Dynamics of a linearly-perturbed May-Leonard competition model

The May--Leonard model was introduced to examine the behavior of three competing populations where rich dynamics, such as limit cycles and nonperiodic cyclic solutions, arise. In this work, we perturb the system by adding the capability of global mutations, allowing one species to evolve to the other two in a linear manner. We find that for small mutation rates the perturbed system not only retains some of the dynamics seen in the classical model, such as the three-species equal-population equilibrium bifurcating to a limit cycle, but also exhibits new behavior. For instance, we capture curves of fold bifurcations where pairs of equilibria emerge and then coalesce. As a result, we uncover parameter regimes with new types of stable fixed points that are distinct from the single- and dual-population equilibria characteristic of the original model. In short, a linear perturbation proves to be not at all trivial, with the modified system exhibiting new behavior captured even with small mutation rates.Comment: 29 pages, 12 figure

Econobiophysics - game of choosing. Model of selection or election process with diverse accessible information

We propose several models applicable to both selection and election processes when each selecting or electing subject has access to different information about the objects to choose from. We wrote special software to simulate these processes. We consider both the cases when the environment is neutral (natural process) as well as when the environment is involved (controlled process)

Collective cell migration in single and dual cell layers

Collective cell migration plays a substantial role in maintaining the cohesion of epithelial cell layers, in wound healing, and in embryonic development. We extend a previously developed one-dimensional continuum mechanical model of cell layer migration based on an assumption of elastic deformation of the cell layer to incorporate stretch-dependent proliferation, which leads to a generalized Stefan problem for the density of the layer. The resulting partial differential equation system is solved numerically using an adaptive finite difference method and similarity solutions are studied analytically. We show the existence of traveling wave solutions with constant wave speed for a large class of constitutive equations for the dependence of proliferation on stretch. We then extend the corresponding two-dimensional model of cell migration to incorporate two adhering cell layers. A numerical method to solve the model equations is based on a level set method for free boundary problems with a domain decomposition method to account for where the migrating cells in each layer are located. We apply the model to experimental migration of epithelial and mesenchymal cell layers during gastrulation, an early phase of development, in animal cap explants of Xenopus laevis embryos to analyze the mechanical properties of each cell layer. Understanding the mechanics of collective cell migration during embryonic development will aid in developing tools to perturb pathological cases such as during wound healing and to aid in the prediction and early detection of birth defects

Developing a gas rocket performance prediction technique

A simple, semi-empirical performance correlation/prediction technique applicable to gaseous and liquid propellant rocket engines is presented. Excellent correlations were attained for over 100 test firings by adjusting the computation of the gaseous mixing of an unreactive, coaxial jet using a correlation factor, F, which resulted in prediction of the experimental combustion efficiency for each firing. Static pressure, mean velocity and turbulence intensity in the developing region of non-reactive coaxial jets, typical of those of coaxial injector elements were determined. Detailed profiles were obtained at twelve axial locations (extending from the nozzle exit for a distance of five diameters) downstream from a single element of the Bell Aerospace H2/O2 19-element coaxial injector. These data are compared with analytical predictions made using both eddy viscosity and turbulence kinetic energy mixing models and available computer codes. Comparisons were disappointing, demonstrating the necessity of developing improved turbulence models and computational techniques before detailed predictions of practical coaxial free jet flows are attempted

Four ultra-short period eclipsing M-dwarf binaries in the WFCAM Transit Survey

We report on the discovery of four ultra-short period (P<0.18 days) eclipsing M-dwarf binaries in the WFCAM Transit Survey. Their orbital periods are significantly shorter than of any other known main-sequence binary system, and are all significantly below the sharp period cut-off at P~0.22 days as seen in binaries of earlier type stars. The shortest-period binary consists of two M4 type stars in a P=0.112 day orbit. The binaries are discovered as part of an extensive search for short-period eclipsing systems in over 260,000 stellar lightcurves, including over 10,000 M-dwarfs down to J=18 mag, yielding 25 binaries with P<0.23 days. In a popular paradigm, the evolution of short period binaries of cool main-sequence stars is driven by loss of angular momentum through magnetised winds. In this scheme, the observed P~0.22 day period cut-off is explained as being due to timescales that are too long for lower-mass binaries to decay into tighter orbits. Our discovery of low-mass binaries with significantly shorter orbits implies that either these timescales have been overestimated for M-dwarfs, e.g. due to a higher effective magnetic activity, or that the mechanism for forming these tight M-dwarf binaries is different from that of earlier type main-sequence stars.Comment: 22 pages, 17 figures, 3 tables Accepted for publication in MNRA