2,941 research outputs found
Catastrophic regime shifts in model ecological communities are true phase transitions
Ecosystems often undergo abrupt regime shifts in response to gradual external
changes. These shifts are theoretically understood as a regime switch between
alternative stable states of the ecosystem dynamical response to smooth changes
in external conditions. Usual models introduce nonlinearities in the
macroscopic dynamics of the ecosystem that lead to different stable attractors
among which the shift takes place. Here we propose an alternative explanation
of catastrophic regime shifts based on a recent model that pictures ecological
communities as systems in continuous fluctuation, according to certain
transition probabilities, between different micro-states in the phase space of
viable communities. We introduce a spontaneous extinction rate that accounts
for gradual changes in external conditions, and upon variations on this control
parameter the system undergoes a regime shift with similar features to those
previously reported. Under our microscopic viewpoint we recover the main
results obtained in previous theoretical and empirical work (anomalous
variance, hysteresis cycles, trophic cascades). The model predicts a gradual
loss of species in trophic levels from bottom to top near the transition. But
more importantly, the spectral analysis of the transition probability matrix
allows us to rigorously establish that we are observing the fingerprints, in a
finite size system, of a true phase transition driven by background
extinctions.Comment: 19 pages, 11 figures, revised versio
Cluster density functional theory for lattice models based on the theory of Mobius functions
Rosenfeld's fundamental measure theory for lattice models is given a rigorous
formulation in terms of the theory of Mobius functions of partially ordered
sets. The free-energy density functional is expressed as an expansion in a
finite set of lattice clusters. This set is endowed a partial order, so that
the coefficients of the cluster expansion are connected to its Mobius function.
Because of this, it is rigorously proven that a unique such expansion exists
for any lattice model. The low-density analysis of the free-energy functional
motivates a redefinition of the basic clusters (zero-dimensional cavities)
which guarantees a correct zero-density limit of the pair and triplet direct
correlation functions. This new definition extends Rosenfeld's theory to
lattice model with any kind of short-range interaction (repulsive or
attractive, hard or soft, one- or multi-component...). Finally, a proof is
given that these functionals have a consistent dimensional reduction, i.e. the
functional for dimension d' can be obtained from that for dimension d (d'<d) if
the latter is evaluated at a density profile confined to a d'-dimensional
subset.Comment: 21 pages, 2 figures, uses iopart.cls, as well as diagrams.sty
(included
Statistical mechanics of ecosystem assembly
We introduce a toy model of ecosystem assembly for which we are able to map
out all assembly pathways generated by external invasions. The model allows to
display the whole phase space in the form of an assembly graph whose nodes are
communities of species and whose directed links are transitions between them
induced by invasions. We characterize the process as a finite Markov chain and
prove that it exhibits a unique set of recurrent states (the endstate of the
process), which is therefore resistant to invasions. This also shows that the
endstate is independent on the assembly history. The model shares all features
with standard assembly models reported in the literature, with the advantage
that all observables can be computed in an exact manner.Comment: Accepted for publication in Physical Review Letter
A theorem on the absence of phase transitions in one-dimensional growth models with onsite periodic potentials
We rigorously prove that a wide class of one-dimensional growth models with
onsite periodic potential, such as the discrete sine-Gordon model, have no
phase transition at any temperature . The proof relies on the spectral
analysis of the transfer operator associated to the models. We show that this
operator is Hilbert-Schmidt and that its maximum eigenvalue is an analytic
function of temperature.Comment: 6 pages, no figures, submitted to J Phys A: Math Ge
Instabilities in complex mixtures with a large number of components
Inside living cells are complex mixtures of thousands of components. It is
hopeless to try to characterise all the individual interactions in these
mixtures. Thus, we develop a statistical approach to approximating them, and
examine the conditions under which the mixtures phase separate. The approach
approximates the matrix of second virial coefficients of the mixture by a
random matrix, and determines the stability of the mixture from the spectrum of
such random matrices.Comment: 4 pages, uses RevTeX 4.
Nonlinear electrodynamics and the Pioneer 10/11 spacecraft anomaly
The occurrence of the phenomenon known as photon acceleration is a natural
prediction of nonlinear electrodynamics (NLED). This would appear as an
anomalous frequency shift in any modeling of the electromagnetic field that
only takes into account the classical Maxwell theory. Thus, it is tempting to
address the unresolved anomalous, steady; but time-dependent, blueshift of the
Pioneer 10/11 spacecrafts within the framework of NLED. Here we show that
astrophysical data on the strength of the magnetic field in both the Galaxy and
the local (super)cluster of galaxies support the view on the major Pioneer
anomaly as a consequence of the phenomenon of photon acceleration. If
confirmed, through further observations or lab experiments, the reality of this
phenomenon should prompt to take it into account in any forthcoming research on
both cosmological evolution and origin and dynamical effects of primordial
magnetic fields, whose seeds are estimated to be very weak.Comment: Final version accepted for publication in Europhysics Letters, uses
EPL style, 7 page
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