STOKES' SYSTEM IN A DOMAIN WITH OSCILLATING BOUNDARY: HOMOGENIZATION AND ERROR ANALYSIS OF AN INTERIOR OPTIMAL CONTROL PROBLEM

Homogenization and error analysis of an optimal interior control problem in the framework of Stokes' system, on a domain with rapidly oscillating boundary, are the subject matters of this article. We consider a three dimensional domain constituted of a parallelepiped with a large number of rectangular cylinders at the top of it. An interior control is applied in a proper subdomain of the parallelepiped, away from the oscillating volume. We consider two types of functionals, namely a functional involving the L-2-norm of the state variable and another one involving its H-1-norm. The asymptotic analysis of optimality systems for both cases, when the cross sectional area of the rectangular cylinders tends to zero, is done here. Our major contribution is to derive error estimates for the state, the co-state and the associated pressures, in appropriate functional spaces.

A DYNAMO MODEL OF MAGNETIC ACTIVITY IN SOLAR-LIKE STARS WITH DIFFERENT ROTATIONAL VELOCITIES

We attempt to provide a quantitative theoretical explanation for the observations that Ca II H/K emission and X-ray emission from solar-like stars increase with decreasing Rossby number (i.e., with faster rotation). Assuming that these emissions are caused by magnetic cycles similar to the sunspot cycle, we construct flux transport dynamo models of 1M(circle dot) stars rotating with different rotation periods. We first compute the differential rotation and the meridional circulation inside these stars from a mean-field hydrodynamics model. Then these are substituted in our dynamo code to produce periodic solutions. We find that the dimensionless amplitude f(m) of the toroidal flux through the star increases with decreasing rotation period. The observational data can be matched if we assume the emissions to go as the power 3-4 of f(m). Assuming that the Babcock-Leighton mechanism saturates with increasing rotation, we can provide an explanation for the observed saturation of emission at low Rossby numbers. The main failure of our model is that it predicts an increase of the magnetic cycle period with increasing rotation rate, which is the opposite of what is found observationally. Much of our calculations are based on the assumption that the magnetic buoyancy makes the magnetic flux tubes rise radially from the bottom of the convection zone. Taking into account the fact that the Coriolis force diverts the magnetic flux tubes to rise parallel to the rotation axis in rapidly rotating stars, the results do not change qualitatively.

An interior penalty method for distributed optimal control problems governed by the biharmonic operator

In this paper, a C-0 interior penalty method has been proposed and analyzed for distributed optimal control problems governed by the biharmonic operator. The state and adjoint variables are discretized using continuous piecewise quadratic finite elements while the control variable is discretized using piecewise constant approximations. A priori and a posteriori error estimates are derived for the state, adjoint and control variables under minimal regularity assumptions. Numerical results justify the theoretical results obtained. The a posteriori error estimators are useful in adaptive finite element approximation and the numerical results indicate that the sharp error estimators work efficiently in guiding the mesh refinement. (C) 2014 Elsevier Ltd. All rights reserved.

GRMHD formulation of highly super-Chandrasekhar rotating magnetized white dwarfs: stable configurations of non-spherical white dwarfs

Here we extend the exploration of significantly super-Chandrasekhar magnetized white dwarfs by numerically computing axisymmetric stationary equilibria of differentially rotating magnetized polytropic compact stars in general relativity (GR), within the ideal magnetohydrodynamic regime. We use a general relativistic magnetohydrodynamic (GRMHD) framework that describes rotating and magnetized axisymmetric white dwarfs, choosing appropriate rotation laws and magnetic field profiles (toroidal and poloidal). The numerical procedure for finding solutions in this framework uses the 3 + 1 formalism of numerical relativity, implemented in the open source XNS code. We construct equilibrium sequences by varying different physical quantities in turn, and highlight the plausible existence of super-Chandrasekhar white dwarfs, with masses in the range of 2-3 solar mass, with central (deep interior) magnetic fields of the order of 10(14) G and differential rotation with surface time periods of about 1-10 s. We note that such white dwarfs are candidates for the progenitors of peculiar, overluminous Type Ia supernovae, to which observational evidence ascribes mass in the range 2.1-2.8 solar mass. We also present some interesting results related to the structure of such white dwarfs, especially the existence of polar hollows in special cases.

