The Heckman-Opdam Markov processes

We introduce and study the natural counterpart of the Dunkl Markov processes in a negatively curved setting. We give a semimartingale decomposition of the radial part, and some properties of the jumps. We prove also a law of large numbers, a central limit theorem, and the convergence of the normalized process to the Dunkl process. Eventually we describe the asymptotic behavior of the infinite loop as it was done by Anker, Bougerol and Jeulin in the symmetric spaces setting in \cite{ABJ}

Exploiting lattice potentials for sorting chiral particles

Several ways are demonstrated of how periodic potentials can be exploited for sorting molecules or other small objects which only differ by their chirality. With the help of a static bias force, the two chiral partners can be made to move along orthogonal directions. Time-periodic external forces even lead to motion into exactly opposite directions.Comment: 4 pages, 4 figure

On hitting times of affine boundaries by reflecting Brownian motion and Bessel processes

Firstly, we compute the distribution function for the hitting time of a linear time-dependent boundary $t\mapsto a+bt,\ a\geq 0,\,b\in \R,$ by a reflecting Brownian motion. The main tool hereby is Doob's formula which gives the probability that Brownian motion started inside a wedge does not hit this wedge. Other key ingredients are the time inversion property of Brownian motion and the time reversal property of diffusion bridges. Secondly, this methodology can also be applied for the three dimensional Bessel process. Thirdly, we consider Bessel bridges from 0 to 0 with dimension parameter $\delta>0$ and show that the probability that such a Bessel bridge crosses an affine boundary is equal to the probability that this Bessel bridge stays below some fixed value.Comment: 32 pages, 2 figure

Rates of convergence of a transient diffusion in a spectrally negative L\'{e}vy potential

We consider a diffusion process $X$ in a random L\'{e}vy potential $\mathbb{V}$ which is a solution of the informal stochastic differential equation \begin{eqnarray*}\cases{dX_t=d\beta_t-{1/2}\mathbb{V}'(X_t) dt,\cr X_0=0,}\end{eqnarray*} ($\beta$ B. M. independent of $\mathbb{V}$). We study the rate of convergence when the diffusion is transient under the assumption that the L\'{e}vy process $\mathbb{V}$ does not possess positive jumps. We generalize the previous results of Hu--Shi--Yor for drifted Brownian potentials. In particular, we prove a conjecture of Carmona: provided that there exists $0<\kappa<1$ such that $\mathbf{E}[e^{\kappa\mathbb{V}_1}]=1$, then $X_t/t^{\kappa}$ converges to some nondegenerate distribution. These results are in a way analogous to those obtained by Kesten--Kozlov--Spitzer for the transient random walk in a random environment.Comment: Published in at http://dx.doi.org/10.1214/009117907000000123 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Liquid transport generated by a flashing field-induced wettability ratchet

We develop and analyze a model for ratchet-driven macroscopic transport of a continuous phase. The transport relies on a field-induced dewetting-spreading cycle of a liquid film with a free surface based on a switchable, spatially asymmetric, periodic interaction of the liquid-gas interface and the substrate. The concept is exemplified using an evolution equation for a dielectric liquid film under an inhomogeneous voltage. We analyse the influence of the various phases of the ratchet cycle on the transport properties. Conditions for maximal transport and the efficiency of transport under load are discussed.Comment: 10 pages, 5 figure

Representation of the Cathedral in French Visual Culture, 1870-1914

This thesis presents an analysis of the way in which northern French cathedrals were represented and understood by artists between 1870 and 1914. The period chosen is of particular interest because of its agitated religious and political context, making a Catholic building such as a cathedral an embodiment of the struggles between church and state under the Third Republic.The issues dealt with in this thesis start with the role played by the representation of French cathedrals in the context of the Annee Terrible of 1870-1871. The analysis of a number of representations from varied sources demonstrates the importance of the notion of nationalism when considering the cathedrals between the FrancoPrussian War and the beginning of World War One. This issue of nationalism is dealt with further with educational material on cathedrals used during the Third Republic.The religious and spiritual side of the cathedral is examined through a range of visual documents presenting images from Catholic painters as well as through the connection established between the Church and the State during the Ralliement.A specific focus is given to painters Camille Pissarro and Maximilien Luce, whose representations of cathedrals need to be assessed in terms of their strong anarchist views. This examination demonstrates how anarchism and religious buildings such as cathedrals could work together in images towards the promotion of the anarchist ideal.Two case studies also allow for a greater depth of understanding of the messages carried by cathedrals between 1870 and 1914. Many artists represented the cathedral churches of Rouen and Paris, and an analysis of these images brings out the range of ideas which can be associated with cathedrals in the visual arts.The French cathedral was an essential figure of the visual arts between 1870 and 1914 because of its power of suggestion. It was in turn a Catholic church, a nationalist emblem, an anarchist symbol, and a motif utilised by artists to experiment with new pictorial ideas. Between 1870 and 1914 it took on significant new artistic and political dimensions