Statistical Analysis and Modelling Aspects of Thermally Driven Turbulence

The present work aims to provide a deeper understanding of thermally driven turbulence and to address some modelling aspects related to the physics of the flow. For this purpose, two idealized systems are investigated by Direct Numerical Simulation: the rotating and non-rotating Rayleigh-Bénard convection. The preliminary study of the flow topologies shows how the coherent structures organise into different patterns depending on the rotation rate. From a statistical perspective, the analysis of the turbulent kinetic energy and temperature variance budgets allows to identify the flow regions where the production, the transport, and the dissipation of turbulent fluctuations occur. To provide a multi-scale description of the flows, a theoretical framework based on the Kolmogorov and Yaglom equations is applied for the first time to the Rayleigh-Bénard convection. The analysis shows how the spatial inhomogeneity modulates the dynamics at different scales and wall-distances. Inside the core of the flow, the space of scales can be divided into an inhomogeneity-dominated range at large scales, an inertial-like range at intermediate scales and a dissipative range at small scales. This classic scenario breaks close to the walls, where the inhomogeneous mechanisms and the viscous/diffusive processes are important at every scale and entail more complex dynamics. The same theoretical framework is extended to the filtered velocity and temperature fields of non-rotating Rayleigh-Bénard convection. The analysis of the filtered Kolmogorov and Yaglom equations reveals the influence of the residual scales on the filtered dynamics both in physical and scale space, highlighting the effect of the relative position between the filter length and the crossover that separates the inhomogeneity-dominated range from the quasi-homogeneous range. The assessment of the filtered and residual physics results to be instrumental for the correct use of the existing Large-Eddy Simulation models and for the development of new ones.

Towards a broader understanding of the effects of tidal forcing on the global ocean circulation

The study of tides and their interactions with the complex dynamics of the global ocean represents a crucial challenge in ocean modelling. This thesis aims to deepen this study from a dynamical point of view, analysing what are the tidal effects on the general circulation of the ocean. We perform different experiments of a mesoscale-permitting global ocean model forced by both atmospheric fields and astronomical tidal potential, and we implement two parametrizations to include in the model tidal phenomena that are currently unresolved, with particular emphasis to the topographic wave drag for locally dissipating internal waves. An additional experiment using a mesoscale-resolving configuration is used to compare the simulated tides at different resolutions with observed data. We find that the accuracy of modelled tides strongly depends on the region and harmonic component of interest, even though the increased resolution allows to improve the modelled topography and resolve more intense internal waves. We then focus on the impact of tides in the Atlantic Ocean and find that tides weaken the overturning circulation during the analysed period from 1981 to 2007, even though the interannual differences strongly change in both amplitude and phase. The zonally integrated momentum balance shows that tide changes the water stratification at the zonal boundaries, modifying the pressure and therefore the geostrophic balance over the entire basin. Finally, we describe the overturning circulation in the Mediterranean Sea computing the meridional and zonal streamfunctions both in the Eulerian and residual frameworks. The circulation is characterised by different cells, and their forcing processes are described with particular emphasis to the role of mesoscale and a transient climatic event. We complete the description of the overturning circulation giving evidence for the first time to the connection between meridional and zonal cells.

Diffusive models and chaos indicators for non-linear betatron motion in circular hadron accelerators

Understanding the complex dynamics of beam-halo formation and evolution in circular particle accelerators is crucial for the design of current and future rings, particularly those utilizing superconducting magnets such as the CERN Large Hadron Collider (LHC), its luminosity upgrade HL-LHC, and the proposed Future Circular Hadron Collider (FCC-hh). A recent diffusive framework, which describes the evolution of the beam distribution by means of a Fokker-Planck equation, with diffusion coefficient derived from the Nekhoroshev theorem, has been proposed to describe the long-term behaviour of beam dynamics and particle losses. In this thesis, we discuss the theoretical foundations of this framework, and propose the implementation of an original measurement protocol based on collimator scans in view of measuring the Nekhoroshev-like diffusive coefficient by means of beam loss data. The available LHC collimator scan data, unfortunately collected without the proposed measurement protocol, have been successfully analysed using the proposed framework. This approach is also applied to datasets from detailed measurements of the impact on the beam losses of so-called long-range beam-beam compensators also at the LHC. Furthermore, dynamic indicators have been studied as a tool for exploring the phase-space properties of realistic accelerator lattices in single-particle tracking simulations. By first examining the classification performance of known and new indicators in detecting the chaotic character of initial conditions for a modulated Hénon map and then applying this knowledge to study the properties of realistic accelerator lattices, we tried to identify a connection between the presence of chaotic regions in the phase space and Nekhoroshev-like diffusive behaviour, providing new tools to the accelerator physics community.

