Molecular dynamics method (MD) has been used for the analysis of fluid field at the atomic and molecular level²⁾, but the calculation cost has been a major bottleneck. Then, in recent years, many scientists are trying to develop new coarse graining methods to increase the speed of calculation. Renormalization molecular dynamics method (RMD)⁶⁾ is one of them. The number of molecules is compressed by applying renormalization group conversion to the Hamiltonian, and simulations are possible at any scales by controlling number of conversion times. The applicability of this method for solids has already been proved, but the applicability for liquids or gases at the micro level has not been shown. In this study, we applied RMD to static argon liquid, gas-liquid layer and argon gas in simple shear flow. We calculated radial distribution function, coefficient of evaporation and viscosity and compared the results with normal MD. As a result, it was possible to shorten the simulation time to 1/13. The obtained results were similar to that of usual MD.

View full abstract

  In this paper, we show that behaviors of Lagrange's top are classified with parameter which at first was introduced to modify the coordinate of the equilibrium point of Euler's equations. The method of classification is as follows. At first, we represent the canonical equations of for Lagrange's top. We then make a parametric survey of potential function, so that we decide a mapping between typical motions of the top and the values of. This approach also makes it clear that there are two different modes of stationary precession and that a sleeping top mode can be reduced from a Lagrange's top. The method of numerical integration is the one which keeps the value of Hamiltonian constant.

View full abstract

  This study aims to realize an assist system for beginners to ride a unicycle as a long term purpose. This paper considers an index to evaluate the prociency in riding a unicycle. The analysis of the relationship between Moment Balancing Point (MBP) and Center of Pressure (CP) on the saddle by rider's action is important. To simulate human riding a unicycle, a Human-Unicycle model is introduced consisting of a unicycle model and an approximation model of a rider with multi-links. The mathematical model and the relationship among torque of the rider's thighs, body and the unicycle wheel are derived by Projection Method. A stabilizing control input is designed by considering the linearized simple unicycle model consisting of a saddle and a wheel. Stable riding of the Human-Unicycle model is simulated by using the torque translated from the stabilizing control input by the torque relationship. The proles of MBP and CP are calculated, and are compared with experimental results. As the result, MBP might be useful as an index for the prociency in riding a unicycle.

View full abstract