Spectral methods for exterior elliptic problems

Spectral approximations for exterior elliptic problems in two dimensions are discussed. As in the conventional finite difference or finite element methods, the accuracy of the numerical solutions is limited by the order of the numerical farfield conditions. A spectral boundary treatment is introduced at infinity which is compatible with the infinite order interior spectral scheme. Computational results are presented to demonstrate the spectral accuracy attainable. Although a simple Laplace problem is examined, the analysis covers more complex and general cases

Kardar-Parisi-Zhang asymptotics for the two-dimensional noisy Kuramoto-Sivashinsky equation

We study numerically the Kuramoto-Sivashinsky (KS) equation forced by external white noise in two space dimensions, that is a generic model for e.g. surface kinetic roughening in the presence of morphological instabilities. Large scale simulations using a pseudospectral numerical scheme allow us to retrieve Kardar-Parisi-Zhang (KPZ) scaling as the asymptotic state of the system, as in the 1D case. However, this is only the case for sufficiently large values of the coupling and/or system size, so that previous conclusions on non-KPZ asymptotics are demonstrated as finite size effects. Crossover effects are comparatively stronger for the 2D case than for the 1D system.Comment: 5 pages, 3 figures; supplemental material available at journal web page and/or on reques

Pseudospectral versus finite-differences schemes in the numerical integration of stochastic models of surface growth

We present a comparison between finite differences schemes and a pseudospectral method applied to the numerical integration of stochastic partial differential equations that model surface growth. We have studied, in 1+1 dimensions, the Kardar, Parisi and Zhang model (KPZ) and the Lai, Das Sarma and Villain model (LDV). The pseudospectral method appears to be the most stable for a given time step for both models. This means that the time up to which we can follow the temporal evolution of a given system is larger for the pseudospectral method. Moreover, for the KPZ model, a pseudospectral scheme gives results closer to the predictions of the continuum model than those obtained through finite difference methods. On the other hand, some numerical instabilities appearing with finite difference methods for the LDV model are absent when a pseudospectral integration is performed. These numerical instabilities give rise to an approximate multiscaling observed in the numerical simulations. With the pseudospectral approach no multiscaling is seen in agreement with the continuum model.Comment: 13 single column pages, RevTeX, 6 eps fig

A Comparison of Measured Crab and Vela Glitch Healing Parameters with Predictions of Neutron Star Models

There are currently two well-accepted models that explain how pulsars exhibit glitches, sudden changes in their regular rotational spin-down. According to the starquake model, the glitch healing parameter, Q, which is measurable in some cases from pulsar timing, should be equal to the ratio of the moment of inertia of the superfluid core of a neutron star (NS) to its total moment of inertia. Measured values of the healing parameter from pulsar glitches can therefore be used in combination with realistic NS structure models as one test of the feasibility of the starquake model as a glitch mechanism. We have constructed NS models using seven representative equations of state of superdense matter to test whether starquakes can account for glitches observed in the Crab and Vela pulsars, for which the most extensive and accurate glitch data are available. We also present a compilation of all measured values of Q for Crab and Vela glitches to date which have been separately published in the literature. We have computed the fractional core moment of inertia for stellar models covering a range of NS masses and find that for stable NSs in the realistic mass range 1.4 +/- 0.2 solar masses, the fraction is greater than 0.55 in all cases. This range is not consistent with the observational restriction Q < 0.2 for Vela if starquakes are the cause of its glitches. This confirms results of previous studies of the Vela pulsar which have suggested that starquakes are not a feasible mechanism for Vela glitches. The much larger values of Q observed for Crab glitches (Q > 0.7) are consistent with the starquake model predictions and support previous conclusions that starquakes can be the cause of Crab glitches.Comment: 8 pages, including 3 figures and 1 table. Accepted for publication in Ap

La reforma agraria agroecológica como camino hacia la sostenibilidad: un estudio de caso en Brasil.

Resumen: El modelo agroexportador actualmente en marcha en Brasil, basado en el agronegocio y los grandes monocultivos para la producción de commodities, tiene intrínsecas limitaciones en alcanzar de manera satisfactoria las múltiples dimensiones de la sostenibilidad planteadas por la agroecología y la soberanía alimentaria. En base a un estudio de caso (un asentamiento campesino agroecológico en la región cañera de Ribeirão Preto, estado de São Paulo), argumentamos que los procesos de transición hacia la sostenibilidad en zonas dominadas por estos grandes monocultivos agroindustriales pueden ser viables a partir de un nuevo modelo de reforma agraria de base agroecológica, que impulse procesos sociales de construcción de alternativas más sostenibles en el campo. Las evidencias obtenidas en la investigación nos permiten plantear que la reforma agraria, y las políticas agroecológicas asociadas, tienen un importante papel de recuperar la agrobiodiversidad y hacer emerger ?memorias campesinas? que de otra forma estarían condenadas al olvido, abriendo las posibilidades para un proceso de recampesinización en contraposición al modelo de desarrollo hegemónico en la región. Concluimos que la perspectiva agroecológica permite una resignificación de la reforma agraria, en la medida que no la restringe a una dimensión solamente económico-productivista, rescatando su naturaleza multidimensionaly rompiendo el histórico divorcio entre la ?cuestión agraria?y la ?cuestión ambiental? en Brasil

