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Notes: We continue our development of a global thermodynamic and stochastic theory of open chemical systems far from equilibrium with an analysis of a broad class of isothermal, multicomponent reaction mechanisms with multiple steady states, studied under the assumption of local equilibrium. We generalize species-specific affinities of reaction intermediates, obtained in prior work for nonautocatalytic reaction mechanisms, to autocatalytic kinetics and define with these affinities an excess free energy differential Fφ. The quantity Fφ is the difference between the work required to reverse a spontaneous concentration change and the work available when the same concentration change is imposed on a system in a reference steady state. The integral of Fφ is in general not a state function; in contrast, the function φdet obtained by integrating Fφ along deterministic kinetic trajectories is a state function, as well as an identifiable term in the time-integrated dissipation. Unlike the total integrated dissipation, φdet remains finite during the infinite duration of the system's relaxation to a steady state and hence φdet can be used to characterize that process. The variational relation δφ≥0 is shown to be a necessary and sufficient thermodynamic criterion for a stable steady state in terms of the excess work of displacement of the intermediates and φdet is a Liapunov function in the domain of attraction of such steady states. Based on these results and earlier work with nonautocatalytic and equilibrating systems, we hypothesize that the stationary distribution of the master equation may be obtained in the form Ps=N exp(−φdet/kT) and provide an analytical argument for this form for macroscopic systems. This generalizes the Einstein fluctuation formula to multivariable systems with multiple steady states, far from equilibrium. In the following article, the utility of the approximation to Ps for systems with single or multiple intermediates, and single or multiple steady states is shown by comparison with numerical solutions of the master equation.

Notes: In this work, we test a hypothesized form for the stationary solution Ps(X,Y) of the stochastic master equation for a reacting chemical system with two reactive intermediates X and Y, and multiple steady states. Thermodynamic analyses and the exact results for nonautocatalytic or equilibrating systems suggest an approximation of the form Pas(X,Y)=N exp(−φ/kT), where the function φ is a line integral of a differential "excess'' work Fφ, which depends on species-specific affinities. The differential Fφ is inexact. In a preceding paper, we have given an analytic argument for the use of the deterministic kinetic trajectory, connecting (X,Y) to the steady state (Xs,Ys) as the path of integration for Fφ. Here, we show that use of the deterministic trajectories leads to a potential φdet which is continuous across the separatrix between the domains of attraction of the two stable steady states in the model studied.We compare the approximate form of Ps(X,Y) thus generated with numerical solutions of the time-dependent master equation in the limit of attainment of a stationary distribution. Because the time required for convergence to the stationary distribution scales as eN with the particle number N in cases with two stable steady states, the numerical work is limited to systems with O(10–100) X and Y particles. System size affects the accuracy of the approximation. To isolate system-size effects, we compare numerical solutions and the corresponding approximations to Ps(X) for two single-intermediate master equations, since the approximation becomes exact in the limit of large particle number for such equations. Based on these comparisons, for the systems with two intermediates, the agreement between the approximation and the numerical solutions is reasonable. The agreement improves as the number of particles increases in those test cases where it has thus far been possible to vary the system size over an order of magnitude. The results obtained by integrating along deterministic trajectories are better than those from straight-line or line-segment paths. The numerical work on small, single-variable systems with two stable steady states leads to two new observations: (i) the relative heights of the steady state peaks in the exact stationary distribution may invert as the system size increases and (ii) an approximation used commonly for particle counting may give results inconsistent with the exact stationary distribution when the particle number is small, while an alternative approximation improves the agreement.

Notes: Developments in measuring the physical mechanisms responsible for strongly driven transverse ion acceleration in the ionosphere are reviewed. Lower-hybrid waves and ion Bernstein waves can be associated very closely with transversely accelerated ions in the auroral ionosphere. In a recent development, very intense and localized lower-hybrid waves have been observed to produce transversely accelerated ions with characteristic energies of 10 eV. The case for current-driven electrostatic oxygen cyclotron waves producing transversely accelerated ions is less compelling.

Notes: An experimental system composed of a standard negative ion source and an Nd:YAG laser is used to study the formation of negative ions by laser impact and the interaction of the laser with the negative ion beam. Using a Q-switched Nd:YAG laser (about 107 W/cm2) impinging on the solid FeS sample of a Cs-sputter source, pulses of negative ions of sulphur with a peak intensity of 3 mA and a width of 150 ns were observed. The time structure of the pulses is measured and shows a complex behavior, not yet fully understood. The same experimental system is used to analyze the production of rare negative ions in the lanthanide and actinide regions and to study their interaction with a laser beam. Cross sections for photodetachment in La− and Th− are measured.

Notes: Vitrinite (woody matter) and spores are generally uncommon or absent in pre-Devonian sediments. To determine organic maturity in the Lower Palaeozoic alternative methods, such as chitinozoan reflectance, must be employed. Chitinozoa are marine, vase-shaped organic-walled microfossils of unknown affinity. The reflectance of incident light from polished chitinozoa walls can provide reliable and accurate maturity data and, due to their relative facies-independency, a high degree of resolution to regional maturity studies. Calibration of the chitinozoan reflectance scale with vitrinite reflectance enables palaeotemperature estimates to be made from pre-Devonian sediments.The range of chitinozoan reflectance for the Welsh Basin is from under 1% to 8%. This corresponds to estimated palaeotemperatures of under 100°C to over 300°C. The regional spatial distribution of organic maturation recorded by chitinozoan reflectance in the Welsh Basin is attributed to palaeobasin form. The increase in reflectance with age in the rocks of the Myddfai Steep Belt and associated areas allows an estimation of a palaeogeothermal gradient. In the Silurian sequences around Llandovery the gradient is calculated to be in the region of 50°C km−1. Similar gradients are derived from other studies (clay minerals, metabasite mineral assemblages, conodont colours). The results from Myddfai Steep Belt suggest the thermal peak occurred during the Acadian event.Chitinozoan reflectivity demonstrates that, with respect to hydrocarbon generation, mature conditions occur on the palaeoplatform, where the sedimentary sequences are relatively thin. Overmature conditions are prevalent in the palaeobasin where there is a thick sedimentary pile which has been subsequently deformed.