Seminars 2013

Janus [1,2] is a special purpose computer designed as a multipurpose reprogramable supercomputer. It is based on a Field-Programmable-Gate-Array (FPGA) processor architecture, which permits us reprogramming the computer's hardware connections structure in order to optimize its performance for each concrete problem to solve.
Encouraged by the good results obtained so far, the Janus Collaboration decided to go an step further developing and designing the new generation Janus dedicated computer, named JanusII [3]. In this talk I will introduce both supercomputers, Janus and JanusII, explaining their internal architectures and the way we profit by their resources and possibilities for the study of spin glasses, paradigm of complex systems. I will also discuss some of the last spin glass aims achieved with Janus.
In addition, there is an international open call to the scientific community for the implementation on new applications on Janus (http://bifi.es/janus).

[1] ‍Janus Collaboration: F. Belletti et al., Computer Physics Communications 178 (3), 208-216, (2008).
[2] ‍Janus Collaboration: F. Belletti et al., Computing in Science & Engineering 11-1, 48-58 (2009).
[3] ‍Janus Collaboration: M. Baity-Jesi, et al., Janus II: a new generation application-driven computer for spin-system simulations, arXiv:1310.1032 (accepted in Computer Physics Communications).

The high-Reynolds-number flow near the corner of a vertical flat plate partially submerged across an uniform stream has been studied using a combination of experimental, numerical and analytical tools. In this configuration, a three dimensional wave forms at the corner of the plate which evolves downstream in a similar way as a time-evolving two dimensional plunging or spilling breaker (depending the occurrence of one or the other type of breaker on the flow conditions). Experiments have been performed submerging a flat plate perpendicular to the free stream in the test section of a recirculating water channel. Experimental results show that the formation and the initial development of the wave is nearly unaffected by the presence of the channel walls and bottom even when their distance to the corner, where the wave originates, is of the order of the size of the wave itself. This is a remarkable observation, that suggests that the formation of the corner wave is a local process in a sense that it is only influenced by the characteristics of the velocity field very near the corner. Moreover, it has been observed that the jet formed when the corner wave adopts the plunging breaker configuration follows a nearly ballistic trajectory, has is the case in two-dimensional unsteady plunging breakers. Theoretical analysis shows that, taking advantage of the slender nature of the flow, the 3D steady problem can be transformed into a two dimensional unsteady one using the so called 2D+T approximation. Together with the high Reynolds number of the flow, the 2D+T approximation makes the problem amenable to be simulated numerically using a Boundary Element Method (BEM). Moreover, a pressure-impulse asymptotic analysis of the flow near the origin of the corner wave has been performed in order to describe the initial evolution of the wave and to clarify the physical mechanisms that lead to its formation. The analysis shows that the flow near the corner exhibits a self similar behavior at short times, although the self-similar solution is physically unattainable due to the existence of two "jetlets" that impinge onto the base of the main jet that causes the wave.

Yves Couder and his coworkers in Paris have discovered a macroscopic particle-wave system exhibiting many features previously thought to be peculiar to the microscopic quantum realm. A small liquid droplet placed on the vibrating surface of a fluid bath, can be made to bounce (essentially indefinitely) provided that the amplitude and frequency of the oscillations is in the "correct range". In particular: (1) The frequency must be high enough that the "impact time" is too short to allow the air layer between the drop and bath to drain to the critical distance at which merger is initiated by van der Waals forces, (2) The maximum vertical acceleration of the free surface must exceed gravity (so the drop can lift of after landing), (3) The operational regime must be below the Faraday instability threshold, so the liquid surface remains (essentially) "flat".
he experiments by Couder involve a millimeter sized droplet on a vibrating bath of silicone oil (viscosity 20-50 times that of water). There, the drop may bounce indefinitely on the free surface, generating a localized field of surface waves that decays with distance from the drop. The drop interacts with this wave field, and undergoes several bifurcations in its behavior as the driving amplitude grows: from bouncing in place at the same frequency as the fluid bath, to a period doubling bifurcation, to spontaneous "walking" on the surface. Walking drops exhibit quantum-like effects in its behavior: diffraction, interference, orbit quantization in rotating frames, etc. Multiple bouncers communicate through their wave fields, and can orbit each other forming "atoms", or "crystal" lattices, etc.
In this talk I will introduce an integral equation that describes the wave-induced force that acts on walking droplets. From this we can write a new guidance equation for walking droplets, that provides insight into their observed quantum behavior. In particular I will consider the behavior of a drop/particle in a rotating frame, and the myriad of patterns that this produces.

