In this contribution, I will describe a suite of methods designed to efficiently characterize the energy landscapes of continuum, Landau-type free energy models. Using wetting morphologies of liquid droplets on structured surfaces, repartitioning of multicomponent lipid membranes on triply periodic minimal surfaces and a multistable liquid crystal device as applications, I will show that the methods allow systematic study of not only the most relevant minimum energy configurations, but also the transition pathways between any two minima, as well as their corresponding energy barriers and transition state configurations. Furthermore, a global view of the free energy landscapes can be visualized using either a disconnectivity graph or a network representation. Different forms of functionals and boundary conditions can be readily implemented, thus allowing these tools to be utilized for a broad range of problems.
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