving vignettes on the astonishing surreal beauty of the marine world. By considering the origin of the science film, by examining Painleve's films and philosophy, and by investigating the role of art and science in society, I argue that artistic science films are valid educational tools that should be used to communicate the wonders of science.
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Milne, Alice Elizabeth. "The Painleve equations : Bäcklund transformations, exact solutions and the isomonodromy deformation method". Thesis, University of Exeter, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.261748.
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Botteghi, Marina. "Coordinate di Painlevé-Gullstrand e buchi neri acustici." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/12057/.
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In questa tesi si introduce il concetto di buco nero acustico come l’analogo sonoro di ciò che rappresenta un buco nero in relatività generale.
In primo luogo verrà quindi illustrata la teoria della gravitazione di Einstein, per poi entrare nel dettaglio della soluzione di Schwarzschild e della nozione di buco nero.
In secondo luogo si dimostrerà come alcuni sistemi, i fluidi disomogenei in movimento, riescano a riprodurre effetti gravitazionali sotto certe condizioni. In particolare si
osserverà come il suono che si propaga in questi fluidi lo faccia lungo delle geodetiche determinate da una "metrica acustica" dipendente da velocità e densità del fluido, che verrà ricavata.
Ciò che permetterà di stabilire l’analogia sarà un’estensione analitica della soluzione di Schwarzschild, quella di Painlevé-Gullstrand: si potrà infatti identificare (formalmente) l’elemento di linea acustico con l’elemento di linea di Painlevé-Gullstrand.
Si troverà che portando la velocità del fluido a una velocità maggiore di quella del suono, nella zona supersonica le onde acustiche non potranno propagarsi controcorrente ma verranno
trascinate nella direzione opposta, come i raggi luminosi vengono trascinati verso la singolarità all’interno dell’orizzonte degli eventi di un buco nero.
La zona supersonica verrà quindi chiamata buco nero acustico.
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Shi, Yang. "Q-discrete Painlevé equation and associated linear problem." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2010. http://tel.archives-ouvertes.fr/tel-00815010.
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Cette thèse est une étude analytique d'équations de Painlevé discrètes(q-discrete Painlevé equations), utilisant le système linéaire associé, dont les équations de Painlevé sont une déformation iso-monodromique. Les équations de Painlevé ont été mises en évidence au début du XXieme siècle, dans une recherche systématique d'équations différentielles ayant des solutions n'ayant pas de singularités dépendant des conditions initiales autres que des pôles. La motivation était de généraliser les fonctions spéciales, tout en contraignant suffisamment le problème. L' idée a été empruntée aux travaux de Sophie Kowalesvki, une contribution fondamentale dans le domaine des systèmes intégrables. Les équations de Painlevé apparaissent aujourd'hui dans un certain nombre de problèmes de physique théorique, dont, pour ne citer que les plus fameux les fonctions de corrélation du modèle d'Ising, et les modèles de mécanique statistique liés aux théories conformes. Un développement apporté par ces résultats venus de la physique théorique est l'émergence de versions discrètes de ces équations. Il est donc particulièrement intéressant de produire de nouvelles solutions de ces équations, puisque la description complète des solutions n'est pas encore disponible. Nous avons surtout étudié les solutions particulières d'un analogue discret de la seconde équation de Painlevé, en utilisant le système linéaire associé construit avec des matrices 2x2. Il est bien connu que, comme leur limites continues, les analogues discrets des équations de Painlevé, admettent, pour des valeurs particulières des paramètres, des solutions particulières rationnelles ou données par des fonctions q-hypergéométriques. Les solutions particulières connues ont des structures de déterminants tout à fait remarquables, et qui peuvent être vues de deux manières différentes. La première fait appel fait appel au ''formalisme bilinéaire'' et est de nature algébrique. La seconde utilise le fait que les équations de Painlevé apparaissent comme la condition de compatibilité d'un système linéaire associé. En examinant ce système linéaire, on peut extraire une information utile sur les équations non-linéaires. En fait ceci permet de mettre en évidence la structure de déterminant des solutions particulières des équations de Painlevé. Pour les équations discrètes, la forme en déterminant des solutions particulières a été déduite par l'approche algébrique. On a montré qu'elles ont une structure similaire à leurs analogues différentiels,modulo quelques différences qui restent à expliquer. Nous avons adopté l'approche analytique et développé la méthode correspondante pour les équations discrètes. Nous avons utilisé le problème linéaire associé à l'équation q-PII, donné en terme de matrices 2x2. Notre résultat majeur est la construction explicite de la forme déterminantale des solutions particulières rationelles et q-hypergéometriques de l'équation q-PII. Ce qui est particulièrement remarquable dans notre méthode est qu'elle utilise l'analyse linéaire q-discrete ''élémentaire'', et est donc très accessible.