Throughout the years nature has inspired some of the best inventions in engineering and medicine, from building airplanes with movable wing surfaces like those of birds to using viruses as a vehicle to deliver genetic materials into cells. In this talk, I will present our work aiming to solve problems in engineering and medicine using nature-inspired approaches. In the first part, I will focus on understanding the adhesive locomotion of gastropods for the design of biomimetic robots. Specifically, some of the critical questions we aim to address are: how do soft-bodied creatures like slugs and snails propel themselves through irregular terrains? Is the rheological properties of the secreted mucus essential, and what lessons can we learn from their crawling mechanism for robotics design? In the second part, we explore the possibility of manipulating cell-cell interactions as a strategy for cartilage regeneration therapy. In particular, we explore the potential of adipose-derived stem cells as a catalyst to stimulate cartilage regeneration by neonatal chondrocytes. The questions we seek to answer are: how can we minimize the number of neonatal chondrocytes, an extremely scarce cell source, needed for cartilage repair? Can we manipulate cell-cell interactions by controlling cell distribution and intercellular distance in 3D to facilitate optimal synergy?

Aerofoil tonal noise is an aeroacoustic phenomenon peculiar of small wind turbines, compressors' blades and UAVs, all applications where a laminar or at least transitional flow can take place. Its investigation spans a period of more than 40 years but up to date no agreement between the researchers has been achieved. The aspects object of research were linked to the flow mechanism causing this acoustic emission and the behaviour in terms of acoustic emission frequency with respect to the free stream velocity.
The aerofoil tonal noise is often referred to as aerofoil self noise. The reason for this appellation resides in the illuminating conjectures of Tam [1], who in 1974 proposed the occurrence of a feedback loop between the hydrodynamic fluctuations and the acoustic waves scattered by those fluctuations. The acoustic waves propagating in the whole field, were causing a forcing of the fluid-dynamic field thus leading to the mutual interaction proper of a feedback loop. In the following years many researchers accepted this explanation introducing new findings and modifications.
In one of the last works on the topic Desquesnes et al. [2] studied the flow mechanism causing tonal emission with a 2D DNS. They investigated the pressure signal in the far field finding a modulation of its amplitude. The period of this modulating envelope was equal to the invert of the separation, in terms of frequency, of the discrete peaks present in the acoustic power spectrum. The cause of this modulation was individuated in a varying phase shift between the disturbances of the boundary layers of the two sides of the aerofoil at the trailing edge.
The results of a wind tunnel campaign by means of high speed PIV and simultaneous microphones measurements are here presented [3]. Furthermore linear stability theory LST in its spatial formulation has been applied to the time-averaged flow fields.
Some important confirmations about the reported flow features under which tonal noise is observed, are obtained. Moreover some new findings have been discovered thus leading to the rejection of some earlier conclusions as well as to the proposition of a new model of the feedback loop.

[1] ‍Tam, C.K.W. (1974). Discrete tones of isolated airfoils. J. Acoust. Soc. Am., 55 (6): 1173-1177.
[2] ‍Desquesnes, G., Terracol, M. and Sagaut, P. (2007). Numerical investigation of the tone noise mechanism over laminar airfoils. J. Fluid. Mech., 591: 155-182.
[3] ‍Pröbsting, S., Serpieri, J. and Scarano, F., (2013). Investigation of tonal noise generation on an airfoil with time-resolved PIV. 19th AIAA/CEAS Aeroacoustics Conf. Berlin, Germany.

Analogue Gravity relies on the observation that certain collective excitations in condensed-matter physics, for example sound waves, have equations of motion that can be written as a relativistic field in a curved space-time. I discuss several consequences, from acoustic black holes in Bose-Einstein condensates over white-hole experiments in a kitchen sink, to the possibility of arriving at acoustic and elastic cloaking with composite metamaterials.

