Multilevel Preconditioning of Discontinuous-Galerkin Spectral Element Methods, Part I: Geometrically Conforming Meshes

This paper is concerned with the design, analysis and implementation of preconditioning concepts for spectral Discontinuous Galerkin discretizations of elliptic boundary value problems. While presently known techniques realize a growth of the condition numbers that is logarithmic in the polynomial degrees when all degrees are equal and quadratic otherwise, our main objective is to realize full robustness with respect to arbitrarily large locally varying polynomial degrees degrees, i.e., under mild grading constraints condition numbers stay uniformly bounded with respect to the mesh size and variable degrees. The conceptual foundation of the envisaged preconditioners is the auxiliary space method. The main conceptual ingredients that will be shown in this framework to yield "optimal" preconditioners in the above sense are Legendre-Gauss-Lobatto grids in connection with certain associated anisotropic nested dyadic grids as well as specially adapted wavelet preconditioners for the resulting low order auxiliary problems. Moreover, the preconditioners have a modular form that facilitates somewhat simplified partial realizations. One of the components can, for instance, be conveniently combined with domain decomposition, at the expense though of a logarithmic growth of condition numbers. Our analysis is complemented by quantitative experimental studies of the main components.Comment: 41 pages, 11 figures; Major revision: rearrangement of the contents for better readability, part on wavelet preconditioner adde

Relativistic spectroscopy of the extreme NLS1 IRAS13224-3809

The narrow line Seyfert 1 (NLS1) IRAS 13224-3809 is the most X-ray variable active galactic nucleus (AGN), exhibiting 0.3-10 keV flux changes of over an order of magnitude within an hour. We report on the results of the 1.5 Ms 2016 XMM-Newton/NuSTAR observing campaign, which revealed the presence of a 0.24c ultra-fast outflow in addition to the well-known strong relativistic reflection. We also summarise other key results of the campaign, such as the first detection of a non-linear RMS-flux relation in an accreting source, correlations between outflow absorption strength/velocity and source flux, and a disconnect between the X-ray and UV emission. Our results are consistent with a scenario where a disk wind is launched close to the black hole, imprinting absorption features into the spectrum and variability.Comment: 6 pages, 7 figures, contributed talk at "Revisiting narrow-line Seyfert 1 galaxies and their place in the Universe" (Padova, April 2018). Accepted for publication in Proceedings of Science, PoS(NLS1-2018)03

The role of translational invariance in non linear gauge theories of gravity

The internal structure of the tetrads in a Poincar\'e non linear gauge theory of gravity is considered. Minkowskian coordinates becomes dynamical degrees of freedom playing the role of Goldstone bosons of the translations. A critical length allowing a covariant expansion similar to the weak field approach is deduced, the zeroth order metric being maximally symmetric (Minkowskian in some cases).Comment: 17 pages, LaTe

Exact Nonequilibrium Work Generating Function for a Small Classical System

We obtain the exact nonequilibrium work generating function (NEWGF), for a small system consisting of a massive Brownian particle connected to internal and external springs. The external work is provided to the system for a finite time interval. The Jarzynski equality (JE), obtained in this case directly from the NEWGF, is shown to be valid for the present model, in an exact way regardless of the rate of external work

Quantum Cosmology in Scalar-Tensor Theories With Non Minimal Coupling

Quantization in the minisuperspace of non minimal scalar-tensor theories leads to a partial differential equation which is non separable. Through a conformal transformation we can recast the Wheeler-DeWitt equation in an integrable form, which corresponds to the minimal coupling case, whose general solution is known. Performing the inverse conformal transformation in the solution so found, we can construct the corresponding one in the original frame. This procedure can also be employed with the bohmian trajectories. In this way, we can study the classical limit of some solutions of this quantum model. While the classical limit of these solutions occurs for small scale factors in the Einstein's frame, it happens for small values of the scalar field non minimally coupled to gravity in the Jordan's frame, which includes large scale factors.Comment: latex, 18 page