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Guerra, Leonor Martinez de Castro. "Mimesis e Alteridade na obra de Jean Painlevé." Master's thesis, Faculdade de Ciências Sociais e Humanas, Universidade Nova de Lisboa, 2013. http://hdl.handle.net/10362/11637.
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Dissertação de mestrado para obtenção do grau de mestre em Ciências da Comunicação, Arte e Comunicação.<br>Parte-se da obra de Jean Painlevé, mais especificamente do objecto (DVD) Science is
Fiction: 23 Films of Jean Painlevé, na tentativa de distinguir o trabalho criativo da arte, da ciência e da
filosofia; as disciplinas lutam entre si contra a Urdoxa de cada uma. Que o discurso científico possa
interessar à arte não é surpreendente, trata-se de satisfazer a sede daqueles que procuram, para além do
que é corrente, o que é vital. Não é com as mesmas ferramentas que arte e ciência procedem a essa
busca, mas ao fazê-lo, partilham a mesma alma e estão expostas à mesma força. Introduz-se a
discussão em torno da mimesis, para elucidar as relações entre realidade, pensamento e linguagem, que
num limite constitui a expressão e o arquivo de uma herança filosófica. Posteriormente, reflecte-se
sobre a dualidade homem/animal, e sobre a afinidade mimética como dimensão central que funda a
possibilidade de emancipação na obra do filósofo. E propõe-se reforçar a dimensão mimética da
constituição do anthropos, isto é, da participação das faculdades estéticas e práticas do sujeito nas
relações de alteridade.
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Alves, Victor César Costa [UNESP]. "Painlevé Integrability and mixed P_III-P_V system solutions." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/149963.
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Previous issue date: 2017-02-21<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>O presente trabalho trata de um abordagem de aplicações em física dos métodos matemáticos de integrabilidade de Painlevé, por outro lado também aborda o formalismo de hierarquias integráveis e o modelo de 2M-bosons onde são usados métodos de equações diferenciais bem como um método para soluções usando aproximantes de Padé.<br>The current work aims at applications of mathematical methods of Painlevé integrability in physics, on the other side it also approaches the integrable hierarchies formalism and the 2M-bose model where differential equations methods are used as well as a method for solutions using Padé approximants.
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Oliveira, Michely Santos. "O problema de Painlevé para campos de Pfaff." Universidade Federal de Viçosa, 2013. http://locus.ufv.br/handle/123456789/4921.
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Previous issue date: 2013-02-25<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>In this work we studied the Painlevé s Problem for Pfaff Fields. The motivation is Painlevé s question about the possibility of giving a bound for the genus of the general solution of an algebraic differential equation in two variables which has a rational first integral. In Some examples for Poincaré and Painlevé problem, Lins Neto found a family of foliations that gave a negative ansewer to this question. In Bounds for sectional genera of varieties invariant under Pfaff fields, Correa Junior and Jardim found a boundle to genera sectional of a projective variety invariant under Pfaff Fields. This work is to study the evidence given by the authors Correa Junior and Jardim.<br>Neste trabalho estudamos o Problema de Painlevé para Campos de Pfaff. A motivação para este estudo foi a questão levantada por Painlevé sobre a possibilidade de limitarmos o gênero da solução geral de uma equação diferencial algébrica em duas variáveis que possui uma integral primeira racional. Em Some examples for Poincaré and Painlevé problem, Lins Neto obteve uma família de folheações holomorfas que deram uma resposta negativa para este problema. Encontrar tal limitante tem sido um problema instigante para muitos matemáticos. Em Bounds for sectional genera of varieties invariant under Pfaff fields, Correa Junior e Jardim obtiveram um limitante para o gênero seccional de uma variedade projetiva invariante por um Campo de Pfaff. Este trabalho consiste em estudar a prova dada pelos autores Correa Junior e Jardim.
