Asymptotic behaviour of two-dimensional time-delayed Navier-Stokes equations

We consider the two-dimensional Navier-Stokes equations with a time-delayed convective term and a forcing term which contains some hereditary features. Some results on existence and uniqueness of solutions are established. We discuss the asymptotic behaviour of solutions and we also show the exponential stability of stationary solutions.

Time-delayed reaction-diffusion fronts

A time-delayed second-order approximation for the front speed in reaction-dispersion systems was obtained by Fort and Méndez [Phys. Rev. Lett. 82, 867 (1999)]. Here we show that taking proper care of the effect of the time delay on the reactive process yields a different evolution equation and, therefore, an alternate equation for the front speed. We apply the new equation to the Neolithic transition. For this application the new equation yields speeds about 10% slower than the previous one

Time-Delayed Theory of the Neolithic Transition in Europe

The classical wave-of-advance model of the neolithic transition (i.e., the shift from hunter-gatherer to agricultural economies) is based on Fisher's reaction-diffusion equation. Here we present an extension of Einstein's approach to Fickian diffusion, incorporating reaction terms. On this basis we show that second-order terms in the reaction-diffusion equation, which have been neglected up to now, are not in fact negligible but can lead to important corrections. The resulting time-delayed model agrees quite well with observations

Time-delayed fronts from biased random walks

We generalize a previous model of time-delayed reaction–diffusion fronts (Fort and Méndez 1999 Phys. Rev. Lett. 82 867) to allow for a bias in the microscopic random walk of particles or individuals. We also present a second model which takes the time order of events (diffusion and reproduction) into account. As an example, we apply them to the human invasion front across the USA in the 19th century. The corrections relative to the previous model are substantial. Our results are relevant to physical and biological systems with anisotropic fronts, including particle diffusion in disordered lattices, population invasions, the spread of epidemics, etc

A matter of time: delayed mate encounter postpones mating window initiation and reduces the strength of female choosiness

Reproductive success is determined by the presence and timing of encounter of mates. The latter depends on species-specific reproductive characteristics (e.g. initiation/duration of the mating window), season, and reproductive strategies (e.g. intensity of choosiness) that may potentially mitigate constraints imposed by mating windows. Despite their potentially crucial role for fitness and population dynamics, limited evidence exists about mating window initiation, duration and reproductive strategies. Here, we experimentally tested the mechanisms of initiation and the duration of the common lizard's Zootoca vivipara mating window, by manipulating the timing of mate encounter and analyzing its effect on (re-)mating probability. We furthermore tested treatment effects on female reproductive strategies, by measuring female choosiness. The timing of mate encounter and season did not significantly affect mating probability. However, a longer delay until mate encounter reduced female choosiness. Re-mating probability decreased with re-mating delay and was independent of mating delay. This indicates that mating window initiation depends on mate encounter, that its duration is fixed, and that plastic reproductive strategies exist. These findings contrast with previous beliefs and shows that mating windows per se may not necessarily constrain reproductive success, which is congruent with rapid range expansion and absence of positive density-effects on reproductive success (Allee effects). In summary, our results show that predicting the effect of mating windows on reproduction is complex and that experimental evidence is essential for evaluating their effect on reproduction and reproductive strategies, both being important determinants of population dynamics and the colonization of new habitats.

Spontaneous cell polarization: Feedback control of Cdc42 GTPase breaks cellular symmetry.

Spontaneous polarization without spatial cues, or symmetry breaking, is a fundamental problem of spatial organization in biological systems. This question has been extensively studied using yeast models, which revealed the central role of the small GTPase switch Cdc42. Active Cdc42-GTP forms a coherent patch at the cell cortex, thought to result from amplification of a small initial stochastic inhomogeneity through positive feedback mechanisms, which induces cell polarization. Here, I review and discuss the mechanisms of Cdc42 activity self-amplification and dynamic turnover. A robust Cdc42 patch is formed through the combined effects of Cdc42 activity promoting its own activation and active Cdc42-GTP displaying reduced membrane detachment and lateral diffusion compared to inactive Cdc42-GDP. I argue the role of the actin cytoskeleton in symmetry breaking is not primarily to transport Cdc42 to the active site. Finally, negative feedback and competition mechanisms serve to control the number of polarization sites.

Time-Delayed Spread of Viruses in Growing Plaques

The spread of viruses in growing plaques predicted by classical models is greater than that measured experimentally. There is a widespread belief that this discrepancy is due to biological factors. Here we show that the observed speeds can be satisfactorily predicted by a purely physical model that takes into account the delay time due to virus reproduction inside infected cells. No free or adjustable parameters are used

Fungicides, seed dresser adjuvants and storage time in the control of Drechslera teres in barley seeds

In experiments conducted in laboratory, the effect of fungicides, seed dresser adjuvants and storage time in the control of Drechslera teres in seeds of barley cultivar BRS Elis, with 58% incidence, was quantified. Fungicides indicated by barley research (carboxin + thiram, difenoconazole and triadimenol) compared with the mixture carbendazim + iprodione were tested. As seed dresser adjuvants, water (500m mL/100 Kg) and a polymer (150 mL/100 Kg) were used. Treated seeds were stored in paper bags and kept in the refrigerator at 5ºC. At 30-day intervals during six months, seeds were plated on semi-selective Reis's medium (1983). The best control was obtained by the mixtures carboxin + thiram and carbendazim + iprodione and the polymer as seed dresser. The control efficiency was improved by the storage time without negatively affecting seed germination. Due to the transmission efficiency, the fungus eradication in seeds should be pursued.

Performance characteristics of positive and negative delayed feedback on chaotic dynamics of directly modulated InGaAsP semiconductor lasers

The chaotic dynamics of directly modulated semiconductor lasers with delayed optoelectronic feedback is studied numerically. The effects of positive and negative delayed optoelectronic feedback in producing chaotic outputs from such lasers with nonlinear gain reduction in its optimum value range is investigated using bifurcation diagrams. The results are confirmed by calculating the Lyapunov exponents. A negative delayed optoelectronic feedback configuration is found to be more effective in inducing chaotic dynamics to such systems with nonlinear gain reduction factor in the practical value range.

Time-delayed fronts from biased random walks

We generalize a previous model of time-delayed reaction–diffusion fronts (Fort and Méndez 1999 Phys. Rev. Lett. 82 867) to allow for a bias in the microscopic random walk of particles or individuals. We also present a second model which takes the time order of events (diffusion and reproduction) into account. As an example, we apply them to the human invasion front across the USA in the 19th century. The corrections relative to the previous model are substantial. Our results are relevant to physical and biological systems with anisotropic fronts, including particle diffusion in disordered lattices, population invasions, the spread of epidemics, etc