Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

Dynamics of Fréedericksz transition in a fluctuating magnetic field

Fréedericksz transition under twist deformation in a nematic layer is discussed when the magnetic field has a random component. A dynamical model which includes the thermal fluctuations of the system is presented. The randomness of the field produces a shift of the instability point. Beyond this instability point the time constant characteristic of the approach to the stationary stable state decreases because of the field fluctuations. The opposite happens for fields smaller than the critical one. The decay time of an unstable state, calculated as a mean first-passage time, is also decreased by the field fluctuations.

Excitability transitions and wave dynamics under spatiotemporal structured noise

We present an analytic and numerical study of the effects of external fluctuations in active media. Our analytical methodology transforms the initial stochastic partial differential equations into an effective set of deterministic reaction-diffusion equations. As a result we are able to explain and make quantitative predictions on the systematic and constructive effects of the noise, for example, target patterns created out of noise and traveling or spiral waves sustained by noise. Our study includes the case of realistic noises with temporal and spatial structures.

Noise-enhanced excitability in bistable activator-inhibitor media

We show that external fluctuations induce excitable behavior in a bistable spatially extended system with activator-inhibitor dynamics of the FitzHugh-Nagumo type. This can be understood as a mechanism for sustained signal propagation in bistable media. The phase diagram of the stochastic system is analytically obtained and numerically verified. For small-noise intensities, front propagation becomes unstable, and excitable pulses arise as the only possible spatiotemporal behavior of the system. For large-noise intensities, on the other hand, the system enters an effective regime of oscillatory behavior, where it exhibits spontaneous nucleation of pulses and synchronized firing.

Noise-induced Brownian motion of spiral waves

We study the erratic displacement of spiral waves forced to move in a medium with random spatiotemporal excitability. Analytical work and numerical simulations are performed in relation to a kinematic scheme, assumed to describe the autowave dynamics for weakly excitable systems. Under such an approach, the Brownian character of this motion is proved and the corresponding dispersion coefficient is evaluated. This quantity shows a nontrivial dependence on the temporal and spatial correlation parameters of the external fluctuations. In particular, a resonantlike behavior is neatly evidenced in terms of the noise correlation time for the particular situation of spatially uniform fluctuations. Actually, this case turns out to be, to a large extent, exactly solvable, whereas a pair of dispersion mechanisms are discussed qualitatively and quantitatively to explain the results for the more general scenario of spatiotemporal disorder.

Multiplicative noise effects on relaxations from marginal states

Relaxational processes in bistable potentials close to marginal conditions are studied under the combined effect of additive and multiplicative fluctuations. Characteristic time scales associated with the first-passage-time-distribution are analytically obtained. Multiplicative noise introduces large effects on the characteristic decay times, which is particularly significant when relaxations are mediated by fluctuations, i.e., below marginality and for small noise intensity. The relevance of our approach with respect to realistic chemical bistable systems experimentally operated under external noise influences is mentioned.

Morphology and segregation in two-component diffusion-limited aggregation

A diffusion-limited-aggregation (DLA) model with two components (A and B species) is presented to investigate the structure of the composite deposits. The sticking probability PAB (=PBA) between the different species is introduced into the original DLA model. By using computer simulation it is shown that various patterns are produced with varying the sticking probabilities PAB (=PBA) and PAA (= PBB), where PAA (=PBB) is the sticking probability between the same species. Segregated patterns can be analyzed under the condition PAB < PAA, assumed throughout the paper. With decreasing sticking probability PAB, a clustering of the same species occurs. With sufficiently small values of both sticking probabilities PAB and PAA, the deposit becomes dense and the segregated patterns of the composite deposit show a striped structure. The effect of the concentration on the pattern morphology is also shown.

Dynamics of transient pattern formation in nematic liquid crystals

We analyze the dynamics of a transient pattern formation in the Fréedericksz transition corresponding to a twist geometry. We present a calculation of the time-dependent structure factor based on a dynamical model which incorporates consistently the coupling of the director field with the velocity flow and also the effect of fluctuations. The appearance and development of a characteristic periodicity is described in terms of the time dependence of the maximum of the structure factor. We find a well-defined time for the appearance of the pattern and a subsequent stage of pattern development in which the characteristic periodicity tends to an asymptotic value.

Fréedericksz transition in a periodic magnetic field

We study the Fréedericksz transition in a twist geometry under the effect of a periodic modulation of the magnitude of the applied magnetic field. We find a shift of the effective instability point and a time-periodic state with anomalously large orientational fluctuations. This time-periodic state occurs below threshold and it is accompanied by a dynamically stabilized spatial pattern. Beyond the instability the emergence of a transient pattern can be significantly delayed by a fast modulation, allowing the observation of pattern selection by slowing down the reorientational dynamics.

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.

