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Productivity of a low-budget computer cluster applied to overcome the n-body problem

Nowicki Tomasz, Gregosiewicz Adam, Łagodowski Zbigniew

Applied Computer Science

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2021

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Vol. 17, no 4

100--109

EN

The classical n-body problem in physics addresses the prediction of individual motions of a group of celestial bodies under gravitational forces and has been studied since Isaac Newton formulated his laws. Nowadays the n-body problem has been recognized in many more fields of science and engineering. Each problem of mutual interaction between objects forming a dynamic group is called as the n-body problem. The cost of the direct algorithm for the problem is O(n2) and is not acceptable from the practical point of view. For this reason cheaper algorithms have been developed successfully reducing the cost to O(nln(n)) or even O(n). Because further improvement of the algorithms is unlikely to happen it is the hardware solutions which can still accelerate the calculations. The obvious answer here is a computer cluster that can preform the calculations in parallel. This paper focuses on the performance of a low-budget computer cluster created on ad hoc basis applied to n-body problem calculation. In order to maintain engineering valuable results a real technical issue was selected to study. It was Discrete Vortex Method that is used for simulating air flows. The pre-sented research included writing original computer code, building a computer cluster, preforming simulations and comparing the results.

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Introduction to n-body simulation of magnetorheological elastomer (MRE) microstructure forming process

Miedzińska D., Łazowski J., Boczkowska A.

Journal of KONES

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2010

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Vol. 17, No. 1

249-253

EN

Magnetorheological elastomers (MREs) are the materials with rheological properties which can be changed in a continuous way, rapidly and reversibly by the applied magnetic field. They are the solid analogues of magnetorheological fluids (MRFs), consisting of magnetically permeable particles (such as iron) added to a viscoelastic polymeric material prior to crosslinking. In the paper the introduction to the n-body simulation of the MRE microstructure forming process is presented. First, the basics of the n-body problem are presented as the planar three-body problem. It is well known, that the planar three-body problem is the problem describing the motion of three point masses in the plane under their mutual Newtonian gravitation. In the paper it is shown how that problem will be applied to the simulation of the phenomena that appeared when the external magnetic field is applied to the chaotically mixed iron particles in the liquid elastomer. Also the physical model of the interactions occurred in such structures are described. The assumptions shown in the paper will be then used for the development of the computer program which calculates the interactions between iron dipoles and describes the movement of the particles in the liquid elastomer under the magnetic field.

3

O osobliwych rozwiązaniach zagadnienia n ciał

Strzelecki P.

Postępy Fizyki

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2005

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T. 56, z. 2

50-56

EN

We discuss some of the mathematical features of the n-body problem and give a popular account of Xia's construction of noncollision singularities for n > 4.