Coupling time-stepping numerical methods and standard aerodynamics codes for instability analysis of flows in complex geometries

The development of a global instability analysis code coupling a time-stepping approach, as applied to the solution of BiGlobal and TriGlobal instability analysis 1, 2 and finite-volume-based spatial discretization, as used in standard aerodynamics codes is presented. The key advantage of the time-stepping method over matrix-formulation approaches is that the former provides a solution to the computer-storage issues associated with the latter methodology. To-date both approaches are successfully in use to analyze instability in complex geometries, although their relative advantages have never been quantified. The ultimate goal of the present work is to address this issue in the context of spatial discretization schemes typically used in industry. The time-stepping approach of Chiba 3 has been implemented in conjunction with two direct numerical simulation algorithms, one based on the typically-used in this context high-order method and another based on low-order methods representative of those in common use in industry. The two codes have been validated with solutions of the BiGlobal EVP and it has been showed that small errors in the base flow do not have affect significantly the results. As a result, a three-dimensional compressible unsteady second-order code for global linear stability has been successfully developed based on finite-volume spatial discretization and time-stepping method with the ability to study complex geometries by means of unstructured and hybrid meshes

Electron transport and azimuthal oscillations in hall thrusters

The Hall Effect Thruster (HET) is a type of satellite electric propulsion device initially developed in the 1960’s independently by USA and the former USSR. The development continued in the shadow during the 1970’s in the Soviet Union to reach a mature status from the technological point of view in the 1980’s. In the 1990’s the advanced state of this Russian technology became known in western countries, which rapidly restarted the analysis and development of modern Hall thrusters. Currently, there are several companies in USA, Russia and Europe manufacturing Hall thrusters for operational use. The main applications of these thrusters are low-thrust propulsion of interplanetary probes, orbital raising of satellites and stationkeeping of geostationary satellites. However, despite the well proven in-flight experience, the physics of the Hall Thruster are not completely understood yet. Over the last two decades large efforts have been dedicated to the understanding of the physics of Hall Effect thrusters. However, the so-called anomalous diffusion, short name for an excessive electron conductivity along the thruster, is not yet fully understood as it cannot be explained with classical collisional theories. One commonly accepted explanation is the existence of azimuthal oscillations with correlated plasma density and electric field fluctuations. In fact, there is experimental evidence of the presence of an azimuthal oscillation in the low frequency range (a few kHz). This oscillation, usually called spoke, was first detected empirically by Janes and Lowder in the 1960s. More recently several experiments have shown the existence of this type of oscillation in various modern Hall thrusters. Given the frequency range, it is likely that the ionization is the cause of the spoke oscillation, like for the breathing mode oscillation. In the high frequency range (a few MHz), electron-drift azimuthal oscillations have been detected in recent experiments, in line with the oscillations measured by Esipchuk and Tilinin in the 1970’s. Even though these low and high frequency azimuthal oscillations have been known for quite some time already, the physics behind them are not yet clear and their possible relation with the anomalous diffusion process remains an unknown. This work aims at analysing from a theoretical point of view and via computer simulations the possible relation between the azimuthal oscillations and the anomalous electron transport in HET. In order to achieve this main objective, two approaches are considered: local linear stability analyses and global linear stability analyses. The use of local linear stability analyses shall allow identifying the dominant terms in the promotion of the oscillations. However, these analyses do not take into account properly the axial variation of the plasma properties along the thruster. On the other hand, global linear stability analyses do account for these axial variations and shall allow determining how the azimuthal oscillations are promoted and their possible relation with the electron transport.

Implicit stochastic Runge-Kutta methods for stochastic differential equations

In this paper we construct implicit stochastic Runge-Kutta (SRK) methods for solving stochastic differential equations of Stratonovich type. Instead of using the increment of a Wiener process, modified random variables are used. We give convergence conditions of the SRK methods with these modified random variables. In particular, the truncated random variable is used. We present a two-stage stiffly accurate diagonal implicit SRK (SADISRK2) method with strong order 1.0 which has better numerical behaviour than extant methods. We also construct a five-stage diagonal implicit SRK method and a six-stage stiffly accurate diagonal implicit SRK method with strong order 1.5. The mean-square and asymptotic stability properties of the trapezoidal method and the SADISRK2 method are analysed and compared with an explicit method and a semi-implicit method. Numerical results are reported for confirming convergence properties and for comparing the numerical behaviour of these methods.

Post-Crisis Lessons for Open Economies

In a systemic perspective, what are the primary transmitters of global competitiveness with the proper coordination mechanism? What are the systemic impacts of the U.S. economy on world markets? Will the United States stay the main engine of world economic growth for quite some time to come, or at least in the current decade? Will and should the United States, as the single largest open economy of the world, be in some way responsible for the provision of global economic stability as a valuable public good? Was the recent crisis predictable? These are the main questions addressed, all of which are answered in a new global context, and the responses are based on some known principles of international economics and economic history.