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Anizan, Anne-Laure. "Paul Painlevé (1863-1933) : un scientifique en politique." Paris, Institut d'études politiques, 2006. https://spire.sciencespo.fr/notice/2441/53r60a8s3kup1vc9kd50h8hsp.
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Le mathématicien Paul Painlevé est un personnage consulaire de la République, un spécialiste de la défense nationale et un leader de la gauche. Dreyfusard, membre de la Ligue des droits de l'Homme, député de Paris, il fait carrière comme républicain socialiste. Pendant la Première Guerre mondiale, ministre des Inventions, il dirige la politique des inventions intéressant la défense nationale et favorise la mobilisation des savants. En 1917, ministre de la Guerre confronté aux mutineries, il nomme Pétain général en chef et prépare l'arrivée des troupes américaines. Dans les années 1920, il dirige la Ligue de la République et est un promoteur du Cartel. En 1925, président du Conseil et ministre de la Guerre, il soutient la répression des révoltes coloniales et la signature des accords de Locarno. Ministre de la Guerre ou de l'Air dans neuf cabinets à la fin des années 1920 et au début des années 1930, il est responsable des grandes réformes de l'armée française. Cette thèse s'intéresse aux structures de la vie politique française sous la Troisième République. Elle étudie le rôle du socialisme indépendant, la possibilité pour ses élus de faire carrière en dehors des grands partis de gauche, la concurrence du phénomène ligueur pour les partis. Elle présente une voie originale d'accès à la fonction parlementaire et la culture militaire d'un civil ministre de la Guerre. Elle analyse la mobilisation scientifique comme aspect de la culture de guerre. Elle porte aussi sur la réforme de l'État en temps de guerre et en temps de paix : implication de l'État dans la recherche, organisation de la présidence du Conseil, évolution des rapports entre exécutif et législatif<br>The mathematician Paul Painlevé was a prominent personality of the French Republic, an expert in the nation's defence and a leader of the French left. A supporter of Captain Dreyfus, a member of the Human Rights League, a député of Paris, he made his career as a republican socialist. In the first world war, as the minister of inventions, he led the research policy regarding the country's defence and encouraged the scientists' involvement in it. As the minister of war in 1917, he had to face the mutinies among the French soldiers, appointed Pétain as the general-in-chief and prepared the US troop' landing. In 1920s, he chaired the Ligue de la République and promoted the Cartel. In 1925, as the président du Conseil and the minister of war, he enforced the repression of rebellions in the colonies and supported the signature of the Locarno agreements. Either as the minister of war or of the air force in nine cabinets from the late 1920s to the early 1930s, he presided over the great reforms of the French army. This thesis focusses on the structures of political life under the Third Republic in France. It studies the part played by independent socialism, the possibility for its elected representatives to thrive outside the mainstream left parties in the context of the competition with the Ligue. It documents an unusual accession to the parliamentary charge and the specific defence culture a civilian who had become the minister of war could have and it analyses the participation of scientists as an aspect of war culture. Lastly it concentrates on the way theState was reformed both in wartime and once peace had been restored through its involvement in research, the organisational changes in the presidence du Conseil and the evolution of the relations between the legislative and executive powers
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Twiton, Michael. "Analysis of Singular Solutions of Certain Painlevé Equations." Thesis, The University of Sydney, 2018. http://hdl.handle.net/2123/18206.
