Turbulence and Passive scalar Advection:
The first part of my PhD thesis (advised by R. Benzi and L. Biferale in Rome University) was devoted to the understanding of one of the most intriguing and long standing problem in the statistical theory of turbulence, i.e. intermittency of the dynamical fields and its small scale universality. Using an exact closure theory based on time-dependent random multiplicative processes, I performed a systematic non perturbative calculation to determine the anomalous scaling exponents in a class of dynamical systems known as 'shell models', whose intermittency is found numerically very close to the real one. I also performed non perturbative calculations together with M.M. Afonso  (Institute de Mécanique des fluides de Toulouse), providing evidence for the recovery of small scale universality in passive scalar advection against disomogeneous large scale fluctuations. The issue of universality has also been addressed in a work (in collaboration with L. Biferale (Rome University), A. Lanotte (CNR) ,  M. Cencini (CNR) and F. Toschi (Eindhoven University))  where, for the first time, we provided  numerical evidence that the zero mode scenario well known for Kraichnan ensembles of passive scalar advection also applies to the non linear Navier-Stokes equations stirred by a random forcing with a power law spectrum. I also gave contribution in the problem of turbulence modelling from the point of view of kinetic theory: a relevant long standing question arises concerning the importance of non-hydrodynamic fields, i.e. high order kinetic moments of the Boltzmann distribution, sometimes called ghost fields. The influence of these high order kinetic modes on the dissipative properties of turbulence dynamics has been studied and controlled in Shell models of turbulence providing a net evidence that the hydrodynamic manifold is very robust towards large fluctuations of non hydrodynamic fields.

Laminar Flows - Hydrodynamic Theory:
The recent blossoming of research in micro-fluidics has prompted renewed interest in the possibility of slip boundary conditions at the contact of a liquid with a solid wall. While many experiments have provided evidence for a violation of the classical no-slip boundary condition at small spatial scales, the physical mechanisms responsible for this phenomenon are still unclear. An interesting possibility is the recent discovery of what appear to be small gas nano-bubbles or pockets attached to the wall. Along these lines, in collaboration with A. Prosperetti (Baltimore, USA) and K. Sugiyama (Fluid Eng. Labs, Tokyo University), I have carried out a rigorous study of slippage properties arising from boundary heterogeneities and surface roughness. We studied the nature of the effective velocity boundary condition for liquid flow over a boundary on which small free-slip islands are randomly distributed and explored the macroscopic consequences of the existence of such drag-reducing structures on a solid wall. This was the first paper in the microfluidics literature of the recent years where the Stokes equation has been coupled to randomly realized boundary conditions using ensemble averaging methods. Also, based on perturbative analysis of the Stokes equations, I was the first one to propose an analytical estimate of the effect of capillarity on the boundary condition, an effect that has been reported experimentally but never controlled from the analytical point of view.

Micro- & Nanofluidics:
In a series of experiments and numerical simulations in collaboration with D. Lohse (Twente University, The Netherlands) I studied the motion of millimetric droplets over super-hydrophobic surfaces. These kind of materials can exhibit high effective contact angles, therefore providing low friction mechanism (the so-called Lotus effect) with a wide range of interdisciplinary applications. When this super-hydrophobic state breaks down, the drop moves to a collapsed state with smaller contact angle. This transition was studied with numerical simulations and led to the first strong evidence of a new filling infiltration named 'zipping wetting'. These results were confronted with experiments using ultrahigh-speed imaging up to 50000fps providing state of the art work where numerics, theory and experiments were joint together. This research was highlighted in the national Dutch Newspaper (see Journal/media coverage section in my CV).

