## Mathematical modelling I will talk about mathematical modelling in the hard sciences at first, in the soft sciences thereafter, with emphasis on essential differences between the two. It may be useful to start with semantics: the "hard" sciences are, in the present context, those (such as the p
Hard versus soft impacts in oscillatory systems modeling
β Scribed by Barbara Blazejczyk-Okolewska; Krzysztof Czolczynski; Tomasz Kapitaniak
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 796 KB
- Volume
- 15
- Category
- Article
- ISSN
- 1007-5704
No coin nor oath required. For personal study only.
β¦ Synopsis
The applicability of the soft and hard impact models in modeling of vibro-impact systems is discussed in the paper. We derive the conditions which allow the same rate of energy dissipation in dynamical systems which use both impact models. The advantages and disadvantages of both models in modeling are discussed. We show that in the case of the stiff base both methods give the same results but the elastic base application of the hard impact model leads to wrong results.
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## Abstract The motivation for this study is the need for accurate numerical models of melt flow instabilities during Czochralski growth of oxides. Such instabilities can lead to undesirable spiralling shapes of the bulk crystals produced by the growing process. The oxide melts are characterized by