13,205 research outputs found
A Frame Work for the Error Analysis of Discontinuous Finite Element Methods for Elliptic Optimal Control Problems and Applications to IP methods
In this article, an abstract framework for the error analysis of
discontinuous Galerkin methods for control constrained optimal control problems
is developed. The analysis establishes the best approximation result from a
priori analysis point of view and delivers reliable and efficient a posteriori
error estimators. The results are applicable to a variety of problems just
under the minimal regularity possessed by the well-posed ness of the problem.
Subsequently, applications of interior penalty methods for a boundary
control problem as well as a distributed control problem governed by the
biharmonic equation subject to simply supported boundary conditions are
discussed through the abstract analysis. Numerical experiments illustrate the
theoretical findings. Finally, we also discuss the variational discontinuous
discretization method (without discretizing the control) and its corresponding
error estimates.Comment: 23 pages, 5 figures, 1 tabl
Quark mass, scale and volume dependence of topological charge density correlator in Lattice QCD
We study the two-point Topological Charge Density Correlator (TCDC) in
lattice QCD with two degenerate flavours of naive Wilson fermions and
unimproved Wilson gauge action at two values of lattice spacings and different
volumes, for a range of quark masses. Configurations are generated with DDHMC
algorithm and smoothed with HYP smearing. In order to shed light on the
mechanisms leading to the observed suppression of topological susceptibility
with respect to the decreasing quark mass and decreasing volume, in this work,
we carry out a detailed study of the two-point TCDC. We have shown that, (1)
the TCDC is negative beyond a positive core and radius of the core shrinks as
lattice spacing decreases, (2) as the volume decreases, the magnitude of the
contact term and the radius of the positive core decrease and the magnitude of
the negative peak increases resulting in the suppression of the topological
susceptibility as the volume decreases, (3) the contact term and radius of the
positive core decrease with decreasing quark mass at a given lattice spacing
and the negative peak increases with decreasing quark mass resulting in the
suppression of the topological susceptibility with decreasing quark mass, (4)
increasing levels of smearing suppresses the contact term and the negative peak
keeping the susceptibility intact and (5) both the contact term and the
negative peak diverge in nonintegrable fashion as lattice spacing decreases.Comment: 7 pages, 5 figures, talk presented at-The 30th International
Symposium on Lattice Field Theory-Lattice 2012, June 24-29, 2012 Cairns,
Australi
A new cellular automata model for city traffic
We present a new cellular automata model of vehicular traffic in cities by
combining ideas borrowed from the Biham-Middleton-Levine (BML) model of city
traffic and the Nagel-Schreckenberg (NaSch) model of highway traffic. The model
exhibits a dynamical phase transition to a completely jammed phase at a
critical density which depends on the time periods of the synchronized signals.Comment: 6 pages, 5 figures, uses Springer Macros 'lncse', to appear in
"Traffic and Granular Flow '99: Social, Traffic, and Granular Dynamics"
edited by D. Helbing, H. J. Herrmann, M. Schreckenberg, and D. E. Wolf
(Springer, Berlin
Cluster formation and anomalous fundamental diagram in an ant trail model
A recently proposed stochastic cellular automaton model ({\it J. Phys. A 35,
L573 (2002)}), motivated by the motions of ants in a trail, is investigated in
detail in this paper. The flux of ants in this model is sensitive to the
probability of evaporation of pheromone, and the average speed of the ants
varies non-monotonically with their density. This remarkable property is
analyzed here using phenomenological and microscopic approximations thereby
elucidating the nature of the spatio-temporal organization of the ants. We find
that the observations can be understood by the formation of loose clusters,
i.e. space regions of enhanced, but not maximal, density.Comment: 11 pages, REVTEX, with 11 embedded EPS file
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