Theoretical values of convective turnover times and Rossby numbers for solar-like, pre-main sequence stars

Magnetic fields are at the heart of the observed stellar activity in late-type stars, and they are presumably generated by a dynamo mechanism at the interface layer between the radiative and the convective stellar regions. Since dynamo models are based on the interaction between differential rotation and convective motions, the introduction of rotation in the ATON 2.3 stellar code allows for explorations regarding a physically consistent treatment of magnetic effects in stellar structure and evolution, even though there are formidable mathematical and numerical challenges involved. As examples, we present theoretical estimates for both the local (tau_c) and global (tau_g) convective turnover times for rotating pre-main sequence solar-type stars, based on up-to-date input physics for stellar models. Our theoretical predictions are compared with the previous ones available in the literature. In addition, we investigate the dependence of the convective turnover time on convection regimes, the presence of rotation and atmospheric treatment. Those estimates, this quantities can be used to calculate the Rossby number, Ro, which is related to the magnetic activity strength in dynamo theories and, at least for main-sequence stars, shows an observational correlation with stellar activity. More important, they can also contribute for testing stellar models against observations. Our theoretical values of tau_c, tau_g and Ro qualitatively agree with those published by Kim & Demarque (1996). By increasing the convection efficiency, tau_g decreases for a given mass. FST models show still lower values. The presence of rotation shifts tau_g towards slightly higher values when compared with non-rotating models. The use of non-gray boundary conditions in the models yields values of tau_g smaller than in the gray approximation.Comment: 10 pages, 14 figures, accepted for publication in A&

Numerical Evolution of axisymmetric vacuum spacetimes: a code based on the Galerkin method

We present the first numerical code based on the Galerkin and Collocation methods to integrate the field equations of the Bondi problem. The Galerkin method like all spectral methods provide high accuracy with moderate computational effort. Several numerical tests were performed to verify the issues of convergence, stability and accuracy with promising results. This code opens up several possibilities of applications in more general scenarios for studying the evolution of spacetimes with gravitational waves.Comment: 11 pages, 6 figures. To appear in Classical and Quantum Gravit

Satellite-to-satellite attitude control of a long-distance spacecraft formation for the Next Generation Gravity Mission

The paperpresentsthedesignandsomesimulatedresultsoftheattitudecontrolofasatelliteformation under studybytheEuropeanSpaceAgencyfortheNextGenerationGravityMission.Theformation consists oftwospacecraftswhich fly morethan200kmapartatanaltitudefromtheEarth'sgroundof between 300and400km.Theattitudecontrolmustkeeptheopticalaxesofthetwospacecraftaligned with amicroradianaccuracy(pointingcontrol).Thisismadepossiblebyspecific opticalsensors accompanyingtheinter-satellitelaserinterferometer,whichisthemainpayloadofthemission.These sensors alloweachspacecrafttoactuateautonomousalignmentafterasuitableacquisitionprocedure. Pointing controlisconstrainedbytheangulardrag-freecontrol,whichisimposedbymissionscience (Earth gravimetryatalowEarthorbit),andmustzerotheangularaccelerationvectorbelow0.01 μrad/s2 in thesciencefrequencyband.Thisismadepossiblebyultrafine accelerometersfromtheGOCE-class, whose measurementsmustbecoordinatedwithattitudesensorstoachievedrag-freeandpointing requirements.EmbeddedModelControlshowshowcoordinationcanbeimplementedaroundthe embedded modelsofthespacecraftattitudeandoftheformationframequaternion.Evidenceand discussion aboutsomecriticalrequirementsarealsoincludedtogetherwithextensivesimulatedresults of twodifferentformationtypes

Existence and approximation of probability measure solutions to models of collective behaviors

In this paper we consider first order differential models of collective behaviors of groups of agents based on the mass conservation equation. Models are formulated taking the spatial distribution of the agents as the main unknown, expressed in terms of a probability measure evolving in time. We develop an existence and approximation theory of the solutions to such models and we show that some recently proposed models of crowd and swarm dynamics fit our theoretic paradigm.Comment: 31 pages, 1 figur