On the Critical Dimension and AC Entropy for Markov Odometers

Markov odometers are natural models for non-homogeneous Markov chains, and are natural generalisations of infinite product measures. We show how to calculate the critical dimension of these measures: this is an invariant which describes the asymptotic growth rate of sums of Radon-Nikodym derivatives. This interesting invariant appears to give a kind of entropy for non-singular odometer actions. The techniques require a law of large numbers for inhomogeneous Markov chains.     

On the Critical Dimension and AC Entropy for Markov Odometers

Markov odometers are natural models for non-homogeneous Markov chains, and are natural generalisations of infinite product measures. We show how to calculate the critical dimension of these measures: this is an invariant which describes the asymptotic growth rate of sums of Radon-Nikodym derivatives. This interesting invariant appears to give a kind of entropy for non-singular odometer actions. The techniques require a law of large numbers for inhomogeneous Markov chains.     

Time-resolved double ionization with few cycle laser pulses

Ionization of D2 launches a vibrational wave packet on the ground state of D+2. Removal of the second electron places a pair of D+ ions onto a Coulombic potential. Measuring the D+ kinetic energy determines the time delay between the first and the second ionization. Caught between a falling ionization and a rapidly rising intensity, the typical lifetime of the D+2 intermediate is less than 5 fs when an intense 8.6 fs laser pulse is used. We simulate Coulomb explosion imaging of the ground state wave function of D2 by a 4 fs optical pulse and compare with our experimental observations.     

Alignment-dependent strong field ionization of molecules

We demonstrate a method to measure strong field laser ionization of aligned molecules. The method employs a macroscopic field-free dynamic alignment, which occurs during revivals of rotational wave packets produced by a femtosecond laser pulse. We investigate the dependence of strong field ionization of N2 on molecular orientation. We determine that N2 molecules are four times more likely to ionize when aligned parallel to the field than when aligned perpendicular to it.     

Modeling High-Resolution Broadband Discourse in Complex Adaptive Systems

Numerous researchers and practitioners have turned to complexity science to better understand human systems. Simulation can be used to observe how the microlevel actions of many human agents create emergent structures and novel behavior in complex adaptive systems. In such simulations, communication between human agents is often modeled simply as message passing, where a message or text may transfer data, trigger action, or inform context. Human communication involves more than the transmission of texts and messages, however. Such a perspective is likely to limit the effectiveness and insight that we can gain from simulations, and complexity science itself. In this paper, we propose a model of how close analysis of discursive processes between individuals (high-resolution), which occur simultaneously across a human system (broadband), dynamically evolve. We propose six different processes that describe how evolutionary variation can occur in texts—recontextualization, pruning, chunking, merging, appropriation, and mutation. These process models can facilitate the simulation of high-resolution, broadband discourse processes, and can aid in the analysis of data from such processes. Examples are used to illustrate each process. We make the tentative suggestion that discourse may evolve to the edge of chaos. We conclude with a discussion concerning how high-resolution, broadband discourse data could actually be collected.     

Acoustic relaxation and internal strains in KCl:CN

Data revealing a previously predicted relaxation peak in the propagation of T_2g mode ultrasound in KCl doped with 15–140 ppm KCN is presented and analyzed. A distribution of activation energies is found; the mean value is identified with a thermal conductivity resonance, and the width of the distribution is taken to confirm Pompi's assumption of internal strains in his analysis of specific heats and electric field dichroism in KCl:CN. The interaction of internal strains with the rotational components of the measuring shear wave suggests new sources for the observed acoustic effects in KCl:CN.     

Insights into the mechanism of N2O reduction by reductively activated N2O reductase from kinetics and spectroscopic studies of pH effects

Nitrous oxide reductase (N2OR) from Achromobacter cycloclastes (Ac) can be reductively activated with reduced methyl viologen over a broad range of pH. Activated Ac N2OR displays a complex activity profile as a function of the pH at which catalytic turnover is measured. Spectroscopic and steady-state kinetics data suggest that [H+] has multiple effects on both the activation and the catalytic reactions. These experimental results are in good agreement with previous theoretical studies, which suggested that the transition state is stabilized by H-bonding interactions between the active site and an N2O-derived intermediate bound to the catalytic CuZ cluster.     

Evolution of the reflection and focusing patterns and stress states in two-fluid cylindrical shell systems subjected to an external shock wave

Several most important features of the hydrodynamic field induced inside a circular cylindrical shell filled with and submerged into different fluids when it is subjected to an external shock wave are considered. This investigation is a follow-up of an earlier study of the two-fluid shell-shock interaction [S. Iakovlev, Interaction between an external shock wave and a cylindrical shell filled with and submerged into different fluids, Journal of Sound and Vibration 322 (2009) 401-437], and it addresses a number of practically important issues not covered in that work. The focus of this study is on the evolution of the respective hydrodynamic patterns in response to the continuous change of the parameters of the fluids, in particular the speed of sound. Along with the analysis of the hydrodynamic patterns it is also demonstrated that when one is concerned with the highest pressure attained inside the shell, the most dangerous combination of the parameters occurs when the ratio of the internal and external acoustic speeds is close to 0.48, with the respective pressure exceeding the maximum incident pressure by more than 110 percent. The effect that the hydrodynamic features discussed have on the stress state of the shell is addressed as well, and it is observed that the maximum tensile stress is significantly affected by the evolution of the considered hydrodynamic features, whereas the maximum compressive stress is not. It is also observed that the maximum tensile stress is very sensitive to the change of the ratio of the acoustic speeds in the internal and external fluids, with as little an increase of the latter as 13 percent resulting in more than doubling of the former in some cases.