Lattice Boltzmann Theory Simulation from nano- to macroscales (Link to my ERC Project):
In collaboration with R. Benzi, L. Biferale (both in Rome University), S. Succi (CNR) and F. Toschi (Eindhoven University) we have developed a computational-theoretical approach based on the Lattice Boltzmann Method (LBM) aimed at the understanding of relevant physical aspects of small scale hydrodynamcs  where confinement may play a relevant role. I initially studied and quantified boundary condition effects (slip, mixed boundary conditions for laminar flows) using the LBM  and proved its potentiality for the simulations of single phase micro-flows at finite Knudsen numbers. I then moved to the description of the interface physics and isothermal multiphase fluid flows mainly from the point of view of LBM's diffuse interface hydrodynamics. I showed how to extend the well know 'Shan-Chen' (SC) model from bulk descriptions to situations where one needs to include interactions with solid walls and model the concept of wetting angles. Moreover, I have been the first to propose the extension of this model to multi-range potentials where one can achieve better realistic control of the interface properties emerging at the hydrodynamical level. Also, in collaboration with X. Shan and H. Chen (EXA Corporation, USA), I proved analytically  that the SC model can be made compliant with an underlying free energy, thus taking a significant step towards reconciling / relating the two most used LBM for multiphase flows, i.e. the SC method and the 'free energy method'. Using the developed approach, I have provided quantitative evidence that the LBM approach correctly captures the essential features of a variety of micro, nano-flows, which cannot be described by atomistic methods for want of computational power. This led to the -first ever done- quantitative comparison of The LBM simulations against molecular dynamics results  on wetting transitions for micro-channel flows with micro-corrugated grooves. Also, studying the old standing Landau-Levich problem for the onset of entrapment of a liquid film out of a bath, I made quantitative comparisons between LBM and fully continuous lubrication hydrodynamics, further extending the prediction of the latter using the results of LBM in a domain where lubrication approximation fails. In a recent paper, again in collaboration with X. Shan and H. Chen, thermal LBM incorporating the effects of external/internal force fields have been placed within the framework of discrete kinetic theory, providing striking evidence on how LBM is able to fully resolve at the same time thermo-hydrodynamical evolutions of complex flows coupled to a fully resolved diffuse interface dynamics. Using these ideas, numerical algorithm based on the lattice Boltzmann method and its applications for simulations of turbulent convection in presence of bubbles, showing appreciable changes in the distribution of pressure, density and temperature fluctuations inside a convective cell.
In recent works, I provided a clear evidence that LBM with multi-range potentials can capture some non trivial dynamical aspects of soft flowing materials both theoretically and numerically. In my recent papers I also started to explore different theoretical formulations of the lattice Boltzmann equation with finite volumes and/or adaptive meshes. 

Lattice Boltzmann on the QPACE Supercomputer (Compressible and Reactive Flows):
I recently started a collaboration with R. Tripiccione, F. Mantovani, S.F. Schifano, M. Pivanto (Ferrara University), with L. Biferale and A. Scagliarini (Rome University) and with F. Toschi (Eindhoven University). We managed to implement a fluid dynamical system on the Qpace supercomputer.  The machine structure is a three-dimensional torus of identical processing nodes, based on IBM's PowerXCell 8i processors. These nodes are tightly coupled by an Xilinx Virtex-5-based FPGA, application-optimized network processor attached to the PowerXCell 8i processor. The three Identical QPACE supercomputers at Jülich Research Centre (University of Regensburg and University of Wuppertal) are as of November 2009 topping the Green500 list of most energy efficient supercomputers in the world and are at the same time ranking at 110, 111 and 112 place on the Top500 list of most powerful supercomputers. In December 2009 we used QPACE to perform the first large scale physics campaign since the machine was commissioned: the challenge is twofold: 

i) adapting a  complex numerical algorithm to the architecture of the Cell

ii) partitioning the computation on a large set of processing elements.

We have studied Rayleigh-Taylor instability with numerical resolutions ever reached before to appreciate the effect of compressibility. We have systematically studied correlation functions and small scale intermittency in both velocity and temperature fields, singling out the effect of the adiabatic gradient in stopping the turbulent fronts while expanding. We are currently performing numerical simulations of reactive flows with the idea to study the emergence of small scale corrections to hydrodynamical fields statistics.

Graphics Processing Unit (GPU) Implementation of Lattice Boltzmann models:
In collaboration with  R. Benzi (Rome University), S. Succi and M.Bernaschi (both in CNR) I have proposed a graphic processing unit GPU implementation of the multicomponent lattice Boltzmann equation with multirange interactions for soft-glassy materials. Performance measurements for flows under shear indicate a GPU/CPU speed up in excess of 10 for 1024^2 grids. Such significant speed up permits to carry out multimillion time-steps simulations of 1024^2 grids within tens of hours of GPU time, thereby considerably expanding the scope of the glassy Lattice Boltzmann simulations toward the investigation of long-time relaxation properties of soft-flowing glassy materials.

 Self-Glassiness in Binary Models (Generalized Landau-Ginzburg models):
In collaboration with  R. Benzi (Rome University), S. Succi and M.Bernaschi (both in CNR) I have presented a new phase-field model for binary fluids exhibiting typical signatures of self-glassiness, such as long-time relaxation, ageing and long-term dynamical arrest. The present model allows the cost of building an interface to become locally zero, while preserving global positivity of the overall surface tension. An important consequence of this property, which we prove analytically, is the emergence of compact configurations of fluid density. Owing to their finite-size support, these ``compactons'' can be arbitrarily superposed, thereby providing a direct link between the ruggedness of the free-energy landscape and morphological complexity in configurational space. The analytical picture is supported by numerical simulations of the proposed phase-field equation.

Sample LBM code for COST school