Fully 3-wave model to study the hard transition to chaotic dynamics in alfven wave-fronts

The derivative nonlinear Schrödinger (DNLS) equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. No matter how small the growth rate of the unstable wave, the four-dimensional flow for the three wave amplitudes and a relative phase, with both resistive damping and linear Landau damping, exhibits chaotic relaxation oscillations that are absent for zero growth-rate. This hard transition in phase-space behavior occurs for left-hand (LH) polarized waves, paralleling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable. The parameter domain developing chaos is much broader than the corresponding domain in a reduced 3-wave model that assumes equal dampings of the daughter waves

High Fidelity Models for Near-Earth Object Dynamics

Motivado por los últimos hallazgos realizados gracias a los recientes avances tecnológicos y misiones espaciales, el estudio de los asteroides ha despertado el interés de la comunidad científica. Tal es así que las misiones a asteroides han proliferado en los últimos años (Hayabusa, Dawn, OSIRIX-REx, ARM, AIMS-DART, ...) incentivadas por su enorme interés científico. Los asteroides son constituyentes fundamentales en la evolución del Sistema Solar, son además grandes concentraciones de valiosos recursos naturales, y también pueden considerarse como objectivos estratégicos para la futura exploración espacial. Desde hace tiempo se viene especulando con la posibilidad de capturar objetos próximos a la Tierra (NEOs en su acrónimo anglosajón) y acercarlos a nuestro planeta, permitiendo así un acceso asequible a los mismos para estudiarlos in-situ, explotar sus recursos u otras finalidades. Por otro lado, las asteroides se consideran con frecuencia como posibles peligros de magnitud planetaria, ya que impactos de estos objetos con la Tierra suceden constantemente, y un asteroide suficientemente grande podría desencadenar eventos catastróficos. Pese a la gravedad de tales acontecimientos, lo cierto es que son ciertamente difíciles de predecir. De hecho, los ricos aspectos dinámicos de los asteroides, su modelado complejo y las incertidumbres observaciones hacen que predecir su posición futura con la precisión necesaria sea todo un reto. Este hecho se hace más relevante cuando los asteroides sufren encuentros próximos con la Tierra, y más aún cuando estos son recurrentes. En tales situaciones en las cuales fuera necesario tomar medidas para mitigar este tipo de riesgos, saber estimar con precisión sus trayectorias y probabilidades de colisión es de una importancia vital. Por ello, se necesitan herramientas avanzadas para modelar su dinámica y predecir sus órbitas con precisión, y son también necesarios nuevos conceptos tecnológicos para manipular sus órbitas llegado el caso. El objetivo de esta Tesis es proporcionar nuevos métodos, técnicas y soluciones para abordar estos retos. Las contribuciones de esta Tesis se engloban en dos áreas: una dedicada a la propagación numérica de asteroides, y otra a conceptos de deflexión y captura de asteroides. Por lo tanto, la primera parte de este documento presenta novedosos avances de apliación a la propagación dinámica de alta precisión de NEOs empleando métodos de regularización y perturbaciones, con especial énfasis en el método DROMO, mientras que la segunda parte expone ideas innovadoras para la captura de asteroides y comenta el uso del “ion beam shepherd” (IBS) como tecnología para deflectarlos. Abstract Driven by the latest discoveries enabled by recent technological advances and space missions, the study of asteroids has awakened the interest of the scientific community. In fact, asteroid missions have become very popular in the recent years (Hayabusa, Dawn, OSIRIX-REx, ARM, AIMS-DART, ...) motivated by their outstanding scientific interest. Asteroids are fundamental constituents in the evolution of the Solar System, can be seen as vast concentrations of valuable natural resources, and are also considered as strategic targets for the future of space exploration. For long it has been hypothesized with the possibility of capturing small near-Earth asteroids and delivering them to the vicinity of the Earth in order to allow an affordable access to them for in-situ science, resource utilization and other purposes. On the other side of the balance, asteroids are often seen as potential planetary hazards, since impacts with the Earth happen all the time, and eventually an asteroid large enough could trigger catastrophic events. In spite of the severity of such occurrences, they are also utterly hard to predict. In fact, the rich dynamical aspects of asteroids, their complex modeling and observational uncertainties make exceptionally challenging to predict their future position accurately enough. This becomes particularly relevant when asteroids exhibit close encounters with the Earth, and more so when these happen recurrently. In such situations, where mitigation measures may need to be taken, it is of paramount importance to be able to accurately estimate their trajectories and collision probabilities. As a consequence, advanced tools are needed to model their dynamics and accurately predict their orbits, as well as new technological concepts to manipulate their orbits if necessary. The goal of this Thesis is to provide new methods, techniques and solutions to address these challenges. The contributions of this Thesis fall into two areas: one devoted to the numerical propagation of asteroids, and another to asteroid deflection and capture concepts. Hence, the first part of the dissertation presents novel advances applicable to the high accuracy dynamical propagation of near-Earth asteroids using regularization and perturbations techniques, with a special emphasis in the DROMO method, whereas the second part exposes pioneering ideas for asteroid retrieval missions and discusses the use of an “ion beam shepherd” (IBS) for asteroid deflection purposes.

