Fastest random walk on a path

In this paper, we consider two convex optimisation problems in order to maximise the mixing rate of a Markov chain on an undirected path. In the first formulation, the holding probabilities of vertices are identical and the transition probabilities from a vertex to its neighbours are equal, whereas the second formulation is the more general reversible Markov chain with the same degree proportional stationary distribution. We derive analytical results on the solutions of the optimisation problems and compare the spectra of the associated transition probability matrices.     

Development of constant output–input force ratio in slider–crank mechanisms

In the slider–crank mechanism whereby output piston force is produced against an input force at crank pin centre, the output force varies rapidly when the crank changes its position. For the applications that require a constant piston pushing force as in feeder mechanisms, a method is needed for identifying the parameters to keep output force at a constant value for any crank angle position. Hence in this study, two methods are shown for a slider–crank mechanism operating in horizontal plane. In the first one, a manual control process to generate a constant piston force and the resulting errors are demonstrated. In the second one, identifying the parameters of a mechanical controller for a readily available slider–crank mechanism in an open force control process and the associated error state are shown. Then, an approach to optimize the results of open force control is explained. Finally, the developed methods are generalized for any orientation of the whole slider–crank mechanism. A user friendly interface is developed to transform all the processes into a computer programme. The effectiveness of the methods are numerically illustrated on examples. The results of these examples show that ±4% deviation from the required output force can be obtained pending on the user’s ability while the optimized open force control process provides a maximum error of ±0.4% without any user intervention during operation.     

Nanocrystallization in Cu-Zr-Al-Sm Bulk Metallic Glasses

Metallurgical and Materials Transactions A - The effect of rare-earth element (Sm) microalloying on the thermal stability and crystallization kinetics of melt-spun ribbons and suction-cast rods of...     

Garfield number: on some characteristics of Eugene Garfield’s first and second order co-authorship networks

In this note we give an overview of the first- and second-order collaboration network reflected by Eugene Garfield’s publications in scientific journals. Although he had only a quite limited number of co-authors and co-publications, his co-authors’ own collaboration networks generate a large world-wide and multidisciplinary coverage. The classical model of co-authorship network is the Erd?s network with the Erd?s Number indicating the shortest co-authorship path through which an author is connected with Paul Erd?s. The two networks, generated by Erd?s and Garfield, respectively, show completely different patterns and characteristics but illustrate the ways how ideas of great scholars and pioneers disseminate and influence the respective scientific communities.