132,401 research outputs found
Moore and more and symmetry
In any spatially discrete model of pedestrian motion which uses a regular
lattice as basis, there is the question of how the symmetry between the
different directions of motion can be restored as far as possible but with
limited computational effort. This question is equivalent to the question ''How
important is the orientation of the axis of discretization for the result of
the simulation?'' An optimization in terms of symmetry can be combined with the
implementation of higher and heterogeniously distributed walking speeds by
representing different walking speeds via different amounts of cells an agent
may move during one round. Therefore all different possible neighborhoods for
speeds up to v = 10 (cells per round) will be examined for the amount of
deviation from radial symmetry. Simple criteria will be stated which will allow
find an optimal neighborhood for each speed. It will be shown that following
these criteria even the best mixture of steps in Moore and von Neumann
neighborhoods is unable to reproduce the optimal neighborhood for a speed as
low as 4.Comment: Proceedings contribution in N. Waldau et al. (editors) "Pedestrian
and Evacuation Dynamics 2005" (2006) pages 297-308. Springer-Verlag Berlin
Heidelberg. ISBN: 978-3-540-47062-
Spontaneous Particle-Hole Symmetry Breaking in the Fractional Quantum Hall Effect
The essence of the fractional quantum Hall effect is believed to be
well captured by the Moore-Read Pfaffian (or anti-Pfaffian) description.
However, an important mystery regarding the formation of the Pfaffian state is
the role of the three-body interaction Hamiltonian that produces the
Pfaffian as an exact ground state and the concomitant particle-hole symmetry
breaking. We show that a two-body interaction Hamiltonian constructed via
particle-hole symmetrization of produces a ground state nearly exactly
approximating the Pfaffian and anti-Pfaffian states, respectively, in the
spherical geometry. More importantly, the ground state energy of is shown
to exhibit a ``Mexican-hat'' structure as a function of particle number in the
vicinity of half filling for a given flux indicating spontaneous particle-hole
symmetry breaking. We do not find any such Mexican-hat signature in the second
Landau level Coulomb interaction at 5/2.Comment: 4 pages, 3 figures, v2 is the final versio
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