A mathematical model called to help coffee lovers
Two mathematicians from the University of Oxford tried to apply mathematical model to calculate what design of the vessel will prevent liquids (e.g., coffee) to pour out of it when driving.
The results of calculations published in the journal SIAM Review.
To understand the basic mechanisms describing the oscillations of the liquid, the authors created a simple model considering only the horizontal vibrations of the container with liquid. It describes the motion of a vessel on a smooth surface under the action of the spring. According to mathematicians, this model gives an idea of the motion of the fluid in the tank, attached to the pendulum, but it is much easier to compute. In addition, they greatly simplify the form of the vessel.
In their model, the researchers took into account the movement of the “arms” the oscillation frequency of walking and the behavior of the “springs” connecting the moving support and the liquid reservoir. The calculations showed that to greatly reduce fluctuations in the liquid by hanging the vessel on the string or pendulum.
The authors hope that future models will take into account vertical oscillations, and more complex forms of liquids. It is also necessary to describe the fluid behaviour at vibrations with a frequency close to the resonance. All of these additions greatly complicate the model and computations, but will make the results more accurate.