Bacterial biofilms may be seen as bacterial aggregates embedded into a polysaccharide matrix with a high resistance against removal processes, which results in a recurrent source of problems in other disciplines (medicine, engineering, etc). The behaviour of these organisms is highly dependent of the physical system in which they are present, thus showing a very high degree of physical complexity. In this seminar we will focus our efforts on describing a mathematical and experimental modelization of biofilms by exposing a different set of case studies. First the dynamics of biofilms in straight ducts is studied. Experiments are performed to obtain statistics about spreading patterns, and a hybrid model (combining a discrete approach for bacterial population with stochastical behaviour rules and a continuum description of outer fields ruling those probabilities) is presented to simulate the biofilm dynamics, obtaining a successfully prediction of the different patterns observed in real experiments (at layers, ripples, streamers, mounds). This part is completed by extending the scope of the model to the formation of biofilm streamers inside a corner flow, where biomass adhesion mechanism becomes relevant. Streamers cross the channel joining both corners as observed experimentally. Additionally we perform a description of more complex dynamics observed in biofilms. An experimental description of biofilm dynamics under pulsatile flows at low Reynolds numbers show spiral patterns not reported yet, supported by a theoretical mechanism of formation based on the competence between flow dynamics and nutrient gradients.

Finite element formulations based on the weak-form Galerkin method in solid and structural mechanics resulted in enormous success. However, extension of these concepts to fluid mechanics and other areas of mechanics where the differential operators are either non-self adjoint or non-linear have met with mixed success. Numerical schemes such as modified weight functions, modified quadrature rule, optimal upwinding etc. have been presented in the literature to alleviate problems encountered with weak form Galerkin procedures in solving non-self adjoint and nonlinear problems outside of solid mechanics.
The lecture presents the formulation and application of the least-squares finite element formulations to the numerical solution of the Navier-Stokes equations governing two-dimensional flows of viscous incompressible fluids. Finite element models of the vorticity-based or velocity gradients-based Navier-Stokes equations are developed using the least-squares technique. The use of least-squares principles leads to a symmetric and positive-definite system of algebraic equations that allow the use of iterative methods for the solution of resulting algebraic equations.
High-order nodal expansions are used to construct the discrete finite element models. The system of equations thus obtained is linearized by Newton's method and solved by the preconditioned conjugate gradient method. Exponentially fast decay of the least-squares functional, which is constructed using the $L_2$ norms of the residuals in the governing equations, is verified for increasing order of the nodal expansions. Numerical results will be presented for several benchmark flow problems to demonstrate the predictive capability and robustness of the least-squares based finite element models.

Radial Basis Function (RBF) methods have become a truly meshless alternative for the interpolation of multidimensional scattered data and the solution of PDEs on irregular domains. Its dependence on the distance between centers makes RBF methods conceptually simple and easy to implement in any dimension or shape of the domain. There are two different formulations for the solution of PDEs: the global RBF method and the local RBF method.
The global RBF formulation yields dense differentiation matrices which are spectrally convergent independently of the node distribution. Its principal drawback is that, as the overall number of centers increases, the condition number of the collocation matrices increases, and this fact restricts the applicability of the method in practical problems. To overcome some of the drawbacks of the global RBF method, the local RBF method was independently proposed by several authors (also known as RBF-FD). Unlike the global RBF method, the RBF-FD method lacks spectral accuracy. However, the main feature of the method is the hability for handling irregular domains using highly sparse differentiation matrices while approximating the differential operators to high order. In this thesis we focus on the RBF-FD method.
In the first part we analyze the convergence properties of the method obtaining novel analytical formulas for the local truncation error as a function of the shape parameter, inter-nodal distance and stencil size. This result proof the existance of a range of values of the shape parameter for which RBF-FD methods are more accurated than FD. Indeed, it usually exists an optimal shape parameter for which the local truncation error cancel outs and the approximation is exact. To leading order, such a value is independent of the inter-nodal distance and only relies on the function and its derivatives. These results allow us to develop novel algorithms for the selection of the shape parameter in the solution of PDEs. In this line, two different strategies are proposed: a node-independent shape parameter, which minimizes the norm of the global error, and a node-dependent shape parameter, which minimizes the local truncation error at each node of the domain. Applications of the present methods have been studied in the solution of classical elastostatic problems, for which it is shown that the accuracy can significantly increased one or two orders of magnitude with respect to finite differences by efficiently tuning the values of shape parameters.
The applicability of the method is explored in the second part of this thesis. In this way, a three-dimensional problem for the propagation of a premixed laminar flame through a duct is solved. The good performance of the method inspires us to implement an RBF-FD method for the numerical study of an idealized Wankel microcombustor, for which the geometry is more complex. The combustible flow field and the combustion process are respectively modeled through the steady Navier-Stokes equations and the combustion model above.

