TY - GEN A1 - Roelly, Sylvie A1 - Thieullen, Michèle T1 - Duality formula for the bridges of a Brownian diffusion : application to gradient drifts N2 - In this paper, we consider families of time Markov fields (or reciprocal classes) which have the same bridges as a Brownian diffusion. We characterize each class as the set of solutions of an integration by parts formula on the space of continuous paths C[0; 1]; R-d) Our techniques provide a characterization of gradient diffusions by a duality formula and, in case of reversibility, a generalization of a result of Kolmogorov. KW - reciprocal processes KW - stochastic bridge KW - mixture of bridges KW - integration by parts formula KW - Malliavin calculus KW - entropy KW - time reversal Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6710 ER - TY - GEN A1 - Roelly, Sylvie A1 - Sortais, Michel T1 - Space-time asymptotics of an infinite-dimensional diffusion having a long- range memory N2 - We develop a cluster expansion in space-time for an infinite-dimensional system of interacting diffusions where the drift term of each diffusion depends on the whole past of the trajectory; these interacting diffusions arise when considering the Langevin dynamics of a ferromagnetic system submitted to a disordered external magnetic field. KW - Random Field Ising Model KW - Langevin Dynamics KW - Interacting Diffusion Processes KW - Space-Time Cluster Expansions Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6700 ER - TY - GEN A1 - Roelly, Sylvie A1 - Dereudre, David T1 - On Gibbsianness of infinite-dimensional diffusions N2 - The authors analyse different Gibbsian properties of interactive Brownian diffusions X indexed by the d-dimensional lattice. In the first part of the paper, these processes are characterized as Gibbs states on path spaces. In the second part of the paper, they study the Gibbsian character on R^{Z^d} of the law at time t of the infinite-dimensional diffusion X(t), when the initial law is Gibbsian. AMS Classifications: 60G15 , 60G60 , 60H10 , 60J60 KW - infinite-dimensional Brownian diffusion KW - Gibbs field KW - cluster expansion Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6692 ER - TY - GEN A1 - Roelly, Sylvie A1 - Dai Pra, Paolo T1 - An existence result for infinite-dimensional Brownian diffusions with non- regular and non Markovian drift N2 - We prove in this paper an existence result for infinite-dimensional stationary interactive Brownian diffusions. The interaction is supposed to be small in the norm ||.||∞ but otherwise is very general, being possibly non-regular and non-Markovian. Our method consists in using the characterization of such diffusions as space-time Gibbs fields so that we construct them by space-time cluster expansions in the small coupling parameter. KW - infinite-dimensional Brownian diffusion KW - space-time Gibbs field KW - cluster expansion Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6684 ER - TY - THES A1 - Andersen, Audrée T1 - Surfactant dynamics at interfaces : a series of second harmonic generation experiments T1 - Surfactant Dynamik an Grenzflächen : eine Studie über SHG-Experimente N2 - Adsorption layers of soluble surfactants enable and govern a variety of phenomena in surface and colloidal sciences, such as foams. The ability of a surfactant solution to form wet foam lamellae is governed by the surface dilatational rheology. Only systems having a non-vanishing imaginary part in their surface dilatational modulus, E, are able to form wet foams. The aim of this thesis is to illuminate the dissipative processes that give rise to the imaginary part of the modulus. There are two controversial models discussed in the literature. The reorientation model assumes that the surfactants adsorb in two distinct states, differing in their orientation. This model is able to describe the frequency dependence of the modulus E. However, it assumes reorientation dynamics in the millisecond time regime. In order to assess this model, we designed a SHG pump-probe experiment that addresses the orientation dynamics. Results obtained reveal that the orientation dynamics occur in the picosecond time regime, being in strong contradiction with the two states model. The second model regards the interface as an interphase. The adsorption layer consists of a topmost monolayer and an adjacent sublayer. The dissipative process is due to the molecular exchange between both layers. The assessment of this model required the design of an experiment that discriminates between the surface compositional term and the sublayer contribution. Such an experiment has been successfully designed and results on elastic and viscoelastic surfactant provided evidence for the correctness of the model. Because of its inherent surface specificity, surface SHG is a powerful analytical tool that can be used to gain information on molecular dynamics and reorganization of soluble surfactants. They are central elements of both experiments. However, they impose several structural elements of the model system. During the course of this thesis, a proper model system has been identified and characterized. The combination of several linear and nonlinear optical techniques, allowed for a detailed picture of the interfacial architecture of these surfactants. N2 - Amphiphile vereinen zwei gegensätzliche Strukturelemente in einem Molekül, eine hydrophile Kopfgruppe und ein hydrophobe, meist aliphatische Kette. Aufgrund der molekularen Asymmetrie erfolgt eine spontane Adsorption an der Wasser-Luft Grenzfläche. Die Adsorptionsschicht verändert die makroskopischen Eigenschaften des Materials, z.B. die Grenzflächenspannung wird erniedrigt. Amphiphile sind zentrale Bauelemente der Kolloid- und Grenzflächenforschung, die Phänomene, wie Schäume ermöglichen. Eine Schaumlamelle besteht aus einem dünnen Wasserfilm, der durch zwei Adsorptionsschichten stabilisiert wird. Die Stabilität der Lamelle wird durch die Grenzflächenrheologie entscheidend geprägt. Die wesentliche makroskopische Größe in diesem Zusammenhang ist das so genannte Grenzflächendilatationsmodul E. Es beschreibt die Fähigkeit des Systems die Gleichgewichtsgrenzflächenspannung nach einer Expansion oder Dilatation der Adsorptionschicht wieder herzustellen. Das Modul E ist eine komplexe Größe, in dem der Imaginärteil direkt mit der Schaumstabilität korreliert. Diese Arbeit widmet sich der Grenzflächenrheologie. In der Literatur werden zwei kontroverse Modelle zur Interpretation dieser Größe diskutiert. Diese Modelle werden experimentell in dieser Arbeit überprüft. Dies erfordert die Entwicklung neuer experimenteller Aufbauten basierend auf nichtlinearen, optischen Techniken. Mit diesen Experimenten konnte eines der Modelle bestätigt werden. KW - Tensid KW - Grenzflächenchemie KW - Nichtlineare Spektroskopie KW - Oscillating Bubble KW - surfactants KW - nonlinear optics KW - surface rheology KW - air-water interface KW - oscillating bubble Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6553 ER -