# Courses

- Portada
- Courses

## Postgraduate

The institute offers an MS program in Industrial Mathematics along two academic years (90 ECTS). Specific information about the master can be found at the link below.

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## Seminars

Short periods of weekly seminars are organized by the institute with speakers belonging to it or from other institutions.

**SEMINARS 2014**

**A spectral theory of linear operators on a Gelfand triplet and its application to dynamics of coupled oscillators**

Hayato Chiba

Kyushu University, Japan

Abstract

The Kuramoto model is a system of ordinary differential equations for describing

synchronization phenomena defined as a coupled phase oscillators. In this talk, an infinite dimensional Kuramoto model is considered, and Kuramoto's conjecture on a bifurcation diagram of the system will be proved.

A linear operator obtained from the linearization of the Kuramoto model has the continuous spectrum on the imaginary axis, so that the usual spectrum theory does not determine the dynamics of the system. To handle such continuous spectra, a new spectral theory of linear operators based on Gelfand triplets is developed. In particular, a generalized eigenvalue is defined. It is proved that a generalized eigenvalue determines the stability and bifurcation of the system.

Date: Wednesday, June 25, 2014

Time: 12:00 a.m.

Room: 2.1 C17 (Sabatini Bld.), Carlos III University

Continuing the Program "Cátedras de Excelencia", next Tuesday, 4 February, at 13:00 p.m., Prof. Vincenzo Capasso, from the University of Milan, will give a lecture entitled:

**The Role of Geometric Randomness in the Mathematical Modelling of Angiogenesis**

Abstract

In biology and medicine we may observe a wide spectrum of formation of patterns, usually due to self-organization phenomena. Patterns are usually explained in terms of a collective behavior driven by "forces", either external and/or internal, acting upon individuals (cells or organisms). In most of these organization phenomena, randomness plays a major role; here we wish to address the issue of the relevance of randomness as a key feature for producing nontrivial geometric patterns in biological structures. As working examples we offer a review of a couple of important case studies involving angiogenesis, i.e. tumor-driven angiogenesis [1], and retina angiogenesis [2]. In both cases the reactants responsible for pattern formation are the cells organizing as a capillary network of vessels, and a family of underlying fields driving the organization, such as nutrients, growth factors and alike.

The strong coupling of the kinetic parameters of the relevant stochastic branching-and-growth of the capillary network, with the family of interacting underlying fields is a major source of complexity from a mathematical and computational point of view.

Thus our main goal is to address the mathematical problem of reduction of the complexity of such systems by taking advantage of its intrinsic multiscale structure; the (stochastic) dynamics of cells will be described at their natural scale (the microscale), while the dynamics of the underlying fields will be described at a larger scale (the macroscale) via deterministic averaged concentrations, by applying suitable "laws of large numbers" at a mesoscale. The intrinsic randomness of the phenomena is responsible of the building up of a realistic stochastic network of vessels.

References

[1] Capasso, V., Morale, D.: Stochastic Modelling of Tumour-induced Angiogenesis.

J. Math. Biol., 58, 219-33 (2009)

[2] Capasso, V., Morale D., Facchetti, G.: The Role of Stochasticity for a

Model of Retinal Angiogenesis, IMA J. Appl. Math. (2012) ; 19 pages;

doi:10.1093/imamat/hxs050

**"Crossover effect in glassy systems and granular gases"**

Antonio Prados Montaño

Universidad de Sevilla

Abstract

The crossover or Kovacs effect is basically the non-monotonic relaxation of a physical quantity to its equilibrium value, from an initial non-equilibrium state. We investigate it in two cases (i) glassy systems (ii) granular gases. In the former, the time evolution of the energy passes through a maximum because the system needs to pass through a more disordered state to reach a typical equilibrium configuration. Within a very simple model, we discuss the relevance of recent linear response results for understanding the Kovacs effect.