(Table 1) Age control and temporal resolution of paleoceanographic records of the North Atlantic

Short-term changes in sea surface conditions controlling the thermohaline circulation in the northern North Atlantic are expected to be especially efficient in perturbing global climate stability. Here we assess past variability of sea surface temperature (SST) in the northeast Atlantic and Norwegian Sea during Marine Isotope Stage (MIS) 2 and, in particular, during the Last Glacial Maximum (LGM). Five high-resolution SST records were established on a meridional transect (53°N-72°N) to trace centennial-scale oscillations in SST and sea-ice cover. We used three independent computational techniques (SIMMAX modern analogue technique, Artificial Neural Networks (ANN), and Revised Analog Method (RAM)) to reconstruct SST from planktonic foraminifer census counts. SIMMAX and ANN reproduced short-term SST oscillations of similar magnitude and absolute levels, while RAM, owing to a restrictive analog selection, appears less suitable for reconstructing "cold end" SST. The SIMMAX and ANN SST reconstructions support the existence of a weak paleo-Norwegian Current during Dansgaard-Oeschger (DO) interstadials number 4, 3, 2, and 1. During the LGM, two warm incursions of 7°C water to occurred in the northern North Atlantic but ended north of the Iceland Faroe Ridge. A rough numerical estimate shows that the near-surface poleward heat transfer from 53° across the Iceland-Faroe Ridge up to to 72° N dropped to less than 60% of the modern value during DO interstadials and to almost zero during DO stadials. Summer sea ice was generally confined to the area north of 70°N and only rarely expanded southward along the margins of continental ice sheets. Internal LGM variability of North Atlantic (>40°N) SST in the GLAMAP 2000 compilation (Sarnthein et al., 2003, doi:10.1029/2002PA000771; Pflaumann et al., 2003, doi:10.1029/2002PA000774) indicates maximum instability in the glacial subpolar gyre and at the Iberian Margin, while in the Nordic Seas, SST was continuously low.

Discrete-time positive periodic systems with state and control constraints

The aim of this paper is to provide an efficient control design technique for discrete-time positive periodic systems. In particular, stability, positivity and periodic invariance of such systems are studied. Moreover, the concept of periodic invariance with respect to a collection of boxes is introduced and investigated with connection to stability. It is shown how such concept can be used for deriving a stabilizing state-feedback control that maintains the positivity of the closed-loop system and respects states and control signals constraints. In addition, all the proposed results can be efficiently solved in terms of linear programming.

Partial state estimation of LTI systems with multiple constant time-delays

Functional observer design for Multi-Input Multi-Output (MIMO) Linear Time-Invariant (LTI) systems with multiple mixed time delays in the states of the system is addressed. Two structures for the design of a minimum-order observer are considered: 1 - delay-dependent, and 2 - internal-delay independent. The parameters of the delay-dependent observer are designed using the Lyapunov Krasovskii approach. The delay-dependent exponential stability of the observer for a specified convergence rate and delay values is guaranteed upon the feasibility of a set of Linear Matrix Inequalities (LMIs) together with a rank condition. Using the descriptor transformation, a modified Jensen's inequality, and improved Park's inequality, the results can be less conservative than the available functional observer design methods that address LTI systems with single state delay. Furthermore, the necessary and sufficient conditions of the asymptotic stability of the internal-delay independent observer are obtained, which are shown to be independent of delay. Two illustrative numerical examples and simulation studies confirm the validity and highlight the performance of the proposed theoretical achievements.

H∞ observer-based control for discrete-time one-sided Lipschitz systems with unknown inputs

This paper investigates the problem of robust observer-based stabilization for a class of one-sided nonlinear discrete-time systems subjected to unknown inputs. We propose a simple simultaneous state and input estimator. A nonlinear controller is then proposed to compensate the effects of unknown inputs and to ensure asymptotic stability in closed loop. Several mathematical artifacts are used to deduce stability conditions expressed in terms of LMIs. To show high performances of the proposed technique, a relevant example is provided with comparisons to recent results.

Las reformas emprendidas en Túnez de la mano del FMI y el BM ¿Precedente para la revolución de los Jazmines?”(1987-2010)

El estallido de la “Revolución de los Jazmines” cuestionó el éxito de un país que por más de dos décadas fue exaltado por el Banco Mundial (BM) y el Fondo Monetario Internacional (FMI) por los logros alcanzados gracias a un programa de restructuración económica. Las exigencias e inconformidades de los manifestantes, que iban más allá de la falta de garantías democráticas, permitieron ver que el país sufría de problemas estructurales relacionados a los altos niveles de desempleo, la precariedad de la situación laboral y la desigualdad. Esta monografía pretende evaluar el papel que tuvieron las reformas económicas y en general el modelo de desarrollo que siguió Túnez de la mano del FMI y el BM, en el surgimiento y consolidación de las condiciones que dieron lugar a la Revolución de los Jazmines a finales del año 2010.

On Convergence of Differential Evolution Over a Class of Continuous Functions With Unique Global Optimum

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms of current interest. Since its inception in the mid 1990s, DE has been finding many successful applications in real-world optimization problems from diverse domains of science and engineering. This paper takes a first significant step toward the convergence analysis of a canonical DE (DE/rand/1/bin) algorithm. It first deduces a time-recursive relationship for the probability density function (PDF) of the trial solutions, taking into consideration the DE-type mutation, crossover, and selection mechanisms. Then, by applying the concepts of Lyapunov stability theorems, it shows that as time approaches infinity, the PDF of the trial solutions concentrates narrowly around the global optimum of the objective function, assuming the shape of a Dirac delta distribution. Asymptotic convergence behavior of the population PDF is established by constructing a Lyapunov functional based on the PDF and showing that it monotonically decreases with time. The analysis is applicable to a class of continuous and real-valued objective functions that possesses a unique global optimum (but may have multiple local optima). Theoretical results have been substantiated with relevant computer simulations.