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The six Painlevé equations can be described as the boundary between the non- integrable- and the trivially integrable-systems. Ever since their discovery they have found numerous applications in mathematics and physics. The solutions of the Painlevé equations are, in most cases, highly transcendental and hence cannot be expressed in closed form. Asymptotic methods do better, and can establish the behaviour of some of the solutions of the Painlevé equations in the neighbourhood of a singularity, such as the point at infinity. Although the quantitative nature of these neighbourhoods is not initially implied from the asymptotic analysis, some regularity results exist for some of the Painlevé equations. In this research, we will present such results for some of the remaining Painlevé equations. In particular, we will provide concrete estimates of the intervals of analyticity of a one-parameter family of solutions of the second Painlevé equation, and estimate the domain of analyticity of a “triply-truncated” solution of the fourth Painlevé equation. In addition we will also deduce the existence of solutions with particular asymptotic behaviour for the discrete Painlevé equations, which are discrete integrable nonlinear systems.
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Gregory, James Philip. "A q-discrete Analogue of the Third Painlevé Equation and its Linear Problem." Thesis, The University of Sydney, 2016. http://hdl.handle.net/2123/15470.
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In this thesis we investigate the rational and Riccati type special solutions for particular parameter values of a q-discrete analogue of the third Painlevé equation, with rational surface A(1) 5 and affine Weyl group (A2 + A1)(1). The general solutions of this equation are highly transcendental in nature. We work closely with an associated system of discrete linear equations, which we refer to as ‘the linear problem.’We demonstrate that the linear problem can be solved both in terms of q-Gamma functions and series expansions for different parameter values of our discrete Painlevé equation. By developing a Schlesinger transformation, which transforms a series expansion of the linear problem for one parameter value to another series expansion of the linear problem for another parameter value, we are able to develop determinantal representations of the rational and Riccati type special solutions. These determinantal forms appear different to those discovered previously by Kajiwara. This technique has only been used to develop the determinantal forms of two other continuous and discrete Painlevé equations and hence the results presented here further indicate its potential.
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Ruy, Danilo Virges. "Equações de Painlevé mistas e modelo PIII-PV simétrico /." São Paulo, 2015. http://hdl.handle.net/11449/124148.
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Orientador: Abraham Hirsz Zimerman<br>Banca: Dionisio Bazeia Filho<br>Banca: Cesar Rogério de Oliveira<br>Banca: Iberê Luiz Caldas<br>Banca: Antônio Lima Santos<br>Resumo: Esta tese aborda a conexão entre modelos integráveis e as equações de Painlevé. Começamos estendendo o método do truncamento modificado afim de encontrar transformações de Bäcklund para a hierarquia mKdV-Liouville e sua redução por auto-similaridade. Com este método, resolvemos parcialmente a conjectura de Kudryashov. Em seguida, estudamos o modelo misto AKNS-Lund-Regge estendido e mostramos que este modelo pode ser reduzido às equações PIV e PV para valores particulares dos parâmetros. Nós também construimos o modelo PIII-PV simétrico afim de unificar alguns casos da equação PIII com a equação PV. Posteriormente, buscamos os vínculos canônicos apropriados que reduzem o modelo 4-bósons ao modelo PIII-PV simétrico. Para isso, elaboramos o método do ansatz de vínculos. Complementarmente, apresentamos um método para encontrar soluções de equações diferenciais em D dimensões no adendo e aplicamos ao modelo 'lâmbda'fi'POT.4<br>Abstract: This thesis studies the connection among integrable models and Painlev'e equations. We begin by extending the modified truncation approach in order to find B¨acklund transformations for the mKdV-Liouville hierarchy and its self-similarity reduction. With this method, we solve Kudryashov's conjecture partially. Then we study the extended mixed AKNS-Lund-Regge model and show this model can be reduced to PIV and PV equation for particular values of the parameters. We also construct the symmetric PIII-PV model in order to unify some cases of the PIII equation with the PV equation. After, we search for canonical constraints for reduce the 4-bose model to the symmetric PIII-PV model. For find the correct constraints, we construct the method of ansatz of constraints. In addition, we show a method for finding solutions for differential equations inD dimensions in the addendum. We also apply this method for the 'lâmbda'fi'POT.4 model<br>Doutor
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Ruy, Danilo Virges [UNESP]. "Equações de Painlevé mistas e modelo PIII-PV simétrico." Universidade Estadual Paulista (UNESP), 2015. http://hdl.handle.net/11449/124148.