Complex-order dynamics in hexapod locomotion

This paper studies the dynamics of foot–ground interaction in hexapod locomotion systems. For that objective the robot motion is characterized in terms of several locomotion variables and the ground is modelled through a non-linear spring-dashpot system, with parameters based on the studies of soil mechanics. Moreover, it is adopted an algorithm with foot-force feedback to control the robot locomotion. A set of model-based experiments reveals the influence of the locomotion velocity on the foot–ground transfer function, which presents complex-order dynamics.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Dinámica Cuántica de Sistemas Complejos: Fundamentos y Aplicaciones. Quantum Dynamics in Complex Systems: Fundamentals and Aplications.

El procedimiento de revertir la dinámica colectiva (diablillo de Loschmidt apresurado) mediante un pulso de radio frecuencia, permite generar un Eco de Loschmidt, es decir la refocalización de una excitación localizada. Alternativamente, en acústica es posible implementar un Espejo de Reversión Temporal, que consiste en la progresiva inyección de una débil excitación ultrasónica en la periferia de un sistema, para construir una excitación que se propaga "hacia atrás". Así, podemos afirmar que es posible revertir y controlar la dinámica. Sin embargo, aún no se posee una comprensión detallada de los mecanismos que gobiernan estos procedimientos. Este proyecto busca responder las preguntas que posibilitan esta comprensión.

Modelling of bird distribution under complex mediterranean landscape dynamics: open habitat birds and fire (MEDFIRE)

Report for the scientific sojourn at the Simon Fraser University, Canada, from July to September 2007. General context: landscape change during the last years is having significant impacts on biodiversity in many Mediterranean areas. Land abandonment, urbanisation and specially fire are profoundly transforming large areas in the Western Mediterranean basin and we know little on how these changes influence species distribution and in particular how these species will respond to further change in a context of global change including climate. General objectives: integrate landscape and population dynamics models in a platform allowing capturing species distribution responses to landscape changes and assessing impact on species distribution of different scenarios of further change. Specific objective 1: develop a landscape dynamic model capturing fire and forest succession dynamics in Catalonia and linked to a stochastic landscape occupancy (SLOM) (or spatially explicit population, SEPM) model for the Ortolan bunting, a species strongly linked to fire related habitat in the region. Predictions from the occupancy or spatially explicit population Ortolan bunting model (SEPM) should be evaluated using data from the DINDIS database. This database tracks bird colonisation of recently burnt big areas (&50 ha). Through a number of different SEPM scenarios with different values for a number of parameter, we should be able to assess different hypothesis in factors driving bird colonisation in new burnt patches. These factors to be mainly, landscape context (i.e. difficulty to reach the patch, and potential presence of coloniser sources), dispersal constraints, type of regenerating vegetation after fire, and species characteristics (niche breadth, etc).

Protein-protein interaction investigated by steered molecular dynamics: the TCR-pMHC complex.

We present a novel steered molecular dynamics scheme to induce the dissociation of large protein-protein complexes. We apply this scheme to study the interaction of a T cell receptor (TCR) with a major histocompatibility complex (MHC) presenting a peptide (p). Two TCR-pMHC complexes are considered, which only differ by the mutation of a single amino acid on the peptide; one is a strong agonist that produces T cell activation in vivo, while the other is an antagonist. We investigate the interaction mechanism from a large number of unbinding trajectories by analyzing van der Waals and electrostatic interactions and by computing energy changes in proteins and solvent. In addition, dissociation potentials of mean force are calculated with the Jarzynski identity, using an averaging method developed for our steering scheme. We analyze the convergence of the Jarzynski exponential average, which is hampered by the large amount of dissipative work involved and the complexity of the system. The resulting dissociation free energies largely underestimate experimental values, but the simulations are able to clearly differentiate between wild-type and mutated TCR-pMHC and give insights into the dissociation mechanism.

Diverse population dynamics of three Anopheles species belonging to the Triannulatus Complex (Diptera: Culicidae)

The Triannulatus Complex of Anopheles (Nyssorhynchus) consists of at least three sibling species, namely Anopheles triannulatus s.s., Anopheles halophylus and a third undescribed member herein referred to as An. triannulatus "C". Sympatric anophelines belonging to species complexes, even though closely related, may exploit different environments such as larval habitats. In this paper we hypothesize that rainfall and seasonal flooding would distinctly influence the availability of larval habitats and consequently the seasonal population dynamics of sympatric members of the Triannulatus Complex. A reflection of this is distinct seasonal biting frequencies exhibited by three members of the Triannulatus Complex at a site in Central Brazil. Population dynamics seem to be influenced by the water level in the local rivers, although biting frequency of all three species was negatively influenced by rainfall. An. triannulatus s.s. was more abundant following the end of the rainy season, but notably 30 to 60 days after flooding. On the other hand, An. halophylus and An. triannulatus C peaked during the middle of the dry season, when water impoundments have no inflow, are somewhat reduced in size and the water becomes brackish. Differences in population dynamics were greater between An. triannulatus s.s. and An. halophylus and An. triannulatus C than between An. halophylus and An. triannulatus C. This might reflect differences in larval habitat exploitation and therefore spatial segregation among these members of the complex.

