A mitotic oscillator with one slowly increasing variable (tau L of the order of hours) and one rapidly increasing variable (tau R of the order of minutes) modulated by a timer (ultradian clock) gives an auto-oscillating solution: cells divide when this relaxation oscillator reaches a critical threshold to initiate a rapid phase of the limit cycle. Increasing values of the velocity constant in t...

We present here a general model for integrase family site-specific recombination using the geometric relationships of the cleavable phosphodiester bonds and the disposition of the recombinase monomers (defined by their binding planes) with respect to them. The 'oscillation model' is based largely on the conformations of the recombinase-bound DNA duplexes and their dynamics within Holliday junct...

Scroll waves are three-dimensional excitation patterns that rotate around a central filament curve; they occur in many physical, biological, and chemical systems. We explicitly derive the equations of motion for scroll wave filaments in reaction-diffusion systems with isotropic diffusion up to third order in the filament's twist and curvature. The net drift components define at every instance o...

When a chemical reaction is driven by an external field, the transition state that the system must pass through as it changes from reactant to product--for example, an energy barrier--becomes time-dependent. We show that for periodic forcing the rate of barrier crossing can be determined through stability analysis of the non-autonomous transition state. Specifically, strong agreement is observe...

The Lotka-Volterra (LV) model of oscillating chemical reactions, characterized by the rate equations has been an active area of research since it was originally posed in the 1920s. In this Review, we present a simple transformation which reduces the two-dimensional LV system to a one-dimensional system modeled by a second-order nonlinear autonomous ordinary differential equation. The formal ana...

Delayed feedback plays a key role in most, if not all chemical oscillators. We derive general results useful in the linear stability analysis of models that explicitly incorporate delay by using differential delay equations. Two models of nonlinear chemical oscillators, the cross-shaped phase diagram model of Boissonade and De Kepper and the Oregonator, are modified by deleting a feedback speci...

Context. This is the first step in a project to combine studies of eclipsing binaries and oscillating stars to probe the interior of Blue Stragglers (BS). This may imply a way to discriminate observationally between different birth mechanisms of BS stars. Aims. We study the open cluster NGC2506 which contains oscillating BS stars and detached eclipsing binaries for which accurate parameters can...

In the previous papers, the idea of “hidden oscillations” has been applied to explain work generation in semiconductor photovoltaic cells and thermoelectric generators. The aim of this paper is firstly to extend this approach to fuel cells and, secondly, to create a unified quantum model for all types of such devices. They are treated as electron pumps powered by heat or chemical engines. The w...