12,251 research outputs found
Numerical simulation of conservation laws with moving grid nodes: Application to tsunami wave modelling
In the present article we describe a few simple and efficient finite volume
type schemes on moving grids in one spatial dimension combined with appropriate
predictor-corrector method to achieve higher resolution. The underlying finite
volume scheme is conservative and it is accurate up to the second order in
space. The main novelty consists in the motion of the grid. This new dynamic
aspect can be used to resolve better the areas with large solution gradients or
any other special features. No interpolation procedure is employed, thus
unnecessary solution smearing is avoided, and therefore, our method enjoys
excellent conservation properties. The resulting grid is completely
redistributed according the choice of the so-called monitor function. Several
more or less universal choices of the monitor function are provided. Finally,
the performance of the proposed algorithm is illustrated on several examples
stemming from the simple linear advection to the simulation of complex shallow
water waves. The exact well-balanced property is proven. We believe that the
techniques described in our paper can be beneficially used to model tsunami
wave propagation and run-up.Comment: 46 pages, 7 figures, 7 tables, 94 references. Accepted to
Geosciences. Other author's papers can be downloaded at
http://www.denys-dutykh.com
Evolution of Robustness and Plasticity under Environmental Fluctuation: Formulation in terms of Phenotypic Variances
The characterization of plasticity, robustness, and evolvability, an
important issue in biology, is studied in terms of phenotypic fluctuations. By
numerically evolving gene regulatory networks, the proportionality between the
phenotypic variances of epigenetic and genetic origins is confirmed. The former
is given by the variance of the phenotypic fluctuation due to noise in the
developmental process; and the latter, by the variance of the phenotypic
fluctuation due to genetic mutation. The relationship suggests a link between
robustness to noise and to mutation, since robustness can be defined by the
sharpness of the distribution of the phenotype. Next, the proportionality
between the variances is demonstrated to also hold over expressions of
different genes (phenotypic traits) when the system acquires robustness through
the evolution. Then, evolution under environmental variation is numerically
investigated and it is found that both the adaptability to a novel environment
and the robustness are made compatible when a certain degree of phenotypic
fluctuations exists due to noise. The highest adaptability is achieved at a
certain noise level at which the gene expression dynamics are near the critical
state to lose the robustness. Based on our results, we revisit Waddington's
canalization and genetic assimilation with regard to the two types of
phenotypic fluctuations.Comment: 23 pages 11 figure
The Clumping Transition in Niche Competition: a Robust Critical Phenomenon
We show analytically and numerically that the appearance of lumps and gaps in
the distribution of n competing species along a niche axis is a robust
phenomenon whenever the finiteness of the niche space is taken into account. In
this case depending if the niche width of the species is above or
below a threshold , which for large n coincides with 2/n, there are
two different regimes. For the lumpy pattern emerges
directly from the dominant eigenvector of the competition matrix because its
corresponding eigenvalue becomes negative. For the lumpy
pattern disappears. Furthermore, this clumping transition exhibits critical
slowing down as is approached from above. We also find that the number
of lumps of species vs. displays a stair-step structure. The positions
of these steps are distributed according to a power-law. It is thus
straightforward to predict the number of groups that can be packed along a
niche axis and it coincides with field measurements for a wide range of the
model parameters.Comment: 16 pages, 7 figures;
http://iopscience.iop.org/1742-5468/2010/05/P0500
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