37,016 research outputs found
Phase transitions in dependence of apex predator decaying ratio in a cyclic dominant system
Cyclic dominant systems, like rock-paper-scissors game, are frequently used
to explain biodiversity in nature, where mobility, reproduction and
intransitive competition are on stage to provide the coexistence of
competitors. A significantly new situation emerges if we introduce an apex
predator who can superior all members of the mentioned three-species system. In
the latter case the evolution may terminate into three qualitatively different
destinations depending on the apex predator decaying ratio . In particular,
the whole population goes extinct or all four species survive or only the
original three-species system remains alive as we vary the control parameter.
These solutions are separated by a discontinuous and a continuous phase
transitions at critical values. Our results highlight that cyclic dominant
competition can offer a stable way to survive even in a predator-prey-like
system that can be maintained for large interval of critical parameter values.Comment: version to appear in EPL. 7 pages, 7 figure
Invasion controlled pattern formation in a generalized multi-species predator-prey system
Rock-scissors-paper game, as the simplest model of intransitive relation
between competing agents, is a frequently quoted model to explain the stable
diversity of competitors in the race of surviving. When increasing the number
of competitors we may face a novel situation because beside the mentioned
unidirectional predator-prey-like dominance a balanced or peer relation can
emerge between some competitors. By utilizing this possibility in the present
work we generalize a four-state predator-prey type model where we establish two
groups of species labeled by even and odd numbers. In particular, we introduce
different invasion probabilities between and within these groups, which results
in a tunable intensity of bidirectional invasion among peer species. Our study
reveals an exceptional richness of pattern formations where five quantitatively
different phases are observed by varying solely the strength of the mentioned
inner invasion. The related transition points can be identified with the help
of appropriate order parameters based on the spatial autocorrelation decay, on
the fraction of empty sites, and on the variance of the species density.
Furthermore, the application of diverse, alliance-specific inner invasion rates
for different groups may result in the extinction of the pair of species where
this inner invasion is moderate. These observations highlight that beyond the
well-known and intensively studied cyclic dominance there is an additional
source of complexity of pattern formation that has not been explored earlier.Comment: 8 pages, 8 figures. To appear in PR
Applications and Sexual Version of a Simple Model for Biological Ageing
We use a simple model for biological ageing to study the mortality of the
population, obtaining a good agreement with the Gompertz law. We also simulate
the same model on a square lattice, considering different strategies of
parental care. The results are in agreement with those obtained earlier with
the more complicated Penna model for biological ageing. Finally, we present the
sexual version of this simple model.Comment: For Int.J.Mod.Phys.C Dec. 2001; 11 pages including 6 fig
Treatment of the infrared contribution: NLO QED evolution as a pedagogic example
We show that the conventional prescription used for DGLAP parton evolution at
NLO has an inconsistent treatment of the contribution from the infrared (IR)
region. We illustrate the problem by studying the simple example of QED
evolution, treating the electron and photon as partons. The deficiency is not
present in a physical approach which removes the IR divergency and allows
calculation in the normal 4-dimensional space.Comment: 15 pages, 2 figures, erratum at the end of the articl
Corrections to Finite Size Scaling in Percolation
A 1/L-expansion for percolation problems is proposed, where L is the lattice
finite length. The square lattice with 27 different sizes L = 18, 22 ... 1594
is considered. Certain spanning probabilities were determined by Monte Carlo
simulations, as continuous functions of the site occupation probability p. We
estimate the critical threshold pc by applying the quoted expansion to these
data. Also, the universal spanning probability at pc for an annulus with aspect
ratio r=1/2 is estimated as C = 0.876657(45)
Improving the Drell-Yan probe of small x partons at the LHC via a k_t cut
We show that the observation of the Drell-Yan production of low-mass
lepton-pairs (M 3) at the LHC can make a
direct measurement of parton distribution functions (PDFs) in the low x region,
x < 10^{-4}. We describe a procedure that greatly reduces the sensitivity of
the predictions to the choice of the factorization scale and, in particular,
show how, by imposing a cutoff on the transverse momentum of the lepton-pair,
the data are able to probe PDFs in the important low scale, low x domain. We
include the effects of the Sudakov suppression factor.Comment: 14 pages, 5 figures, version to be published in EPJC, with expanded
explanatio
Physical factorisation scheme for PDFs for non-inclusive applications
We introduce the physical factorisation scheme, which is necessary to
describe observables which are `not completely inclusive'. We derive the
formulae for NLO DGLAP evolution in this scheme, and also for the `rotation' of
the conventional MSbar PDFs into the physical representation. Unlike, the MSbar
prescription, where, for example, the gluon PDF at NLO obtains an admixture of
the quark-singlet PDF, and vice-versa, the physical approach does not mix
parton PDFs of different types. That is, the physical approach retains the
precise quantum numbers of each PDF. The NLO corrections to DGLAP evolution in
the physical scheme are less than those in the MSbar case, indicating a better
convergence of the perturbative series
The LHC can probe small x PDFs; the treatment of the infrared region
First, we show how to reduce the sensitivity of the NLO predictions of the
Drell-Yan production of low-mass, lepton-pairs, at high rapidity, to the choice
of factorization scale. In this way, observations of this process at the LHC
can make direct measurements of parton distribution functions in the low x
domain; x < 10^{-4}. Second, we find an inconsistency in the conventional NLO
treatment of the infrared region. We illustrate the problem using the NLO
coefficient function of Drell-Yan production.Comment: 5 pages, 1 figure, contribution to the Proceedings of
"Diffraction2012", Puerto del Carmen, Lanzarote, Spain, Sept. 10-15th, 201
- …