Cold black holes and conformal continuations

We study Einstein gravity minimally coupled to a scalar field in a static, spherically symmetric space-time in four dimensions. Black hole solutions are shown to exist for a phantom scalar field whose kinetic energy is negative. These ``scalar black holes'' have an infinite horizon area and zero Hawking temperature and are termed ``cold black holes'' (CBHs). The relevant explicit solutions are well-known in the massless case (the so-called anti-Fisher solution), and we have found a particular example of a CBH with a nonzero potential $V(\phi)$. All CBHs with $V(\phi) \not \equiv 0$ are shown to behave near the horizon quite similarly to those with a massless field. The above solutions can be converted by a conformal transformation to Jordan frames of a general class of scalar-tensor theories of gravity, but CBH horizons in one frame are in many cases converted to singularities in the other, which gives rise to a new type of conformal continuation.Comment: 15 pages, late

Process approach: the way to improve the quality of high-tech products

В статье представлен процесс регламентации бизнес-процесса «Изготовление источников питания», описанного с использованием методологии IDEF0 и программного продукта Business Studio 4.0 на примере подразделения, которое занимается разработкой и изготовлением сварочных источников тока. При моделировании процесса изготовления источников питания была построена матрица атрибутов, в которой определены цели и задачи процессов, владельцы на каждом этапе процесса, несущие ответственность за ход и за результат, определены входы и выходы (документы) процесса, а также критерии результативности и/или эффективности процесса, для осуществления оперативного управления на всех этапах изготовления конечной продукции. В результате работы был разработан комплект документов, в состав которого вошли: регламент процесса изготовления источников тока, положение о подразделении, должностные инструкции сотрудников, участвующих в процессе. Деятельность по регламентации процесса проводилась в рамках подготовки подразделения к сертификации в соответствии с требованиями стандарта ГОСТ РВ 0015-002-2012 «Система разработки и постановки продукции на производство военной техники. Системы менеджмента качества. Общие требования» в системе добровольной сертификации «Военный регистр»

Falsifying Tree Level String Motivated Bouncing Cosmologies

The string effective action at tree level contains, in its bosonic sector, the Einstein-Hilbert term, the dilaton, and the axion, besides scalar and gauge fields coming from the Ramond-Ramond sector. The reduction to four dimensions brings to scene moduli fields. We generalize this effective action by introducing two arbitrary parameters, $\omega$ and $m$, connected with the dilaton and axion couplings. In this way, more general frameworks can be analyzed. Regular solutions with a bounce can be obtained for a range of (negative) values of the parameter $\omega$ which, however, exclude the pure string configuration ($\omega = - 1$). We study the evolution of scalar perturbations in such cosmological scenarios. The predicted primordial power spectrum decreases with the wavenumber with spectral index $n_s=-2$, in contradiction with the results of the $WMAP$. Hence, all such effective string motivated cosmological bouncing models seem to be ruled out, at least at the tree level approximation.Comment: Latex file, 19 pages, 3 figures in eps forma

On exact time-averages of a massive Poisson particle

In this work we study, under the Stratonovich definition, the problem of the damped oscillatory massive particle subject to a heterogeneous Poisson noise characterised by a rate of events, \lambda (t), and a magnitude, \Phi, following an exponential distribution. We tackle the problem by performing exact time-averages over the noise in a similar way to previous works analysing the problem of the Brownian particle. From this procedure we obtain the long-term equilibrium distributions of position and velocity as well as analytical asymptotic expressions for the injection and dissipation of energy terms. Considerations on the emergence of stochastic resonance in this type of system are also set forth.Comment: 21 pages, 5 figures. To be published in Journal of Statistical Mechanics: Theory and Experimen

Poincare gauge invariance and gravitation in Minkowski spacetime

A formulation of Poincare symmetry as an inner symmetry of field theories defined on a fixed Minkowski spacetime is given. Local P gauge transformations and the corresponding covariant derivative with P gauge fields are introduced. The renormalization properties of scalar, spinor and vector fields in P gauge field backgrounds are determined. A minimal gauge field dynamics consistent with the renormalization constraints is given.Comment: 36 pages, latex-fil