The Proper Generalized Decomposition With Application In Problems Of Dynamics

In this paper we address the new reduction method called Proper Generalized Decomposition (PGD) which is a discretization technique based on the use of separated representation of the unknown fields, specially well suited for solving multidimensional parametric equations. In this case, it is applied to the solution of dynamics problems. We will focus on the dynamic analysis of an one-dimensional rod with a unit harmonic load of frequency (ω) applied at a point of interest. In what follows, we will present the application of the methodology PGD to the problem in order to approximate the displacement field as the sum of the separated functions. We will consider as new variables of the problem, parameters models associated with the characteristic of the materials, in addition to the frequency. Finally, the quality of the results will be assessed based on an example.

Computational and Experimental Modelling of Mooring Lines Dynamics for Offshore Floating Wind Turbines

El cálculo de cargas de aerogeneradores flotantes requiere herramientas de simulación en el dominio del tiempo que consideren todos los fenómenos que afectan al sistema, como la aerodinámica, la dinámica estructural, la hidrodinámica, las estrategias de control y la dinámica de las líneas de fondeo. Todos estos efectos están acoplados entre sí y se influyen mutuamente. Las herramientas integradas se utilizan para calcular las cargas extremas y de fatiga que son empleadas para dimensionar estructuralmente los diferentes componentes del aerogenerador. Por esta razón, un cálculo preciso de las cargas influye de manera importante en la optimización de los componentes y en el coste final del aerogenerador flotante. En particular, el sistema de fondeo tiene gran impacto en la dinámica global del sistema. Muchos códigos integrados para la simulación de aerogeneradores flotantes utilizan modelos simplificados que no consideran los efectos dinámicos de las líneas de fondeo. Una simulación precisa de las líneas de fondeo dentro de los modelos integrados puede resultar fundamental para obtener resultados fiables de la dinámica del sistema y de los niveles de cargas en los diferentes componentes. Sin embargo, el impacto que incluir la dinámica de los fondeos tiene en la simulación integrada y en las cargas todavía no ha sido cuantificada rigurosamente. El objetivo principal de esta investigación es el desarrollo de un modelo dinámico para la simulación de líneas de fondeo con precisión, validarlo con medidas en un tanque de ensayos e integrarlo en un código de simulación para aerogeneradores flotantes. Finalmente, esta herramienta, experimentalmente validada, es utilizada para cuantificar el impacto que un modelos dinámicos de líneas de fondeo tienen en la computación de las cargas de fatiga y extremas de aerogeneradores flotantes en comparación con un modelo cuasi-estático. Esta es una información muy útil para los futuros diseñadores a la hora de decidir qué modelo de líneas de fondeo es el adecuado, dependiendo del tipo de plataforma y de los resultados esperados. El código dinámico de líneas de fondeo desarrollado en esta investigación se basa en el método de los Elementos Finitos, utilizando en concreto un modelo ”Lumped Mass” para aumentar su eficiencia de computación. Los experimentos realizados para la validación del código se realizaron en el tanque del École Céntrale de Nantes (ECN), en Francia, y consistieron en sumergir una cadena con uno de sus extremos anclados en el fondo del tanque y excitar el extremo suspendido con movimientos armónicos de diferentes periodos. El código demostró su capacidad para predecir la tensión y los movimientos en diferentes posiciones a lo largo de la longitud de la línea con gran precisión. Los resultados indicaron la importancia de capturar la dinámica de las líneas de fondeo para la predicción de la tensión especialmente en movimientos de alta frecuencia. Finalmente, el código se utilizó en una exhaustiva evaluación del efecto que la dinámica de las líneas de fondeo tiene sobre las cargas extremas y de fatiga de diferentes conceptos de aerogeneradores flotantes. Las cargas se calcularon para tres tipologías de aerogenerador flotante (semisumergible, ”spar-buoy” y ”tension leg platform”) y se compararon con las cargas obtenidas utilizando un modelo cuasi-estático de líneas de fondeo. Se lanzaron y postprocesaron más de 20.000 