Instantons and Fluctuations in a Lagrangian Model of Turbulence

We perform a detailed analytical study of the Recent Fluid Deformation (RFD) model for the onset of Lagrangian intermittency, within the context of the Martin-Siggia-Rose-Janssen-de Dominicis (MSRJD) path integral formalism. The model is based, as a key point, upon local closures for the pressure Hessian and the viscous dissipation terms in the stochastic dynamical equations for the velocity gradient tensor. We carry out a power counting hierarchical classification of the several perturbative contributions associated to fluctuations around the instanton-evaluated MSRJD action, along the lines of the cumulant expansion. The most relevant Feynman diagrams are then integrated out into the renormalized effective action, for the computation of velocity gradient probability distribution functions (vgPDFs). While the subleading perturbative corrections do not affect the global shape of the vgPDFs in an appreciable qualitative way, it turns out that they have a significant role in the accurate description of their non-Gaussian cores.Comment: 32 pages, 9 figure

The Onset of Intermittency in Stochastic Burgers Hydrodynamics

We study the onset of intermittency in stochastic Burgers hydrodynamics, as characterized by the statistical behavior of negative velocity gradient fluctuations. The analysis is based on the response functional formalism, where specific velocity configurations - the viscous instantons - are assumed to play a dominant role in modeling the left tails of velocity gradient probability distribution functions. We find, as expected on general grounds, that the field theoretical approach becomes meaningful in practice only if the effects of fluctuations around instantons are taken into account. Working with a systematic cumulant expansion, it turns out that the integration of fluctuations yields, in leading perturbative order, to an effective description of the Burgers stochastic dynamics given by the renormalization of its associated heat kernel propagator and the external force-force correlation function.Comment: 10 pages, 6 figure

Tailoring the Ti surface via electropolishing nanopatterning as a route to obtain highly ordered TiO2 nanotubes

Highly ordered TiO2 nanotubes (NTs) were synthesized by the electrochemical anodization of Tifoils subjected to electropolishing (EP) pre-treatment. We found that the Ti surface roughnessplays an important role in the onset of pore nucleation in enhancing the local focusing effect ofthe electrical field. Additionally, EP induces the formation of dimple structures on the metalsurface, which can work as a pre-pattern prior to anodization. These shallow ripples lead to apreferentially ordered pore nucleation, offering an organizational improvement of the anodicoxide NTs. We found that, depending on the EP applied potential, the roughness and the spatialperiod of the ripple-like structures varies from 82 nm and from 12230 nm, respectively. Suchtuning allowed us to focus on the influence of the initial Ti pre-surface topography features onthe NTs length, organization, and hexagonal arrangement quality, as well as diameter anddensity. Our results show that an EP under 10 V is the most suitable to obtain a small Ti surfaceroughness, the largest NT length (40% enhancement), and the effective improvement of theordered hexagonal NTs arrays over larger areas. Furthermore, the NTs dimensions (porediameters and density) were also found to depend on the initial Ti surface topography. The use ofoptimized EP allows us to obtain highly hexagonal self-ordered samples at a reduced timeand cost