Homogenization induced by chaotic mixing and diffusion in an oscillatory chemical reaction

A model for an imperfectly mixed batch reactor with the chlorine dioxide-iodine-malonic acid (CDIMA) reaction, with the mixing being modelled by chaotic advection, is considered. The reactor is assumed to be operating in oscillatory mode and the way in which an initial spatial perturbation becomes homogenized is examined. When the kinetics are such that the only stable homogeneous state is oscillatory then the perturbation is always entrained into these oscillations. The rate at which this occurs is relatively insensitive to the chemical effects, measured by the Damkohler number, and is comparable to the rate of homogenization of a passive contaminant. When both steady and oscillatory states are stable, spatially homogeneous states, two possibilities can occur. For the smaller Damkohler numbers, a localized perturbation at the steady state is homogenized within the background oscillations. For larger Damkohler numbers, regions of both oscillatory and steady behavior can co-exist for relatively long times before the system collapses to having the steady state everywhere. An interpretation of this behavior is provided by the one-dimensional Lagrangian filament model, which is analyzed in detail

Magnetosphere-Ionosphere Coupling Through E-region Turbulence: Anomalous Conductivities and Frictional Heating

Global magnetospheric MHD codes using ionospheric conductances based on laminar models systematically overestimate the cross-polar cap potential during storm time by up to a factor of two. At these times, strong DC electric fields penetrate to the E region and drive plasma instabilities that create turbulence. This plasma density turbulence induces non-linear currents, while associated electrostatic field fluctuations result in strong anomalous electron heating. These two effects will increase the global ionospheric conductance. Based on the theory of non-linear currents developed in the companion paper, this paper derives the correction factors describing turbulent conductivities and calculates turbulent frictional heating rates. Estimates show that during strong geomagnetic storms the inclusion of anomalous conductivity can double the total Pedersen conductance. This may help explain the overestimation of the cross-polar cap potentials by existing MHD codes. The turbulent conductivities and frictional heating presented in this paper should be included in global magnetospheric codes developed for predictive modeling of space weather.Comment: 13 pages, 5 figures, 2nd of two companion paper

Effects of electrojet turbulence on a magnetosphere-ionosphere simulation of a geomagnetic storm

Ionospheric conductance plays an important role in regulating the response of the magnetosphere‐ionosphere system to solar wind driving. Typically, models of magnetosphere‐ionosphere coupling include changes to ionospheric conductance driven by extreme ultraviolet ionization and electron precipitation. This paper shows that effects driven by the Farley‐Buneman instability can also create significant enhancements in the ionospheric conductance, with substantial impacts on geospace. We have implemented a method of including electrojet turbulence (ET) effects into the ionospheric conductance model utilized within geospace simulations. Our particular implementation is tested with simulations of the Lyon‐Fedder‐Mobarry global magnetosphere model coupled with the Rice Convection Model of the inner magnetosphere. We examine the impact of including ET‐modified conductances in a case study of the geomagnetic storm of 17 March 2013. Simulations with ET show a 13% reduction in the cross polar cap potential at the beginning of the storm and up to 20% increases in the Pedersen and Hall conductance. These simulation results show better agreement with Defense Meteorological Satellite Program observations, including capturing features of subauroral polarization streams. The field‐aligned current (FAC) patterns show little differences during the peak of storm and agree well with Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) reconstructions. Typically, the simulated FAC densities are stronger and at slightly higher latitudes than shown by AMPERE. The inner magnetospheric pressures derived from Tsyganenko‐Sitnov empirical magnetic field model show that the inclusion of the ET effects increases the peak pressure and brings the results into better agreement with the empirical model.This material is based upon work supported by NASA grants NNX14AI13G, NNX13AF92G, and NNX16AB80G. The National Center for Atmospheric Research is sponsored by the National Science Foundation. This work used the XSEDE and TACC computational facilities, supported by National Science Foundation grant ACI-1053575. We would like to acknowledge high-performance computing support from Yellowstone (ark:/85065/d7wd3xhc) provided by NCAR's Computational and Information Systems Laboratory, sponsored by the National Science Foundation. We thank the AMPERE team and the AMPERE Science Center for providing the Iridium derived data products. All model output, simulation codes, and analysis routines are being preserved on the NCAR High-Performance Storage System and will be made available upon written request to the lead author of this publication. (NNX14AI13G - NASA; NNX13AF92G - NASA; NNX16AB80G - NASA; National Science Foundation; ACI-1053575 - National Science Foundation

