A Two-Step Model of Human Entrainment: A Quantitative Study of Circadian Period and Phase of Entrainment.

One of the essential characteristics of an authentic circadian clock is that the free-running period sustains an approximately 24-hour cycle. When organisms are exposed to an external stimulus, the endogenous oscillators synchronize to the cycling environment signal in a process known as entrainment. These environmental cues perform an important role in resetting the phase and period of the circadian clock. A "generalized assumption" states that when an organism has a short period, it will experience a phase advance, while an organism with a long period experiences a phase delay. Despite widespread use, this positive relationship relating period to the phase of entrainment does not describe all known experimental data. We developed a two-step entrainment model to explain a broader range of results as well as provide more quantitative analysis. We prove existence and stability of periodic orbits and given analytical solutions of the range of entrainment, fit the phase trajectory over the entire entrainment process to data from a published study for 12 subjects in extended day cycles, i.e., longer than 24 h. Our simulations closely replicated the phase data and predicted correctly the phase of entrainment. We investigate the factors related to the rate of entrainment (ROE) and present the three-dimensional parameter spaces, illustrating the various behaviors of the phase of entrainment and ROE. Our findings can be applied to diagnostics and treatments for patients with sleep disorders caused by shift work or jet lag.

Modeling Tree Growth Taking into Account Carbon Source and Sink Limitations.

Increasing CO2 concentrations are strongly controlled by the behavior of established forests, which are believed to be a major current sink of atmospheric CO2. There are many models which predict forest responses to environmental changes but they are almost exclusively carbon source (i.e., photosynthesis) driven. Here we present a model for an individual tree that takes into account the intrinsic limits of meristems and cellular growth rates, as well as control mechanisms within the tree that influence its diameter and height growth over time. This new framework is built on process-based understanding combined with differential equations solved by numerical method. Our aim is to construct a model framework of tree growth for replacing current formulations in Dynamic Global Vegetation Models, and so address the issue of the terrestrial carbon sink. Our approach was successfully tested for stands of beech trees in two different sites representing part of a long-term forest yield experiment in Germany. This model provides new insights into tree growth and limits to tree height, and addresses limitations of previous models with respect to sink-limited growth.

Lateral chirality-sorting optical forces.

The transverse component of the spin angular momentum of evanescent waves gives rise to lateral optical forces on chiral particles, which have the unusual property of acting in a direction in which there is neither a field gradient nor wave propagation. Because their direction and strength depends on the chiral polarizability of the particle, they act as chirality-sorting and may offer a mechanism for passive chirality spectroscopy. The absolute strength of the forces also substantially exceeds that of other recently predicted sideways optical forces.