Turbulent jet noise is a technological problem of great importance that has received continuous attention for decades. While state-of-the-art numerical simulations are today capable of simultaneously predicting turbulence and its radiated sound, a theoretical framework enabling fast prediction in order to guide noise-control efforts is incomplete. In this direction, the peak noise radiation in the aft direction of high-speed jets has been linked to the dynamics of the large-scale wavepackets existing in the flow: intermittent, advecting disturbances that are correlated over distances far exceeding the integral scales of turbulence, the signatures of which can be distinguished in the vortical turbulent region and in the acoustic near and far fields.
The present research uses parabolized stability equations (PSE) in order to model the statistical wavepackets as instability waves of the turbulent mean flow for subsonic and ideally-expanded supersonic round jets. The theoretical framework and algorithmic details will be discussed. Extensive comparisons and validations are performed against experimental measurements and data from large eddy simulations, demonstrating the utility of PSE in modeling (i) the large-scale structures in the velocity field, (ii) the pressure signature in the acoustic near-field and (iii) the highly directional peak noise in the acoustic far-field.

Interacting time and space scales are universal. They frequently go hand in hand with coupled phenomena which can be observed in nature and man-made systems. Such mutiscale coupled phenomena are fundamental to our knowledge about all the systems surrounding us, ranging from such global systems as the climate of our planet, to such tiny ones as quantum dots, and all the way down to the building blocks of life such as nucleic acid biological molecules.
In this talk I will provide an overview of some coupled multiscale problems that we face in studying physical, engineering, and biological systems. I will start from considering tiny objects, known as low dimensional nanostructures, and will give examples on why the nanoscale is becoming increasingly important in the applications affecting our everyday lives. By using fully coupled mathematical models, I will show how to build on the previous results in developing a new theory, while analyzing the influence of coupled multiscale effects on properties of these tiny objects.
The remaining part of the talk I will devote to coupled multiscale problems in studying biological structures constructed from ribonucleic acid (RNA). As compared to deoxyribonucleic acid (DNA) and some other bio-molecules, RNA offers not only a much greater variety of interactions but also great conformational flexibility, making it an important functional material in many bioengineering and medical applications. Examples of numerical simulations of such biological structures will be shown, based on our developed coarse-grained methodologies.

Space exploration vehicles frequently employ cabin environments that are not at standard sea level atmospheric conditions. NASA's Constellation Program considers a human space exploration cabin environment of reduced ambient pressure and increased oxygen concentration. This enhanced oxygen and reduced pressure atmosphere (approximately 56 kPa and 32 the Space Exploration Atmosphere, SEA, and while it reduces preparation time for EVAs by reducing the risk of decompression sickness it may have a significant impact on the flammability of materials. In this presentation the work being conducted at the University of California Berkeley regarding the flammability of materials in environments similar to those expected in those future space based facilities, i.e., micro-gravity, low velocity flow, elevated oxygen concentrations, and reduced pressures, is reviewed. A description of the equipment and facilities used in those studies and a summary of the results will be presented.

The behavior of vibrated fluids and, in particular, the surface or interfacial instabilities that commonly arise in these systems have been the subject of continued experimental and theoretical attention since Faraday's seminal experiments in 1831. Both orientation and frequency are critical in determining the response of the fluid to excitation. Low frequencies are associated with sloshing while higher frequencies may generate Faraday waves or cross-waves, depending on whether the axis of vibration is perpendicular or parallel to the interface. In addition, high frequency vibrations are known to produce large scale reorientation of the fluid (vibroequilibria), an effect that becomes especially pronounced in the absence of gravity. We describe the results of experimental and theoretical investigations into the effect of vibrations on fluid interfaces, particularly the interaction between Faraday waves and cross-waves.
Experiments utilize a dual-axis shaker configuration that permits two independent forcing frequencies, amplitudes, and phases to be varied. Theoretical results, based on the analysis of reduced models, and on numerical simulations, are described and compared to experiment. In particular, the nonlinear Schrodinger equation models used to study cross-waves since Jones (JFM 138, 1984) are extended to include surface tension and to allow the inhomogeneous forcing term to vary on the same lengthscale as the cross-wave modulation, an assumption that is needed for high frequency (large aspect ratio) experiments such as ours.

