Breadth-first serialisation of trees and rational languages

We present here the notion of breadth-first signature and its relationship with numeration system theory. It is the serialisation into an infinite word of an ordered infinite tree of finite degree. We study which class of languages corresponds to which class of words and,more specifically, using a known construction from numeration system theory, we prove that the signature of rational languages are substitutive sequences.Comment: 15 page

Finite size scaling of current fluctuations in the totally asymmetric exclusion process

We study the fluctuations of the current J(t) of the totally asymmetric exclusion process with open boundaries. Using a density matrix renormalization group approach, we calculate the cumulant generating function of the current. This function can be interpreted as a free energy for an ensemble in which histories are weighted by exp(-sJ(t)). We show that in this ensemble the model has a first order space-time phase transition at s=0. We numerically determine the finite size scaling of the cumulant generating function near this phase transition, both in the non-equilibrium steady state and for large times.Comment: 18 pages, 11 figure

Cohomology of groups of diffeomorphims related to the modules of differential operators on a smooth manifold

Let $M$ be a manifold and $T^*M$ be the cotangent bundle. We introduce a 1-cocycle on the group of diffeomorphisms of $M$ with values in the space of linear differential operators acting on $C^{\infty} (T^*M).$ When $M$ is the $n$-dimensional sphere, $S^n$, we use this 1-cocycle to compute the first-cohomology group of the group of diffeomorphisms of $S^n$, with coefficients in the space of linear differential operators acting on contravariant tensor fields.Comment: arxiv version is already officia

On sl(2)-equivariant quantizations

By computing certain cohomology of Vect(M) of smooth vector fields we prove that on 1-dimensional manifolds M there is no quantization map intertwining the action of non-projective embeddings of the Lie algebra sl(2) into the Lie algebra Vect(M). Contrariwise, for projective embeddings sl(2)-equivariant quantization exists.Comment: 09 pages, LaTeX2e, no figures; to appear in Journal of Nonlinear Mathematical Physic

Critical parameters for the partial coalescence of a droplet

The partial coalescence of a droplet onto a planar liquid/liquid interface is investigated experimentally by tuning the viscosities of both liquids. The problem mainly depends on four dimensionless parameters: the Bond number (gravity vs. surface tension), the Ohnesorge numbers (viscosity in both fluids vs. surface tension), and the density relative difference. The ratio between the daughter droplet size and the mother droplet size is investigated as a function of these dimensionless numbers. Global quantities such as the available surface energy of the droplet has been measured during the coalescence. The capillary waves propagation and damping are studied in detail. The relation between these waves and the partial coalescence is discussed. Additional viscous mechanisms are proposed in order to explain the asymmetric role played by both viscosities.Comment: 16 pages, 14 figures, submitted to Physical Review

A numerical approach to large deviations in continuous-time

We present an algorithm to evaluate the large deviation functions associated to history-dependent observables. Instead of relying on a time discretisation procedure to approximate the dynamics, we provide a direct continuous-time algorithm, valuable for systems with multiple time scales, thus extending the work of Giardin\`a, Kurchan and Peliti (PRL 96, 120603 (2006)). The procedure is supplemented with a thermodynamic-integration scheme, which improves its efficiency. We also show how the method can be used to probe large deviation functions in systems with a dynamical phase transition -- revealed in our context through the appearance of a non-analyticity in the large deviation functions.Comment: Submitted to J. Stat. Mec

Natural and projectively equivariant quantizations by means of Cartan Connections

The existence of a natural and projectively equivariant quantization in the sense of Lecomte [20] was proved recently by M. Bordemann [4], using the framework of Thomas-Whitehead connections. We give a new proof of existence using the notion of Cartan projective connections and we obtain an explicit formula in terms of these connections. Our method yields the existence of a projectively equivariant quantization if and only if an \sl(m+1,\R)-equivariant quantization exists in the flat situation in the sense of [18], thus solving one of the problems left open by M. Bordemann.Comment: 13 page