# Gallery — Math

Gallery Items tagged Math

Show all Gallery Items Mimetic postprocessing for LFRic
We describe what mimetic interpolation is and why it is critical for some pre- and post-processing tasks. A simple test case shows how using bilinear interpolation for a flux calculation introduces numerical errors that depend on the grid, the number of segments and the number of quadrature points. In contrast, mimetic interpolation will return the exact result regardless of the grid resolution and the number of segments.
Alex Pletzer and Wolfgang Hayek and Jorge Bornemann Forced Van Der Pol's Equation
This work is going to analyze the Forced Van Der Pol's Equation which is used to analyze the electric circuit. In 1927, Balthasar Van Der Pol observed the stable oscillation and heard some irregular noise in vacuum tube circuit. He then proposed the Forced Van Der Pol's Equation to analyze the circuit and suggested the concept of limit cycle and Chaos to explain his observation. In this work, We would like to analyze behavior of the model by observing the phase space, time series, bifurcation diagram and power spectrum. Those points in the figures are calculated by Runge-Kutta Method with the aid of MATLAB. For a better understanding, the RLC circuit, which is a electric circuit consisting the a resistor, an inductor and a capacitor, will be used as an example for explaining the properties. Apart from electric circuit, the Forced Van Der Pol's Equation can be applied to dynamic systems in different aspect, such as the artificial heart, economic market and so on. Therefore, we suggest this work to all students since the Forced Van Der Pol's Equation can be applied to many majors, like Mathematics, Physics, Economics, Sociology, Biology, Engineering and so on.
Wallace, Homer