Magnetosphere-Ionosphere Coupling Through E-region Turbulence 1: Energy Budget

During periods of intense geomagnetic activity, strong electric fields and currents penetrate from the magnetosphere into high-latitude ionosphere where they dissipate energy, form electrojets, and excite plasma instabilities in the E-region ionosphere. These instabilities give rise to plasma turbulence which induces non-linear currents and strong anomalous electron heating (AEH) as observed by radars. These two effects can increase the global ionospheric conductances. This paper analyzes the energy budget in the electrojet, while the companion paper applies this analysis to develop a model of anomalous conductivity and frictional heating useful in large-scale simulations and models of the geospace environment. Employing first principles, this paper proves for the general case an earlier conjecture that the source of energy for plasma turbulence and anomalous heating equals the work by external field on the non-linear current. Using a two-fluid model of an arbitrarily magnetized plasma and the quasilinear approximation, this paper describes the energy conversion process, calculates the partial sources of anomalous heating, and reconciles the apparent contradiction between the inherently 2-D non-linear current and the 3-D nature of AEH.Comment: 13 pages, 1 figure; 1st of two companion paper

Flow-distributed spikes for Schnakenberg kinetics

This is the post-print version of the final published paper. The final publication is available at link.springer.com by following the link below. Copyright @ 2011 Springer-Verlag.We study a system of reaction–diffusion–convection equations which combine a reaction–diffusion system with Schnakenberg kinetics and the convective flow equations. It serves as a simple model for flow-distributed pattern formation. We show how the choice of boundary conditions and the size of the flow influence the positions of the emerging spiky patterns and give conditions when they are shifted to the right or to the left. Further, we analyze the shape and prove the stability of the spikes. This paper is the first providing a rigorous analysis of spiky patterns for reaction-diffusion systems coupled with convective flow. The importance of these results for biological applications, in particular the formation of left–right asymmetry in the mouse, is indicated.RGC of Hong Kon

Predicting magnetospheric dynamics with a coupled sun-to-Earth model: challenges and first results

Results from the first Sun-to-Earth coupled numerical model developed at the Center for Integrated Space Weather Modeling are presented. The model simulates physical processes occurring in space spanning from the corona of the Sun to the Earth's ionosphere, and it represents the first step toward creating a physics-based numerical tool for predicting space weather conditions in the near-Earth environment. Two 6- to 7-d intervals, representing different heliospheric conditions in terms of the three-dimensional configuration of the heliospheric current sheet, are chosen for simulations. These conditions lead to drastically different responses of the simulated magnetosphere-ionosphere system, emphasizing, on the one hand, challenges one encounters in building such forecasting tools, and on the other hand, emphasizing successes that can already be achieved even at this initial stage of Sun-to-Earth modeling

Effective dynamics of an electrically charged string with a current

Equations of motion for an electrically charged string with a current in an external electromagnetic field with regard to the first correction due to the self-action are derived. It is shown that the reparametrization invariance of the free action of the string imposes constraints on the possible form of the current. The effective equations of motion are obtained for an absolutely elastic charged string in the form of a ring (circle). Equations for the external electromagnetic fields that admit stationary states of such a ring are revealed. Solutions to the effective equations of motion of an absolutely elastic charged ring in the absence of external fields as well as in an external uniform magnetic field are obtained. In the latter case, the frequency at which one can observe radiation emitted by the ring is evaluated. A model of an absolutely nonstretchable charged string with a current is proposed. The effective equations of motion are derived within this model, and a class of solutions to these equations is found.Comment: 14 pages, 3 figures, format changed, minor change