The European way out of recession

This paper proposes a two-regime Bounce-Back Function augmented Self-Exciting Threshold AutoRegression (SETAR) which allows for various shapes of recoveries from the recession regime. It relies on the bounce-back effects first analyzed in a Markov-Switching setup by Kim, Morley and Piger [2005] and recently extended by Bec, Bouabdallah and Ferrara [2011a]. This approach is then applied to post-1973 quarterly growth rates of French, German, Italian, Spanish and Euro area real GDPs. Both the linear autoregression and the standard SETAR without bounce-back effect null hypotheses are strongly rejected against the Bounce-Back augmented SETAR alternative in all cases but Italy. The relevance of our proposed model is further assessed by the comparison of its short-term forecasting performances with the ones obtained from a linear autoregression and a standard SETAR. It turns out that the bounce-back models one-step ahead forecasts generally outperform the other ones, and particularly so during the last recovery period in 2009Q3-2010Q4.Threshold autoregression, bounce-back effects, asymmetric business cycles.

Lyapunov exponents of heavy particles in turbulence

Lyapunov exponents of heavy particles and tracers advected by homogeneous and isotropic turbulent flows are investigated by means of direct numerical simulations. For large values of the Stokes number, the main effect of inertia is to reduce the chaoticity with respect to fluid tracers. Conversely, for small inertia, a counter-intuitive increase of the first Lyapunov exponent is observed. The flow intermittency is found to induce a Reynolds number dependency for the statistics of the finite time Lyapunov exponents of tracers. Such intermittency effects are found to persist at increasing inertia.Comment: 4 pages, 4 figure

Acceleration statistics of heavy particles in turbulence

We present the results of direct numerical simulations of heavy particle transport in homogeneous, isotropic, fully developed turbulence, up to resolution $512^3$ ($R_\lambda\approx 185$). Following the trajectories of up to 120 million particles with Stokes numbers, $St$, in the range from 0.16 to 3.5 we are able to characterize in full detail the statistics of particle acceleration. We show that: ({\it i}) The root-mean-squared acceleration $a_{\rm rms}$ sharply falls off from the fluid tracer value already at quite small Stokes numbers; ({\it ii}) At a given $St$ the normalised acceleration $a_{\rm rms}/(\epsilon^3/\nu)^{1/4}$ increases with $R_\lambda$ consistently with the trend observed for fluid tracers; ({\it iii}) The tails of the probability density function of the normalised acceleration $a/a_{\rm rms}$ decrease with $St$. Two concurrent mechanisms lead to the above results: preferential concentration of particles, very effective at small $St$, and filtering induced by the particle response time, that takes over at larger $St$.Comment: 10 pages, 3 figs, 2 tables. A section with new results has been added. Revised version accepted for pubblication on Journal of Fluid Mechanic

Dynamics and statistics of heavy particles in turbulent flows

We present the results of Direct Numerical Simulations (DNS) of turbulent flows seeded with millions of passive inertial particles. The maximum Taylor's Reynolds number is around 200. We consider particles much heavier than the carrier flow in the limit when the Stokes drag force dominates their dynamical evolution. We discuss both the transient and the stationary regimes. In the transient regime, we study the growt of inhomogeneities in the particle spatial distribution driven by the preferential concentration out of intense vortex filaments. In the stationary regime, we study the acceleration fluctuations as a function of the Stokes number in the range [0.16:3.3]. We also compare our results with those of pure fluid tracers (St=0) and we find a critical behavior of inertia for small Stokes values. Starting from the pure monodisperse statistics we also characterize polydisperse suspensions with a given mean Stokes.Comment: 13 pages, 10 figures, 2 table

Heavy particle concentration in turbulence at dissipative and inertial scales

Spatial distributions of heavy particles suspended in an incompressible isotropic and homogeneous turbulent flow are investigated by means of high resolution direct numerical simulations. In the dissipative range, it is shown that particles form fractal clusters with properties independent of the Reynolds number. Clustering is there optimal when the particle response time is of the order of the Kolmogorov time scale $\tau_\eta$. In the inertial range, the particle distribution is no longer scale-invariant. It is however shown that deviations from uniformity depend on a rescaled contraction rate, which is different from the local Stokes number given by dimensional analysis. Particle distribution is characterized by voids spanning all scales of the turbulent flow; their signature in the coarse-grained mass probability distribution is an algebraic behavior at small densities.Comment: 4 RevTeX pgs + 4 color Figures included, 1 figure eliminated second part of the paper completely revise

