Tracking bifurcating solutions of a model biological pattern generator

We study heterogeneous steady-state solutions of a cell-chemotaxis model for generating biological spatial patterns in two-dimensional domains with zero flux boundary conditions. We use the finite-element package ENTWIFE to investigate bifurcation from the uniform solution as the chemotactic parameter varies and as the domain scale and geometry change. We show that this simple cell-chemotaxis model can produce a remarkably wide and surprising range of complex spatial patterns

Competition of spatial and temporal instabilities under time delay near codimension-two Turing-Hopf bifurcations

Competition of spatial and temporal instabilities under time delay near the codimension-two Turing-Hopf bifurcations is studied in a reaction-diffusion equation. The time delay changes remarkably the oscillation frequency, the intrinsic wave vector, and the intensities of both Turing and Hopf modes. The application of appropriate time delay can control the competition between the Turing and Hopf modes. Analysis shows that individual or both feedbacks can realize the control of the transformation between the Turing and Hopf patterns. Two dimensional numerical simulations validate the analytical results.Comment: 13 pages, 6 figure

SIRS dynamics on random networks: simulations and analytical models

The standard pair approximation equations (PA) for the Susceptible-Infective-Recovered-Susceptible (SIRS) model of infection spread on a network of homogeneous degree $k$ predict a thin phase of sustained oscillations for parameter values that correspond to diseases that confer long lasting immunity. Here we present a study of the dependence of this oscillatory phase on the parameter $k$ and of its relevance to understand the behaviour of simulations on networks. For $k=4$, we compare the phase diagram of the PA model with the results of simulations on regular random graphs (RRG) of the same degree. We show that for parameter values in the oscillatory phase, and even for large system sizes, the simulations either die out or exhibit damped oscillations, depending on the initial conditions. This failure of the standard PA model to capture the qualitative behaviour of the simulations on large RRGs is currently being investigated.Comment: 6 pages, 3 figures, WIPP to be published in Conference proceedings Complex'2009 February 23-25, Shanghai, Chin

Reduction of Algebraic Parametric Systems by Rectification of their Affine Expanded Lie Symmetries

Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equations. We apply this principle by finding some \emph{affine derivations} that induces \emph{expanded} Lie point symmetries of considered system. By rewriting original problem in an invariant coordinates set for these symmetries, we \emph{reduce} the number of involved parameters. We present an algorithm based on this standpoint whose arithmetic complexity is \emph{quasi-polynomial} in input's size.Comment: Before analysing an algebraic system (differential or not), one can generally reduce the number of parameters defining the system behavior by studying the system's Lie symmetrie

The influence of risk perception in epidemics: a cellular agent model

Our work stems from the consideration that the spreading of a disease is modulated by the individual's perception of the infected neighborhood and his/her strategy to avoid being infected as well. We introduced a general ``cellular agent'' model that accounts for a hetereogeneous and variable network of connections. The probability of infection is assumed to depend on the perception that an individual has about the spreading of the disease in her local neighborhood and on broadcasting media. In the one-dimensional homogeneous case the model reduces to the DK one, while for long-range coupling the dynamics exhibits large fluctuations that may lead to the complete extinction of the disease

Adaptalight: An inexpensive PAR sensor system for daylight harvesting in a Micro Indoor Smart Hydroponic System

Environmental changes and the reduction in arable land have led to food security concerns around the world, particularly in urban settings. Hydroponic soilless growing methods deliver plant nutrients using water, conserving resources and can be constructed nearly anywhere. Hydroponic systems have several complex attributes that need to be managed, and this can be daunting for the layperson. Micro Indoor Smart Hydroponics (MISH) leverage Internet of Things (IoT) technology to manage the complexities of hydroponic techniques, for growing food at home for everyday citizens. Two prohibitive costs in the advancement of MISH systems are power consumption and equipment expense. Reducing cost through harvesting ambient light can potentially reduce power consumption but must be done accurately to sustain sufficient plant yields. Photosynthetic Active Radiation (PAR) meters are commercially used to measure only the light spectrum that plants use, but are expensive. This study presents Adaptalight, a MISH system that harvests ambient light using an inexpensive AS7265x IoT sensor to measure PAR. The system is built on commonly found IoT technology and a well-established architecture for MISH systems. Adpatalight was deployed in a real-world application in the living space of an apartment and experiments were carried out accordingly. A two-phase experiment was conducted over three months, each phase lasting 21 days. Phase one measured the IoT sensor’s capability to accurately measure PAR. Phase two measured the ability of the system to harvest ambient PAR light and produce sufficient yields, using the calibrated IoT sensor from phase one. The results showed that the Adaptalight system was successful in saving a significant amount of power, harvesting ambient PAR light and producing yields with no significant differences from the control. The amount of power savings would be potentially greater in a location with more ambient light. Additionally, the findings show that, when calibrated, the AS7265x sensor is well suited to accurately measure PAR light in MISH systems

The 1:1 resonance in Extrasolar Systems: Migration from planetary to satellite orbits

We present families of symmetric and asymmetric periodic orbits at the 1/1 resonance, for a planetary system consisting of a star and two small bodies, in comparison to the star, moving in the same plane under their mutual gravitational attraction. The stable 1/1 resonant periodic orbits belong to a family which has a planetary branch, with the two planets moving in nearly Keplerian orbits with non zero eccentricities and a satellite branch, where the gravitational interaction between the two planets dominates the attraction from the star and the two planets form a close binary which revolves around the star. The stability regions around periodic orbits along the family are studied. Next, we study the dynamical evolution in time of a planetary system with two planets which is initially trapped in a stable 1/1 resonant periodic motion, when a drag force is included in the system. We prove that if we start with a 1/1 resonant planetary system with large eccentricities, the system migrates, due to the drag force, {\it along the family of periodic orbits} and is finally trapped in a satellite orbit. This, in principle, provides a mechanism for the generation of a satellite system: we start with a planetary system and the final stage is a system where the two small bodies form a close binary whose center of mass revolves around the star.Comment: to appear in Cel.Mech.Dyn.Ast

The Geologic Setting of Coal and Carbonaceous Material, Narragansett Basin, Southeastern New England

Guidebook to geologic field studies in Rhode Island and adjacent areas: The 73rd annual meeting of the New England Intercollegiate Geological Conference, October 16-18, 1981: Trip B-