Excel as Tool for Modeling , Dynamic Simulation and Visualization ofMechanical Motion
One of the most important tasks in teaching of mechanics is to use a suitable method for developing of theoreticallyacquired knowledge. Drawing on her own experience, the author has found that the best method to be used is the system approach.System approach is closely connected to the modeling,computer simulation and dynamic visualization. Theory of the systems, modeling and computer simulation are disciplines with its own theory and research methodology. Modeling and computer simulation (M&S) can be understand as one of the most important method in teaching of mathematics and simultaneously can be use as suitable method for practical developing of theoretically acquired knowledge. Case study, described in the paper, presentspossibility of dynamic visualization of mechanical motion – trajectory of ballistic shot. The solution is demonstrated in MS Excel worksheet and chart. Key-Words:Animation, computer simulation, mathematical modeling, system approach, visualization.
Mastermind: method of the system approach in the algorithm development and computer simulation
One of the most important tasks in teaching of algorithm development and programming is to use a suitable method of developing theoretical knowledge of algorithm development and programming. Drawing on his own experience, the author has found that the best method to be used is the system approach. This method, described in the paper, is presented through the computer simulation of real process - solution of the Mastermind board game. The solution is demonstrated progressively - it starts with the mathematical analysis of the problem, then the strategy of the solution and algorithm development is presented and finally the computer simulation program in MS Excel is shown. A case study of the system approach as a suitable method of the algorithm development thinking is presented in the paper step by step; the text also emphasizes multidisciplinary learning of university students.
Collagen dynamics in articular cartilage under osmotic pressure
Cartilage is a complex biological tissue consisting of collagen, proteoglycans and water. The structure and molecular mobility of the collagen component of cartilage were studied by 13C solid‐state NMR spectroscopy as a function of hydration. The hydration level of cartilage was adjusted between fully hydrated (∼80 wt% H2O) and highly dehydrated (∼30 wt% H2O) using the osmotic stress technique. Thus, the conditions of mechanical load could be simulated and the response of the tissue macromolecules to mechanical stress is reported. From the NMR measurements, the following results were obtained. (i) Measurements of motionally averaged dipolar 1H–13C couplings were carried out to study the segmental mobility in cartilage collagen at full hydration. Backbone segments undergo fast motions with amplitudes of ∼35° whereas the collagen side‐chains are somewhat more mobile with amplitudes between 40 and 50°. In spite of the high water content of cartilage, collagen remains essentially rigid. (ii) No chemical shift changes were observed in 13C cross‐polarization magic angle spinning spectra of cartilage tissue at varying hydration indicating that the collagen structure was not altered by application of high osmotic stress. (iii) The 1H–13C dipolar coupling values detected for collagen signals respond to dehydration. The dipolar coupling values gradually increase upon cartilage dehydration, reaching rigid limit values at ∼30 wt% H2O. This indicates that collagen is essentially dehydrated in cartilage tissue under very high mechanical load, which provides insights into the elastic properties of cartilage collagen, although the mechanical pressures applied here exceed the physiological limit. Copyright © 2006 John Wiley & Sons, Ltd.