Weakening processes in thrust faults: insights from the Monte Perdido thrust fault (southern Pyrenees, Spain)

The Monte Perdido thrust fault (southern Pyrenees) consists of a 6-m-thick interval of intensely deformed clay-bearing rocks. The fault zone is affected by a pervasive pressure solution seam and numerous shear surfaces. Calcite extensional-shear veins are present along the shear surfaces. The angular relationships between the two structures indicate that shear surfaces developed at a high angle (70°) to the local principal maximum stress axis r1. Two main stages of deformation are present. The first stage corresponds to the development of calcite shear veins by a combination of shear surface reactivation and extensional mode I rupture. The second stage of deformation corresponds to chlorite precipitation along the previously reactivated shear surfaces. The pore fluid factor k computed for the two deformation episodes indicates high fluid pressures during the Monte Perdido thrust activity. During the first stage of deformation, the reactivation of the shear surface was facilitated by a suprahydrostatic fluid pressure with a pore fluid factor kv equal to 0.89. For the second stage, the fluid pressure remained still high (with a k value ranging between 0.77 and 0.84) even with the presence of weak chlorite along the shear surfaces. Furthermore, evidence of hydrostatic fluid pressure during calcite cement precipitation supports that incremental shear surface reactivations are correlated with cyclic fluid pressure fluctuations consis- tent with a fault-valve model.

Shallow-platform palaeoenvironmental conditions recorded in deep-shelf sediments: C and stable isotopes in Upper Jurassic sections of southern Germany (Oxfordian-Kimmeridgian)

A high-resolution carbon and oxygen isotope analysis of Late Oxfordian-Early Kimmeridgian deep-shelf sediments of southern Germany is combined with investigation of nannofossil assemblage composition and sedimentological interpretations in order to evaluate the impact of regional palaeoenvironmental conditions on isotopic composition of carbonates. This study suggests that carbonate mud was essentially derived from the Jura shallow platform environments and also that the isotopic signature of carbonates deposited in the Swabian Alb deep shelf indirectly expresses the palaeoenvironmental evolution of the platform. Short-term fluctuations in delta(13) C and delta(18)O are probably controlled by changes in salinity (fresh-water input versus evaporation) in platform environments. Long-term fluctuations in carbon and oxygen isotope record throughout the Late Oxfordian-Early Kimmeridgian result from the interplay of increasing temperature and decreasing humidity, which both control the trophic level. Changes from mesotrophic to oligotrophic conditions in platform environments and in the deep-shelf surface waters are inferred. During the Late Oxfordian (Bimammatum Subzone to Planula Zone), the delta(13)C curve displays a positive shift of about 1 parts per thousand, which is comparable in intensity to global perturbations of the carbon cycle. This evident isotopic shift has not been documented yet in other basinal settings. It can be reasonably explained by local palaeoenvironmental changes on the Jura platform (salinity, temperature, and nutrient availability) that controlled platform carbonate production, and the geochemistry of overlying waters. However, increasing carbonate production on the Jura platform and related positive delta(13)C shifts recorded in the Swabian Alb deep shelf are the regional signatures of climatic changes affecting other palaeogeographical domains of Europe in which the carbonate production increased throughout the Late Oxfordian. (C) 2002 Elsevier Science B.V. All rights reserved.

Seasonal patterns op biomass variation of Ruppia cirrhosa (Petagna) Grande and Potamageton pectinatus L. in a coastal logoon

Coastal lagoons where salinity varies within a wide range during the year are colonized by euryhaline macrophytes which can develop extensive beds. Seasonal changes in biomass of Ruppia cirrhosa and Potamogeton pectinatus were studied in Tancada Lagoon (Ebro Delta, NE Spain) in order to reveal the environmental factors controlling their population development. Ruppia cirrhosa occupy a larger area of the lagoon than Potarnogeton pectinatus. Their maximum above ground biomasses are also different (495 g m-2 and 351 g m-2 ash free dry weight, respectively). Below ground biomass of Ruppia cirrhosa is between 9 and 53 % of the above ground biomass, while it is 3-40 % for Potamogeton pectinatus. Chlorophyll a contents show fluctuations similar to biomass. Low salinity and high turbidity caused by freshwater inflows favour Potamogeton expansion, while Ruppia development is favoured by high salinity and transparent water.

The adaptive function of melanin-based coloration in the tawny owl (Strix aluco) ; the proximate role of the melanocortin system