casos de carga definidos por la norma IEC 61400-3 siguiendo todos los requerimientos que una entidad certificadora requeriría a un diseñador industrial de aerogeneradores flotantes. Los resultados mostraron que el impacto de la dinámica de las líneas de fondeo, tanto en las cargas de fatiga como en las extremas, se incrementa conforme se consideran elementos situados más cerca de la plataforma: las cargas en la pala y en el eje sólo son ligeramente modificadas por la dinámica de las líneas, las cargas en la base de la torre pueden cambiar significativamente dependiendo del tipo de plataforma y, finalmente, la tensión en las líneas de fondeo depende fuertemente de la dinámica de las líneas, tanto en fatiga como en extremas, en todos los conceptos de plataforma que se han evaluado. ABSTRACT The load calculation of floating offshore wind turbine requires time-domain simulation tools taking into account all the phenomena that affect the system such as aerodynamics, structural dynamics, hydrodynamics, control actions and the mooring lines dynamics. These effects present couplings and are mutually influenced. The results provided by integrated simulation tools are used to compute the fatigue and ultimate loads needed for the structural design of the different components of the wind turbine. For this reason, their accuracy has an important influence on the optimization of the components and the final cost of the floating wind turbine. In particular, the mooring system greatly affects the global dynamics of the floater. Many integrated codes for the simulation of floating wind turbines use simplified approaches that do not consider the mooring line dynamics. An accurate simulation of the mooring system within the integrated codes can be fundamental to obtain reliable results of the system dynamics and the loads. The impact of taking into account the mooring line dynamics in the integrated simulation still has not been thoroughly quantified. The main objective of this research consists on the development of an accurate dynamic model for the simulation of mooring lines, validate it against wave tank tests and then integrate it in a simulation code for floating wind turbines. This experimentally validated tool is finally used to quantify the impact that dynamic mooring models have on the computation of fatigue and ultimate loads of floating wind turbines in comparison with quasi-static tools. This information will be very useful for future designers to decide which mooring model is adequate depending on the platform type and the expected results. The dynamic mooring lines code developed in this research is based in the Finite Element Method and is oriented to the achievement of a computationally efficient code, selecting a Lumped Mass approach. The experimental tests performed for the validation of the code were carried out at the `Ecole Centrale de Nantes (ECN) wave tank in France, consisting of a chain submerged into a water basin, anchored at the bottom of the basin, where the suspension point of the chain was excited with harmonic motions of different periods. The code showed its ability to predict the tension and the motions at several positions along the length of the line with high accuracy. The results demonstrated the importance of capturing the evolution of the mooring dynamics for the prediction of the line tension, especially for the high frequency motions. Finally, the code was used for an extensive assessment of the effect of mooring dynamics on the computation of fatigue and ultimate loads for different floating wind turbines. The loads were computed for three platforms topologies (semisubmersible, spar-buoy and tension leg platform) and compared with the loads provided using a quasi-static mooring model. More than 20,000 load cases were launched and postprocessed following the IEC 61400-3 guideline and fulfilling the conditions that a certification entity would require to an offshore wind turbine designer. The results showed that the impact of mooring dynamics in both fatigue and ultimate loads increases as elements located closer to the platform are evaluated; the blade and the shaft loads are only slightly modified by the mooring dynamics in all the platform designs, the tower base loads can be significantly affected depending on the platform concept and the mooring lines tension strongly depends on the lines dynamics both in fatigue and extreme loads in all the platform concepts evaluated.

