On the basis of general considerations, we propose a Langevin equation accounting for critical phenomena occurring in the presence of two symmetric absorbing states. We study its phase diagram by mean-field arguments and direct numerical integration in physical dimensions. Our findings fully account for and clarify the intricate picture known so far from the aggregation of partial results obtained with microscopic models. We argue that the direct transition from disorder to one of two absorbing states is best described as a (generalized) voter critical point and show that it can be split into an Ising and a directed percolation transition in dimensions larger than one.

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.

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.PACS numbers: 02.50.-r,64.60.Ht 87.14.GgThe DNA thermal melting transition (also called denaturation, coiling, or un-zipping) occurs when, above a certain critical temperature, the double-stranded DNA molecule unravels into two separate coils, while for smaller temperatures (pre-melting stage) only localized openings or bubbles exist [1]. This phase transition is of importance for DNA duplication and transcription, and many studies have scrutinized its nature (whether first or second order), trying to pin down the relevant traits of the rich phenomenology experimentally observed (a nonexhaustive list of references is [2,3,4,5,6,7]). Moreover, it has been suggested that the dynamics of a DNA molecule in its pre-melting stage may play a role in its own transcription initiation. Indeed, bubbles are determined by sequence specificity and they have been reported to occur with high probability in the neighborhood of the, functionally relevant, transcription start site (TSS) and near other regulatory sites, facilitating further microbiological activity [7,8,9].This relation between thermal dynamics and biological functionality has been claimed to be borne out by experimental data from real promoter DNA sequences and is supported by results from a theoretical model (see below) [8,9]. Even if this might differ from biological, protein mediated processes, studies of thermal properties of the DNA by itself are a first step forward in understanding more complex situations [1] (see [10] for a different view).Let us mention some observations in this context, which have been the object of recent analyses. Even though one would expect that adenine-thymine (AT-)rich regions should be more prone to sustain bubbles than guanine-cytosine-(GC-)rich ones (as AT pairs bind the two strands more weakly than GC ones [1]), counterintuitive situations in which this is not the case have been reported [7,11]. In the same vein, the dependence of bubble formation on the specific base-pair sequence was reported to be highly nonlocal: Upon mutation of two AT base-pairs into two (stronger) GC base-pairs near the TSS, rendering a specific promoter sequence completely inactive for transcription, the opening profiles of the original sequence and its mutant var...

We introduce a Langevin equation describing the pinning-depinning phase transition experienced by Kardar-Parisi-Zhang interfaces in the presence of a bounding "lower-wall". This provides a continuous description for this universality class, complementary to the different and already well documented one for the case of an "upper-wall". The Langevin equation is written in terms of a field that is not an orderparameter, in contrast to standard approaches, and is studied both by employing a systematic mean-field approximation and by means of a recently introduced efficient integration scheme. Our findings are in good agreement with known results from microscopic models in this class, while the numerical precision is improved. This Langevin equation constitutes a sound starting point for further analytical calculations, beyond mean-field, needed to shed more light on this poorly understood universality class.

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 paraboliccylinder 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.