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000829086.pdf: 649617 bytes, checksum: d3f00788fe458b7e00736119967fad0f (MD5)<br>Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)<br>Esta tese aborda a conexão entre modelos integráveis e as equações de Painlevé. Começamos estendendo o método do truncamento modificado afim de encontrar transformações de Bäcklund para a hierarquia mKdV-Liouville e sua redução por auto-similaridade. Com este método, resolvemos parcialmente a conjectura de Kudryashov. Em seguida, estudamos o modelo misto AKNS-Lund-Regge estendido e mostramos que este modelo pode ser reduzido às equações PIV e PV para valores particulares dos parâmetros. Nós também construimos o modelo PIII-PV simétrico afim de unificar alguns casos da equação PIII com a equação PV. Posteriormente, buscamos os vínculos canônicos apropriados que reduzem o modelo 4-bósons ao modelo PIII-PV simétrico. Para isso, elaboramos o método do ansatz de vínculos. Complementarmente, apresentamos um método para encontrar soluções de equações diferenciais em D dimensões no adendo e aplicamos ao modelo 'lâmbda'fi'POT.4<br>This thesis studies the connection among integrable models and Painlev'e equations. We begin by extending the modified truncation approach in order to find B¨acklund transformations for the mKdV-Liouville hierarchy and its self-similarity reduction. With this method, we solve Kudryashov's conjecture partially. Then we study the extended mixed AKNS-Lund-Regge model and show this model can be reduced to PIV and PV equation for particular values of the parameters. We also construct the symmetric PIII-PV model in order to unify some cases of the PIII equation with the PV equation. After, we search for canonical constraints for reduce the 4-bose model to the symmetric PIII-PV model. For find the correct constraints, we construct the method of ansatz of constraints. In addition, we show a method for finding solutions for differential equations inD dimensions in the addendum. We also apply this method for the 'lâmbda'fi'POT.4 model<br>FAPESP: 2010/18110-9
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Lindblom, Ove. "Painlevé analysis and transformations for nonlinear partial differential equations." Doctoral thesis, Luleå tekniska universitet, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-16794.
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Nonlinear partial differential equations play a fundamental role in the description of many physical models. In order to get a complete understanding of the phenomena which are modeled it is important to obtain exact analytic solutions. In this thesis several methods are investigated to construct analytic solutions and to classify nonlinear partial differential equations with respect to those methods. The main emphasis is on the Painlevé analysis and transformations of partial differential equations (PDEs). The Painlevé analysis for PDEs was introduced by a group of American Mathematicians in 1983. Since then many integrable equations are studied by use of this analysis. For example this analysis plays a major role in the study of soliton equations and other integrable PDEs. More recently several scientists have become interested in extending the analysis to non-integrable equations. In this thesis we investigate several non-integrable PDEs of Mathematical Physics such as the Boltzmann equations and d'Alembert-type wave equations in multidimensions. These equations model different physical phenomena in particle dynamics and wave motion. We show that the Bateman equation provides a structure for the singularity manifold for some classes of equations. This fact is applied to obtain several new solutions to the equations of interest. The second major theme of this thesis is the transformation properties of nonlinear PDEs. Two-dimensional d'Alembert-type equations invariant under Lie symmetry subalgebras of Lorenz- and conformal-type are classified. A hierarchy of linearizable evolution equations is also derived by use of a generalized hodograph transformation. This result sets the stage for a new classification of linearizable evolution equations.<br>Godkänd; 2001; 20061114 (haneit)
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Masoero, Davide. "Essays on the Painlevé first equation and the cubic oscillator." Doctoral thesis, SISSA, 2010. http://hdl.handle.net/20.500.11767/4151.
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Little, Steven. "INTEGRABILITY OF A SINGULARLY PERTURBED MODEL DESCRIBING GRAVITY WATER WAVES ON A SURFACE OF FINITE DEPTH." Master's thesis, University of Central Florida, 2008. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3285.
