50 research outputs found
Efficiency of a stirred chemical reaction in a closed vessel
We perform a numerical study of the reaction efficiency in a closed vessel.
Starting with a little spot of product, we compute the time needed to complete
the reaction in the container following an advection-reaction-diffusion
process. Inside the vessel it is present a cellular velocity field that
transports the reactants. If the size of the container is not very large
compared with the typical length of the velocity field one has a plateau of the
reaction time as a function of the strength of the velocity field, . This
plateau appears both in the stationary and in the time-dependent flow. A
comparison of the results for the finite system with the infinite case (for
which the front speed, , gives a simple estimate of the reacting time)
shows the dramatic effect of the finite size.Comment: 4 pages, 4 figure
Linear and anomalous front propagation in system with non Gaussian diffusion: the importance of tails
We investigate front propagation in systems with diffusive and sub-diffusive
behavior. The scaling behavior of moments of the diffusive problem, both in the
standard and in the anomalous cases, is not enough to determine the features of
the reactive front. In fact, the shape of the bulk of the probability
distribution of the transport process, which determines the diffusive
properties, is important just for pre-asymptotic behavior of front propagation,
while the precise shape of the tails of the probability distribution determines
asymptotic behavior of front propagation.Comment: 7 pages, 3 figure
Reaction spreading on percolating clusters
Reaction-diffusion processes in two-dimensional percolating structures are
investigated. Two different problems are addressed: reaction spreading on a
percolating cluster and front propagation through a percolating channel. For
reaction spreading, numerical data and analytical estimates show a power-law
behavior of the reaction product as M(t) \sim t^dl, where dl is the
connectivity dimension. In a percolating channel, a statistically stationary
traveling wave develops. The speed and the width of the traveling wave are
numerically computed. While the front speed is a low-fluctuating quantity and
its behavior can be understood using a simple theoretical argument, the front
width is a high-fluctuating quantity showing a power-law behavior as a function
of the size of the channelComment: 7 pages, 8 figure
Invasions in heterogeneous habitats in the presence of advection
We investigate invasions from a biological reservoir to an initially empty,
heterogeneous habitat in the presence of advection. The habitat consists of a
periodic alternation of favorable and unfavorable patches. In the latter the
population dies at fixed rate. In the former it grows either with the logistic
or with an Allee effect type dynamics, where the population has to overcome a
threshold to grow. We study the conditions for successful invasions and the
speed of the invasion process, which is numerically and analytically
investigated in several limits. Generically advection enhances the downstream
invasion speed but decreases the population size of the invading species, and
can even inhibit the invasion process. Remarkably, however, the rate of
population increase, which quantifies the invasion efficiency, is maximized by
an optimal advection velocity. In models with Allee effect, differently from
the logistic case, above a critical unfavorable patch size the population
localizes in a favorable patch, being unable to invade the habitat. However, we
show that advection, when intense enough, may activate the invasion process.Comment: 16 pages, 11 figures J. Theor. Biol. to appea
Discreteness effects in a reacting system of particles with finite interaction radius
9 pages.-- PACS numbers: 05.40.-a, 82.39.-k, 82.40.-g.-- Final full-text version of the paper available at: http://dx.doi.org/10.1103/PhysRevE.76.031139.An autocatalytic reacting system with particles interacting at a finite distance is studied. We investigate the effects of the discrete-particle character of the model on properties like reaction rate, quenching phenomenon, and front propagation, focusing on differences with respect to the continuous case. We introduce a renormalized reaction rate depending both on the interaction radius and the particle density, and we relate it to macroscopic observables (e.g., front speed and front thickness) of the system.We have benefited from a MEC-MIUR joint program (Italy-Spain Integral Actions). C.L. acknowledges support from FEDER and MEC (Spain), through project CONOCE2 (FIS2004-00953). A.V. and D.V. acknowledge support from PRIN-MIUR project "Dinamica Statistica di sistemi a molti e pochi gradi di libertà"
Front speed in reactive compressible stirred media
We investigated a nonlinear advection-diffusion-reaction equation for a
passive scalar field. The purpose is to understand how the compressibility can
affect the front dynamics and the bulk burning rate. We study two classes of
flows: periodic shear flow and cellular flow both in the case of fast advection
regime, analysing the system at varying the extent of compressibility and the
reaction rate. We find that the bulk burning rate in a shear flow increases
with compressibility intensity.
Furthermore, the faster the reaction the more important the difference with
respect to the laminar case. The effect has been quantitatively measured and it
turns out to be generally little. For the cellular flow, the two extreme cases
have been investigated, with the whole perturbation situated either in the
centre of the vortex or in the periphery. The dependence in this case does not
show a monotonic scaling with different behaviour in the two cases. The
enhancing remains modest and always less than 20%Comment: 9 pages, 5 figures, under press on Physical Review E (2013
Markovian approximation in foreign exchange markets
In this paper we test the random walk hypothesis on the high frequency
dataset of the bid--ask Deutschemark/US dollar exchange rate quotes registered
by the inter-bank Reuters network over the period October 1, 1992 to September
30, 1993. Then we propose a stochastic model for price variation which is able
to describe some important features of the exchange market behavior. Besides
the usual correlation analysis we have verified the validity of this model by
means of other approaches inspired by information theory . These techniques are
not only severe tests of the approximation but also evidence some aspects of
the data series which have a clear financial relevance.Comment: 19 pages, LaTeX, uses elsart.cls and JournalOfFinance.sty, 7 eps
figures, submitted to J. of Int. Money and Financ
Inverse velocity statistics in two dimensional turbulence
We present a numerical study of two-dimensional turbulent flows in the
enstrophy cascade regime, with different large-scale forcings and energy sinks.
In particular, we study the statistics of more-than-differentiable velocity
fluctuations by means of two recently introduced sets of statistical
estimators, namely {\it inverse statistics} and {\it second order differences}.
We show that the 2D turbulent velocity field, , cannot be simply
characterized by its spectrum behavior, . There
exists a whole set of exponents associated to the non-trivial smooth
fluctuations of the velocity field at all scales. We also present a numerical
investigation of the temporal properties of measured in different
spatial locations.Comment: 9 pages, 12 figure