Vibrational population relaxation of carbon monoxide in the heme pocket of photolyzed carbonmonoxy myoglobin: Comparison of time-resolved mid-IR absorbance experiments and molecular dynamics simulations

The vibrational energy relaxation of carbon monoxide in the heme pocket of sperm whale myoglobin was studied by using molecular dynamics simulation and normal mode analysis methods. Molecular dynamics trajectories of solvated myoglobin were run at 300 K for both the δ- and ɛ-tautomers of the distal His-64. Vibrational population relaxation times of 335 ± 115 ps for the δ-tautomer and 640 ± 185 ps for the ɛ-tautomer were estimated by using the Landau–Teller model. Normal mode analysis was used to identify those protein residues that act as the primary “doorway” modes in the vibrational relaxation of the oscillator. Although the CO relaxation rates in both the ɛ- and δ-tautomers are similar in magnitude, the simulations predict that the vibrational relaxation of the CO is faster in the δ-tautomer with the distal His playing an important role in the energy relaxation mechanism. Time-resolved mid-IR absorbance measurements were performed on photolyzed carbonmonoxy hemoglobin (Hb13CO). From these measurements, a T1 time of 600 ± 150 ps was determined. The simulation and experimental estimates are compared and discussed.

A bcr-3 isoform of RARα-PML potentiates the development of PML-RARα-driven acute promyelocytic leukemia

Acute promyelocytic leukemia (APML) most often is associated with the balanced reciprocal translocation t(15;17) (q22;q11.2) and the expression of both the PML-RARα and RARα-PML fusion cDNAs that are formed by this translocation. In this report, we investigated the biological role of a bcr-3 isoform of RARα-PML for the development of APML in a transgenic mouse model. Expression of RARα-PML alone in the early myeloid cells of transgenic mice did not alter myeloid development or cause APML, but its expression significantly increased the penetrance of APML in mice expressing a bcr-1 isoform of PML-RARα (15% of animals developed APML with PML-RARα alone vs. 57% with both transgenes, P < 0.001). The latency of APML development was not altered substantially by the expression of RARα-PML, suggesting that it does not behave as a classical “second hit” for development of the disease. Leukemias that arose from doubly transgenic mice were less mature than those from PML-RARα transgenic mice, but they both responded to all-trans retinoic acid in vitro. These findings suggest that PML-RARα drives the development of APML and defines its basic phenotype, whereas RARα-PML potentiates this phenotype via mechanisms that are not yet understood.

Structure of a biological oxygen sensor: A new mechanism for heme-driven signal transduction

The FixL proteins are biological oxygen sensors that restrict the expression of specific genes to hypoxic conditions. FixL’s oxygen-detecting domain is a heme binding region that controls the activity of an attached histidine kinase. The FixL switch is regulated by binding of oxygen and other strong-field ligands. In the absence of bound ligand, the heme domain permits kinase activity. In the presence of bound ligand, this domain turns off kinase activity. Comparison of the structures of two forms of the Bradyrhizobium japonicum FixL heme domain, one in the “on” state without bound ligand and one in the “off” state with bound cyanide, reveals a mechanism of regulation by a heme that is distinct from the classical hemoglobin models. The close structural resemblance of the FixL heme domain to the photoactive yellow protein confirms the existence of a PAS structural motif but reveals the presence of an alternative regulatory gateway.