The granular gas case is quite different, since it is an intrinsically out-of-equilibrium system due to the continuous loss of energy in collisions. By introducing a simple energy input mechanism, the granular gas reaches an out-of-equilibrium steady state. A simple à la Kovacs protocol is investigated, for which a crossover effect is also displayed. Interestingly, it becomes anomalous for large enough inelasticity: the granular temperature (kinetic energy) shows a minimum instead of a maximum.

Date: Thursday, January 9th, 2014

Time: 12:00

Room: 2.1C19 (Sabatini Bld.), Carlos III University

## SEMINARS 2013

**The Janus family: a dedicated computer generation**

Sergio Pérez Gaviro

ARAID Foundation,

Institute for Biocomputation and Physics of Complex Systems (BIFI)

Universidad de Zaragoza

Abstract

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).

References:

[1] Janus Collaboration: F. Belletti et al., Computer Physics Communications 178 (3), p. 208-216, 2008.

[2] Janus Collaboration: F. Belletti et al., Computing in Science & Engineering 11 (1), p. 48-58, 2009.

[3] Janus Collaboration: M. Baity-Jesi, et al., arXiv:1310.1032 (accepted in Computer Physics Communications).

Date: Tuesday, December 10th, 2013

Time: 1:00 p.m.

Room: 2.1C19 (Sabatini Bld.), Carlos III University

**A macroscopic particle-wave system: Theoretical investigation of walking droplets**

Rodolfo R. Rosales

Professsor of Applied Mathematics

Department of Mathematics,

Massachusetts Institute of Technology

(joint work with Anand Oza, and John W. M. Bush)

Abstract

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".

The 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.

Date: Tuesday, November 5th, 2013

Time: 1:00 p.m.

Room: 2.1C19 (Sabatini Bld.), Carlos III University

**Corner waves downstream from a partially submerged vertical plate**

Javier Rodríguez-Rodríguez

Universidad Carlos III de Madrid

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.

Date: Tuesday, October 29th, 2013

Time: 1:00 p.m.

Room: 2.1 C19 (Sabatini Bld.), Carlos III University

**Capturing Nature's Creativity in Robotics & Tissue Regeneration**

Janice Lai

Stanford University

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?

Date: Tuesday, October 22nd, 2013

Time: 1:00 p.m.

Room: 2.1 C19 (Sabatini Bld.), Carlos III University

**On aerofoil tonal noise**

Jacopo Serpieri

Delft University of Technology

Faculty of Aerospace Engineering, Aerodynamics Section

Abstract

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 , 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. 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 . 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.

Date: Monday, October 14th, 2013

Time: 1:00 p. m.

Room: 2.1 C19 (Sabatini Bld.), Carlos III University

**From Analogue Gravity to Elastic Cloaking**

Gil Jannes

Grupo de Modelización y Simulación Numérica,

Universidad Carlos III de Madrid

Abstract

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.

Date: Tuesday, October 8th, 2013

Time: 1:00 p.m.

Room: 2.1 C19 (Sabatini Bld.), Carlos III University

**Least-Squares Finite Element Models of Flows of Incompressible Fluids **

J. N. Reddy

Advanced Computational Mechanics Laboratory

Department of Mechanical Engineering

Texas A & M University

College Station, Texas 77843-3123

e-mail: jnreddy@tamu.edu

Abstract

Finite element formulations based on the weak-form Galerkin method in solid and tructural 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 L2 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.

Date: Tuesday, 2nd July, 2013

Time: 12:30 a.m.

Room: 2.1.C17 (Sabatini Bld.), Carlos III University

**The RBF-FD Method: Developments and Applications**

Víctor Bayona Revilla

Universidad Carlos III de Madrid

Abstract

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 for 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 in a way that considerably restricts the applicability of the method. 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 ability 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 proves the existence of a range of values of the shape parameter for which RBF-FD are more accurate than FD methods. Indeed, it usually exists an optimal shape parameter for which the local truncation error cancels out and the approximation becomes 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. Both strategies have been applied to the solution of classical elastostatic problems and it is shown that their accuracy with respect to FD methods can be significantly increased in one or two orders of magnitude by efficiently tuning the values of shape parameters.

