Interatomic interaction potentials are compared using a molecular dynamics modeling method to choose the simplest, but most effective, model describe of copper nanoparticles and graphene flakes. Three considered: (1) bond-order potential; (2) hybrid embedded-atom-method Morse (3) potential. The is investigated for crumpled filled with determine possibility obtaining composite mechanical propert...

Inspired by the works of Forman on discrete Morse theory, which is a combinatorial adaptation to cell complexes of classical Morse theory on manifolds, we introduce a discrete analogue of the stratified Morse theory of Goresky and MacPherson [17]. We describe the basics of this theory and prove fundamental theorems relating the topology of a general simplicial complex with the critical simplice...

The goal of coverage path planning is to determine a path that passes a detector over all points in an environment. This work prescribes a provably complete coverage path planner for robots in unknown spaces. We achieve coverage using Morse decompositions which are exact cellular decompositions whose cells are defined in terms of critical points of Morse functions. Generically, two critical poi...

A pair of pants is a genus zero orientable surface with three boundary components. A pants decomposition of a surface is a finite collection of unordered pairwise disjoint simple closed curves embedded in the surface that decompose the surface into pants. In this paper we present two Morse theory based algorithms for pants decomposition of a surface mesh. Both algorithms operates on a choice of...

bond-order conservation-morse potential (boc-mp) method is used to carry out the calculationon the co2+ h20 system. one of the best catalysts for methanol synthesis in catalytic reductionof co2 with h2o is cu/zno/a1203 whose surface is supported by with some amount of pd orga. reduction of co2 with h20 on cu will result in methanol formation; while on ni will lead tomethane formation. in the me...

The counting function on the natural numbers defines a discrete Morse-Smale complex with a cohomology for which topological quantities like Morse indices, Betti numbers or counting functions for critical points of Morse index are explicitly given in number theoretical terms. The Euler characteristic of the Morse filtration is related to the Mertens function, the Poincaré-Hopf indices at critica...

The goal of coverage path planning is to determine a path that passes a detector over all points in an environment. This work prescribes a provably complete coverage path planner for robots in unknown spaces. We achieve coverage using Morse decompositions which are exact cellular decompositions whose cells are defined in terms of critical points of Morse functions. Generically, two critical poi...

In this paper, a novel shore-based S-band microwave Doppler coherent wave radar (Microwave Ocean Remote SEnsor (MORSE)) is designed to improve wave measurements. Marine radars, which operate in the X band, have been widely used for ocean monitoring because of their low cost, small size and flexibility. However, because of the non-coherent measurements and strong absorption of X-band radio waves...

Morse theory provides a powerful framework to study the topology of a manifold from a function de ned on it, but discrete constructions have remained elusive due to the di culty of translating smooth concepts to the discrete setting. Consider the problem of approximating the Morse-Smale (MS) complex of a Morse function from a point cloud and an associated nearest neighbor graph (NNG). While fol...

In this paper we primarily consider the family of elliptic PDEs ∆u+ f(u) = 0 on the square region Ω = (0, 1)× (0, 1) with zero Dirichlet boundary condition. Following our previous analysis and numerical approximations which relied on the variational characterization of solutions as critical points of an “action” functional, we consider Newton’s method on the gradient of that functional. We use ...