Measures with infinite Lyapunov exponents for the periodic Lorentz gas

We study invariant measures for the periodic Lorentz gas which are supported on the set of points with infinite Lyapunov exponents. We construct examples of such measures which are measures of maximal entropy and ones which are not.     

Statistical-thermodynamic approach to a chaotic dynamical system: Exactly solvable examples

The static and dynamic properties of a chaotic attractor of a two-dimensional map are studied, which belongs to a particular class of piecewise continuous invertible maps. Coverings of a natural size to cover the attractor are introduced, so that the microscopic information of the attractor is written on each box composing the cover. The statistical thermodynamics of the scaling indices and the size indices of the boxes is formulated. Analytic forms of the free energy functions of the scaling indices and the size indices of the boxes are obtained for examples of a hyperbolic and a nonhyperbolic chaotic attractor. The statistical thermodynamics of local Lyapunov exponents is also studied and a relation between the thermodynamics of scaling indices and of local Lyapunov exponents is invetigated. For the nonhyperbolic example, the free energy and entropy functions of local Lyapunov exponents are obtained in analytic forms. These results display the existence of phase transitions. A phase transition is seen in the thermodynamics of scaling indices also.     

Chemical Vapor Generation with Slurry Sampling: A Review of Applications to Atomic and Mass Spectrometry

Abstract

A critical review of published analytical methods and techniques for chemical vapor generation (CVG) with slurry sample introduction for detection by atomic and mass spectrometry is presented. The nstrumentation used for the reaction as well as separation and transport of the species, influence of chemical and physical factors, and efficiency of the process are considered. A brief comparison of detection limits obtained with atomic absorption, emission, and fluorescence as well as mass spectrometry along with practical applications to analytical samples are summarized. The current state-of-the-art, including advantages and limitations of this approach, is discussed.     

A Photon Force and Flow for Dissipative Structuring: Application to Pigments,Plants and Ecosystems

Through a modern derivation of Planck’s formula for the entropy of an arbitrary beam of photons, we derive a general expression for entropy production due to the irreversible process of the absorption of an arbitrary incident photon spectrum in material and its dissipation into an infrared-shifted grey-body emitted spectrum, with the rest being reflected or transmitted. Employing the framework of Classical Irreversible Thermodynamic theory, we define the generalized thermodynamic flow as the flow of photons from the incident beam into the material and the generalized thermodynamic force is, then, the entropy production divided by the photon flow, which is the entropy production per unit photon at a given wavelength. We compare the entropy production of different inorganic and organic materials (water, desert, leaves and forests) under sunlight and show that organic materials are the greater entropy-producing materials. Intriguingly, plant and phytoplankton pigments (including chlorophyll) reach peak absorption exactly where entropy production through photon dissipation is maximal for our solar spectrum 430<λ<550 nm, while photosynthetic efficiency is maximal between 600 and 700 nm. These results suggest that the evolution of pigments, plants and ecosystems has been towards optimizing entropy production, rather than photosynthesis. We propose using the wavelength dependence of global entropy production as a biosignature for discovering life on planets of other stars.     

A lattice gas coupled to two thermal reservoirs: Monte Carlo and field theoretic studies

We investigate the collective behavior of an Ising lattice gas, driven to non-equilibrium steady states by being coupled to two thermal baths. Monte Carlo methods are applied to a two-dimensional system in which one of the baths is fixed at infinite temperature. Both generic long range correlations in the disordered state and critical properties near the second order transition are measured. Anisotropic scaling, a key feature near criticality, is used to extract and some critical exponents. On the theoretical front, a continuum theory, in the spirit of Landau-Ginzburg, is presented. Being a renormalizable theory, its predictions can be computed by standard methods of -expansions and found to be consistent with simulation data. In particular, the critical behavior of this system belongs to a universality class which is quite different from the uniformly driven Ising model. Received 4 October 2000