A C-0 Interior Penalty Method for a Fourth-order Variational Inequality of the Second Kind

In this article, we propose a C-0 interior penalty ((CIP)-I-0) method for the frictional plate contact problem and derive both a priori and a posteriori error estimates. We derive an abstract error estimate in the energy norm without additional regularity assumption on the exact solution. The a priori error estimate is of optimal order whenever the solution is regular. Further, we derive a reliable and efficient a posteriori error estimator. Numerical experiments are presented to illustrate the theoretical results. (c) 2015Wiley Periodicals, Inc.

High Loading of Pd Nanoparticles by Interior Functionalization of MOFs for Heterogeneous Catalysis

In this report, the issue related to nanoparticle (NP) agglomeration upon increasing their loading amount into metal-organic frameworks (MOFs) has been addressed by functionalization of MOFs with alkyne groups. The alkynophilicity of the Pd2+ (or other noble metals) ions has been utilized successfully for significant loading of Pd NPs into alkyne functionalized MOFs. It has been shown here that the size and loading amount of Pd NPs are highly dependent on the surface area and pore width of the MOFs. The loading amount of Pd NPs was increased monotonically without altering their size distribution on a particular MOF. Importantly, the distinct role of alkyne groups for Pe(2+) stabilization has also been demonstrated by performing a control experiment considering a MOF without an alkyne moiety. The preparation of NPs involved two distinct steps viz. adsorption of metal ions inside MOFs and reduction of metal ions. Both of these steps were monitored by microscopic techniques. This report also demonstrates the applicability of Pd@MOF NPs as extremely efficient heterogeneous catalysts for Heck-coupling and hydrogenation reactions of aryl bromides or iodides and alkenes, respectively.

[B_Muskiz_Muñatones] Documentación geométrica de la muralla interior del Castillo de Muñatones (Muskiz, Bizkaia)

[ES] Este proyecto corresponde a una continuación del que documenta la torre central y que se realizó en 2005. Dicho trabajo puede consultarse también es este repositorio:

Niveles de nutrientes y pigmentos fotosintéticos en el Río de la Plata interior (55°-59°W 34°-36°S)

The "Río de la Plata" River is one of the less studied systems of the basin with respect to its biological and ecological aspects. Twenty four and twenty seven surface stations were sample on September 22-23 and November 22-23, 1982, respectively. The section studied is part of the zone called inner "Río de la Plata" River. The discharge was 29.000 m3/s in September and 45.200 m3/s in November. Total phosphorus (PT), total organic nitrogen (NOT), chemical oxygen demad (COT) and total cholrophyll were measured. Dissolved oxygen (DO), turbidity (TURB), pH and electrical conductivity (K20) were also measured at the surface with a HORIBA U7 sensor on November 1982. PT was 72-208 mg/m3 and 66-205 mg/m3 in September and November repectively; the higher values were near the Argentinian coast and the outer zone. NOT was 33-106 µM and 49-117 µM and CHL was 1.4-5.8 mg/m3 and 1.3-9.4 mg/m3. TURB was between 44 and 240 NTU in November; the maximun value were obseved in the central zone. Steep K20 gradients were found near both coast. The reduced organic carbon load into the lower and external part of the "Río de la Plata" River was estimated. (Document contains 40 pages.)

Vozes saudosas, da eloquencia do espirito, do zelo, e eminente sabedoria do Padre Antonio Vieira, da Companhia de Jesus, pregador de sua magestade, e príncipe dos oradores evangélicos : acompanhadas com hum fidelissimo echo, que sonoramente resulta do interior da obra clavis prophetarum : concorda no fim a suavidade das musas em elogios raros : tudo reverente dedica ao principe nosso senhor o p. Andre de Barros Da Companhia de Jesus, Academico do numero da Academia Real da Historia portugueza

Padre Antônio Vieira nasceu em Lisboa em 6 de novembro de 1608 e morreu na Bahia em 18 de julho de 1697. Ordenado sacerdote em 1634, logo se destacou como excepcional pregador. Exerceu importante papel politico e diplomático durante o reinado de D. João IV e fez do púlpito uma tribuna a serviço da nação, em guerra com a Espanha. De 1652 a 1661 atuou como missionário no Maranhão. Em Portugal foi denunciado como herético ao Tribunal da Inquisição. Doente e encarcerado defendeu-se com extraordinário vigor, mas foi condenado a internamento numa casa jesuítica e proibido de pregar. Retirou-se em 1681 para o Brasil, onde trabalhou na edição completa dos Sermoens, iniciada em 1679. Este é o primeiro volume de Vozes saudosas, cuja edição foi executada pelo Padre Jesuíta André de Barros,após a morte do autor. Trata-se de uma compilação de texto, contendo "vários tratados sobre o Brasil escritos por Antonio Vieira, mas nenhum sermão" , como esclarece Borba de Moraes. Vozes saudosas foi o titulo atribuído à obra pelo seu compilador, como uma homenagem ao autor, que ele compara a Sêneca. O segundo tomo de Vozes saudosas foi também publicado pelo Padre André de Barros, em 1748, no livro Sermões vários e tratados ainda não impressos do grande Padre Antonio Vieira... volume 15.

