Ultrasonic velocity data on hydrocarbon mixtures was shown by Wang and Nur [JASA 89, 2725 (1991)] to agree quite well with the predictions of a simple mixing rule (volume average of velocity). The same data is reanalyzed using Wood's formula and the time average approximation. Wood's formula for acoustic velocity is shown to be always less than the time average formula, which is itself always l...

We study three quantities that can each be viewed as the time needed for a finite irreducible Markov chain to “forget” where it started. One of these is the mixing time, the minimum mean length of a stopping rule that yields the stationary distribution from the worst starting state. A second is the forget time, the minimum mean length of any stopping rule that yields the same distribution from ...

In this paper, the dynamics of elementary cellular automaton (ECA) rule 73 is investigated under the framework of the bi-infinite symbolic sequence space. This paper provides a rigorous mathematical analysis for the evolution of symbol sequences in some subsystems of rule 73. ECA rule 73, a member of Wolfram’s class III and Chua’s complex Bernoulli-shift rules, defines many more subsystems with...

Considering light transport in disordered media, the medium is often treated as an effective requiring accurate evaluation of refractive index. Because its simplicity, Maxwell-Garnett (MG) mixing rule widely used, although restriction to particles much smaller than wavelength rarely satisfied. Using 3D finite-difference time-domain simulations, we show that MG theory indeed fails for large part...

This article describes a simple probabilistic diagnostic system for a fan-powered mixing box. Several types of electrical and damper failures are diagnosed. Empirical data is available for modeling the normal operation of the mixing box, but no empirical data is available for failure states and models of failure states must be constructed from expert knowledge. The distribution over operational...

We identify a ‘‘ selection rule’’ for N resonances in the presence of QCD mixing effects. We quantify these mixing effects from existing data and predict amplitudes for exciting 20 representations in SU(6), which are forbidden in strict diquark models. By classifying Particle-Data-Group (PDG) states at N 2, we show that N ! K , K , K , K , and J= ! pN are ideal probes of baryon dynamics and for...

The purpose of this paper is to point out that an asymptotic rule A+B/u for the ultimate ruin probability applies to a wide class of dependent risk processes, in continuous or discrete time. That dependence is incorporated through a mixing model in the individual claim amount distributions. Several special mixing distributions are examined in detail and some close-form formulas are derived. Cla...

Direct Monte Carlo simulation of internal energies of departure for binary mixtures of geological interest are gathered and compared to those calculated using a linear mixing rule. Simulation results for gas–oil, oil–oil, and oil–water mixtures show that the linear mixing rule used in the Gibbs–Helmholtz Constrained (GHC) equation of state framework gives accurate approximations of binary mixtu...