The applicability of the method is explored in the second part of this thesis. This way, a three-dimensional problem for the propagation of a premixed laminar flame through a duct, has been solved. The good performance of the method inspires us to implement an RBF-FD method for the numerical study of an idealized Wankel microcombustor, whose geometry is more complex. The combustible flow field is modeled through the steady Navier-Stokes equations and the combustion process follows the combustion model above.

Date: Monday, June 24th, 2013

Time: 12:30 a.m.

Room: 2.1.C19 (Sabatini Bld.), Carlos III University

**Models for large-scale turbulent structures on jets and their radiated noise**

Daniel Rodríguez Alvarez

California Institute of Technology and

Universidad Politécnica de Madrid

Abstract

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.

Date: Friday, June 14th, 2013

Time: 12:30 a.m.

Room: 2.1.C19 (Sabatini Bld.), Carlos III University

Continuing the Program "Cátedras de Excelencia del Banco de Santander y la Universidad Carlos III de Madrid", next Thursday, 16th May at 12:30 a.m., Prof. Roderick Melnik will give a lecture entitled:

**Multiple Scales and Coupled Phenomena in Nature and Mathematical Models**

Abstract

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.

**Flammability of Materials in Spacecrafts **

Angel Carlos Fernandez-Pello Sanchez

University of California at Berkeley

Abstract

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% O2) is known as 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.

Date: Wednesday, May, 16th 2013

Time: 12:30 a.m.

Room: 2.1.C17 (Sabatini Bld.), Carlos III University

**Vibrated fluids: Faraday waves, cross-waves, and vibroequilibria**

Jeffrey Porter

Universidad Politécnica de Madrid

Abstract

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.

Date: Friday, May, 10th 2013

Time: 12:30 a.m.

Room: 2.1.C19 (Sabatini Bld.), Carlos III University

**Well-posed and ill-posed regimes in
μ(I)-rheology for granular materials**

David Schaeffer

Duke University

(colaboración con P. Bohorquez y N. Gray)

Abstract

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 *μ(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 *μ(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 *μ(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 *μ(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 *μ(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* μ(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.

Date: Friday, May, 10th 2013

Time: 12:30 a.m.

Room: 2.1.C19 (Sabatini Bld.), Carlos III University

**Coupled Mathematical Models for Multi-Phase Materials:
Nonlinear Dynamics and Numerical Approximations**

Roderick Melnik

Wilfrid Laurier University

Waterloo, Canada

Abstract

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.

Date: Wednesday, March, 20th 2013

Time: 12:30 a.m.

Room: 2.1.D03 (Sabatini Bld.), Carlos III University

**Elasto-Inertial Turbulence**

Julio Soria

Department of Mechanical and Aerospace Engineering

Monash University, Australia

Abstract

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.

Date: Thursday, March, 7th 2013

Time: 4:00 p.m.

Room: 7.1.H03 (Juan Benet Bld., wing H), Carlos III University

**Unsteady characteristic of a shallow porous cylinder wake**

Wernher Brevis

Sheffield Fluid Mechanics Group

University of Sheffield

Abstract

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 arepresented. 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.

Date: Wednesday, February, 27th 2013

Time: 12:30 a.m.

Room: 7.1.H01 (Juan Benet Bld., wing H), Carlos III University

## SEMINARS 2012

**Structural and functional relationship in materials, catalysts and environmental systems**

Konstantinos Christoforidis

Modelling and Numerical Simulation

Carlos III University, Madrid

Abstract

Material science and catalytic systems play a very important role in many man-kind activities as well as in nature. This can be easily understood if we consider that more than 90% of the chemical industry has catalysis-related processes. In nature, enzymes are the commonest and most efficient catalysts found. Taking this into account, the idea of transferring principles from nature to a chemistry lab and mimicking enzymatic reactions by synthetic catalysts looks very promising in an effort to produce highly active and selective catalysts. On the other hand solid materials used as heterogeneous catalysts (i.e. semiconductors, metal oxides), have advantages towards industrial applications. However, in order to achieve the ultimate goal of producing materials with improved properties and to understand in depth environmental systems, analysis in atomic scale and electronic level are considered mandatory. Towards this objective, the utilization of in-situ spectroscopic characterization techniques under real working conditions and computational chemistry have gained significance with respect to the most commonly used classical characterization methodology.

