Importance Of Stochastic Effects Research Articles

The role of impacts on the atmospheres on the moons of outer giants

ABSTRACTWe investigate the comparative effect of impacts by trans-Neptunian Objects on the atmospheres of the moons Ganymede, Callisto, Europa, and Titan. We derive an analytic prescription for the ‘stalling mass’ (i.e. the atmosphere mass at which equilibrium between erosion and volatile delivery occurs), which is tested against a numerical model, demonstrating that the behaviour of the atmosphere matches the analytic prediction, albeit with stochastic events causing orders of magnitude variability. We find that bombardment, neglecting other effects, predicts atmosphere erosion on Ganymede, Callisto, and Europa leading to masses in quantitative agreement with the observed atmospheres. The predicted masses are relatively insensitive to the impactor size and velocity distributions, but sensitive to impactor density and volatile content. Crucially, we find that in this model the frequent arrival of 1–20 km-sized objects sets the quiescent atmosphere masses of the different moons, with atmospheres returning to these levels on ∼100 Myr time-scales at current bombardment levels, and larger impactors causing stochastic excursions to larger atmosphere masses. This quiescent level is higher on Titan than the Jovian moons due to the typically slower impact velocities, but to recreate Titan’s massive current atmosphere an additional volatiles contribution is needed, which may be provided by impact-triggered outgassing. If so, the predicted mass is then dependent on the outgassing efficiency and the volatile mass contained in the crust, both of which are uncertain. This work highlights the role that impacts may have played in shaping the atmosphere evolution of outer Solar system moons, and the importance of stochastic effects.

Some Dynamic Aspects of Hematopoietic Stem Cells

Hematopoiesis is the process responsible for maintaining the number of circulating blood cells that are undergoing continuous turnover. At the root of this process are the hematopoietic stem cells (HSC). In the following we discuss various dynamic aspects of HSC behavior ranging from the number of active stem cells, their expansion during ontogeny and the importance of stochastic effects on their behavior. We show how mathematical modeling of HSC behavior can provide important insights on these cells and clarify the implications of these dynamical aspects on healthy and sick individuals, as such providing rational explanations for relevant clinical observations on disorders that originate in this group of cells.

SEEDLING SURVIVAL AND GROWTH OF THREE FOREST TREE SPECIES: THE ROLE OF SPATIAL HETEROGENEITY

Spatial heterogeneity in microenvironments may provide unique regeneration niches for trees and may promote forest diversity. We examined how heterogeneity in understory cover, mineral nutrients, and moisture and their interactions with canopy gaps contribute to the coexistence of three common, co-occuring tree species. We measured survival and height growth of 1080 seedlings of Acer rubrum (red maple), Liriodendron tulipifera (yellow poplar), and Quercus rubra (red oak) that were planted in one of five understory treatments: removal of understory vegetation, trenched, trenched plus removal of understory vegetation, fertilization, and a control. Understory treatments were replicated in 12 paired gap and canopy environments. Survivorship varied among species, with Q. rubra having the highest probability of surviving beyond the 1135-day experiment (probability = 0.64), followed by A. rubrum (probability = 0.27) and L. tulipifera (probability = 0.07). Although canopy gaps and understory treatments had large effects on survivorship, species survival rankings changed little across microenvironments; Q. rubra had the highest survival in all microenvironments. In contrast to survival, L. tulipifera had a relative growth rate for height that was three times greater than that of A. rubrum and Q. rubra in high-resource microenvironments. There was broad overlap among species in relative growth rates in the remaining seven microenvironments, with no clear top-ranked species. Differences in seedling growth and survival across these 10 microenvironments may contribute to the coexistence of two of the three species studied, L. tulipifera and Q. rubra, but not A. rubrum. Q. rubra had higher survival than A. rubrum and L. tulipifera in all microenvironments, but L. tulipifera tended to grow faster than A. rubrum and Q. rubra in high-resource microenvironments. Despite the generally poor performance of A. rubrum, it was the only surviving species in some quadrats at the end of the experiment, indicating that stochastic effects, in conjunction with broad niche overlap, may also contribute to species coexistence. The importance of stochastic effects will probably increase when differential fecundity across these three species is considered because the high fecundity of A. rubrum offsets survival and growth disadvantages of its seedlings through their greater total abundance.

Stochastic influences on pattern formation in Rayleigh-Bénard convection: Ramping experiments.

We report on computer-enhanced shadowgraph flow-visualization and heat-flux measurements of pattern formation in convective flows in a thin fluid layer of depth {ital d} that is heated from below. Most of the experiments were conducted in a cylindrical container of radius {ital r} and aspect ratio {Gamma}=={ital r}/{ital d}=10. The temperature of the top plate of the container was held constant while the heat current through the fluid was linearly ramped in time, resulting in a temperature difference {Delta}{ital T} between the bottom and top plates. After initial transients ended, the reduced Rayleigh number {epsilon}=={Delta}{ital T}/{Delta}{ital T}{sub {ital c}}{minus}1, where {Delta}{ital T}{sub {ital c}} is the critical temperature difference for the onset of convection, increased linearly with ramp rate {beta} such that {epsilon}({ital t})={beta}{ital t}. When time was scaled by the vertical thermal diffusion time, our ramp rates were in the range 0.01{le}{beta}{le}0.30. When the sidewalls of the cell were made of conventional plastic materials, a concentric pattern of convection rolls was always induced by dynamic sidewall forcing. When sidewalls were made of a gel that had virtually the same thermal diffusivity as the fluid, pattern formation occurred independent of cell geometry. In the earliest stages the patterns were thenmore » composed of irregularly arranged cells and varied randomly between experimental runs. The same random cellular flow was also observed in samples of square horizontal cross section. The results demonstrate the importance of stochastic effects on pattern formation in this system. However, an explanation of the measured convective heat current in terms of theoretical models requires that the noise source in these models have an intensity that is four orders of magnitude larger than that of thermal noise.« less