Arp2/3 complex and actin dynamics are required for actin-based mitochondrial motility in yeast

The Arp2/3 complex is implicated in actin polymerization-driven movement of Listeria monocytogenes. Here, we find that Arp2p and Arc15p, two subunits of this complex, show tight, actin-independent association with isolated yeast mitochondria. Arp2p colocalizes with mitochondria. Consistent with this result, we detect Arp2p-dependent formation of actin clouds around mitochondria in intact yeast. Cells bearing mutations in ARP2 or ARC15 genes show decreased velocities of mitochondrial movement, loss of all directed movement and defects in mitochondrial morphology. Finally, we observe a decrease in the velocity and extent of mitochondrial movement in yeast in which actin dynamics are reduced but actin cytoskeletal structure is intact. These results support the idea that the movement of mitochondria in yeast is actin polymerization driven and that this movement requires Arp2/3 complex.

Glass transition in DNA from molecular dynamics simulations.

Molecular dynamics simulations of the oligonucleotide duplex d(CGCGCG)2 in aqueous solution are used to investigate the glass transition phenomenon. The simulations were performed at temperatures in the 20 K to 340 K range. The mean square atomic fluctuations showed that the behavior of the oligonucleotide duplex was harmonic at low temperatures. A glass transition temperature at 223 K to 234 K was inferred for the oligonucleotide duplex, which is in agreement with experimental observations. The largest number of hydrogen bounds between the polar atoms of the oligonucleotide duplex and the water molecules was obtained at the glass transition temperature. With increasing temperature we observed a decrease in the average lifetime of the hydrogen bonds to water molecules.

Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model

We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation including additive white noise and Gilbert damping. Using a collective variable theory with no adjustable parameters we derive an equation of motion for the vortices with stochastic forces which are shown to represent white noise with an effective diffusion constant linearly dependent on temperature. We solve these stochastic equations of motion by means of a Green's function formalism and obtain the mean vortex trajectory and its variance. We find a non-standard time dependence for the variance of the components perpendicular to the driving force. We compare the analytical results with Langevin dynamics simulations and find a good agreement up to temperatures of the order of 25% of the Kosterlitz-Thouless transition temperature. Finally, we discuss the reasons why our approach is not appropriate for higher temperatures as well as the discreteness effects observed in the numerical simulations.

The emergence of classical behaviour in magnetic adatoms

A wide class of nanomagnets shows striking quantum behaviour, known as quantum spin tunnelling (QST): instead of two degenerate ground states with opposite magnetizations, a bonding-antibonding pair forms, resulting in a splitting of the ground-state doublet with wave functions linear combination of two classically opposite magnetic states, leading to the quenching of their magnetic moment. Here we study how QST is destroyed and classical behaviour emerges in the case of magnetic adatoms, where, contrary to larger nanomagnets, the QST splitting is in some instances bigger than temperature and broadening. We analyze two different mechanisms for the renormalization of the QST splitting: Heisenberg exchange between different atoms, and Kondo exchange interaction with the substrate electrons. Sufficiently strong spin-substrate and spin-spin coupling renormalize the QST splitting to zero allowing the environmental decoherence to eliminate superpositions between classical states, leading to the emergence of spontaneous magnetization. Importantly, we extract the strength of the Kondo exchange for various experiments on individual adatoms and construct a phase diagram for the classical to quantum transition.

Evolution of the landscape of Madeira Island: long-term vegetation dynamics

The aim of this thesis was to evaluate historical change of the landscape of Madeira Island and to assess spatial and temporal vegetation dynamics. In current research diverse “retrospective techniques”, such as landscape repeat photography, dendrochronology, and research of historical records were used. These, combined with vegetation relevés, aimed to gather information about landscape change, disturbance history, and vegetation successional patterns. It was found that landscape change, throughout 125 years, was higher in the last five decades manly driven by farming abandonment, building growth and exotic vegetation coverage increase. Pristine vegetation was greatly destroyed since early settlement and by the end of the nineteenth century native vegetation was highly devastated due to recurrent antropogenic disturbances. These actions also helped to block plant succession and to modify floristical assemblages, affecting as well as species richness. In places with less hemeroby, although significant growth of vegetation of lower seral stages was detected, the vegetation of most mature stages headed towards unbalance between recovery and loss, being also very vulnerable to exotic species encroachment. Recovery by native vegetation also occurred in areas formerly occupied by exotic plants and agriculture but it was almost negligible. Vegetation recovery followed the successional model currently proposed, attesting the model itself. Yet, succession was slower than espected, due to lack of favourable conditions and to recurrent disturbances. Probable tempus of each seral stage was obtained by growth rates of woody taxa estimated through dendrochronology. The exotic trees which were the dominant trees in the past (Castanea sativa and Pinus pinaster) almost vanished. Eucalyptus globulus, the current main tree of the exotic forest is being replaced by other cover types as Acacia mearnsii. The latter, along with Arundo donax, Cytisus scoparius and Pittosporum undulatum are currently the exotic species with higher invasive behaviour. However, many other exotic species have also proved to be highly pervasive and came together with the ones referred above to prevent native vegetation regeneration, to diminish biological diversity, and to block early successional phases delaying native forest recovery.

