Structure of intermediate shocks in collisionsless anisotropic Hall-magnetohydrodynamics plasma models

The existence of discontinuities within the double-adiabatic Hall-magnetohydrodynamics (MHD) model is discussed. These solutions are transitional layers where some of the plasma properties change from one equilibrium state to another. Under the assumption of traveling wave solutions with velocity C and propagation angle θ with respect to the ambient magnetic field, the Hall-MHD model reduces to a dynamical system and the waves are heteroclinic orbits joining two different fixed points. The analysis of the fixed points rules out the existence of rotational discontinuities. Simple considerations about the Hamiltonian nature of the system show that, unlike dissipative models, the intermediate shock waves are organized in branches in parameter space, i.e., they occur if a given relationship between θ and C is satisfied. Electron-polarized (ion-polarized) shock waves exhibit, in addition to a reversal of the magnetic field component tangential to the shock front, a maximum (minimum) of the magnetic field amplitude. The jumps of the magnetic field and the relative specific volume between the downstream and the upstream states as a function of the plasma properties are presented. The organization in parameter space of localized structures including in the model the influence of finite Larmor radius is discussed

Interaction of spatially overlapping standing electromagnetic solitons in plasmas

Numerical investigations on mutual interactions between two spatially overlapping standing electromagnetic solitons in a cold unmagnetized plasma are reported. It is found that an initial state comprising of two overlapping standing solitons evolves into different end states, depending on the amplitudes of the two solitons and the phase difference between them. For small amplitude solitons with zero phase difference, we observe the formation of an oscillating bound state whose period depends on their initial separation. These results suggest the existence of a bound state made of two solitons in the relativistic cold plasma fluid model.

Comparative study about the use of two and three-dimensional methods in surface finishing characterization

The increasing number of works related to the surface texture characterization based on 3D information, makes convenient rethinking traditional methods based on two-dimensional measurements from profiles. This work compares results between measurements obtained using two and three-dimensional methods. It uses three kinds of data sources: reference surfaces, randomly generated surfaces and measured. Preliminary results are presented. These results must be completed trying to cover a wider number of possibilities according to the manufacturing process and the measurement instrumentation since results can vary quite significantly between them.

Symmetry issues in Directly Irradiated Targets

In direct drive Inertial Confinement Fusion (ICF), the typical laser beam to laser beam angle is around 30o. This fact makes the study of the irradiation symmetry agenuine 3D problem. In this paper we use the three dimensional version of the MULTI hydrocode to assess the symmetry of such ICF implosions. More specifically, we study a shock-ignition proposal for the Laser-M´egajoule facility (LMJ) in which two of the equatorial beam cones are used to implode and pre compress a spherical capsule (the “reference” capsule of HiPER project) made of 0.59 mg of pure Deuterium-Tritium mixture. The symmetry of this scheme is analysed and optimized to get a design inside the operating limits of LMJ. The studied configuration has been found essentially axial-symmetric, so that the use of 2D hydrocodes would be appropriate for this specific situation

Systematic analysis of direct-drive baseline designs for shock ignition with the Laser MégaJoule

We present direct-drive target design studies for the laser mégajoule using two distinct initial aspect ratios (A = 34 and A = 5). Laser pulse shapes are optimized by a random walk method and drive power variations are used to cover a wide variety of implosion velocities between 260 km/s and 365 km/s. For selected implosion velocities and for each initial aspect ratio, scaled-target families are built in order to find self-ignition threshold. High-gain shock ignition is also investigated in the context of Laser MégaJoule for marginally igniting targets below their own self-ignition threshold.

Fast ignition by quasimonoenergetic ion beams

The potential of quasimonoenergetic ion beams for fast ignition (FI) of fusion targets is investigated. Lithium, carbon, aluminium and vanadium ions have been considered here to determine the optimal kinetic energy for each ion type. Our calculations show that the ignition energies of those beams impinging on a standard fuel configuration are similar. However, they are obtained for very different ion energies. Assuming that the ions can be focused onto 10 ?m spots, a new irradiation scheme that reduces substantially the ignition energies is proposed. The combination of using intermediate ions, such as 5.5 GeV vanadium, and the new irradiation scheme allows one to reduce the number of ions required for ignition by roughly three orders of magnitude when compared with the standard proton FI scheme.