In this seminar, the application of in-situ characterization methodologies, to study catalytic systems and the synthesis of nanomaterials under real conditions will be presented regarding bio-mimetic and metal oxide catalysts. The advantages on understanding the underlying mechanism and establishing structural/functional relationship will be discussed.

Date: Friday, November, 23rd 2012

Time: 12:30 a.m.

Room: 2.1.C19 (Sabatini Bld.), Carlos III University

**Analysing the structure of graphene at the atomic level**

J. H. Warner

Department of Materials,

University of Oxford

Abstract

Defects in graphene influence its electronic, chemical, magnetic and mechanical

properties. In this talk I will discuss how we can study defects and their impact on the

structure of graphene at the single atom level. We produce synthetic graphene by chemical vapour deposition and transfer it to TEM grids for analysis. Using Oxford's JEOL 2200 HRTEM fitted with spherical aberration correctors and a monochromator for the electron gun, we can achieve 80pm spatial resolution at a low accelerating voltage of 80kV. We have developed techniques to introduce defects in a defined spatial location with 10nm precision and study there stability and dynamics. Edge dislocation pairs are formed by sputtering carbon atoms along the zig sag direction and lead to substantial distortion of the lattice. We map out the strain sensors from these dislocation using geometric phase analysis. These results provide some of the most detailed knowledge to date on the true atomic form of defects in graphene.

Date: Friday, November, 30th 2012

Time: 12:30 a.m.

Room: 2.1.C19 (Sabatini Bld.), Carlos III University

**Spin dynamics in one dimension: any surprises?**

Eugene Sherman

Department of Physical Chemistry, The University of the Basque Country, 48080 Bilbao, Spain

IKERBASQUE Basque Foundation for Science, Bilbao, 48011, Bizkaia, Spain

Abstract

We analyze spin dynamics in one dimensional systems and find that despite

simplicity they show interesting surprises. We concentrate on two effects: spin-dependent tunneling and spin relaxation and noise.

First, we analyze spin dynamics in the tunneling decay of a localized particle in the presence of spin-orbit coupling. The spin polarization at a short time scale is affected by initial state while at long times both the probability and the spin density exhibit diffraction-in-time phenomenon. We find that tunneling in general can be characterized by a new parameter, the tunneling length, which can be seen in the spin precession.

Next, we consider the effects of random potentials in one-dimensional nanosystems and develop a theory of spin relaxation there. A theory of spin noise in semiconductor nanowires considered as prospective elements for spintronics will be presented.

In these structures spin-orbit coupling can be realized as a random function of coordinate. We demonstrate that the spin relaxation can be very slow and the resulting noise power spectrum diverges as frequency goes to zero.

Date: Wednesday, November, 7th 2012

Time: 12:30 a.m.

Room: 2.1.D03 (Sabatini Bld.), Carlos III University

**POD-based reduced order models to speed up the numerical integration of unsteady problems**

Filippo Terragni

(Modelling and Numerical Simulation Group - uc3m)

Abstract

Various ideas and methods involving local proper orthogonal decomposition (POD) and Galerkin projection are presented aiming at accelerating the numerical integration of nonlinear time dependent parabolic problems.

The proposed approach combines, in interspersed time intervals, short runs with a given numerical solver and reduced order models constructed by expanding the solution of the problem into appropriate POD modes (which span a POD manifold) and Galerkin projecting some evolution equations onto that linear basis. The POD manifold is completely calculated from the outset and only updated as time proceeds according to the dynamics, which yields an adaptive and flexible procedure.