Permutation Entropy Based Analysis of Complex Signals for Characterising Change in System Dynamics

Timely detection of sudden change in dynamics that adversely affect the performance of systems and quality of products has great scientific relevance. This work focuses on effective detection of dynamical changes of real time signals from mechanical as well as biological systems using a fast and robust technique of permutation entropy (PE). The results are used in detecting chatter onset in machine turning and identifying vocal disorders from speech signal.Permutation Entropy is a nonlinear complexity measure which can efficiently distinguish regular and complex nature of any signal and extract information about the change in dynamics of the process by indicating sudden change in its value. Here we propose the use of permutation entropy (PE), to detect the dynamical changes in two non linear processes, turning under mechanical system and speech under biological system.Effectiveness of PE in detecting the change in dynamics in turning process from the time series generated with samples of audio and current signals is studied. Experiments are carried out on a lathe machine for sudden increase in depth of cut and continuous increase in depth of cut on mild steel work pieces keeping the speed and feed rate constant. The results are applied to detect chatter onset in machining. These results are verified using frequency spectra of the signals and the non linear measure, normalized coarse-grained information rate (NCIR).PE analysis is carried out to investigate the variation in surface texture caused by chatter on the machined work piece. Statistical parameter from the optical grey level intensity histogram of laser speckle pattern recorded using a charge coupled device (CCD) camera is used to generate the time series required for PE analysis. Standard optical roughness parameter is used to confirm the results.Application of PE in identifying the vocal disorders is studied from speech signal recorded using microphone. Here analysis is carried out using speech signals of subjects with different pathological conditions and normal subjects, and the results are used for identifying vocal disorders. Standard linear technique of FFT is used to substantiate thc results.The results of PE analysis in all three cases clearly indicate that this complexity measure is sensitive to change in regularity of a signal and hence can suitably be used for detection of dynamical changes in real world systems. This work establishes the application of the simple, inexpensive and fast algorithm of PE for the benefit of advanced manufacturing process as well as clinical diagnosis in vocal disorders.

Statistics and kinetics of single-molecule electron transfer dynamics in complex environments: A simulation model study

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Single molecule electron transfer dynamics in complex environments

We propose a new theoretical approach to study the kinetics of the electron transfer (ET) under the dynamical influence of the complex environments with the first passage times (FPT) of the reaction events. By measuring the mean and high order moments of FPT and their ratios, the full kinetics of ET, especially the dynamical transitions across different temperature zones, is revealed. The potential applications of the current results to single molecule electron transfer are discussed.

Application of a bounded upwinding scheme to complex fluid dynamics problems

This paper is concerned with an overview of upwinding schemes, and further nonlinear applications of a recently introduced high resolution upwind differencing scheme, namely the ADBQUICKEST [V.G. Ferreira, F.A. Kurokawa, R.A.B. Queiroz, M.K. Kaibara, C.M. Oishi, J.A.Cuminato, A.F. Castelo, M.F. Tomé, S. McKee, assessment of a high-order finite difference upwind scheme for the simulation of convection-diffusion problems, International Journal for Numerical Methods in Fluids 60 (2009) 1-26]. The ADBQUICKEST scheme is a new TVD version of the QUICKEST [B.P. Leonard, A stable and accurate convective modeling procedure based on quadratic upstream interpolation, Computer Methods in Applied Mechanics and Engineering 19 (1979) 59-98] for solving nonlinear balance laws. The scheme is based on the concept of NV and TVD formalisms and satisfies a convective boundedness criterion. The accuracy of the scheme is compared with other popularly used convective upwinding schemes (see, for example, Roe (1985) [19], Van Leer (1974) [18] and Arora & Roe (1997) [17]) for solving nonlinear conservation laws (for example, Buckley-Leverett, shallow water and Euler equations). The ADBQUICKEST scheme is then used to solve six types of fluid flow problems of increasing complexity: namely, 2D aerosol filtration by fibrous filters; axisymmetric flow in a tubular membrane; 2D two-phase flow in a fluidized bed; 2D compressible Orszag-Tang MHD vortex; axisymmetric jet onto a flat surface at low Reynolds number and full 3D incompressible flows involving moving free surfaces. The numerical simulations indicate that this convective upwinding scheme is a good generic alternative for solving complex fluid dynamics problems. © 2012.