Correlation Dimension of Complex Networks

We propose a new measure to characterize the dimension of complex networks based on the ergodic theory of dynamical systems. This measure is derived from the correlation sum of a trajectory generated by a random walker navigating the network, and extends the classical Grassberger-Procaccia algorithm to the context of complex networks. The method is validated with reliable results for both synthetic networks and real-world networks such as the world air-transportation network or urban networks, and provides a computationally fast way for estimating the dimensionality of networks which only relies on the local information provided by the walkers.

Horizontal visibility graphs generated by type-I intermittency

The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associatedHVgraphs.We showhowthe alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values for several network parameters. In particular, we predict that the characteristic power-law scaling of the mean length of laminar trend sizes is fully inherited by the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of block entropy functionals defined on the graph. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization-group framework, where the fixed points of its graph-theoretical renormalization-group flow account for the different types of dynamics.We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibits extremal entropic properties.

Quasiperiodic graphs at the onset of chaos

We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identities between entropy growth rates and generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued fraction characterizes each family. We illustrate our results for the so-called golden, silver, and bronze numbers

Phase transitions in number theory: from the birthday problem to Sidon sets

In this work, we show how number theoretical problems can be fruitfully approached with the tools of statistical physics. We focus on g-Sidon sets, which describe sequences of integers whose pairwise sums are different, and propose a random decision problem which addresses the probability of a random set of k integers to be g-Sidon. First, we provide numerical evidence showing that there is a crossover between satisfiable and unsatisfiable phases which converts to an abrupt phase transition in a properly defined thermodynamic limit. Initially assuming independence, we then develop a mean-field theory for the g-Sidon decision problem. We further improve the mean-field theory, which is only qualitatively correct, by incorporating deviations from independence, yielding results in good quantitative agreement with the numerics for both finite systems and in the thermodynamic limit. Connections between the generalized birthday problem in probability theory, the number theory of Sidon sets and the properties of q-Potts models in condensed matter physics are briefly discussed

Theory of intermittency applied to classical pathological cases

The classical theory of intermittency developed for return maps assumes uniform density of points reinjected from the chaotic to laminar region. Though it works fine in some model systems, there exist a number of so-called pathological cases characterized by a significant deviation of main characteristics from the values predicted on the basis of the uniform distribution. Recently, we reported on how the reinjection probability density (RPD) can be generalized. Here, we extend this methodology and apply it to different dynamical systems exhibiting anomalous type-II and type-III intermittencies. Estimation of the universal RPD is based on fitting a linear function to experimental data and requires no a priori knowledge on the dynamical model behind. We provide special fitting procedure that enables robust estimation of the RPD from relatively short data sets (dozens of points). Thus, the method is applicable for a wide variety of data sets including numerical simulations and real-life experiments. Estimated RPD enables analytic evaluation of the length of the laminar phase of intermittent behaviors. We show that the method copes well with dynamical systems exhibiting significantly different statistics reported in the literature. We also derive and classify characteristic relations between the mean laminar length and main controlling parameter in perfect agreement with data provided by numerical simulations

Advances in global instability computations: from incompressible to hypersonic flow

