the aim of this research is to calculate the elastic constants and bulk modulus of cu-20 wt% ni random nanoalloy. the molecular dynamics simulation technique was used to calculate the mechanical properties in npt ensemble. the interaction between atoms as well as cohesive energy in the nanoalloy modeled systems was calculated by morse et al. two body potential. also the temperature of the syste...

Let f be a Morse function on a closed manifold M , and v be a Riemannian gradient of f satisfying the transversality condition. The classical construction (due to Morse, Smale, Thom, Witten), based on the counting of flow lines joining critical points of the function f associates to these data the Morse complex M * (f, v). In the present paper we introduce a new class of vector fields (f-gradie...

Within a one-dimensional semi-classical model with a Morse potential the possibility of infrared multi-photon dissociation of vibrationally excited nitrogen oxide was studied. The dissociation thresholds of typical driving forces and couplings were found to be similar, which indicates that the results were robust to variations of the potential and of the definition of dissociation rate. PACS: 4...

A. In this paper we use Morse theory and the gradient flow of a Morse-Smale function to compute the linking number of a two-component link L in S 3 , by counting the signed number of gradient flow lines passing through each component of L. We will also use three Morse-Smale functions and their gradient flows, to compute Milnor's triple linking number of three-component links by counting ...

This paper, as a continuing work of [1], focus on establishing the fact that if we equip a reciprocal multi-agent (RMA) system with a triangulated Laman graph (TLG), then the associated potential function is generically an equivariant Morse function, i.e., there are only finitely many critical orbits each of which is nondegenerate. Though this assumption on the potential function of being an eq...

We consider a self-propelled particle system which has been used to describe certain types of collective motion of animals, such as fish schools and bird flocks. Interactions between particles are specified by means of a pairwise potential, repulsive at short ranges and attractive at longer ranges. The exponentially decaying Morse potential is a typical choice, and is known to reproduce certain...

We consider a semilinear Neumann problem with an indefinite and unbounded potential and an asymmetric reaction that crosses at least the principal eigenvalue of the operator −Δ + βI in H1(Ω), β being the potential function. Using a combination of variational methods, with truncation and perturbation techniques and Morse theory, we prove multiplicity theorems providing precise sign information f...

We discuss generic smooth maps from smooth manifolds to smooth surfaces, which we call "Morse 2-functions," and homotopies between such maps. The two central issues are to keep the fibers connected, in which case the Morse 2-function is "fiber-connected," and to avoid local extrema over one-dimensional submanifolds of the range, in which case the Morse 2-function is "indefinite." This is founda...

2. MORSE E.P., SHAKARJI C.M., SRINIVASAN V., 2018, A Brief Analysis of recent ISO Tolerancing Standards and Their Potential Impact on Digitization Manufacturing, Procedia CIRP, 75, 11–18. https://doi.org./10.1016/ J.Procir.2018.04.080. Google Scholar

In 1974, Mark Goresky and Robert MacPherson began their development of intersection homology theory (see [24] in these volumes), and their first paper on this topic appeared in 1980; see [12]. At that time, they were missing a fundamental tool which was available for the study of smooth manifolds; they had no Morse Theory for stratified spaces. Goresky and MacPherson wished to have a Stratified...