The effect of an electric field on the local stoichiometry of front waves in an ionic chemical system

A model based on an autocatalytic, two-step reaction mechanismincluding two ionic components (of the same charge) and twonon-ionic components, where both reactions are of second orderoverall, is considered when an electric field is applied tothe system. The model is motivated by experimental observationson the iodate-arsenous acid system. The travelling wave equationsare examined first and conditions obtained for the existenceand form of these waves. These conditions are then used to interpretthe results obtained from numerical simulations of the fullsystem. These results display all the main features observedexperimentally, the change in the local stoichiometry and thepossible wave annihilation for sufficiently strong fields. Themodel provides a clear explanation for these features as wellas predicting new features not reported from the experiments.The main one of which is the occurrence of an internal wavepropagating in the reacted part of the system in the directioninduced by the applied field.     

Oscillations and waves in the Belousov-Zhabotinskii reaction in a finite medium

Travelling reaction-diffusion waves are considered in a finite medium. The model considered is a simplified model of the Belousov-Zhabotinskii reaction, described mathematically by the two-variable Oregonator. A one-dimensional problem consisting of three regions is considered. Regions I (x 0) and III (x 1) act as reservoirs with fixed concentrations of the reactant X (the autocatalyst, hypobromous acid (HBrO₂)), where the concentration of X in regions I and III may be different. Region II represents a catalyst-loaded membrane, within which species X can diffuse while species Z (the oxidized form of the metal-ion catalyst (Ce(IV))) is fixed spatially. The large time behaviour of the system is considered and both stable steady states and periodic spatio-temporal structures are seen.     

Steady mixed convection boundary-layer flow over a vertical flat surface in a porous medium filled with water at 4°C: variable surface heat flux

The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water at 4°C (maximum density) when the surface heat flux varies as x ^m and the velocity outside the boundary layer varies as x ^(1+2m)/2, where x measures the distance from the leading edge, is discussed. Assisting and opposing flows are considered with numerical solutions of the governing equations being obtained for general values of the flow parameters. For opposing flows, there are dual solutions when the mixed convection parameter λ is greater than some critical value λ _c (dependent on the power-law index m). For assisting flows, solutions are possible for all values of λ. A lower bound on m is found, m > −1 being required for solutions. The nature of the critical point λ _c is considered as well as various limiting forms; the forced convection limit (λ = 0), the free convection limit (λ → ∞) and the limits as m → ∞ and as m → −1.     

The effect of a radical scavenger on the propagation of flames in an exothermic-endothermic system

The propagation of a premixed laminar flame supported by an exothermic chemical reaction under adiabatic conditions but subject to inhibition through parallel endothermic chemical processes is considered. These consist of the endothermic decomposition of an inhibitor W leading to the formation of a ‘radical scavenger’ S, which acts as a catalyst for the removal of active radicals X through an additional termination step. The heat loss through the endothermic reaction and the action of the radical scavenger, represented by the parameters α and ρ, both have a strong quenching effect on wave propagation. The dependence of the flame velocity c on α and ρ is determined by numerical integration of the flame equations for a range of values of the other parameters. The (ρ ,c) curve can have at least one turning point, the (α,c) curve can be monotone or it can have one or three turning points, depending on the values of the parameters β, representing the rate at which inhibitor is consumed, μ, the ratio of the activation energies of the reactants and the Lewis numbers. The additional feature caused by the scavenger is that the (α, c) curve has a turning point for any (μ, β) parameter pair if ρ is sufficiently large. A new feature of the model is that, for non-zero values of ρ, there can be four solutions below critical values of α. This behaviour is confirmed by a high activation energy analysis, which also reveals some additional features of the flame structure resulting from the presence of the radical scavenger.AMS subject classification: 80A25, 35K57, 35B32     

The effects of an electric field on an autocatalytic ionic reaction in a system with high ionic strength

The effects of an applied electric field on an ionic autocatalyticreaction with a quadratic rate law are considered, where thereacting species, A⁺ and B⁺, are present in a system which alsoincludes non-reacting species C^- and D⁺. The conditions areestablished under which the general terms which describe theelectric field effects in the reaction-diffusion equations canbe simplified to those used in previous studies, where theseeffects are modelled by linear advection terms. The resultingequations are then studied in detail by first obtaining conditionsfor the existence of travelling waves of permanent form. Thisdiscussion shows that _B, the ratio of the diffusion coefficientsof B⁺ and A⁺, is a critical parameter, with different formsof behaviour arising for _B < 1 and _B > 1. This analysisis augmented by obtaining solutions valid for large times andlarge values of (the dirnensionless applied field). Numericalsolutions of initial-value problems are obtained for a rangeof values of and _B, guided by and interpreted through the analysispreviously obtained. These numerical integrations show the formationof reaction fronts, with the possibility of greatly increasedreaction rates caused by the applied electric field, as wellas propagating electrophoretic fronts in B⁺ being formed incases where a reaction front is also initiated. There is alsothe possibility of separate electrophoretic fronts in A⁺ andB⁺ being formed, which become increasingly separated as timeincreases with the reaction being completely inhibited.     

Octopamine increases the excitability of neurons in the snail feeding system by modulation of inward sodium current but not outward potassium currents

Background  

Although octopamine has long been known to have major roles as both transmitter and modulator in arthropods, it has only recently been shown to be functionally important in molluscs, playing a role as a neurotransmitter in the feeding network of the snail Lymnaea stagnalis. The synaptic potentials cannot explain all the effects of octopamine-containing neurons on the feeding network, and here we test the hypothesis that octopamine is also a neuromodulator.     

How to Determine the Amplitude-Phase Structure of a 2D Optical Field and a 2D Complex Transfer Function, with the Effect of the Medium Described by Convolution

We consider the solution to the phase problem in optics in application to registration and analysis of the amplitude–phase structure of twodimensional optical fields that form or transmit images, as well as the amplitude–phase structure of transfer and spread functions of media, in which light propagates, or those of systems that form fields or images. The idea of our method is to introduce two additional modulators that visualize phase information. We consider two variants of optical schemes designed for analyzing the amplitudephase characteristics of twodimensional optical fields as well as twodimensional complex transfer and spread functions. These schemes are special because the twodimensional structure of the fields is transmitted at a distance in a disturbing medium or system and four independent twodimensional intensity distributions are to be registered in the course of processing the twodimensional fields. To solve the problem, the first additional modulation preceding the transmitting medium is introduced in the scheme. Then the spectrum of spatial frequencies is formed by the optical system. The second additional spatial modulation is applied either in the optical system plane (the first variant of the scheme) or in the plane of spatial frequencies formed by the optical system (the second variant). A separate optical system is used for registration in the plane of spatial frequencies in the first variant of the scheme and in the image plane in the second variant. The intensity distributions obtained make it possible to solve the problem.     

Inhibition of flame propagation by an endothermic reaction

The propagation of a premixed laminar flame supported by anexothermic chemical reaction under adiabatic conditions butsubject to inhibition through a parallel endothermic chemicalprocess is considered. The heat loss through the endothermicreaction, represented by the dimensionless parameter ; has astrong quenching effect on wave propagation. The temperatureprofile can have a front or a pulse structure depending on therelative values of the parameters and ß; the latterrepresents the rate at which inhibitor is consumed relativeto the consumption of fuel. The wave speed–cooling parameter() curves are determined for various values of the other parameters.These curves can be monotone decreasing or S-shaped, dependingon the value of ß and the ratio of the activationenergies of the reactants. This gives the possibility of havingeither one, two or three different flame velocities for thesame value of the cooling parameter .