Esta tesis constituye un gran avance en el conocimiento del estudio y análisis de inestabilidades hidrodinámicas desde un punto de vista físico y teórico, como consecuencia de haber desarrollado innovadoras técnicas para la resolución computacional eficiente y precisa de la parte principal del espectro correspondiente a los problemas de autovalores (EVP) multidimensionales que gobiernan la inestabilidad de flujos con dos o tres direcciones espaciales inhomogéneas, denominados problemas de estabilidad global lineal. En el contexto del trabajo de desarrollo de herramientas computacionales presentado en la tesis, la discretización mediante métodos de diferencias finitas estables de alto orden de los EVP bidimensionales y tridimensionales que se derivan de las ecuaciones de Navier-Stokes linealizadas sobre flujos con dos o tres direcciones espaciales inhomogéneas, ha permitido una aceleración de cuatro órdenes de magnitud en su resolución. Esta mejora de eficiencia numérica se ha conseguido gracias al hecho de que usando estos esquemas de diferencias finitas, técnicas eficientes de resolución de problemas lineales son utilizables, explotando el alto nivel de dispersión o alto número de elementos nulos en las matrices involucradas en los problemas tratados. Como más notable consecuencia cabe destacar que la resolución de EVPs multidimensionales de inestabilidad global, que hasta la fecha necesitaban de superordenadores, se ha podido realizar en ordenadores de sobremesa. Además de la solución de problemas de estabilidad global lineal, el mencionado desarrollo numérico facilitó la extensión de las ecuaciones de estabilidad parabolizadas (PSE) lineales y no lineales para analizar la inestabilidad de flujos que dependen fuertemente en dos direcciones espaciales y suavemente en la tercera con las ecuaciones de estabilidad parabolizadas tridimensionales (PSE-3D). Precisamente la capacidad de extensión del novedoso algoritmo PSE-3D para el estudio de interacciones no lineales de los modos de estabilidad, desarrollado íntegramente en esta tesis, permite la predicción de transición en flujos complejos de gran interés industrial y por lo tanto extiende el concepto clásico de PSE, el cuál ha sido empleado exitosamente durante las pasadas tres décadas en el mismo contexto para problemas de capa límite bidimensional. Típicos ejemplos de flujos incompresibles se han analizado en este trabajo sin la necesidad de recurrir a restrictivas presuposiciones usadas en el pasado. Se han estudiado problemas vorticales como es el caso de un vórtice aislado o sistemas de vórtices simulando la estela de alas, en los que la homogeneidad axial no se impone y así se puede considerar la difusión viscosa del flujo. Además, se ha estudiado el chorro giratorio turbulento, cuya inestabilidad se utiliza para mejorar las características de funcionamiento de combustores. En la tesis se abarcan adicionalmente problemas de flujos compresibles. Se presenta el estudio de inestabilidad de flujos de borde de ataque a diferentes velocidades de vuelo. También se analiza la estela formada por un elemento rugoso aislado en capa límite supersónica e hipersónica, mostrando excelentes comparaciones con resultados obtenidos mediante simulación numérica directa. Finalmente, nuevas inestabilidades se han identificado en el flujo hipersónico a Mach 7 alrededor de un cono elíptico que modela el vehículo de pruebas en vuelo HIFiRE-5. Los resultados comparan favorablemente con experimentos en vuelo, lo que subraya aún más el potencial de las metodologías de análisis de estabilidad desarrolladas en esta tesis. ABSTRACT The present thesis constitutes a step forward in advancing the frontiers of knowledge of fluid flow instability from a physical point of view, as a consequence of having been successful in developing groundbreaking methodologies for the efficient and accurate computation of the leading part of the spectrum pertinent to multi-dimensional eigenvalue problems (EVP) governing instability of flows with two or three inhomogeneous spatial directions. In the context of the numerical work presented in this thesis, the discretization of the spatial operator resulting from linearization of the Navier-Stokes equations around flows with two or three inhomogeneous spatial directions by variable-high-order stable finite-difference methods has permitted a speedup of four orders of magnitude in the solution of the corresponding two- and three-dimensional EVPs. This improvement of numerical performance has been achieved thanks to the high-sparsity level offered by the high-order finite-difference schemes employed for the discretization of the operators. This permitted use of efficient sparse linear algebra techniques without sacrificing accuracy and, consequently, solutions being obtained on typical workstations, as opposed to the previously employed supercomputers. Besides solution of the two- and three-dimensional EVPs of global linear instability, this development paved the way for the extension of the (linear and nonlinear) Parabolized Stability Equations (PSE) to analyze instability of flows which depend in a strongly-coupled inhomogeneous manner on two spatial directions and weakly on the third. Precisely the extensibility of the novel PSE-3D algorithm developed in the framework of the present thesis to study nonlinear flow instability permits transition prediction in flows of industrial interest, thus extending the classic PSE concept which has been successfully employed in the same context to boundary-layer type of flows over the last three decades. Typical examples of incompressible flows, the instability of which was analyzed in the present thesis without the need to resort to the restrictive assumptions used in the past, range from isolated vortices, and systems thereof, in which axial homogeneity is relaxed to consider viscous diffusion, as well as turbulent swirling jets, the instability of which is exploited in order to improve flame-holding properties of combustors. The instability of compressible subsonic and supersonic leading edge flows has been solved, and the wake of an isolated roughness element in a supersonic and hypersonic boundary-layer has also been analyzed with respect to its instability: excellent agreement with direct numerical simulation results has been obtained in all cases. Finally, instability analysis of Mach number 7 ow around an elliptic cone modeling the HIFiRE-5 flight test vehicle has unraveled flow instabilities near the minor-axis centerline, results comparing favorably with flight test predictions.

