Mixing statistical approach

The optimal formulations were obtained using a statistical approach (D-optimal design) and the particles obtained with these formulations had high relaxivities (20-25 s mM ) and small particle sizes (80-100 nm). These formulations appeared to be highly stable in blood, since no change in Ti relaxivity was observed when they where mixed with whole blood. 

This last part or phase is traditionally thought of as "the audit." It can be accomplished in two basic ways either using a random number statistical approach or by a percentage or line approach. In conducting an audit, it is important to remember that some types of errors (usually the small ones) are random, for example, a simple transcription error at the end of a long calculation, while others follow patterns and can have a cumulative impact, such as an unacceptable calibration curve or even sample mix-up. 

Box counting methods. These are simple statistical approaches to describe the mixing of a small... 

Two-particle correlation functions. A statistical approach to quantify the mixing of a heterogeneity that is represented by many particles is to calculate the distances between each pair of particles and compute the cumulative histogram H(r) which is the number of particle pairs that have a distance of less than r. The slope of log(H) versus log(r) within a particular range of r indicates the spatial dimension of the particle distribution. For example, if in a two-dimensional box calculation... 

This statistical approach can be readily extended to mixed dispersions of different antifoams. Thus, the probability of a bubble surviving in the presence of two different antifoam dispersions of species, 1 and 2, respectively, is obviously from which we may deduce by analogy with Equation 5.26 that we can write... 

From a statistical approach, leading to the same result, the ideal entropy of mixing is also designated as the configurational entropy A Sc. 

Understanding the role of surface roughness in mixed lubrication is a first step toward the microscopic study of tribology. It has been an effort for more than 30 years, starting from statistic models, but it is the deterministic approach that provides a powerful means to explore the tribological events occurring at the micrometre scale. 

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