Ballistic and diffusive corrections to front propagation in the presence of multiplicative noise

We study the dynamics of reaction-diffusion fronts under the influence of multiplicative noise. An approximate theoretical scheme is introduced to compute the velocity of the front and its diffusive wandering due to the presence of noise. The theoretical approach is based on a multiple scale analysis rather than on a small noise expansion and is confirmed with numerical simulations for a wide range of the noise intensity. We report on the possibility of noise sustained solutions with a continuum of possible velocities, in situations where only a single velocity is allowed without noise.

Propagation in a thermal graviton background

It is well known that radiative corrections evaluated in nontrivial backgrounds lead to effective dispersion relations which are not Lorentz invariant. Since gravitational interactions increase with energy, gravity-induced radiative corrections could be relevant for the trans-Planckian problem. As a first step to explore this possibility, we compute the one-loop radiative corrections to the self-energy of a scalar particle propagating in a thermal bath of gravitons in Minkowski spacetime. We obtain terms which originate from the thermal bath and which indeed break the Lorentz invariance that possessed the propagator in the vacuum. Rather unexpectedly, however, the terms which break Lorentz invariance vanish in the high three-momentum limit. We also found that the imaginary part, which gives the rate of approach to thermal equilibrium, vanishes at one loop.

Telegrapher's equation with variable propagation speeds

All derivations of the one-dimensional telegraphers equation, based on the persistent random walk model, assume a constant speed of signal propagation. We generalize here the model to allow for a variable propagation speed and study several limiting cases in detail. We also show the connections of this model with anomalous diffusion behavior and with inertial dichotomous processes.

In vivo T-lymphocyte tolerance in the absence of thymic clonal deletion mediated by hematopoietic cells.

Thymic negative selection renders the developing T-cell repertoire tolerant to self-major histocompatability complex (MHC)/peptide ligands. The major mechanism of induction of self-tolerance is thought to be thymic clonal deletion, ie, the induction of apoptotic cell death in thymocytes expressing a self-reactive T-cell receptor. Consistent with this hypothesis, in mice deficient in thymic clonal deletion mediated by cells of hematopoietic origin, a twofold to threefold increased generation of mature thymocytes has been observed. Here we describe the analysis of the specificity of T lymphocytes developing in the absence of clonal deletion mediated by hematopoietic cells. In vitro, targets expressing syngeneic MHC were readily lysed by activated CD8(+) T cells from deletion-deficient mice. However, proliferative responses of T cells from these mice on activation with syngeneic antigen presenting cells were rather poor. In vivo, deletion-deficient T cells were incapable of induction of lethal graft-versus-host disease in syngeneic hosts. These data indicate that in the absence of thymic deletion mediated by hematopoietic cells functional T-cell tolerance can be induced by nonhematopoietic cells in the thymus. Moreover, our results emphasize the redundancy in thymic negative selection mechanisms.

Front propagation in spatially modulated media

A two-dimensional reaction-diffusion front which propagates in a modulated medium is studied. The modulation consists of a spatial variation of the local front velocity in the transverse direction to that of the front propagation. We study analytically and numerically the final steady-state velocity and shape of the front, resulting from a nontrivial interplay between the local curvature effects and the global competition process between different maxima of the control parameter. The transient dynamics of the process is also studied numerically and analytically by means of singular perturbation techniques.

Self-organizing propagation patterns from dynamic self-assembly in monolayers

Propagation of localized orientational waves, as imaged by Brewster angle microscopy, is induced by low intensity linearly polarized light inside axisymmetric smectic-C confined domains in a photosensitive molecular thin film at the air/water interface (Langmuir monolayer). Results from numerical simulations of a model that couples photoreorientational effects and long-range elastic forces are presented. Differences are stressed between our scenario and the paradigmatic wave phenomena in excitable chemical media.

Metastability and front propagation in the first-order optical Fréedericksz transition

A general dynamical model for the first-order optical Fréedericksz transition incorporating spatial transverse inhomogeneities and hydrodynamic effects is discussed in the framework of a time-dependent Ginzburg-Landau model. The motion of an interface between two coexisting states with different director orientations is considered. A uniformly translating front solution of the dynamical equations for the motion of that interface is described.

Front propagation in the A+B->2A reaction under subdiffusion

We consider an irreversible autocatalytic conversion reaction A+B->2A under subdiffusion described by continuous-time random walks. The reactants transformations take place independently of their motion and are described by constant rates. The analog of this reaction in the case of normal diffusion is described by the Fisher-Kolmogorov-Petrovskii-Piskunov equation leading to the existence of a nonzero minimal front propagation velocity, which is really attained by the front in its stable motion. We show that for subdiffusion, this minimal propagation velocity is zero, which suggests propagation failure.

