The Navier-Stokes Equations with Particle Methods

The non-stationary nonlinear Navier-Stokes equations describe the motion of a viscous incompressible fluid flow for 0weak sense.

The Navier-Stokes Equations with Time Delay

In the present paper we use a time delay epsilon > 0 for an energy conserving approximation of the nonlinear term of the non-stationary Navier-Stokes equations. We prove that the corresponding initial value problem (N_epsilon)in smoothly bounded domains G \subseteq R^3 is well-posed. Passing to the limit epsilon \rightarrow 0 we show that the sequence of stabilized solutions has an accumulation point such that it solves the Navier-Stokes problem (N_0) in a weak sense (Hopf).

Ground state correlation energy of the Be-sequence for Z = 4-20 in MCDF approximation

The ground state (J = 0) electronic correlation energy of the 4-electron Be-sequence is calculated in the Multi-Configuration Dirac-Fock approximation for Z = 4-20. The 4 electrons were distributed over the configurations arising from the 1s, 2s, 2p, 3s, 3p and 3d orbitals. Theoretical values obtained here are in good agreement with experimental correlation energies.

Zur Approximation der Gleichungen von Navier-Stokes

In der vorliegenden Arbeit betrachten wir die Strömung einer zähen, inkompressiblen, instationären Flüssigkeit in einem dreidimensionalen beschränkten Gebiet, deren Verhalten wird mit den instationären Gleichungen von Navier-Stokes beschrieben. Diese Gleichungen gelten für viele wichtige Strömungsprobleme, beispielsweise für Luftströmungen weit unterhalb der Schallgeschwindigkeit, für Wasserströmungen, sowie für flüssige Metalle. Im zweidimensionalen Fall konnten für die Navier-Stokes-Gleichungen bereits weitreichende Existenz-, Eindeutigkeits- und Regularitätsaussagen bewiesen werden. Im allgemeinen dreidimensionalen Fall, falls also die Daten keinen Kleinheitsannahmen unterliegen, hat man bisher lediglich Existenz und Eindeutigkeit zeitlich lokaler starker Lösungen nachgewiesen. Außerdem existieren zeitlich global so genannte schwache Lösungen, deren Regularität für den Nachweis der Eindeutigkeit im dreidimensionalen Fall allerdings nicht ausreicht. Somit bleibt die Lücke zwischen der zeitlich lokalen, eindeutigen starken Lösung und den zeitlich globalen, nicht eindeutigen schwachen Lösungen der Navier-Stokes-Gleichungen im dreidimensionalen Fall weiterhin offen. Das renommierte Clay Mathematics Institute hat dieses Problem zu einem von sieben Millenniumsproblemen erklärt und für seine Lösung eine Million US-Dollar ausgelobt. In der vorliegenden Arbeit wird ein neues Approximationsverfahren für die Navier-Stokes-Gleichungen entwickelt, das auf einer Kopplung der Eulerschen und Lagrangeschen Beschreibung zäher Strömungen beruht.

Asymptotic model for shape resonance control of diatomics by intense non-resonant light: universality in the single-channel approximation

Non-resonant light interacting with diatomics via the polarizability anisotropy couples different rotational states and may lead to strong hybridization of the motion. The modification of shape resonances and low-energy scattering states due to this interaction can be fully captured by an asymptotic model, based on the long-range properties of the scattering (Crubellier et al 2015 New J. Phys. 17 045020). Remarkably, the properties of the field-dressed shape resonances in this asymptotic multi-channel description are found to be approximately linear in the field intensity up to fairly large intensity. This suggests a perturbative single-channel approach to be sufficient to study the control of such resonances by the non-resonant field. The multi-channel results furthermore indicate the dependence on field intensity to present, at least approximately, universal characteristics. Here we combine the nodal line technique to solve the asymptotic Schrödinger equation with perturbation theory. Comparing our single channel results to those obtained with the full interaction potential, we find nodal lines depending only on the field-free scattering length of the diatom to yield an approximate but universal description of the field-dressed molecule, confirming universal behavior.

Feature Point Detection and Curve Approximation for Early Processing of Freehand Sketches

Freehand sketching is both a natural and crucial part of design, yet is unsupported by current design automation software. We are working to combine the flexibility and ease of use of paper and pencil with the processing power of a computer to produce a design environment that feels as natural as paper, yet is considerably smarter. One of the most basic steps in accomplishing this is converting the original digitized pen strokes in the sketch into the intended geometric objects using feature point detection and approximation. We demonstrate how multiple sources of information can be combined for feature detection in strokes and apply this technique using two approaches to signal processing, one using simple average based thresholding and a second using scale space.