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Our work is closely connected with the problem of splitting of separatrices (breaking of homoclinic orbits) in a singularly perturbed model describing gravity water waves on a surface of finite depth. The singularly perturbed model is a family of singularly perturbed fourth-order nonlinear ordinary differential equations, parametrized by an external parameter (in addition to the small parameter of the perturbations). It is known that in general separatrices will not survive a singular perturbation. However, it was proven by Tovbis and Pelinovsky that there is a discrete set of exceptional values of the external parameter for which separatrices do survive the perturbation. Since our family of equations can be written in the Hamiltonian form, the question is whether or not survival of separatrices implies integrability of the corresponding equation. The complete integrability of the system is examined from two viewpoints: 1) the existence of a second first integral in involution (Liouville integrability), and 2) the existence of single-valued, meromorphic solutions (complex analytic integrability). In the latter case, a singular point analysis is done using the technique given by Ablowitz, Ramani, and Segur (the ARS algorithm) to determine whether the system is of Painlevé-type (P-type), lacking movable critical points. The system is shown by the algorithm to fail to be of P-type, a strong indication of nonintegrability.<br>M.S.<br>Department of Mathematics<br>Sciences<br>Mathematical Science MS
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Biava, Pedro. "A ideia de cinema científico presente na obra de Jean Painlevé." Pontifícia Universidade Católica de São Paulo, 2015. https://tede2.pucsp.br/handle/handle/13306.
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Previous issue date: 2015-03-09<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>Jean Painlevé s (1902-1989) scientific cinema is filled with
elements that turned his analysis into an important source to study the
relation between Art and Science during the first decades of the 20th
century, especially in France. The filmmaker s work is composed of
more than 200 movies, performed throughout more than six decades of
work as a filmmaker, scientist and Science propagator.
Painlevé used cinema as a research and scientific propagation
instrument, and he used a particular mixture of technical and narrative
resources to perform his work. He connected surrealist art to scientific
objectivity, always seeking to show the spectator his own enchantment
for scientific research. Some of his films became a reference for the
Science documentarians that followed him. It is the case of The
Seahorse (1934), his most popular film. It gathers images that were
never seen before about the birth of babies from this species, where the
male has the role of giving birth offspring.
Painlevé used a narrative that mixed technical and scientific
information along with dramatic and comical elements. It s possible to
notice how his work helped Science become more accessible and
popular. His work had Marine Biology as a main theme, but he worked
with other scientific themes that interested him in Physics, Chemistry
and other areas.
Using cinema as a source of science history research is not only
a tool that allows an analysis of the technical evolution of image
capturing, but it´s also a sociocultural understanding of the historical
context in which the cinematographic technique was used. Analyzing
the films as part of the documents studied in the research was essential
in the process.
Besides an extensive filmography, Painlevé left a series of written
material talking about cinema, which helped understand his vision of
Science, and the role he assigned to cinema in the context of scientific
development. In this dissertation, the objective was to cross information
presented in these films and texts to understand the aspects of Science
History in his work<br>O cinema científico de Jean Painlevé (1902-1989) é repleto de
elementos que tornaram sua análise uma fonte importante para estudar
a relação entre arte e ciência nas primeiras décadas do século XX, em
especial na França. Sua obra é composta por mais de 200 filmes,
realizados ao longo de mais de seis décadas de trabalho como
cineasta, cientista e divulgador da ciência.
Painlevé utilizou o cinema como instrumento de pesquisa e
divulgação científica, e fez uso de uma mistura particular de recursos
técnicos e narrativos para realizar seu trabalho. Uniu a arte surrealista
à objetividade científica, sempre buscando apresentar ao espectador o
encantamento que ele próprio tinha pela pesquisa científica. Alguns de
seus filmes tornaram-se referência para os documentaristas de ciência
que o sucederam. É o caso de O Cavalo Marinho (1934), seu filme
mais popular e que reúne imagens, até então inéditas, do nascimento
de filhotes dessa espécie que tem no macho, o papel de gestor das
crias.
