Advanced thermal barrier coating systems

Current state-of-the-art thermal barrier coating (TBC) systems consist of partially stabilized zirconia coatings plasma sprayed over a MCrAlY bond coat. Although these systems have excellent thermal shock properties, they have shown themselves to be deficient for a number of diesel and aircraft applications. Two ternary ceramic plasma coatings are discussed with respect to their possible use in TBC systems. Zirconia-ceria-yttria (ZCY) coatings were developed with low thermal conductivities, good thermal shock resistance and improved resistance to vanadium containing environments, when compared to the baseline yttria stabilized zirconia (YSZ) coatings. In addition, dense zirconia-titania-yttria (ZTY) coatings were developed with particle erosion resistance exceeding conventional stabilized zirconia coatings. Both coatings were evaluated in conjunction with a NiCr-Al-Co-Y2O3 bond coat. Also, multilayer or hybrid coatings consisting of the bond coat with subsequent coatings of zirconia-ceria-yttria and zirconia-titania-yttria were evaluated. These coatings combine the enhanced performance characteristics of ZCY with the improved erosion resistance of ZTY coatings. Improvement in the erosion resistance of the TBC system should result in a more consistent delta T gradient during service. Economically, this may also translate into increased component life simply because the coating lasts longer

Assessing the effect of advertising expenditures upon sales: a Bayesian structural time series model

We propose a robust implementation of the Nerlove--Arrow model using a Bayesian structural time series model to explain the relationship between advertising expenditures of a country-wide fast-food franchise network with its weekly sales. Thanks to the flexibility and modularity of the model, it is well suited to generalization to other markets or situations. Its Bayesian nature facilitates incorporating \emph{a priori} information (the manager's views), which can be updated with relevant data. This aspect of the model will be used to present a strategy of budget scheduling across time and channels.Comment: Published at Applied Stochastic Models in Business and Industry, https://onlinelibrary.wiley.com/doi/full/10.1002/asmb.246

Measurement of entropy production rate in compressible turbulence

The rate of change of entropy $\dot S$ is measured for a system of particles floating on the surface of a fluid maintained in a turbulent steady state. The resulting coagulation of the floaters allows one to relate $\dot S$ to the velocity divergence and to the Lyapunov exponents characterizing the behavior of this system. The quantities measured from experiments and simulations are found to agree well with the theoretical predictions.Comment: 7 Pages, 4 figures, 1 tabl

Ergodicity Breaking in a Deterministic Dynamical System

The concept of weak ergodicity breaking is defined and studied in the context of deterministic dynamics. We show that weak ergodicity breaking describes a weakly chaotic dynamical system: a nonlinear map which generates subdiffusion deterministically. In the non-ergodic phase non-trivial distribution of the fraction of occupation times is obtained. The visitation fraction remains uniform even in the non-ergodic phase. In this sense the non-ergodicity is quantified, leading to a statistical mechanical description of the system even though it is not ergodic.Comment: 11 pages, 4 figure

Chaotic properties of systems with Markov dynamics

We present a general approach for computing the dynamic partition function of a continuous-time Markov process. The Ruelle topological pressure is identified with the large deviation function of a physical observable. We construct for the first time a corresponding finite Kolmogorov-Sinai entropy for these processes. Then, as an example, the latter is computed for a symmetric exclusion process. We further present the first exact calculation of the topological pressure for an N-body stochastic interacting system, namely an infinite-range Ising model endowed with spin-flip dynamics. Expressions for the Kolmogorov-Sinai and the topological entropies follow.Comment: 4 pages, to appear in the Physical Review Letter

Separation of trajectories and its Relation to Entropy for Intermittent Systems with a Zero Lyapunov exponent

One dimensional intermittent maps with stretched exponential separation of nearby trajectories are considered. When time goes infinity the standard Lyapunov exponent is zero. We investigate the distribution of $\lambda_{\alpha}= \sum_{i=0}^{t-1} \ln \left| M'(x_i) \right|/t^{\alpha}$, where $\alpha$ is determined by the nonlinearity of the map in the vicinity of marginally unstable fixed points. The mean of $\lambda_{\alpha}$ is determined by the infinite invariant density. Using semi analytical arguments we calculate the infinite invariant density for the Pomeau-Manneville map, and with it obtain excellent agreement between numerical simulation and theory. We show that \alpha \left is equal to Krengel's entropy and to the complexity calculated by the Lempel-Ziv compression algorithm. This generalized Pesin's identity shows that \left and Krengel's entropy are the natural generalizations of usual Lyapunov exponent and entropy for these systems.Comment: 12 pages, 10 figure

Wave packet autocorrelation functions for quantum hard-disk and hard-sphere billiards in the high-energy, diffraction regime

We consider the time evolution of a wave packet representing a quantum particle moving in a geometrically open billiard that consists of a number of fixed hard-disk or hard-sphere scatterers. Using the technique of multiple collision expansions we provide a first-principle analytical calculation of the time-dependent autocorrelation function for the wave packet in the high-energy diffraction regime, in which the particle's de Broglie wave length, while being small compared to the size of the scatterers, is large enough to prevent the formation of geometric shadow over distances of the order of the particle's free flight path. The hard-disk or hard-sphere scattering system must be sufficiently dilute in order for this high-energy diffraction regime to be achievable. Apart from the overall exponential decay, the autocorrelation function exhibits a generally complicated sequence of relatively strong peaks corresponding to partial revivals of the wave packet. Both the exponential decay (or escape) rate and the revival peak structure are predominantly determined by the underlying classical dynamics. A relation between the escape rate, and the Lyapunov exponents and Kolmogorov-Sinai entropy of the counterpart classical system, previously known for hard-disk billiards, is strengthened by generalization to three spatial dimensions. The results of the quantum mechanical calculation of the time-dependent autocorrelation function agree with predictions of the semiclassical periodic orbit theory.Comment: 24 pages, 13 figure

Random walk approach to the d-dimensional disordered Lorentz gas

A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic expression for the diffusion constant in arbitrary number of dimensions d is obtained. The result corresponds to an Enskog-like correction to the Boltzmann prediction, being exact in the dilute limit, and better or nearly exact in comparison to renormalized kinetic theory predictions for all allowed densities in d=2,3. Extensive numerical simulations were also performed to elucidate the role of the approximations involved.Comment: 5 pages, 5 figure

Power-law tail distributions and nonergodicity

We establish an explicit correspondence between ergodicity breaking in a system described by power-law tail distributions and the divergence of the moments of these distributions.Comment: 4 pages, 1 figure, corrected typo