Local evolution equations for non-Markovian processes

A Fokker-Planck equation approach for the treatment of non-Markovian stochastic processes is proposed. The approach is based on the introduction of fictitious trajectories sharing with the real ones their local structure and initial conditions. Different statistical quantities are generated by different construction rules for the trajectories, which coincide only in the Markovian case. The merits and limitations of the approach are discussed and applications to transport in ratchets and to anomalous diffusion are illustated.Comment: Latex, 11 pages, 1 eps figur

Lagrangian dispersion characteristics in the Western Mediterranean

Dispersion characteristics in the Western Mediterranean are analyzed using data from Coastal Ocean Dynamics Experiment (CODE) and Surface Velocity Program (SVP) surface drifters deployed in the period 1986–2017. Results are presented in terms of absolute dispersion A2 (mean-squared displacement of drifter individuals) and of relative dispersion (D2; mean square separation distance of drifter pairs). Moreover, the dispersion characteristics are estimated for different initial separation distances (D0) between particles: smaller, larger, or comparable with the internal Rossby radius of deformation. Results show the presence of a quasiballistic regime for absolute dispersion at small time scales and the nonlocal relative dispersion regime related to the submesoscale activities for scales smaller than the internal Rossby radius. At intermediate times, two anomalous absolute dispersion regimes (elliptic and hyperbolic regimes) related with the flow topology are observed, although the relative dispersion involves the Richardson and shear/ballistic regimes only for D0 smaller than the Rossby radius. During the subsequent 20–30 days, absolute dispersion shows quasirandom walk regime and relative dispersion follows the diffusive regime for scales larger than 100 km for which pair velocities are uncorrelated

Spreading of Lagrangian Particles in the Black Sea: A Comparison between Drifters and a High-Resolution Ocean Model

The Lagrangian dispersion statistics of the Black Sea are estimated using satellite-tracked drifters, satellite altimeter data and a high-resolution ocean model. Comparison between the in-situ measurements and the model reveals good agreement in terms of the surface dispersion. The mean sub-basin coherent structures and currents of the Black Sea are well reproduced by the model. Seasonal variability of the dispersion in the upper (15 m), intermediate (150 m) and deep (750 m) layers are discussed with a special focus of the role of sub-basin scale structures and currents on the turbulent dispersion regimes. In terms of the surface relative dispersion, the results show the presence of the three known turbulent exponential, Richardson and diffusive-like regimes. The non-local exponential regime is only detected by the model for scales <10 km, while the local Richardson regime occurs between 10 and 100 km in all cases due to the presence of an inverse energy cascade range, and the diffusive-like regime is well detected for the largest distance by drifters (100–300 km) in winter/spring. Regarding the surface absolute dispersion, it reflects the occurrence of both quasi-ballistic and random-walk regimes at small and large times, respectively, while the two anomalous hyperbolic (5/4) and elliptic (5/3) regimes, which are related to the topology of the Black Sea, are detected at intermediate times. At depth, the signatures of the relative and absolute dispersion regimes shown in the surface layer are still valid in most cases. The absolute dispersion is anisotropic; the zonal component grows faster than the meridional component in any scenario

Clustering dynamics of Lagrangian tracers in free-surface flows

We study the formation of clusters of passive Lagrangian tracers in a non-smooth turbulent flow in a flat free-slip surface as a model for particle dynamics on free surfaces. Single particle and pair dispersion show different behavior for short and large times: on short times particles cluster exponentially rapidly until patches of the size of the divergence correlation length are depleted; on larger times the pair dispersion is dominated by almost ballistic hopping between clusters. We also find that the distribution of particle density is close to algebraic and can trace this back to the exponential distribution of the divergence field of the surface flow.Comment: 5 pages, 5 Postscript figure

Dynamics of a small neutrally buoyant sphere in a fluid and targeting in Hamiltonian systems

We show that, even in the most favorable case, the motion of a small spherical tracer suspended in a fluid of the same density may differ from the corresponding motion of an ideal passive particle. We demonstrate furthermore how its dynamics may be applied to target trajectories in Hamiltonian systems.Comment: See home page http://lec.ugr.es/~julya

The Mixing and Transport Properties of the Intra Cluster Medium: a numerical study using tracers particles

We present a study of the mixing properties of the simulated intra cluster Medium, using tracers particles that are advected by the gas flow during the evolution of cosmic structures. Using a sample of seven galaxy clusters (with masses in the range of M=2-3 10^14Msol/h) simulated with a peak resolution of 25kpc/h up to the distance of two virial radii from their centers, we investigate the application of tracers to some important problems concerning the mixing of the ICM. The transport properties of the evolving ICM are studied through the analysis of pair dispersion statistics and mixing distributions. As an application, we focus on the transport of metals in the ICM. We adopt simple scenarios for the injection of metal tracers in the ICM, and find remarkable differences of metallicity profiles in relaxed and merger systems, also through the analysis of simulated emission from Doppler-shifted Fe XXIII lines.Comment: 19 pages, 24 figures, Astronomy and Astrophysics accepted; Final version after language editing and updating the bibliograph

