Role of 3D printing technology in dynamical systems applications
Shibabrat Naik, Stephen Wiggins
Understanding chemical reactions using dynamical systems theory is based on using the geometric view of the structures underlying the solutions of the equations of motion. The equations are derived from the potential energy due to the molecular configurations involved in the reaction. In both of these aspects, that is the geometry of the potential energy surfaces and the phase space structures, visualization in the real space of the physical world using 3D printing facility is increasing the educational and hands-on learning experience. In our research project supported by CHAMPS (EPSRC Grant No. EP/P021123/1) we used the 3D-printing facility in the School of Mathematics for prototyping a potential energy surface in the dissociation of ozone available in the literature (dx.doi.org/10.1021/ed500683g). This potential energy function at constant total energy is an 3D volume specified by a function obtained from fitting electronic energies and can be used in dynamical systems analysis of the dissociation.
The image on the left shows the generated prototype using the 3D printer and on the right is the image in the virtual space generated using the Sketchfab Labs (https://sketchfab.com/3d-models/potential-energy-in-dissociation-of-ozone-59a7e742edea4c1bba11ff3123c0312e). The hands-on experience of a 3D prototype makes the geometric methods used in phase space perspective of chemical reaction dynamics accessible to a wider audience. In addition, we are planning to use the 3D printing facility to build some of the many mathematical objects called phase space structures that come out of dynamical systems analysis of chemical reactions. This will be useful for educational and conference presentation purposes.