18,172 research outputs found
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
Symmetry Aspects in Nonrelativistic Multi-Scalar Field Models and Application to a Coupled Two-Species Dilute Bose Gas
We discuss unusual aspects of symmetry that can happen due to entropic
effects in the context of multi-scalar field theories at finite temperature. We
present their consequences, in special, for the case of nonrelativistic models
of hard core spheres. We show that for nonrelativistic models phenomena like
inverse symmetry breaking and symmetry non-restoration cannot take place, but a
reentrant phase at high temperatures is shown to be possible for some region of
parameters. We then develop a model of interest in studies of Bose-Einstein
condensation in dilute atomic gases and discuss about its phase transition
patterns. In this application to a Bose-Einstein condensation model, however,
no reentrant phases are found.Comment: 8 pages, 1 eps figure, IOP style. Based on a talk given by R. O.
Ramos at the QFEXT05 workshop, Barcelona, Spain, September 5-9, 2005. One
reference was update
Testing static game theory with dynamic experiments: a case study of public goods
Game theory provides predictions of behavior in many one-shot games. On the other hand, most experimenters usually play repeated games with subjects, to provide experience. To avoid subjects rationally employing strategies that are appropriate for the repeated game, experimenters typically employ a "random strangers" design in which subjects are randomly paired with others in the session. There is some chance that subjects will meet in multiple rounds, but it is claimed that this chance is so small that subjects will behave as if they are in a one-shot environment. We present evidence from public goods experiments that this claim is not always true.Game theory, experiments, public goods
Social norms and social choice
Experiments can provide rich information on behavior conditional on the institutional rules of the game being imposed by the experimenter. We consider what happens when the subjects are allowed to choose the institution through a simple social choice procedure. Our case study is a setting in which sanctions may or may not be allowed to encourage "righteous behavior". Laboratory experiments show that some subjects in public goods environments employ costly sanctions against other subjects in order to enforce what appears to be a social norm of contribution. We show that this artificial society is not an attractive place to live, by any of the standard social choice criteria. If it came about because of evolutionary forces, as speculated, then The Blind Watchmaker was having one of his many bad days at the workbench. In fact, none of our laboratory societies with perfect strangers matching ever chose to live in such a world. Our findings suggest that the conditions under which a group or a society would choose a constitution that is based on voluntary costly sanctions are very special.
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