Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

Stochastic generation of homogeneous isotropic turbulence with well-defined-spectra

A precise and simple computational model to generate well-behaved two-dimensional turbulent flows is presented. The whole approach rests on the use of stochastic differential equations and is general enough to reproduce a variety of energy spectra and spatiotemporal correlation functions. Analytical expressions for both the continuous and the discrete versions, together with simulation algorithms, are derived. Results for two relevant spectra, covering distinct ranges of wave numbers, are given.

Reaction-diffusion fronts under stochastic advection

We study front propagation in stirred media using a simplified modelization of the turbulent flow. Computer simulations reveal the existence of the two limiting propagation modes observed in recent experiments with liquid phase isothermal reactions. These two modes respectively correspond to a wrinkled although sharp propagating interface and to a broadened one. Specific laws relative to the enhancement of the front velocity in each regime are confirmed by our simulations.

Dynamical properties of nonmarkovian stochastic differential equations

We study nonstationary non-Markovian processes defined by Langevin-type stochastic differential equations with an OrnsteinUhlenbeck driving force. We concentrate on the long time limit of the dynamical evolution. We derive an approximate equation for the correlation function of a nonlinear nonstationary non-Markovian process, and we discuss its consequences. Non-Markovicity can introduce a dependence on noise parameters in the dynamics of the correlation function in cases in which it becomes independent of these parameters in the Markovian limit. Several examples are discussed in which the relaxation time increases with respect to the Markovian limit. For a Brownian harmonic oscillator with fluctuating frequency, the non-Markovicity of the process decreases the domain of stability of the system, and it can change an infradamped evolution into an overdamped one.

Stochastic processes induced by dichotomous markov noise: Some exact dynamical results

Stochastic processes defined by a general Langevin equation of motion where the noise is the non-Gaussian dichotomous Markov noise are studied. A non-FokkerPlanck master differential equation is deduced for the probability density of these processes. Two different models are exactly solved. In the second one, a nonequilibrium bimodal distribution induced by the noise is observed for a critical value of its correlation time. Critical slowing down does not appear in this point but in another one.

Microbial biomass and activity in litter during the initial development of pure and mixed plantations of Eucalyptus grandis and Acacia mangium

Studies on microbial activity and biomass in forestry plantations often overlook the role of litter, typically focusing instead on soil nutrient contents to explain plant and microorganism development. However, since the litter is a significant source of recycled nutrients that affect nutrient dynamics in the soil, litter composition may be more strongly correlated with forest growth and development than soil nutrient contents. This study aimed to test this hypothesis by examining correlations between soil C, N, and P; litter C, N, P, lignin content, and polyphenol content; and microbial biomass and activity in pure and mixed second-rotation plantations of Eucalyptus grandis and Acacia mangium before and after senescent leaf drop. The numbers of cultivable fungi and bacteria were also estimated. All properties were correlated with litter C, N, P, lignin and polyphenols, and with soil C and N. We found higher microbial activity (CO2 evolution) in litter than in soil. In the E. grandis monoculture before senescent leaf drop, microbial biomass C was 46 % higher in litter than in soil. After leaf drop, this difference decreased to 16 %. In A. mangium plantations, however, microbial biomass C was lower in litter than in soil both before and after leaf drop. Microbial biomass N of litter was approximately 94 % greater than that of the soil in summer and winter in all plantations. The number of cultivable fungi and bacteria increased after leaf drop, especially so in the litter. Fungi were also more abundant in the E. grandis litter. In general, the A. mangium monoculture was associated with higher levels of litter lignin and N, especially after leaf drop. In contrast, the polyphenol and C levels in E. grandis monoculture litter were higher after leaf drop. These properties were negatively correlated with total soil C and N. Litter in the mixed stands had lower C:N and C:P ratios and higher N, P, and C levels in the microbial biomass. This suggests more effective nutrient cycling in mixed plantations in the long term, greater stimulation of microbial activity in litter and soil, and a more sustainable system in general.

Diffusion of passive scalars under stochastic convection

The diffusion of passive scalars convected by turbulent flows is addressed here. A practical procedure to obtain stochastic velocity fields with well¿defined energy spectrum functions is also presented. Analytical results are derived, based on the use of stochastic differential equations, where the basic hypothesis involved refers to a rapidly decaying turbulence. These predictions are favorable compared with direct computer simulations of stochastic differential equations containing multiplicative space¿time correlated noise.

