Generalisation of the Eyring–Kramers Transition Rate Formula to Irreversible Diffusion Processes

In the small noise regime, the average transition time between metastable states of a reversible diffusion process is described at the logarithmic scale by Arrhenius’ law. The Eyring–Kramers formula classically provides a subexponential prefactor to this large deviation estimate. For irreversible diffusion processes, the equivalent of Arrhenius’ law is given by the Freidlin–Wentzell theory. In this paper, we compute the associated prefactor and thereby generalise the Eyring–Kramers formula to irreversible diffusion processes. In our formula, the role of the potential is played by Freidlin–Wentzell’s quasipotential, and a correction depending on the non-Gibbsianness of the system along the minimum action paths is highlighted. Our study assumes some properties for the vector field: (1) attractors are isolated points, (2) the dynamics restricted to basin of attraction boundaries are attracted to single points (which are saddle-points of the vector field). We moreover assume that the minimum action paths that connect attractors to adjacent saddle-points (the instantons) have generic properties that are summarised in the conclusion. At a technical level, our derivation combines an exact computation for the first-order WKB expansion around the instanton and an exact computation of the first-order match asymptotics expansion close to the saddle-point. While the results are exact once a formal expansion is assumed, the validity of these asymptotic expansions remains to be proven.     

Large Eddy and Reynolds-Averaged Navier - Stokes Simulations of Turbulent Flow Over an Airfoil

A Large Eddy Simulation (LES) of turbulent flow over an airfoil near stall is performed. Results of the LES are compared with those of Reynolds-Averaged Navier-Stokes (RANS) simulations using two well-known turbulence models, namely the Baldwin-Lomax model and the Spalart-Allmaras model. The subgrid scale model used for the LES is the filtered structure function model. All simulations are performed using the same structured multi-block code. In order to reduce the CPU time, an implicit time stepping method is used for the LES. The purpose of this study is to show the possibilities and limitations of LES of complex flows associated with aeronautical applications using state of the art simulation techniques. Typical flow features are captured by the LES such as the adverse-pressure gradient and flow retardation. Visualization of instantaneous flow fields shows the typical streaky structures in the near-wall region.     

Recurrence properties of sequences of integers

In order to study the recurrence of sequences of integers, we investigate their L2-exactness and Θ-Hartman property (Θ being a set of rational numbers). Two classes of sequences of integers are well studied, which are return times relative to a weakly mixing system and Bernoulli random sequences.     

Strange baryon resonance production in sqrt s NN=200 GeV p+p and Au+Au collisions

We report the measurements of Sigma(1385) and Lambda(1520) production in p+p and Au+Au collisions at sqrt[s{NN}]=200 GeV from the STAR Collaboration. The yields and the p(T) spectra are presented and discussed in terms of chemical and thermal freeze-out conditions and compared to model predictions. Thermal and microscopic models do not adequately describe the yields of all the resonances produced in central Au+Au collisions. Our results indicate that there may be a time span between chemical and thermal freeze-out during which elastic hadronic interactions occur.     

Large time behavior and asymptotic stability of the 2D Euler and linearized Euler equations

We study the asymptotic behavior and the asymptotic stability of the 2D Euler equations and of the 2D linearized Euler equations close to parallel flows. We focus on flows with spectrally stable profiles U(y) and with stationary streamlines y=y₀ (such that U^′(y₀)=0), a case that has not been studied previously. We describe a new dynamical phenomenon: the depletion of the vorticity at the stationary streamlines. An unexpected consequence is that the velocity decays for large times with power laws, similarly to what happens in the case of the Orr mechanism for base flows without stationary streamlines. The asymptotic behaviors of velocity and the asymptotic profiles of vorticity are theoretically predicted and compared with direct numerical simulations. We argue on the asymptotic stability of this ensemble of flow profiles even in the absence of any dissipative mechanisms.     

Strangeness enhancement in Cu-Cu and Au-Au collisions at √S(NN)=200 GeV

We report new STAR measurements of midrapidity yields for the Λ, Λ[over ˉ], K(S)(0), Ξ(-), Ξ[over ˉ](+), Ω(-), Ω[over ˉ](+) particles in Cu+Cu collisions at √S(NN)==200 GeV, and midrapidity yields for the Λ, Λ[over ˉ], K(S)(0) particles in Au+Au at √S(NN)==200 GeV. We show that, at a given number of participating nucleons, the production of strange hadrons is higher in Cu+Cu collisions than in Au+Au collisions at the same center-of-mass energy. We find that aspects of the enhancement factors for all particles can be described by a parametrization based on the fraction of participants that undergo multiple collisions.     

Photochimie d'heterocycles azotes—V : Reactions de photosubstitution en serie heterocyclique: cas des p-nitrophenyl-1 pyrazoles et imidazoles

The photosubstitution reactions of eight 1-p-nitrophenylpyrazoles and two 1-p-nitrophenylimidazoles bearing different substituents in the heterocyclic ring have been studied. In the case of pyrazole derivatives, among the different nucleophiles utilized, only the acetate, cyanate and cyanide ions gave identifiable products. The two first ones lead to the 4-formyl derivative of the starting material. With the cyanide ion the reaction is more complicated, not only the 4-cyano derivative is formed but also the 4-carboxamido and several reduced products: p-amino, p-formamido, p-acetamido, p-carbamate and p-azoxypheny 1-1 pyrazoles. In the case of 1-p-nitrophenylimidazoles, the only interesting results have been obtained with the cyanide ion: formation of cyano- and hydroxymethylene-imidazoles.