10,050 research outputs found
On the Numerical Dispersion of Electromagnetic Particle-In-Cell Code : Finite Grid Instability
The Particle-In-Cell (PIC) method is widely used in relativistic particle
beam and laser plasma modeling. However, the PIC method exhibits numerical
instabilities that can render unphysical simulation results or even destroy the
simulation. For electromagnetic relativistic beam and plasma modeling, the most
relevant numerical instabilities are the finite grid instability and the
numerical Cherenkov instability. We review the numerical dispersion relation of
the electromagnetic PIC algorithm to analyze the origin of these instabilities.
We rigorously derive the faithful 3D numerical dispersion of the PIC algorithm,
and then specialize to the Yee FDTD scheme. In particular, we account for the
manner in which the PIC algorithm updates and samples the fields and
distribution function. Temporal and spatial phase factors from solving
Maxwell's equations on the Yee grid with the leapfrog scheme are also
explicitly accounted for. Numerical solutions to the electrostatic-like modes
in the 1D dispersion relation for a cold drifting plasma are obtained for
parameters of interest. In the succeeding analysis, we investigate how the
finite grid instability arises from the interaction of the numerical 1D modes
admitted in the system and their aliases. The most significant interaction is
due critically to the correct represenation of the operators in the dispersion
relation. We obtain a simple analytic expression for the peak growth rate due
to this interaction.Comment: 25 pages, 6 figure
From Bad to Good: Fitness Reversals and the Ascent of Deleterious Mutations
Deleterious mutations are considered a major impediment to adaptation, and there are straightforward expectations for the rate at which they accumulate as a function of population size and mutation rate. In a simulation model of an evolving population of asexually replicating RNA molecules, initially deleterious mutations accumulated at rates nearly equal to that of initially beneficial mutations, without impeding evolutionary progress. As the mutation rate was increased within a moderate range, deleterious mutation accumulation and mean fitness improvement both increased. The fixation rates were higher than predicted by many population-genetic models. This seemingly paradoxical result was resolved in part by the observation that, during the time to fixation, the selection coefficient (s) of initially deleterious mutations reversed to confer a selective advantage. Significantly, more than half of the fixations of initially deleterious mutations involved fitness reversals. These fitness reversals had a substantial effect on the total fitness of the genome and thus contributed to its success in the population. Despite the relative importance of fitness reversals, however, the probabilities of fixation for both initially beneficial and initially deleterious mutations were exceedingly small (on the order of 10(ā5) of all mutations)
Children's construction task performance and spatial ability: controlling task complexity and predicting mathematics performance.
This paper presents a methodology to control construction task complexity and examined the relationships between construction performance and spatial and mathematical abilities in children. The study included three groups of children (N = 96); ages 7-8, 10-11, and 13-14 years. Each group constructed seven pre-specified objects. The study replicated and extended previous findings that indicated that the extent of component symmetry and variety, and the number of components for each object and available for selection, significantly predicted construction task difficulty. Results showed that this methodology is a valid and reliable technique for assessing and predicting construction play task difficulty. Furthermore, construction play performance predicted mathematical attainment independently of spatial ability
Anisotropy effects in a mixed quantum-classical Heisenberg model in two dimensions
We analyse a specific two dimensional mixed spin Heisenberg model with
exchange anisotropy, by means of high temperature expansions and Monte Carlo
simulations. The goal is to describe the magnetic properties of the compound
(NBu_{4})_{2}Mn_{2}[Cu(opba)]_{3}\cdot 6DMSO\cdot H_{2}O which exhibits a
ferromagnetic transition at . Extrapolating our analysis on the
basis of renormalisation group arguments, we find that this transition may
result from a very weak anisotropy effect.Comment: 8 pages, 10 Postscript figure
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