Comparing Basal Area Diameter Distributions Estimated by Tree Species and for the Entire Stock in a Mixed Stand

Summary

Stochastic semiclassical equations for weakly inhomogeneous cosmologies

Semiclassical Einstein-Langevin equations for arbitrary small metric perturbations conformally coupled to a massless quantum scalar field in a spatially flat cosmological background are derived. Use is made of the fact that for this problem the in-in or closed time path effective action is simply related to the Feynman-Vernon influence functional which describes the effect of the ``environment,'' the quantum field which is coarse grained here, on the ``system,'' the gravitational field which is the field of interest. This leads to identify the dissipation and noise kernels in the in-in effective action, and to derive a fluctuation-dissipation relation. A tensorial Gaussian stochastic source which couples to the Weyl tensor of the spacetime metric is seen to modify the usual semiclassical equations which can be veiwed now as mean field equsations. As a simple application we derive the correlation functions of the stochastic metric fluctuations produced in a flat spacetime with small metric perturbations due to the quantum fluctuations of the matter field coupled to these perturbations.

Stochastic semiclassical cosmological models

We consider the classical stochastic fluctuations of spacetime geometry induced by quantum fluctuations of massless nonconformal matter fields in the early Universe. To this end, we supplement the stress-energy tensor of these fields with a stochastic part, which is computed along the lines of the Feynman-Vernon and Schwinger-Keldysh techniques; the Einstein equation is therefore upgraded to a so-called Einstein-Langevin equation. We consider in some detail the conformal fluctuations of flat spacetime and the fluctuations of the scale factor in a simple cosmological model introduced by Hartle, which consists of a spatially flat isotropic cosmology driven by radiation and dust.

Stochastic semiclassical gravity

In the first part of this paper, we show that the semiclassical Einstein-Langevin equation, introduced in the framework of a stochastic generalization of semiclassical gravity to describe the back reaction of matter stress-energy fluctuations, can be formally derived from a functional method based on the influence functional of Feynman and Vernon. In the second part, we derive a number of results for background solutions of semiclassical gravity consisting of stationary and conformally stationary spacetimes and scalar fields in thermal equilibrium states. For these cases, fluctuation-dissipation relations are derived. We also show that particle creation is related to the vacuum stress-energy fluctuations and that it is enhanced by the presence of stochastic metric fluctuations.

Stochastic semiclassical fluctuations in Minkowski spacetime

The semiclassical Einstein-Langevin equations which describe the dynamics of stochastic perturbations of the metric induced by quantum stress-energy fluctuations of matter fields in a given state are considered on the background of the ground state of semiclassical gravity, namely, Minkowski spacetime and a scalar field in its vacuum state. The relevant equations are explicitly derived for massless and massive fields arbitrarily coupled to the curvature. In doing so, some semiclassical results, such as the expectation value of the stress-energy tensor to linear order in the metric perturbations and particle creation effects, are obtained. We then solve the equations and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. In the conformal field case, explicit results are obtained. These results hint that gravitational fluctuations in stochastic semiclassical gravity have a non-perturbative behavior in some characteristic correlation lengths.

Species selectivity of mixed-lineage leukemia/trithorax and HCF proteolytic maturation pathways.

Site-specific proteolytic processing plays important roles in the regulation of cellular activities. The histone modification activity of the human trithorax group mixed-lineage leukemia (MLL) protein and the cell cycle regulatory activity of the cell proliferation factor herpes simplex virus host cell factor 1 (HCF-1) are stimulated by cleavage of precursors that generates stable heterodimeric complexes. MLL is processed by a protease called taspase 1, whereas the precise mechanisms of HCF-1 maturation are unclear, although they are known to depend on a series of sequence repeats called HCF-1(PRO) repeats. We demonstrate here that the Drosophila homologs of MLL and HCF-1, called Trithorax and dHCF, are both cleaved by Drosophila taspase 1. Although highly related, the human and Drosophila taspase 1 proteins display cognate species specificity. Thus, human taspase 1 preferentially cleaves MLL and Drosophila taspase 1 preferentially cleaves Trithorax, consistent with coevolution of taspase 1 and MLL/Trithorax proteins. HCF proteins display even greater species-specific divergence in processing: whereas dHCF is cleaved by the Drosophila taspase 1, human and mouse HCF-1 maturation is taspase 1 independent. Instead, human and Xenopus HCF-1PRO repeats are cleaved in vitro by a human proteolytic activity with novel properties. Thus, from insects to humans, HCF proteins have conserved proteolytic maturation but evolved different mechanisms.