Acceleration of heavy and light particles in turbulence: comparison between experiments and direct numerical simulations

We compare experimental data and numerical simulations for the dynamics of inertial particles with finite density in turbulence. In the experiment, bubbles and solid particles are optically tracked in a turbulent flow of water using an Extended Laser Doppler Velocimetry technique. The probability density functions (PDF) of particle accelerations and their auto-correlation in time are computed. Numerical results are obtained from a direct numerical simulation in which a suspension of passive pointwise particles is tracked, with the same finite density and the same response time as in the experiment. We observe a good agreement for both the variance of acceleration and the autocorrelation timescale of the dynamics; small discrepancies on the shape of the acceleration PDF are observed. We discuss the effects induced by the finite size of the particles, not taken into account in the present numerical simulations.Comment: 7 pages, 4 figure

Caustics and Intermittency in Turbulent Suspensions of Heavy Particles

The statistics of velocity differences between very heavy inertial particles suspended in an incompressible turbulent flow is found to be extremely intermittent. When particles are separated by distances within the viscous subrange, the competition between quiet regular regions and multi-valued caustics leads to a quasi bi-fractal behavior of the particle velocity structure functions, with high-order moments bringing the statistical signature of caustics. Contrastingly, for particles separated by inertial-range distances, the velocity-difference statistics is characterized in terms of a local H\"{o}lder exponent, which is a function of the scale-dependent particle Stokes number only. Results are supported by high-resolution direct numerical simulations. It is argued that these findings might have implications in the early stage of rain droplets formation in warm clouds.Comment: 4 pages, 6 figure

Anisotropic clustering of inertial particles in homogeneous shear flow

Recently, clustering of inertial particles in turbulence has been thoroughly analyzed for statistically homogeneous isotropic flows. Phenomenologically, spatial homogeneity of particles configurations is broken by the advection of a range of eddies determined by the Stokes relaxation time of the particles which results in a multi-scale distribution of local concentrations and voids. Much less is known concerning anisotropic flows. Here, by addressing direct numerical simulations (DNS) of a statistically steady particle-laden homogeneous shear flow, we provide evidence that the mean shear preferentially orients particle patterns. By imprinting anisotropy on large scales velocity fluctuations, the shear indirectly affects the geometry of the clusters. Quantitative evaluation is provided by a purposely designed tool, the angular distribution function of particle pairs (ADF), which allows to address the anisotropy content of particles aggregates on a scale by scale basis. The data provide evidence that, depending on the Stokes relaxation time of the particles, anisotropic clustering may occur even in the range of scales where the carrier phase velocity field is already recovering isotropy. The strength of the singularity in the anisotropic component of the ADF quantifies the level of fine scale anisotropy, which may even reach values of more than 30% direction-dependent variation in the probability to find two close-by particles at viscous scale separation.Comment: To appear in Journal Fluid Mechanics 200

Superdiffusion of massive particles induced by multi-scale velocity fields

We study drag-induced diffusion of massive particles in scale-free velocity fields, where superdiffusive behavior emerges due to the scale-free size distribution of the vortices of the underlying velocity field. The results show qualitative resemblance to what is observed in fluid systems, namely the diffusive exponent for the mean square separation of pairs of particles and the preferential concentration of the particles, both as a function of the response time.Comment: 5 pages, 5 figures. Accepted for publication in EP

Stretching in a model of a turbulent flow

Using a multi-scaled, chaotic flow known as the KS model of turbulence, we investigate the dependence of Lyapunov exponents on various characteristics of the flow. We show that the KS model yields a power law relation between the Reynolds number and the maximum Lyapunov exponent, which is similar to that for a turbulent flow with the same energy spectrum. Our results show that the Lyapunov exponents are sensitive to the advection of small eddies by large eddies, which can be explained by considering the Lagrangian correlation time of the smallest scales. We also relate the number of stagnation points within a flow to the maximum Lyapunov exponent, and suggest a linear dependence between the two characteristics.Comment: 7 pages, 10 figure