Segunda viagem ao interior do Brasil : Espirito Santo

As Voyages... são estudos completos, abrangendo todos os aspectos das regiões percorridas; servem de subsídio ao estudo das condições de vida no Brasil no século passado. "Fonte primordial de informações sobre os prédios coloniais do Rio de Janeiro, Minas Gerais, São Paulo, Santa Catarina e Goiás. Poucas obras no gênero atingem o valor de Saint-Hilarire. São clássicas e indispensáveis para o estudo do sul do Brasil, antes da Independência" segundo Borba de Moraes.

Ensaio sobre a theoria das torrentes, e rios : que contem os meios mais simples de obstar aos seus estragos, de estreitar o seu leito e facilitar a sua navegação, sirga, e fluctuação, acompanhado de huma discussão a respeito da navegação interior da França, e terminado pelo projeto de tornar Paris em Porto Maritimo, fazendo subir à véla pelo Seine as embarcações, que parão em Rouen

Seguido da Indagação da mais vantajosa construcção dos diques por Mrs. Bossut e Viallet ; e de hum extracto da architectura hydraulica de M. Belidor... ; terminado pelo tratado pratico da medida das aguas correntes, e uso da taboa parabolica do P. D. Francisco Maria de Regi ; de Ordem de Sua Alteza Real o Principe Regente Nosso Senhor traduzidos por Manoel Jacinto Nogueira da Gama.

Black holes in the early universe, in compact binaries, and as energy sources inside solar-type stars

This thesis consists of three separate studies of roles that black holes might play in our universe.

In the first part we formulate a statistical method for inferring the cosmological parameters of our universe from LIGO/VIRGO measurements of the gravitational waves produced by coalescing black-hole/neutron-star binaries. This method is based on the cosmological distance-redshift relation, with "luminosity distances" determined directly, and redshifts indirectly, from the gravitational waveforms. Using the current estimates of binary coalescence rates and projected "advanced" LIGO noise spectra, we conclude that by our method the Hubble constant should be measurable to within an error of a few percent. The errors for the mean density of the universe and the cosmological constant will depend strongly on the size of the universe, varying from about 10% for a "small" universe up to and beyond 100% for a "large" universe. We further study the effects of random gravitational lensing and find that it may strongly impair the determination of the cosmological constant.

In the second part of this thesis we disprove a conjecture that black holes cannot form in an early, inflationary era of our universe, because of a quantum-field-theory induced instability of the black-hole horizon. This instability was supposed to arise from the difference in temperatures of any black-hole horizon and the inflationary cosmological horizon; it was thought that this temperature difference would make every quantum state that is regular at the cosmological horizon be singular at the black-hole horizon. We disprove this conjecture by explicitly constructing a quantum vacuum state that is everywhere regular for a massless scalar field. We further show that this quantum state has all the nice thermal properties that one has come to expect of "good" vacuum states, both at the black-hole horizon and at the cosmological horizon.

In the third part of the thesis we study the evolution and implications of a hypothetical primordial black hole that might have found its way into the center of the Sun or any other solar-type star. As a foundation for our analysis, we generalize the mixing-length theory of convection to an optically thick, spherically symmetric accretion flow (and find in passing that the radial stretching of the inflowing fluid elements leads to a modification of the standard Schwarzschild criterion for convection). When the accretion is that of solar matter onto the primordial hole, the rotation of the Sun causes centrifugal hangup of the inflow near the hole, resulting in an "accretion torus" which produces an enhanced outflow of heat. We find, however, that the turbulent viscosity, which accompanies the convective transport of this heat, extracts angular momentum from the inflowing gas, thereby buffering the torus into a lower luminosity than one might have expected. As a result, the solar surface will not be influenced noticeably by the torus's luminosity until at most three days before the Sun is finally devoured by the black hole. As a simple consequence, accretion onto a black hole inside the Sun cannot be an answer to the solar neutrino puzzle.