Colour polymorphism is common in wild population. One of the main questioning of evolutionary biologists is to understand how different colour variants could have evolved and be maintained in fluctuating environments, a selective process that forces individuals to constantly adapt their strategies in order to survive. This issue is particularly true for traits that are genetically inherited. Natural selection erodes genotypes with lowest fitness (less adapted), reducing in turn global genetic variation within population. In this context, the study of the evolution and maintenance of melanin- based coloration is relevant since inter-individual variation in the deposition of these pigments is common in animal and plant kingdoms and is under strong genetic control. In this thesis, I focus on the specific case of the tawny owl (Strix aluco), a species displaying continuous variation in reddish pheomelanin-based coloration. Interestingly, empirical studies highlighted covariations between melanin-based coloration and important behavioural, physiological and life history traits. Recently, a genetic model pointed out the melanocortin system and their pleiotropic effects as a potential regulator of these covariations. Accordingly, this PhD thesis further investigates colour-specific behavioural, physiological, or life history strategies, while examining the proximate mechanisms underlying these reaction norms. We found that differently coloured tawny owls differently resolve fundamental trade-off between offspring number and quality (Chapter 1), light melanic individuals producing many low- quality offspring and dark, melanic ones producing few high-quality offspring. These reproductive strategies are likely to induce alternative physiological constraints. Indeed, we demonstrated that light melanic individuals produced higher levels of reactive oxygen species (ROS, Chapter 2), but also expressed higher levels of antioxidant (GSH, Chapters 2 & 3). Interestingly, we showed that light melanic breeding females could modulate their POMC prohormone levels according to the environmental conditions, while dark reddish ones produced constant levels of this prohormone {Chapter 4). Finally, we highlighted colour-specific patterns of prohormone convertase 1 (PCI) gene expression (Chapter 5), an enzyme responsible for POMC prohormone processing to ACTH and a- MSH, for instance. Altogether, these results provide strong evidence of colour-specific strategies, light and melanic tawny owls better coping with stressful and relaxed environments, respectively. Variation in melanin-based coloration is likely to be maintained by the heterogeneity of our study area and strong environmental stochasticity within and between years, these process favouring differently coloured tawny owls at different periods of time. From a proximate point of view, this PhD thesis supports the hypothesis that covariations between phenotypic traits and melanin-based coloration stems from the melanocortin system, especially the fundamental role of POMC gene expression and its processing to melanocortin peptides. - Le polymorphisme de couleur est une variation phénotypique très fréquente dans la nature. En biologie évolutive, une des problématiques clés est donc de comprendre comment différent morphes de couleur peuvent être apparus et maintenus au cours du temps dans des environnements aussi variables que les nôtres, surtout que ces fluctuations forcent ces morphes à s'adapter constamment pour assurer leur survie. Cette thématique est particulièrement réelle lorsque les variations phénotypiques sont héréditaires et donc sous forte influence génétique. La sélection naturelle a en effet le pouvoir d'éroder rapidement la variation génétique en éliminant les génotypes mal adaptés. Dans ce sens, l'étude de l'évolution, et de la maintenance de la coloration mélanique est donc tout à fait pertinente car la variation de coloration entre individus est très répandue à travers les règnes animal et végétal et sous forte influence génétique. Dans cette thèse, je me suis concentré sur le cas spécifique de la chouette hulotte (Strix aluco), une espèce présentant une variation continue dans la déposition de pigments pheomélaniques roux. De précédentes études ont déjà montré que cette variation de coloration était associée avec des variations de traits comportementaux, physiologiques ou d'histoire de vie. Récemment, une étude a souligné l'importance du système des mélanocortines et de leurs effets pléiotropes dans la régulation de ces covariations. En conséquence, cette thèse de doctoral a pour but d'étudier un peu plus les stratégies comportementales, physiologiques ou d'histoire de vie spécifiques à chaque morphe de couleur, tout en examinant un peu plus les mécanismes proximaux potentiellement à la base de ces normes de réactions. Nous constatons tout d'abord que les morphes de couleurs étaient associés à différentes stratégies dans la résolution de compromis telle que la production de beaucoup de jeunes ou des jeunes de qualité (Chapitre 1). Les morphes gris (dit peu mélaniques) ont tendance à produire beaucoup de jeunes mains de moindre qualité, alors que les morphes roux (dit fortement mélaniques) produisent moins de jeunes mais de meilleure qualité. Ces stratégies sont susceptibles alors d'induire certaines contraintes physiologiques. Par exemple, nous montrons que les morphes gris produisent plus de dérivés réactifs de l'oxygène (ROS, Chapitre 2), mais aussi plus d'antioxydants (GSH, Chapitres 2 & 3). Nous montrons ensuite que les femelles grises ont une plus grande capacité à moduler leur niveau de POMC prohormone dans le sang en fonction des conditions environnementales, alors que les femelles rousses gardent un niveau constant (Chapitre 4). Finalement, nous démontrons que les patterns d'expression du gène codant pour la prohormone convertase 1 varient chez des jeunes issus de parents gris ou roux (Chapitre 5). Ceci est particulièrement intéressant car cette enzyme permet de scinder la POMC prohormone en plusieurs peptides importants tels que l'ACTH ou l'a-MSH. En conclusion, ces résultats démontrent qu'il y a bel et bien des stratégies évolutives différentes entre les morphes de couleurs, les chouettes hulottes grises et rousses étant respectivement plus adaptés à des environnements stressants ou favorables. L'hétérogénéité de notre zone d'étude et la stochasticité environnementale qui caractérise ses habitats pourraient donc agir comme une source de sélection temporelle, laquelle favoriserait les différents morphes de couleurs à diverses périodes. D'un point de vue plus proximale maintenant, cette thèse de doctorat soutient l'hypothèse que les covariations observées entre la coloration mélanique et des traits phénotypiques importants sont modulées par les effets pléiotropes du système des mélanocortines, et met en avant le rôle prépondérant que pourrait jouer l'expression du gène POMC et sa post traduction en mélanocortines.