Enhanced pulse propagation in non-linear arrays of oscillators

The propagation of a pulse in a nonlinear array of oscillators is influenced by the nature of the array and by its coupling to a thermal environment. For example, in some arrays a pulse can be speeded up while in others a pulse can be slowed down by raising the temperature. We begin by showing that an energy pulse (one dimension) or energy front (two dimensions) travels more rapidly and remains more localized over greater distances in an isolated array (microcanonical) of hard springs than in a harmonic array or in a soft-springed array. Increasing the pulse amplitude causes it to speed up in a hard chain, leaves the pulse speed unchanged in a harmonic system, and slows down the pulse in a soft chain. Connection of each site to a thermal environment (canonical) affects these results very differently in each type of array. In a hard chain the dissipative forces slow down the pulse while raising the temperature speeds it up. In a soft chain the opposite occurs: the dissipative forces actually speed up the pulse, while raising the temperature slows it down. In a harmonic chain neither dissipation nor temperature changes affect the pulse speed. These and other results are explained on the basis of the frequency vs energy relations in the various arrays

Wave propagation in a medium with disordered excitability

The effect of quenched disorder on the propagation of autowaves in excitable media is studied both experimentally and numerically in relation to the light-sensitive Belousov-Zhabotinsky reaction. The spatial disorder is introduced through a random distribution with two different levels of transmittance. In one dimension the (time-averaged) wave speed is smaller than the corresponding to a homogeneous medium with the mean excitability. Contrarily, in two dimensions the velocity increases due to the roughening of the front. Results are interpreted using kinematic and scaling arguments. In particular, for d = 2 we verify a theoretical prediction of a power-law dependence for the relative change of the propagation speed on the disorder amplitude.

Regular wave propagation out of noise in chemical active media

A pacemaker, regularly emitting chemical waves, is created out of noise when an excitable photosensitive Belousov-Zhabotinsky medium, strictly unable to autonomously initiate autowaves, is forced with a spatiotemporal patterned random illumination. These experimental observations are also reproduced numerically by using a set of reaction-diffusion equations for an activator-inhibitor model, and further analytically interpreted in terms of genuine coupling effects arising from parametric fluctuations. Within the same framework we also address situations of noise-sustained propagation in subexcitable media.

External Fluctuations in Front Propagation

We study the effects of external noise in a one-dimensional model of front propagation. Noise is introduced through the fluctuations of a control parameter leading to a multiplicative stochastic partial differential equation. Analytical and numerical results for the front shape and velocity are presented. The linear-marginal-stability theory is found to increase its range of validity in the presence of external noise. As a consequence noise can stabilize fronts not allowed by the deterministic equation.

Self-organizing propagation patterns from dynamic self-assembly in monolayers

Propagation of localized orientational waves, as imaged by Brewster angle microscopy, is induced by low intensity linearly polarized light inside axisymmetric smectic-C confined domains in a photosensitive molecular thin film at the air/water interface (Langmuir monolayer). Results from numerical simulations of a model that couples photoreorientational effects and long-range elastic forces are presented. Differences are stressed between our scenario and the paradigmatic wave phenomena in excitable chemical media.

The ecological significance of arbuscular mycorrhizal fungal effects on clonal reproduction in plants

The population ecology of clonal plants depends on the number and distribution of ramets formed during growth. Variation in clonal reproduction has previously been explained by variation in effects of abiotic resource heterogeneity and by plant genotypic variation. Different co-occurring species of the mutualistic arbuscular mycorrhizal fungi (AMF) have been shown to differentially alter growth traits of Prunella vulgaris which we hypothesize would lead to changes in clonal reproduction. Two experiments were carried out to test whether different co-occurring mycorrhizal fungi significantly influence clonal reproduction of P. vulgaris whether this effect also occurs when P. vulgaris is growing in an artificial plant community and how the effects compare with plant genotype effects on clonal growth of P. vulgaris. In the first experiment the number of ramets of P. vulgaris growing in a plant community of simulated calcareous grassland was significantly affected by inoculation with different mycorrhizal fungi. The number of ramets produced by P. vulgaris differed by a factor of up to 1.8 with different mycorrhizal fungi. The fungal effects on the number of new ramets were independent of their effects on the biomass of P. vulgaris. In a second experiment 17 different genotypes of P. vulgaris were inoculated with different mycorrhizal fungi. There were significant main effects of genotypes and mycorrhizal fungi on clonal reproduction of P. vulgaris. The effect of different mycorrhizal fungi contributed more than the effect of plant genotype to variation in size and ramet production. However mean stolon length and spacer length which determine the spatial arrangement of ramets were only significantly affected by plant genotype. There were no mycorrhizal fungal X plant genotype interactions on clonal growth of P. vulgaris indicating that there is no obvious evidence that selection pressures would favor further coevolution between P. vulgaris and mycorrhizal fungal species. In natural communities plants can be colonized by several different AMF at the same time. The effect of the mixed AMF treatment on the growth and clonal reproduction of P. vulgaris could not be predicted from the responses of the plants to the single AMF To what extent however the patterns of colonization by different AMF differ among plants in a natural community is unknown. Since the effects of AMF on growth and clonal reproduction occur on a population of P. vulgaris in a microcosm plant community and because the effects are also as great as those caused by plant genotypic variation we conclude that the effects are strong enough to potentially affect population size and variation of clonal plants in communities.