Characterization of Particulate Mixtures by In-Line Measurments

The quality of particulate mixtures influences strongly the efficiency of downstream process steps. The design or optimization of mixing processes requires fast and accurate methods for determining mixture quality. This paper describes an optical method for the in-line concentration measurement of the key (tracer) component in particulate mixtures with fiber optical probes. Small fluctuations of tracer concentration equivalent to a low concentration variance represent a high degree of mixing. Monochromatic light penetrates via fiber optical probes into a powder sample. A photometer measures the intensity of the diffuse reflected light. If the tracer differs in colour from the other components of the mixture its concentration can be determined. Three types of fiber optical probes were tested. For calibration two series of mixed samples covering a broad concentration range were prepared, one consisting of white Al(OH)₃ and dark SiC and the other of Al(OH)₃ and a much finer green pigment. The calibration graphs are described by the Kubelka-Munk theory. The influence of changes in particle size on the signals is reduced by choosing a probe with an angled arrangement of the fibers. The sample mass of the probes is estimated to ca. 0.01 g, based on comparison with random mixtures at different tracer concentrations. In-line measurements provide extensive data sets which allow advanced statistical intepretations of mixing processes.     

The renormalized variational theory: Its structure,interpretation, and relation to other methods

We apply the Ritz variational principle to a renormalized form of the Iwamoto-Yamada cluster expansion, restricting our discussion to infinite systems. The structure of the resulting theory is governed by the renormalization which keeps track of the normalization denominator in the expectation value. The single-particle potential for hole states (u_i) is introduced as a Lagrange multiplier in the variational principle, and the self-consistent choice of u_i guarantees that the renormalization factors are determined correctly. The importance of the renormalization is illustrated by a discussion of the two-body approximation to our theory. The general formalism is evaluated in more detail for the representation Ψ_T = exp(S)Φ of the trial wave function. Very fundamental considerations show that the theory is especially adapted to that choice of Ψ_T. In addition, if we use that choice of Ψ_T the self-consistent single-particle energies are directly related to experiment, and the theory is almost identical to renormalized Brueckner theory. Thus we are able to clarify many aspects of the latter. We also discuss the relation to the theory of Coester and Kümmel.     

A Retrial BMAP/PH/N System

A multi-server retrial queueing model with Batch Markovian Arrival Process and phase-type service time distribution is analyzed. The continuous-time multi-dimensional Markov chain describing the behavior of the system is investigated by means of reducing it to the corresponding discrete-time multi-dimensional Markov chain. The latter belongs to the class of multi-dimensional quasi-Toeplitz Markov chains in the case of a constant retrial rate and to the class of multi-dimensional asymptotically quasi-Toeplitz Markov chains in the case of an infinitely increasing retrial rate. It allows to obtain the existence conditions for the stationary distribution and to elaborate the algorithms for calculating the stationary state probabilities.