Ergodic properties of a model for turbulent dispersion of inertial particles

We study a simple stochastic differential equation that models the dispersion of close heavy particles moving in a turbulent flow. In one and two dimensions, the model is closely related to the one-dimensional stationary Schroedinger equation in a random delta-correlated potential. The ergodic properties of the dispersion process are investigated by proving that its generator is hypoelliptic and using control theory

Caustics in turbulent aerosols

Networks of caustics can occur in the distribution of particles suspended in a randomly moving gas. These can facilitate coagulation of particles by bringing them into close proximity, even in cases where the trajectories do not coalesce. We show that the long-time morphology of these caustic patterns is determined by the Lyapunov exponents lambda_1, lambda_2 of the suspended particles, as well as the rate J at which particles encounter caustics. We develop a theory determining the quantities J, lambda_1, lambda_2 from the statistical properties of the gas flow, in the limit of short correlation times.Comment: 4 pages, 3 figure

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

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

Finite-time Lyapunov exponents of deep neural networks

We compute how small input perturbations affect the output of deep neural networks, exploring an analogy between deep networks and dynamical systems, where the growth or decay of local perturbations is characterised by finite-time Lyapunov exponents. We show that the maximal exponent forms geometrical structures in input space, akin to coherent structures in dynamical systems. Ridges of large positive exponents divide input space into different regions that the network associates with different classes. These ridges visualise the geometry that deep networks construct in input space, shedding light on the fundamental mechanisms underlying their learning capabilities.Comment: 6 pages, 4 figure

Chemical, enantioselective, and sensory analysis of a cholinesterase inhibitor essential oil from coreopsis triloba S.F. Blake (asteraceae)

The fresh leaves of Coreopsis triloba S.F. Blake, collected at Cerro Villonaco in Loja, Ecuador, were investigated with respect to their essential oil (EO). The chemical composition was determined qualitatively through gas chromatography coupled with mass spectrometry (GC-MS) and quantitatively by gas chromatography coupled with flame ionization (GC-FID), using relative response factors (RRF) based on the enthalpy of combustion. The essential oil contained between 92.5% and 93.4% of monoterpene hydrocarbons, with (E)-β-ocimene being the main component (35.2–35.9%), followed by β-phellandrene (24.6–25.0%), α-pinene (15.3–15.9%), myrcene (10.9–11.0%), sabinene (2.2–2.4%), (Z)-β-ocimene (1.5%), and germacrene D (1.2–1.3%). The enantiomeric distribution of α-pinene, β-pinene, limonene, and germacrene D was also determined. The main components responsible for the aroma were identified through aroma extract dilution analysis (AEDA), a gas chromatography-olfactometry (GC-O) based technique, being α-pinene, β-pinene (0.6%), terpinolene (0.1%), α-copaene (0.1–0.3%), β-phellandrene, and (E)-4,8-dimethyl-1,3,7-nonatriene (0.1–0.2%) the main olfactory constituents according to the decreasing factor of dilution (FD) order. The biological tests showed IC50 inhibition values of 42.2 and 6.8 µg/mL for acetylcholinesterase (AChE) and butyrylcholinesterase (BChE), respectively

Response of the Adriatic Sea to the atmospheric anomaly in 2003

Unusual weather conditions over the southern Europe and the Mediterranean area in 2003 significantly impacted the oceanographic properties of the Adriatic Sea. To document these changes, both in the atmosphere and the sea, anomalies from the normal climate were calculated. The winter 2003 was extremely cold, whereas the spring/summer period was extremely warm. The air temperature in June was more than 3 standard deviations above the average. On the other hand, precipitation and river runoff were extremely low between February and August. The response of the sea was remarkable, especially in surface salinity during spring and summer, with values at least one standard deviation above the average. Analysis of thermohaline properties in the middle Adriatic showed the importance of two phenomena responsible for the occurrence of exceptionally high salinity: (1) enhanced inflow of saline Levantine Intermediate Water (LIW) in the Adriatic, and (2) extremely low precipitation and river runoff, accompanied with strong evaporation. Two large-scale atmospheric indices: NAOI (North Atlantic Oscillation Index) and MOI (Mediterranean Oscillation Index), although generally correlated to the Adriatic climate, failed to describe anomalies in 2003. The air pressure gradients used for the definition of both indices significantly decreased in 2003 due to the presence of the high pressure areas over most of Europe and the northern Atlantic, and were actually responsible for the observed anomalies above and in the Adriatic

The analytic structure of 2D Euler flow at short times

Using a very high precision spectral calculation applied to the incompressible and inviscid flow with initial condition $\psi_0(x_1, x_2) = \cos x_1+\cos 2x_2$, we find that the width $\delta(t)$ of its analyticity strip follows a $\ln(1/t)$ law at short times over eight decades. The asymptotic equation governing the structure of spatial complex-space singularities at short times (Frisch, Matsumoto and Bec 2003, J.Stat.Phys. 113, 761--781) is solved by a high-precision expansion method. Strong numerical evidence is obtained that singularities have infinite vorticity and lie on a complex manifold which is constructed explicitly as an envelope of analyticity disks.Comment: 19 pages, 14 figures, published versio