Painlevé fez uso de uma narrativa que mesclava informações
técnicas e cientificas com elementos dramáticos e cômicos. É possível
perceber como seu trabalho ajudou a tornar a ciência mais acessível e
popular. Sua obra teve como temática principal a biologia marinha, mas
tratou de outros temas da ciência que lhe interessavam, na física,
química e em outras áreas.
O uso do cinema como fonte de pesquisa da história da ciência é
uma ferramenta que permitiu não apenas uma análise da evolução
técnica do registro de imagens, mas também um entendimento sócio
cultural do contexto histórico em que a técnica cinematográfica foi
utilizada. Analisar os filmes, como parte dos documentos estudados na
pesquisa, foi fundamental no processo.
Além da extensa filmografia, Painlevé deixou uma série de
escritos tratando do cinema que auxiliaram na compreensão de sua
visão de ciência e do papel que ele atribuía ao cinema no contexto do
desenvolvimento científico. Nessa dissertação, buscou-se fazer um
cruzamento das informações presentes nestes filmes e textos para
compreender os aspectos da História da Ciência presentes em sua
obra
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Hamery, Roxane. "Jean Painlevé (1902-1989) : un cinéaste au service de la science." Rennes 2, 2004. http://www.theses.fr/2004REN20016.
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La production et la longue carrière de Jean Painlevé, réalisateur de court métrage, documentariste associé aux domaines spécialisés du cinéma scientifique ou du film d'enseignement, demeurent, pour une large part, méconnues alors qu'il fut un fervent défenseur d'un cinéma populaire et intelligent, un membre important des institutions du septième art ainsi qu'une figure reconnue de l'avant-garde des années 20. C'est peut être cet éclectisme qui a jusqu'ici empêché de dresser un panorama cohérent de ses multiples activités et de saisir la personnalité de cet homme farouchement indépendant. Afin de réévaluer ce parcours cinématographique original et engagé, cette thèse a pour ambition de retracer l'œuvre de Jean Painlevé et d'étudier l'évolution esthétique de ses films dans le cadre d'une analyse contextuelle. Ce portrait contrasté se présente comme celui d'un artiste exigeant, autant dans la réalisation de ses films que dans ses combats militants<br>Jean Painlevé, short film director and documentarist, usually associated with the specialized genres of scientific cinema and educational film, has, throughout his long career, produced an impressive amount of work which remains for a large part scarcely known. He was however an ardent promoter of an instructive yet popular cinema, an eminent member of the institutions of the seven arts and a major pioneer of the avant-garde of the twenties. Up to now, this eclecticism may have impeded the attempts to draw up all these various activities into a coherent panorama and to understand the complex personality of the strongly independent man behind them. The aim of this thesis is the reassessment of this original cinematographic career; it will follow Painlevé's works step by step and will also examine his aesthetic evolution in a contextual analysis. This contrasted portrait fits a never satisfied artist involved with the same passion in the making of films or in militant struggles as well
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Roffelsen, Pieter. "On the global asymptotic analysis of a q-discrete Painlevé equation." Thesis, The University of Sydney, 2017. http://hdl.handle.net/2123/16601.
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In this thesis we make effective the global asymptotic analysis of a nonlinear q-difference Painlevé equation, whose initial value space is a rational surface of type A1(1) according to Sakai's classification. This equation can be thought of as an eight parameter generalisation of the celebrated sixth Painlevé equation, where the reduction to the differential equation goes via the continuum limit of its symmetric form. The first part of the thesis is concerned with the local asymptotic analysis of solutions near the critical points of the q-difference equation, the origin and infinity. A conjecturally complete list of possible asymptotic behaviours is found near both critical points. It is shown that, upon taking the continuum limit, the list essentially coincides with that of critical behaviours of solutions of the sixth Painlevé equation, obtained by Guzzetti. In the second part of the thesis, the integrability of the equation under consideration is exploited, to solve the nonlinear connection problem, which entails explicitly relating the critical behaviours of solutions near the two different critical points. This is done by employing a q-analog of the isomonodromic deformation method to a q-difference Lax pair devised by Yamada. The direct monodromy problem is solved, both for critical behaviours near the origin and infinity, by showing that near the critical points, the connection problem of Yamada's system factorises in two copies of a simpler connection problem, which can be solved explicitly. Comparison of the results, leads to explicit parametric connection formulae for critical behaviours of the q-difference Painlevé equation.