In addition, some properties concerning the weak dependence of the POD modes on time and possible parameters in the problem are exploited in order to increase the flexibility and efficiency of the low dimensional models, which turns out to be especially interesting in the computation of bifurcations.

In this talk, the results obtained by applying the developed techniques to the approximation of transient dynamics and the simulation of attractors in bifurcation problems are presented and discussed. The test problems considered to illustrate the various ideas are the 1D complex Ginzburg-Landau equation and the unsteady, laminar flow in a 2D driven cavity.

Date: Friday, October, 26th 2012

Time: 12:30 a.m.

Room: 2.1.C17 (Sabatini Bld.), Carlos III University

**Magnetic Resonance Imaging: a tool for investigating fluid flows**

Filippo Coletti

(Mechanical Engineering Department, Stanford University)

Abstract

Magnetic Resonance Imaging (MRI) is a well-established technique in the medical community, able to produce tomographic and volumetric images of the human body. MRI can also be used to perform accurate velocimetry in fluid flows, thanks to the phase-sensitivity of the MR signal to particle motion. In the last decade the full potential of MRI-based techniques to investigate engineering flows has been demonstrated. In this seminar recent applications will be presented in which mean velocity and scalar fields are measured with high spatial resolution. Those include: three-dimensional diffusers, jets in cross-flow, turbine blade cooling configurations, compact heat exchangers, and flow in porous media. The advantages of the technique emerge: the capability of providing three-dimensional fields in complex geometries, with high data yield and without the need of optical access. The potential for developments in areas such as environmental and biomedical engineering is discussed.

Date: Thursday, June, 28th 2012

Time: 12:30 am

Room: 2.3.B04 (Sabatini Bld.), Carlos III University

**Coherent dynamics of electrons in ac driven quantum dot arrays **

Gloria Platero

(Instituto de Ciencia de Materiales de Madrid - ICMM, CSIC)

Abstract

A powerful method of manipulating the coherent dynamics of quantum particles is to control the phase of their tunnelling. We will show how such phases can be produced in two distinct and complementary ways. We have considered the dynamics of two interacting electrons hopping on a quasi-one dimensional lattice with a non-trivial topology, threaded by a uniform magnetic flux, and study the effect of adding a time-periodic ac electric field. We will show that the dynamical phases produced by the driving field can combine with the familiar Aharonov-Bohm phases arising from the magnetic flux to give precise control over the dynamics and localization of the particles, even in the presence of strong particle interactions [1].

Recent electron spin resonance experiments measure coherent spin rotations of one single electron, a fundamental ingredient for quantum operations.

We will show how it is possible to manipulate electron charge and spin dynamics in double and triple quantum dots by means of ac magnetic fields.

We demonstrate that by tuning the the field intensity, frequency and the phase difference between the fields within each dot, charge localization can be achieved. Furthermore, ac magnetic fields are also able to induce spin locking, i.e., to freeze the electronic spin, at certain field parameters and symmetry configurations [2].

Spin Blockade has been measured in transport experiments through double quantum dots. We will discuss the effect of ac magnetic fields on spin blockade and we will show that ac magnetic fields can not only remove spin blockade, but also restore it due to collective rotations of the two spins at certain parameters of the field [3].

[1] *C.E. Creffield and G. Platero, Phys. Rev. Lett., 105, 086804 (2010).*

[2] *A. Gómez-León and G. Platero, Phys. Rev. B (RC), 84, 121310(R) (2011).*

[3] *M. Busl et al., Phys. Rev. B, 81, 121306(R) (2010); R. Sánchez et al., Phys. Rev. B, 77, 165312 (2008).*

Date: Wednesday, February, 8th 2012

Time: 12:30 am

Room: 2.3.B04 (Sabatini Bld.), Carlos III University

All the information concerning the seminars from 2003 to date can be found at: