On the geometrical representation of phase equilibria

In order to achieve a rational and optimal representation of thermodynamic information in a two-dimensional plot for multicomponent systems, three types of equilibrium phase dia-grams are investigated with regard to their topology. These three types are 1) diagrams in which the coordinates are given by two generalized thermodynamic potential functions ; 2) diagrams in which one generalized thermodynamic potential function is replaced by a ratio of conjugate extensive variables; 3) diagrams in which both generalized thermody-namic potential functions are replaced by ratios of conjugate extensive variables. In the second part of this investigation, the general considerations are used to calculate and construct phase diagrams of ternary systems of the kindA-B-X. It is shown that the pro-posed representations, especially the ones using logp X ₂-n _A/(n _A +n _B ) as generalized thermodynamic potential and conjugate extensive variable coordinates (which are topo-logically analogous to the well knownT- x _i -diagrams of binary systems) allow conclusions of practical importance to be drawn. The ternary systems discussed in detail are Co-Ni-O, Ag-Cu-Cl, Cu-Ni-S, Pb-Sn-Cl, Ag-Sb-S, Mg-Ni-O, Fe-Cr-O, and Fe-Ni-O.     

A geometrical statistical analysis of structural changes-I the chord intercepts of the diminishing phase of the: Tammann system at a time t

The Taramann system represents an idealized transforming system of one component. It is statistically completely defined by special conditions of the nucleation and the growth. Its microstructure (topology) at a time t contains two phases. From this microstructure we make a linear analysis in a thought experiment. We derive the distribution function of the lengths of the chord intercepts of the diminishing phase as well as some other quantities characterizing the microstructure at time t.     

Distortions and disappearances of geometrical patterns

Prolonged observation of a stationary grating has a number of perceptual consequences. Initially the lines appear well-resolved and straight. The lines then take on a wavy and oscillating appearance, which is followed by scintillation of the pattern. The scintillations are often accompanied by cloudy disappearances of the grating. A streaming or scintillating aftereffect is visible subsequently, upon viewing a homogeneous surface. The literature concerning these effects is reviewed and several experiments are reported which examined the apparent waviness and scintillating disappearances. The basis for the apparent waviness remains unresolved. It is suggested that the scintillations are produced by small involuntary eye movements over the contours and that the associated disappearances might be due to binocular rivalry.     

Approximate Derivation of Critical Buckling Load

This paper proposes an approximate derivation for the critical buckling load of a column, based on the application of a uniformly loaded beam's midspan moment and deflection to the buckled column's rotational equilibrium. The curvature of a pin-ended member, when it buckles under axial load, is similar to the curvature assumed by the same member when it deflects under a uniformly distributed load applied transversely along its entire length. Euler's famous equation for critical buckling load is based, of course, on the former assumption, in which the deflected column assumes the shape of a sine curve. However, dividing a uniformly loaded beam's midspan moment by its deflection provides a conservative result for the critical buckling load, within 3% of Euler's value, that can be derived solely on the basis of these commonly used beam equations.     

Threshold effect in visual perception of geometrical figures

Filtering of the input image has been shown to play a central role in several aspects of visual perception. In our experiments in visual perception of the area of geometrical figures the orientation in random dot patterns, and some visual illusions, we have shown that a threshold effect inferred from the filtering of the input image produces a perceptual error. This error has been explained by using the concept of Image Function. The present paper is a brief review of our experimental results and of the models we have proposed.     

Derivation of subgroups from dyadic interactions.

This article presents a simulation study that compares several methods for deriving empirical subgroups from sociometric data. The Monte Carlo study was used to investigate how well the methods recovered the subgroup structure that had been built into the actors' and partners' modes. Forty-eight sociomatrices were generated using a 2–4?×?3 factorial design. The factors included the number of individuals in the network, the true number of subgroups into which the individuals were classified, the proportion of individuals falling into each of the subgroups, the structure of the dyadic interactions, and the clarity of the subgroup structure. On the basis of the simulation study's results, subgroups were derived for two real data sets. The first data set described the relations in a monastery (S. F. Sampson, 1968). The second data set described the referral network of a service provider (P. H. Reingen & J. B. Kernan, 1986). (PsycINFO Database Record (c) 2010 APA, all rights reserved)