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Singh, Shonal. "Spaces of initial values of differential equations with the Painlevé property." Thesis, The University of Sydney, 2018. http://hdl.handle.net/2123/18114.
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In this thesis, we study the spaces of initial values of some differential equations with the Painlevé property. The first part of our study begins by introducing the standard techniques associated with such spaces by discussing the well known example of the second Painlevé equation P_II. We then apply these techniques to the cases of linearisable second-order ordinary differential equations (ODEs) and a fourth-order analogue of P_II with particular emphasis on the solutions and structure of the singularities. We explicitly show that the initial value spaces of these ODEs can be regularised for family of general solutions while special family of solutions containing fewer free parameters than the equations’ orders require an infinite number of resolutions or blow ups. To complement our study, we also consider the spaces of initial values of partial differential equations (PDEs). Our examples are Burgers’ and the Korteweg-de Vries equations, whose movable singularities are described by Laurent expansions of the solutions around an arbitrary noncharacteristic manifold. We embed the initial values of these PDEs in complex projective spaces of the appropriate respective dimension and resolve base loci in the corresponding space. As in the ODE case, the initial value space is best understood as a foliation. It is interesting to observe that for both the PDEs, generic initial values are resolved by a finite number of blow ups, while certain initial values lead to an infinite number of blow ups. We provide evidence to show that the latter cases correspond to implicit special solutions. All of the resolutions are described explicitly. Our results suggest that the geometric framework of initial value spaces for the Painlevé equations extends to integrable PDEs. While not all the correspondences between the two frameworks are pursued in this thesis, they suggest tantalising rich directions for future research.
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Ruy, Danilo Virges [UNESP]. "Estrutura hamiltoniana da hierarquia PIV." Universidade Estadual Paulista (UNESP), 2011. http://hdl.handle.net/11449/92036.
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ruy_dv_me_ift.pdf: 500107 bytes, checksum: fef6f049175c290422f569aa7ad7e26e (MD5)<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>Esta dissertação trata da construção de hierarquias compatíveis com a equação PIV a partir dos modelos: AKNS, dois bósons e dois bósons quadráticos. Também são construidos os problema linear de Jimbo-Miwa dos três modelos e discutimos a hamiltoniana correspondente a equação PIV a partir do formalismo lagrangiano<br>This dissertation contains the construction of compatible hierarchies with the PIV equation from the models: AKNS, two-boson and quadratic two-boson. Also it is build the Jimbo-Miwa linear problem for the three models and we discuss the hamiltonian corresponding to fouth Painlevé equation from the Lagrangian formalism
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Ruy, Danilo Virges. "Estrutura hamiltoniana da hierarquia PIV /." São Paulo : [s.n.], 2011. http://hdl.handle.net/11449/92036.
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Orientador: Abraham Hirsz Zimerman<br>Banca: Iberê Luiz Caldas<br>Banca: Roberto André Kraenkel<br>Resumo: Esta dissertação trata da construção de hierarquias compatíveis com a equação PIV a partir dos modelos: AKNS, dois bósons e dois bósons quadráticos. Também são construidos os problema linear de Jimbo-Miwa dos três modelos e discutimos a hamiltoniana correspondente a equação PIV a partir do formalismo lagrangiano<br>Abstract: This dissertation contains the construction of compatible hierarchies with the PIV equation from the models: AKNS, two-boson and quadratic two-boson. Also it is build the Jimbo-Miwa linear problem for the three models and we discuss the hamiltonian corresponding to fouth Painlevé equation from the Lagrangian formalism<br>Mestre
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Sakai, Hidetaka. "Rational surfaces associated with affine root systems and geometry of the Painlevé equations." 京都大学 (Kyoto University), 1999. http://hdl.handle.net/2433/181435.
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