Statistical behavior

Statistical behavior of a reacting mixture in isotropic turbulence. The Physics of Fluids 1, 42-47. 

The statistical behavior of interest is encapsulated in the equilibrium probability density function P )( q c). This PDF is determined by an appropriate ensemble-dependent, dimensionless [6] configurational energy 6( q, c). The relationship takes the generic form 

The statistic models consider surface roughness as a stochastic process, and concern the averaged or statistic behavior of lubrication and contact. For instance, the average flow model, proposed by Patir and Cheng [2], combined with the Greenwood and Williamsons statistic model of asperity contact [3] has been one of widely accepted models for mixed lubrication in early times. 

This hypothetical equivalent chain should resemble in statistical behavior the actual chain of given size n and mean extension v.  

RESONANCES IN UNIMOLECULAR DISSOCIATION FROM MODE-SPECIFIC TO STATISTICAL BEHAVIOR 

Standardized long-term measurements provide reliable information on statistical behavior of atmospheric aerosols, far beyond what could be obtained in short-term campaign-wise measurements. Although data from a period of only two years is shown, the results already provide a previously unavailable variety of information on the sub-micron aerosol physical properties and variability in Europe. Such information would also be hard to achieve based on information collected from separately managed stations, especially if the instrumentation and data handling are not harmonized. 

Brumer, P. (1981), Intramolecular Energy Transfer Theories for the Onset of Statistical Behavior, Adv. Chem. Phys. 47, 201. 

Because of the deep potential well and small exoergicity, conventional wisdom will then predict a long-lived complex being involved in the title reaction and the statistical behavior might be borne out.1,22 23 

R. Schinke, H.-M. Keller, M. Stumpf, C. Beck, D. H. Mordaunt, and A. J. Dobbyn, Adv. Chem. Phys., Vol. 101, Resonances in Unimolecular Dissociation From Mode-Specific to Statistical Behavior. 

While many methods for parameter estimation have been proposed, experience has shown some to be more effective than others. Since most phenomenological models are nonlinear in their adjustable parameters, the best estimates of these parameters can be obtained from a formalized method which properly treats the statistical behavior of the errors associated with all experimental observations. For reliable process-design calculations, we require not only estimates of the parameters but also a measure of the errors in the parameters and an indication of the accuracy of the data. 

When describing polymer tactlcity, one should attempt to obtain the highest complete "n-ad" distribution available as well as a simple "comonomer" distribution. In connection with such a measurement, the mean sequence lengths may offer a viable alternative to the simple m versus r distribution. Useful relationships, which are helpful in establishing particular statistical behaviors, are available. 

The topic of capillarity concerns interfaces that are sufficiently mobile to assume an equilibrium shape. The most common examples are meniscuses, thin films, and drops formed by liquids in air or in another liquid. Since it deals with equilibrium configurations, capillarity occupies a place in the general framework of thermodynamics in the context of the macroscopic and statistical behavior of interfaces rather than the details of their molectdar structure. In this chapter we describe the measurement of surface tension and present some fundamental results. In Chapter III we discuss the thermodynamics of liquid surfaces. 

The LST, on the other hand, explicitly takes into account all correlations (up to an arbitrary order) that arise between different cells on a given lattice, by considering the probabilities of local blocks of N sites. For one dimensional lattices, for example, it is simply formulated as a set of recursive equations expressing the time evolution of the probabilities of blocks of length N (to be defined below). As the order of the LST increases, so does the accuracy with which the LST is able to predict the statistical behavior of a given rule. 

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