Dynamics of the Developing Chick Chorioallantoic Membrane Assessed by Stereology, Allometry, Immunohistochemistry and Molecular Analysis.

The chick chorioallantoic membrane (CAM) is a widely used model for the study of angiogenesis, tumour growth, as well as drug efficacy. In spite of this, little is known about the developmental alteration from its appearance to the time of hatching. In the current study the CAM has been studied by classical stereology and allometry. Expression levels of selected angiogenesis-related molecules were estimated by RT-PCR and cell dynamics assessed by proliferation and apoptosis assays. Absolute CAM volume increased from a low of 0.47 ± 0.11 cm3 at embryonic day 8 (E8) to a high of 2.05 ± 0.27 cm3 at E18, and then decreased to 1.6 ± 0.47 cm3 at E20. On allometric analysis, three growth phases were identifiable. Between E8-13 (phase I), the CAM grew fastest; moderately in phase II (E13-18) but was regressing in phase III (E18-20). The chorion, the mesenchyme and the allantoic layers grew fastest in phase I, but moderately in phase II. The mesenchyme grew slowly in phase III while the chorion and allantois were regressing. Chorionic cell volume increased fastest in phase I and was regressing in phase III. Chorionic capillaries grew steadily in phase I and II but regressed in phase III. Both the chorion and the allantois grew by intrinsic cell proliferation as well as recruitment of cells from the mesenchyme. Cell proliferation was prominent in the allantois and chorion early during development, declined after E17 and apoptosis started mainly in the chorion from E14. VEGFR2 expression peaked at E11 and declined steadily towards E20, VEGF peaked at E13 and E20 while HIF 1α had a peak at E11 and E20. Studies targeting CAM growth and angiogenesis need to take these growth phases into consideration.

Tropically-driven climate shifts in southwestern Europe during MIS 19, a low eccentricity interglacial

The relative roles of high- versus low-latitude forcing of millennial-scale climate variability are still not well understood. Here we present terrestrial–marine climate profiles from the southwestern Iberian margin, a region particularly affected by precession, that show millennial climate oscillations related to a nonlinear response to the Earth's precession cycle during Marine Isotope Stage (MIS) 19. MIS 19 has been considered the best analogue to our present interglacial from an astronomical point of view due to the reduced eccentricity centred at 785 ka. In our records, seven millennial-scale forest contractions punctuated MIS 19 superimposed to two orbitally-driven Mediterranean forest expansions. In contrast to our present interglacial, we evidence for the first time low latitude-driven 5000-yr cycles of drying and cooling in the western Mediterranean region, along with warmth in the subtropical gyre related to the fourth harmonic of precession. These cycles indicate repeated intensification of North Atlantic meridional moisture transport that along with decrease in boreal summer insolation triggered ice growth and may have contributed to the glacial inception, at ∼774 ka. The freshwater fluxes during MIS 19ab amplified the cooling events in the North Atlantic promoting further cooling and leading to MIS 18 glaciation. The discrepancy between the dominant cyclicity observed during MIS 1, 2500-yr, and that of MIS 19, 5000-yr, challenges the similar duration of the Holocene and MIS 19c interglacials under natural boundary conditions.

Higher mathematics. A text-book for classical and engineering colleges.

"Bibliography ... general works on the history of mathematics in the nineteenth century": p. 568-570.