Predicción de la velocidad crítica de flameo mediante el uso de modelos aeroelásticos extrapolados en tiempo real con datos de vuelo

La Aeroelasticidad fue definida por Arthur Collar en 1947 como "el estudio de la interacción mutua entre fuerzas inerciales, elásticas y aerodinámicas actuando sobre elementos estructurales expuestos a una corriente de aire". Actualmente, esta definición se ha extendido hasta abarcar la influencia del control („Aeroservoelasticidad‟) e, incluso, de la temperatura („Aerotermoelasticidad‟). En el ámbito de la Ingeniería Aeronáutica, los fenómenos aeroelásticos, tanto estáticos (divergencia, inversión de mando) como dinámicos (flameo, bataneo) son bien conocidos desde los inicios de la Aviación. Las lecciones aprendidas a lo largo de la Historia Aeronáutica han permitido establecer criterios de diseño destinados a mitigar la probabilidad de sufrir fenómenos aeroelásticos adversos durante la vida operativa de una aeronave. Adicionalmente, el gran avance experimentado durante esta última década en el campo de la Aerodinámica Computacional y en la modelización aeroelástica ha permitido mejorar la fiabilidad en el cálculo de las condiciones de flameo de una aeronave en su fase de diseño. Sin embargo, aún hoy, los ensayos en vuelo siguen siendo necesarios para validar modelos aeroelásticos, verificar que la aeronave está libre de inestabilidades aeroelásticas y certificar sus distintas envolventes. En particular, durante el proceso de expansión de la envolvente de una aeronave en altitud/velocidad, se requiere predecir en tiempo real las condiciones de flameo y, en consecuencia, evitarlas. A tal efecto, en el ámbito de los ensayos en vuelo, se han desarrollado diversas metodologías que predicen, en tiempo real, las condiciones de flameo en función de condiciones de vuelo ya verificadas como libres de inestabilidades aeroelásticas. De entre todas ellas, aquella que relaciona el amortiguamiento y la velocidad con un parámetro específico definido como „Margen de Flameo‟ (Flutter Margin), permanece como la técnica más común para proceder con la expansión de Envolventes en altitud/velocidad. No obstante, a pesar de su popularidad y facilidad de aplicación, dicha técnica no es adecuada cuando en la aeronave a ensayar se hallan presentes no-linealidades mecánicas como, por ejemplo, holguras. En particular, en vuelos de ensayo dedicados específicamente a expandir la envolvente en altitud/velocidad, las condiciones de „Oscilaciones de Ciclo Límite‟ (Limit Cycle Oscillations, LCOs) no pueden ser diferenciadas de manera precisa de las condiciones de flameo, llevando a una determinación excesivamente conservativa de la misma. La presente Tesis desarrolla una metodología novedosa, basada en el concepto de „Margen de Flameo‟, que permite predecir en tiempo real las condiciones de „Ciclo Límite‟, siempre que existan, distinguiéndolas de las de flameo. En una primera parte, se realiza una revisión bibliográfica de la literatura acerca de los diversos métodos de ensayo existentes para efectuar la expansión de la envolvente de una aeronave en altitud/velocidad, el efecto de las no-linealidades mecánicas en el comportamiento aeroelástico de dicha aeronave, así como una revisión de las Normas de Certificación civiles y militares respecto a este tema. En una segunda parte, se propone una metodología de expansión de envolvente en tiempo real, basada en el concepto de „Margen de Flameo‟, que tiene en cuenta la presencia de no-linealidades del tipo holgura en el sistema aeroelástico objeto de estudio. Adicionalmente, la metodología propuesta se valida contra un modelo aeroelástico bidimensional paramétrico e interactivo programado en Matlab. Para ello, se plantean las ecuaciones aeroelásticas no-estacionarias de un perfil bidimensional en la formulación espacio-estado y se incorpora la metodología anterior a través de un módulo de análisis de señal y otro módulo de predicción. En una tercera parte, se comparan las conclusiones obtenidas con las expuestas en la literatura actual y se aplica la metodología propuesta a resultados experimentales de ensayos en vuelo reales. En resumen, los principales resultados de esta Tesis son: 1. Resumen del estado del arte en los métodos de ensayo aplicados a la expansión de envolvente en altitud/velocidad y la influencia de no-linealidades mecánicas en la determinación de la misma. 2. Revisión de la normas de Certificación Civiles y las normas Militares en relación a la verificación aeroelástica de aeronaves y los límites permitidos en presencia de no-linealidades. 