48,217 research outputs found
Stochastic and Discrete Time Models of Long-Range Turbulent Transport in the Scrape-Off Layer
Two dimensional stochastic time model of scrape-off layer (SOL) turbulent
transport is studied. Instability arisen in the system with respect to the
stochastic perturbations of both either density or vorticity reveals itself in
the strong outward bursts of particle density propagating ballistically across
the SOL. The stability and possible stabilization of the cross- field turbulent
system depend very much upon the reciprocal correlation time between density
and vorticity fluctuations. Pdf of the particle flux for the large magnitudes
of flux events can be modelled with a simple discrete time toy model of random
walks concluding at a boundary. The spectra of wandering times feature the pdf
of particle flux in the model and qualitatively reproduce the experimental
statistics of transport events.Comment: 21 pages,11 figure
Homogeneous and Scalable Gene Expression Regulatory Networks with Random Layouts of Switching Parameters
We consider a model of large regulatory gene expression networks where the
thresholds activating the sigmoidal interactions between genes and the signs of
these interactions are shuffled randomly. Such an approach allows for a
qualitative understanding of network dynamics in a lack of empirical data
concerning the large genomes of living organisms. Local dynamics of network
nodes exhibits the multistationarity and oscillations and depends crucially
upon the global topology of a "maximal" graph (comprising of all possible
interactions between genes in the network). The long time behavior observed in
the network defined on the homogeneous "maximal" graphs is featured by the
fraction of positive interactions () allowed between genes.
There exists a critical value such that if , the
oscillations persist in the system, otherwise, when it tends to
a fixed point (which position in the phase space is determined by the initial
conditions and the certain layout of switching parameters). In networks defined
on the inhomogeneous directed graphs depleted in cycles, no oscillations arise
in the system even if the negative interactions in between genes present
therein in abundance (). For such networks, the bidirectional edges
(if occur) influence on the dynamics essentially. In particular, if a number of
edges in the "maximal" graph is bidirectional, oscillations can arise and
persist in the system at any low rate of negative interactions between genes
(). Local dynamics observed in the inhomogeneous scalable regulatory
networks is less sensitive to the choice of initial conditions. The scale free
networks demonstrate their high error tolerance.Comment: LaTeX, 30 pages, 20 picture
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