Self-similarity of parallel machines

Self-similarity is a property of physical systems that describes how to scale parameters such that dissimilar systems appear to be similar. Computer systems are self-similar if certain ratios of computational forces, also known as computational intensities, are equal. Two machines with different computational power, different network bandwidth and different inter-processor latency behave the same way if they have the same ratios of forces. For the parallel conjugate gradient algorithm studied in this paper, two machines are self-similar if and only if the ratio of one force describing latency effects to another force describing bandwidth effects is the same for both machines. For the two machines studied in this paper, this ratio, which we call the mixing coefficient, is invariant as problem size and processor count change. The two machines have the same mixing coefficient and belong to the same equivalence class.     

Die Auslegung von Kühlerkondensatoren zur partiellen Kondensation von Dämpfen aus strömenden Gas/Dampf-Gemischen

Dimensioning of cooler condensers for partial condensation of vapours from gas-vapour mixtures . This contribution surveys present knowledge in the field of partial condensation with related hints about dimensioning cooler condensers. In case of an atmospheric and slightly increased pressure and moderate shearing forces of the gas-vapour mixture on the condensate film being formed, the film theory is sufficient. However, it is necessary to include the Stefan correction for unilateral diffusion. High sharing forces lead to entrainment. The results of the few experimental publications show that the film theory is no longer valid immediately before entrainment is reached. Nor can it be used in the area of high pressure. There are not enough experimentally and theoretically proved correlations for dimensioning so that it is necessary to use empirically found average overall heattransfer coefficients. The use of well-known correlations to determine limits of entrainment makes it possible to prove whether the film theory is valid or not in every single case.     

Energierückgewinnung bei der Konvektionstrocknung mit Hilfe von Membranen

Thermal drying of solid materials is one of the most energy-intensive process steps as, in most cases, the recuperation of the high latent heat in water vapour is either not possible or uneconomical. Particularly in convective drying processes, in which hot gases are used as heat carriers, the level of energy in the vapours leaving the dryer is very low. One starting point for significant recuperation of energy is the development of efficient membranes with which it is possible to selectively separate water vapour from exhaust gas or air. After separation, the water vapour can be recirculated – using the principle of mechanical vapour recompression – as hot steam into the drying process. The feasibility of this process can be demonstrated in a laboratory unit. It is possible, by using this process, to reduce the energy used for convection drying to about 25% of the usual requirement. As far as the use of primary energy is concerned, up to 50% can be saved by using a gas motor for the compressor and utilizing the heat produced in the drying process.     

A metric space for computer programs and the principle of computational least action

We define a normed metric space for computer programs and derive from it the Principle of Computational Least Action. In our model, programs follow trajectories determined by Newton’s equation of motion in an abstract computational phase space and generate computational action as they evolve. A program’s action norm is the L ₁-norm of its action function, and its distance from other programs is the distance derived from the action norm. The Principle of Computational Least Action states the goal of performance optimization as finding the program with the smallest action norm. We illustrate this principle by analyzing a simple program.

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