17 research outputs found
Critical wetting of a class of nonequilibrium interfaces: A mean-field picture
A self-consistent mean-field method is used to study critical wetting
transitions under nonequilibrium conditions by analyzing Kardar-Parisi-Zhang
(KPZ) interfaces in the presence of a bounding substrate. In the case of
positive KPZ nonlinearity a single (Gaussian) regime is found. On the contrary,
interfaces corresponding to negative nonlinearities lead to three different
regimes of critical behavior for the surface order-parameter: (i) a trivial
Gaussian regime, (ii) a weak-fluctuation regime with a trivially located
critical point and nontrivial exponents, and (iii) a highly non-trivial
strong-fluctuation regime, for which we provide a full solution by finding the
zeros of parabolic-cylinder functions. These analytical results are also
verified by solving numerically the self-consistent equation in each case.
Analogies with and differences from equilibrium critical wetting as well as
nonequilibrium complete wetting are also discussed.Comment: 11 pages, 2 figure
Simplified Langevin approach to the Peyrard-Bishop-Dauxois model of DNA
A simple Langevin approach is used to study stationary properties of the
Peyrard-Bishop-Dauxois model for DNA, allowing known properties to be recovered
in an easy way. Results are shown for the denaturation transition in
homogeneous samples, for which some implications, so far overlooked, of an
analogy with equilibrium wetting transitions are highlighted. This analogy
implies that the order-parameter, asymptotically, exhibits a second order
transition even if it may be very abrupt for non-zero values of the stiffness
parameter. Not surprisingly, we also find that for heterogeneous DNA, within
this model the largest bubbles in the pre-melting stage appear in
adenine-thymine rich regions, while we suggest the possibility of some sort of
not strictly local effects owing to the merging of bubbles.Comment: 4 pages, 2 figure
When can species abundance data reveal non-neutrality?
Species abundance distributions (SAD) are probably ecology's most well-known empirical pattern, and over the last decades many models have been proposed to explain their shape. There is no consensus over which model is correct, because the degree to which different processes can be discerned from SAD patterns has not yet been rigorously quantified. We present a power calculation to quantify our ability to detect deviations from neutrality using species abundance data. We study non-neutral stochastic community models, and show that the presence of non-neutral processes is detectable if sample size is large enough and/or the amplitude of the effect is strong enough. Our framework can be used for any candidate community model that can be simulated on a computer, and determines both the sampling effort required to distinguish between alternative processes, and a range for the strength of non-neutral processes in communities whose patterns are statistically consistent with neutral theory. We find that even data sets of the scale of the 50 Ha forest plot on Barro Colorado Island, Panama, are unlikely to be large enough to detect deviations from neutrality caused by competitive interactions alone, though the presence of multiple non-neutral processes with contrasting effects on abundance distributions may be detectable
Critical wetting of a class of nonequilibrium interfaces: A computer simulation study
Critical wetting transitions under nonequilibrium conditions are studied
numerically and analytically by means of an interface-displacement model
defined by a Kardar-Parisi-Zhang equation, plus some extra terms representing a
limiting, short-ranged attractive wall. Its critical behavior is characterized
in detail by providing a set of exponents for both the average height and the
surface order-parameter in one dimension. The emerging picture is qualitatively
and quantitatively different from recently reported mean-field predictions for
the same problem. Evidence is shown that the presence of the attractive wall
induces an anomalous scaling of the interface local slopes.Comment: 7 pages, 8 figure
Absorbing state phase transitions with a non-accessible vacuum
We analyze from the renormalization group perspective a universality class of
reaction-diffusion systems with absorbing states. It describes models where the
vacuum state is not accessible, as the set of reactions together
with creation processes of the form with . This class
includes the (exactly solvable in one-dimension) {\it reversible} model as a particular example, as well as many other {\it
non-reversible} reactions, proving that reversibility is not the main feature
of this class as previously thought. By using field theoretical techniques we
show that the critical point appears at zero creation-rate (in accordance with
exact results), and it is controlled by the well known pair-coagulation
renormalization group fixed point, with non-trivial exactly computable critical
exponents in any dimension. Finally, we report on Monte-Carlo simulations,
confirming all field theoretical predictions in one and two dimensions for
various reversible and non-reversible models.Comment: 6 pages. 3 Figures. Final version as published in J.Stat.Mec
Langevin equations for nonequilibrium phase transition
Contiene un resumen en castellanoTesis realizada en colaboraciĂłn con el Instituto Carlos I de FĂsica TeĂłrica y ComputacionalTesis Univ. Granada. Departamento de Electromagnetismo y FĂsica de la Materia. LeĂda el 27 del 4 del 200
Probabilty of rejecting the neutral null model as a function of the strength of non-neutrality, for different levels of diversity in the metacommunity.
<p>The parameters are: for HL/LOGS: <i>m</i> = 10<sup>â3</sup> and <i>Ξ</i> = 25 (blue multiplication signs), <i>Ξ</i> = 50 (red triangles), <i>Ξ</i> = 200 (green plus signs); for PC/LOGS, <i>m</i> = 10<sup>â3</sup> and <i>Ξ</i> = 10 (black circles), <i>Ξ</i> = 50 (red triangles), <i>Ξ</i> = 200 (green plus signs); for HL/EVEN and PC/EVEN, <i>m</i> = 10<sup>â3</sup> and <i>S</i><sub><i>T</i></sub> = 20 (black circles), <i>S</i><sub><i>T</i></sub> = 50 (red triangles), <i>S</i><sub><i>T</i></sub> = 500 (green plus signs); for IF/LOGS, <i>m</i> = 0.1 and <i>Ξ</i> = 10 (black circles), <i>Ξ</i> = 100 (red triangles), <i>Ξ</i> = 1000 (green plus signs); for IF/EVEN <i>m</i> = 0.1 and <i>S</i><sub><i>T</i></sub> = 50 (black circles), <i>S</i><sub><i>T</i></sub> = 100 (red triangles), <i>S</i><sub><i>T</i></sub> = 200 (green plus signs). In all cases <i>J</i> = 2000.</p