Measure Fields for Function Approximation

The computation of a piecewise smooth function that approximates a finite set of data points may be decomposed into two decoupled tasks: first, the computation of the locally smooth models, and hence, the segmentation of the data into classes that consist on the sets of points best approximated by each model, and second, the computation of the normalized discriminant functions for each induced class. The approximating function may then be computed as the optimal estimator with respect to this measure field. We give an efficient procedure for effecting both computations, and for the determination of the optimal number of components.

An Equivalence Between Sparse Approximation and Support Vector Machines

In the first part of this paper we show a similarity between the principle of Structural Risk Minimization Principle (SRM) (Vapnik, 1982) and the idea of Sparse Approximation, as defined in (Chen, Donoho and Saunders, 1995) and Olshausen and Field (1996). Then we focus on two specific (approximate) implementations of SRM and Sparse Approximation, which have been used to solve the problem of function approximation. For SRM we consider the Support Vector Machine technique proposed by V. Vapnik and his team at AT&T Bell Labs, and for Sparse Approximation we consider a modification of the Basis Pursuit De-Noising algorithm proposed by Chen, Donoho and Saunders (1995). We show that, under certain conditions, these two techniques are equivalent: they give the same solution and they require the solution of the same quadratic programming problem.

A First approximation to the realism/idealism debate about the external world

El text intenta fer una primera aproximació al debat contemporani entre realistes i anti-realistes sobre el món empíric, centrant-se en les posicions de Putnam i Nagel. El seu objectiu principal és el d'entendre les motivacions de les posicions i l'estructura actual del debat, i el d'establir les característiques que hauria de tenir qualsevol posició satisfactòria

An approximation to the digital divide among low income people in Colombia, Mexico and Perú: two composite indexes

El estudio analiza los determinantes de uso y acceso a las tecnologías de información y comunicación en personas de bajos ingresos en pasases como Colombia, México y Perú. El punto central está en analizar las diferencias entre países de acuerdo a diferentes variables socioeconómicas. Se encuentra que la variable que más explica el nivel de acceso digital es la escolaridad. De otro lado no se encuentra una brecha por género sino en Perú. Los resultados también indican que cuando solo se tienen en cuenta las tecnologías más ‘avanzadas’, las diferencias entre la población son más notorias

Sunlight disinfects? Free media in weak democracies

Free media may not favor political accountability when other democratic institutions are weak, and may even bring undesirable unintended consequences. We propose a simple model in which politicians running for office may engage in coercion to obtain votes. A media scandal that exposes these candidates increases their coercion effort to offset the negative popularity shock. This may result in the tainted politicians actually increasing their vote share. We provide empirical evidence from one recent episode in the political history of Colombia, the ‘parapolitics’ scandal featuring politicians colluding with illegal armed paramilitary groups to obtain votes. We show that colluding candidates not only get more votes than their clean competitors, but also concentrate them in areas where coercion is more likely (namely, areas with more paramilitary presence, less state presence, and more judicial inefficiency). Harder to reconcile with other explanations and as a direct test of the effects of media exposure, we compare tainted candidates exposed before elections to those exposed after. We find that those exposed before elections get as many votes as those exposed once elected, but their electoral support is more strongly concentrated in places where coercion is more likely. Our re

An approximation to the informal-formal wage gap in Colombia 2008-2012

This document provides recent evidence about the persistency of wage gaps between formal and informal workers in Colombia by using a non-parametric method proposed by Ñopo (2008a). Over a rich dataset at a household level during 2008-2012, it is found that formal workers earn between 30 to 60 percent more, on average, than informal workers. Despite of the formality definition - structuralist or institucionalist- adopted, it is clear that formal workers have more economic advantages than informal ones, but after controlling by demographic and labor variables an important fraction of the gap still remains unexplained.

Beyond divide and rule : weak dictators, natural resources and civil conflict

We propose a model where an autocrat rules over an ethnically divided society. The dictator selects the tax rate over domestic production and the nation’s natural resources to maximize his rents under the threat of a regime-switching revolution. We show that a weak ruler may let the country plunge in civil war to increase his personal rents. Inter-group fighting weakens potential opposition to the ruler, thereby allowing him to increase fiscal pressure. We show that the presence of natural resources exacerbates the incentives of the ruler to promote civil conflict for his own profit, especially if the resources are unequally distributed across ethnic groups. We validate the main predictions of the model using cross-country data over the period 1960-2007, and show that our empirical results are not likely to be driven by omitted observable determinants of civil war incidence or by unobservable country-specific heterogeneity.

An approximation to the standard of living index: the Colombian case

El documento busca mostrar las principales propiedades de un indicador de estándar de vida dentro del enfoque teórico de Amartya Sen. Establecemos un puente entre conceptos tales como: bienestar económico, bienestar, logro de agencia y estándar de vida. La metodología del Optimal scaling fue usada para probar las propiedades de Monotonicidad, No independencia de alternativas irrelevantes, Concavidad, informatividad y sustituibilidad.

The effect of skewness and kurtosis on the Kenward-Roger approximation when group distributions differ

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