Wafer-scale detachable monocrystalline Germanium nanomembranes for the growth of III-V materials and substrate reuse

Germanium (Ge) is increasingly used as a substrate for high-performance optoelectronic, photovoltaic, and electronic devices. These devices are usually grown on thick and rigid Ge substrates manufactured by classical wafering techniques. Nanomembranes (NMs) provide an alternative to this approach while offering wafer-scale lateral dimensions, weight reduction, limitation of waste, and cost effectiveness. Herein, we introduce the Porous germanium Efficient Epitaxial LayEr Release (PEELER) process, which consists of the fabrication of wafer-scale detachable monocrystalline Ge NMs on porous Ge (PGe) and substrate reuse. We demonstrate monocrystalline Ge NMs with surface roughness below 1 nm on top of nanoengineered void layer enabling layer detachment. Furthermore, these Ge NMs exhibit compatibility with the growth of III-V materials. High-resolution transmission electron microscopy (HRTEM) characterization shows Ge NMs crystallinity and high-resolution X-ray diffraction (HRXRD) reciprocal space mapping endorses high-quality GaAs layers. Finally, we demonstrate the chemical reconditioning process of the Ge substrate, allowing its reuse, to produce multiple free-standing NMs from a single parent wafer. The PEELER process significantly reduces the consumption of Ge during the fabrication process which paves the way for a new generation of low-cost flexible optoelectronics devices.Comment: 17 pages and 6 figures along with 3 figures in supporting informatio

Photoconversion Optimization of Pulsed-Laser-Deposited p-CZTS/n-Si-Nanowires Heterojunction-Based Photovoltaic Devices

We report on the achievement of novel photovoltaic devices based on the pulsed laser deposition (PLD) of p-type Cu2ZnSnS4 (CZTS) layers onto n-type silicon nanowires (SiNWs). To optimize the photoconversion efficiency of these p-CZTS/n-SiNWs heterojunction devices, both the thickness of the CZTS films and the length of the SiNWs were independently varied in the (0.3&ndash;1.0 &micro;m) and (1&ndash;6 &micro;m) ranges, respectively. The k&euml;sterite CZTS films were directly deposited onto the SiNWs/Si substrates by means of a one-step PLD approach at a substrate temperature of 300 &deg;C and without resorting to any post-sulfurization process. The systematic assessment of the PV performance of the ITO/p-CZTS/n-SiNWs/Al solar cells, as a function of both SiNWs&rsquo; length and CZTS film thickness, has led to the identification of the optimal device characteristics. Indeed, an unprecedented power conversion efficiency (PCE) as high as ~5.5%, a VOC of 400 mV, a JSC of 26.3 mA/cm2 and a FF of 51.8% were delivered by the devices formed by SiNWs having a length of 2.2 &micro;m along with a CZTS film thickness of 540 nm. This PCE value is higher than the current record efficiency (of 5.2%) reported for pulsed-laser-deposited-CZTS (PLD-CZTS)-based solar cells with the classical SLG/Mo/CZTS/CdS/ZnO/ITO/Ag/MgF2 device architecture. The relative ease of depositing high-quality CZTS films by means of PLD (without resorting to any post deposition treatment) along with the gain from an extended CZTS/Si interface offered by the silicon nanowires make the approach developed here very promising for further integration of CZTS with the mature silicon nanostructuring technologies to develop novel optoelectronic devices

Turbulent dispersion properties from a model simulation of the western Mediterranean Sea

Using a high-resolution primitive equation model of the western Mediterranean Sea, we analyzed the dispersion properties of a set of homogeneously distributed, passive particle pairs. These particles were initially separated by different distances D-0 (D-0 = 5.55, 11.1 and 16.65 km), and were seeded in the model at initial depths of 44 and 500 m. This realistic ocean model, which reproduces the main features of the regional circulation, puts into evidence the three well-known regimes of relative dispersion. The first regime due to the chaotic advection at small scales lasts only a few days (3 days at 44m depth, a duration comparable with the integral timescale), and the relative dispersion is then exponential. In the second regime, extending from 3 to 20 days, the relative dispersion has a power law t(alpha) where alpha tends to 3 as D-0 becomes small. In the third regime, a linear growth of the relative dispersion is observed starting from the twentieth day. For the relative diffusivity, the D-2 growth is followed by the Richardson regime D-4/3. At large scales, where particle velocities are decorrelated, the relative diffusivity is constant. At 500m depth, the integral timescale increases (> 4 days) and the intermediate regime becomes narrower than that at 44m depth due to the weaker effect of vortices (this effect decreases with depth). The turbulent properties become less intermittent and more homogeneous and the Richardson law takes place