3. Desarrollo de una metodología de expansión de envolvente basada en el Margen de Flameo. 4. Validación de la metodología anterior contra un modelo aeroelástico bidimensional paramétrico e interactivo programado en Matlab/Simulink. 5. Análisis de los resultados obtenidos y comparación con resultados experimentales. ABSTRACT Aeroelasticity was defined by Arthur Collar in 1947 as “the study of the mutual interaction among inertia, elastic and aerodynamic forces when acting on structural elements surrounded by airflow”. Today, this definition has been updated to take into account the Controls („Aeroservoelasticity‟) and even the temperature („Aerothermoelasticity‟). Within the Aeronautical Engineering, aeroelastic phenomena, either static (divergence, aileron reversal) or dynamic (flutter, buzz), are well known since the early beginning of the Aviation. Lessons learned along the History of the Aeronautics have provided several design criteria in order to mitigate the probability of encountering adverse aeroelastic phenomena along the operational life of an aircraft. Additionally, last decade improvements experienced by the Computational Aerodynamics and aeroelastic modelization have refined the flutter onset speed calculations during the design phase of an aircraft. However, still today, flight test remains as a key tool to validate aeroelastic models, to verify flutter-free conditions and to certify the different envelopes of an aircraft. Specifically, during the envelope expansion in altitude/speed, real time prediction of flutter conditions is required in order to avoid them in flight. In that sense, within the flight test community, several methodologies have been developed to predict in real time flutter conditions based on free-flutter flight conditions. Among them, the damping versus velocity technique combined with a Flutter Margin implementation remains as the most common technique used to proceed with the envelope expansion in altitude/airspeed. However, although its popularity and „easy to implement‟ characteristics, several shortcomings can adversely affect to the identification of unstable conditions when mechanical non-linearties, as freeplay, are present. Specially, during test flights devoted to envelope expansion in altitude/airspeed, Limits Cycle Oscillations (LCOs) conditions can not be accurately distinguished from those of flutter and, in consequence, it leads to an excessively conservative envelope determination. The present Thesis develops a new methodology, based on the Flutter Margin concept, that enables in real time the prediction of the „Limit Cycle‟ conditions, whenever they exist, without degrading the capability of predicting the flutter onset speed. The first part of this Thesis presents a review of the state of the art regarding the test methods available to proceed with the envelope expansion of an aircraft in altitude/airspeed and the effect of mechanical non-linearities on the aeroelastic behavior. Also, both civil and military regulations are reviewed with respect aeroelastic investigation of air vehicles. The second part of this Thesis proposes a new methodology to perform envelope expansion in real time based on the Flutter Margin concept when non-linearities, as freeplay, are present. Additionally, this methodology is validated against a Matlab/Slimulink bidimensional aeroelastic model. This model, parametric and interactive, is formulated within the state-space field and it implements the proposed methodology through two main real time modules: A signal processing module and a prediction module. The third part of this Thesis compares the final conclusions derived from the proposed methodology with those stated by the flight test community and experimental results. In summary, the main results provided by this Thesis are: 1. State of the Art review of the test methods applied to envelope expansion in altitude/airspeed and the influence of mechanical non-linearities in its identification. 2. Review of the main civil and military regulations regarding the aeroelastic verification of air vehicles and the limits set when non-linearities are present. 3. Development of a methodology for envelope expansion based on the Flutter Margin concept. 4. A Matlab/Simulink 2D-[aeroelastic model], parametric and interactive, used as a tool to validate the proposed methodology. 5. Conclusions driven from the present Thesis and comparison with experimental results.