We remark that the power diagrams from computer science are the spines of amoebas in algebraic geometry, or the hypersurfaces in tropical geometry. Our concept of a Morse poset generalizes to power diagrams. We show that there exists a discrete Morse function on the coherent triangulation, dual to the power diagram, such that its critical set equals the Morse poset of the power diagram. In the ...

It is proved that the critical cells of a discrete Morse function in the sense of Forman on a finite regular CW complex can always be detected by a polyhedral Morse function in the sense of Banchoff on an appropriate embedding in Euclidean space of the barycentric subdivision of the complex. The proof is stated in terms of discrete Morse functions on a class of posets that is slightly broader t...

We examine semilinear Neumann problems driven by the Laplacian plus an unbounded and indefinite potential. The reaction is a Carathéodory function which exhibits linear growth near ±∞. We allow for resonance to occur with respect to a nonprincipal nonnegative eigenvalue, and we prove several multiplicity results. Our approach uses critical point theory, Morse theory and the reduction method (th...

The Variational Method is applied within the context of Supersymmetric Quantum Mechanics to provide information about the energy and eigenfunction of the lowest levels of a Hamiltonian. The approach is illustrated by the case of the Morse potential applied to several diatomic molecules and the results are compared with stablished results.

A simple one-dimensional lattice model is suggested to describe the experimentally observed plateau in force-stretching diagrams for some macromolecules. This chain model involves the nearest-neighbor interaction of a Morse-like potential (required to have a saturation branch) and a harmonic second-neighbor coupling. Under an external stretching applied to the chain ends, the intersite Morse-li...

A short-ranged pairwise Morse potential is used to model colloidal clusters with planar morphologies. Potential and free energy global minima as well as rearrangement paths, obtained by basin-hopping global optimisation and discrete path sampling, are characterised. The potential and free energy landscapes are visualised using disconnectivity graphs. The short-ranged potential is found to favou...