Progress in understanding granular flow has been greatly hampered by the lack of satisfactory constitutive equations. Historically, the concept of a Coulomb material, based on rate-independent plasticity, was introduced to describe granular materials. On substitution into the equations for conservation of mass and momentum, this constitutive relation leads to a system of evolution equations loosely analogous to the Navier-Stokes equations; friction gives rise to a term that formally resembles viscosity. However, it turns out that this system is ill-posed. Numerous higher-order, non-local theories have been introduced in an attempt to resolve this difficulty; while many of these are well-posed, they are invariably quite complicated, perhaps unnecessarily so.
In the last decade the French school (GDR MIDI) proposed a natural modification of the Coulomb constitutive equation. In this theory the coefficient of friction varies with the shear rate (which is measured by a nondimensional inertial number $I$); this property leads to the name $\mu(I)$-rheology. Their equation, which is based on experiments of flow down inclined planes and on dimensional analysis, retains a level of simplicity comparable to Coulomb material.
In this talk we analyze the well-posedness of the governing equations using $\mu(I)$-rheology. Specifically, we show that these evolution equations are well-posed for a large range of deformation rates but become ill-posed at extremes of slow or fast deformation. It is known that additional effects, not represented in $\mu(I)$-rheology, become important in these two extremes. Thus, the present mathematical result and physical understanding of granular materials support one another.
On the numerical side, several authors have adapted a recently proposed finite volume method for solving the Navier-Stokes equations to problems with $\mu(I)$-rheology. In this method, the pressure viscosity contribution is evaluated explicitly; this is appropriate for viscosity in the Navier-Stokes equations (where the viscosity operator is elliptic) but questionable for the not-necessarily-elliptic operator that occurs in $\mu(I)$-rheology. Reflecting this mismatch, numerical results using this method show no indication of ill-posedness: i.e., they do not reproduce the stability properties of the PDE derived assuming $\mu(I)$-rheology. To better capture the behavior of the PDE, we propose a PISO-like method that evaluates implicitly the viscous pressure contributions, and we derive a new pressure equation based on the Schur complement. We present numerical simulations to illustrate that our method does capture ill-posedness as predicted by theory.

Coupled nonlinear mathematical models are essential in describing most natural phenomena, processes, and man-made systems. From large scale mathematical models of climate to modelling of quantum mechanical effects coupling and nonlinearity go often hand and hand. Coupled dynamic systems of partial differential equations (PDEs) provide a foundation for the description of many such systems, processes, and phenomena. In majority of cases, however, their solutions are not amenable to analytical treatments and the development, analysis, and applications of effective numerical approximations for such models become a core element in their studies.
In this talk we will focus on mathematical models that are based on the Landau framework of phase transformations based on non-monotone free energy functions. Phase transformations are universal phenomena, and one specific example that we will consider in this talk is motivated by mesoscopic mathematical models for the description of multi-phase solid materials. Such models provide an intermediate length scale description between the atomistic level and the level that is usually used for bulk materials. In particular, we will discuss several classes of problems where non-equilibrium phenomena such as phase transformations are important, focusing on the dynamics of materials with shape memory. The talk will provide further insight into their application areas, the development of computationally efficient reduction procedures for their 3D modelling, and the construction of fully conservative schemes for solving the associated problems.

Direct numerical simulations of channel flow with Reynolds numbers ranging from 1,000 to 10,000 (based on the bulk and the channel height) have been used to study the formation and dynamics of elastic instabilities and their effects on a polymeric flow. The dynamics of turbulence generated and controlled by polymer additives has been investigated from the perspective of the coupling between polymer dynamics and flow structures.

In this work the result of laboratory flow visualisations and Large Scale Particle Image Velocimetry measurements of the wake developed after three emerged square arrays of rigid cylinders in a shallow water flow are presented. It is observed that for all cases a steady wake is developed downstream the array and it is followed by a vortex street pattern. It is shown that not always higher porosities produce a more extended steady wake and reduced turbulent intensities. It is also shown that in two cases the dominant wake frequency remain constant, and indication that the solid volume fractions do not affect the wake frequency. It is also observed that this frequency was also present within the slow steady wake in one of the measured cases, which could be evidence of an instability initiated within the cylinder array. Based on a Dynamic Mode Decomposition and Wavelet analysis of two and one-dimensional time series a description of the dominant coherent structures in the near and far field is presented. A discussion regarding the use of fractal arrays will be also presented.