Second-order hyperbolic Fuchsian systems. Gowdy spacetimes and the Fuchsian numerical algorithm

This is the second part of a series devoted to the singular initial value problem for second-order hyperbolic Fuchsian systems. In the first part, we defined and investigated this general class of systems, and we established a well-posedness theory in weighted Sobolev spaces. This theory is applied here to the vacuum Einstein equations for Gowdy spacetimes admitting, by definition, two Killing fields satisfying certain geometric conditions. We recover, by more direct and simpler arguments, the well-posedness results established earlier by Rendall and collaborators. In addition, in this paper we introduce a natural approximation scheme, which we refer to as the Fuchsian numerical algorithm and is directly motivated by our general theory. This algorithm provides highly accurate, numerical approximations of the solution to the singular initial value problem. In particular, for the class of Gowdy spacetimes under consideration, various numerical experiments are presented which show the interest and efficiency of the proposed method. Finally, as an application, we numerically construct Gowdy spacetimes containing a smooth, incomplete, non-compact Cauchy horizon.Comment: 22 pages. A shortened version is included in: F. Beyer and P.G. LeFloch, Second-order hyperbolic Fuchsian systems and applications, Class. Quantum Grav. 27 (2010), 24501

Polarized semi-inclusive electroweak structure functions at next-to-leading-order

We present a next-to-leading order (NLO) computation of the full set of polarized and unpolarized electroweak semi-inclusive DIS (SIDIS) structure functions, whose knowledge is crucial for a precise extraction of polarized parton distributions. We focus on the phenomenology of the polarized structure functions for the kinematical conditions that could be reached in an Electron-Ion-Collider. We show that the NLO corrections are sizeable, particularly in the small-$x$ range. We test the sensitivity of these structure functions on certain quark distributions and compare it to the situation of inclusive DIS and electromagnetic SIDIS.Comment: 17 pages, 5 figure

On tree-decompositions of one-ended graphs

A graph is one-ended if it contains a ray (a one way infinite path) and whenever we remove a finite number of vertices from the graph then what remains has only one component which contains rays. A vertex $v$ {\em dominates} a ray in the end if there are infinitely many paths connecting $v$ to the ray such that any two of these paths have only the vertex $v$ in common. We prove that if a one-ended graph contains no ray which is dominated by a vertex and no infinite family of pairwise disjoint rays, then it has a tree-decomposition such that the decomposition tree is one-ended and the tree-decomposition is invariant under the group of automorphisms. This can be applied to prove a conjecture of Halin from 2000 that the automorphism group of such a graph cannot be countably infinite and solves a recent problem of Boutin and Imrich. Furthermore, it implies that every transitive one-ended graph contains an infinite family of pairwise disjoint rays

Gift Exchange in the Lab - It is not (only) how much you give ...

An important aspect in determining the effectiveness of gift exchange relations in labor markets is the ability of the worker to “repay the gift” to the employer. To test this hypothesis, we conduct a real effort laboratory experiment where we vary the wage and the effect of the worker’s effort on the manager’s payoff. Furthermore we collect additional information that allows us to control for the workers’ ability and whether they can be classified as reciprocal or not. From our agency model of reciprocal motivation we derive non-trivial predictions about which is the marginal worker (in terms of ability) affected by our experimental variation and how different types of individuals, selfish and reciprocal, will react to it. Our model does substantially better than other theories in organizing the data.reciprocity, fairness, real effort experiment, personality tests