相关论文: Revisiting the Complexity of Finding Globally Mini…

In this chapter the physical aspects of the global optimization of the geometry of atomic clusters are elucidated. In particular, I examine the structural principles that determine the nature of the lowest-energy structure, the physical…

In this paper we consider the problem of characterizing the minimum energy configurations of a finite system of particles interacting between them due to attracting or repulsive forces given by a certain inter molecular potential. We limit…

The computational complexity of the "cluster minimization problem" is revisited [L. T. Wille and J. Vennik, J. Phys. A 18, L419 (1985)]. It is argued that the original NP-hardness proof does not apply to pairwise potentials of physical…

A new atomic cluster structure corresponding to the global minimum of the 98-atom Lennard-Jones cluster has been found using a variant of the basin-hopping global optimization algorithm. The new structure has an unusual tetrahedral symmetry…

Minimum energy configurations in celestial mechanics are investigated. It is shown that this is not a well defined problem for point-mass celestial mechanics but well-posed for finite density distributions. This naturally leads to a…

We study minimum energy configurations of $N$ particles in $\R^3$ of charge -1 (`electrons') in the potential of $M$ particles of charges $Z_\alpha>0$ (`atomic nuclei'). In a suitable large-N limit, we determine the asymptotic electron…

Locating the global minimum of a complex potential energy surface is facilitated by considering a homotopy, namely a family of surfaces that interpolate continuously from an arbitrary initial potential to the system under consideration.…

This contribution gives a short review of recent theoretical advances in most topics of nuclear cluster physics concentrating, however, around {$\alpha$} particle clustering. Along the route, the point of view will be critical mentioning…

Complexity theory as practiced by physicists and computational complexity theory as practiced by computer scientists both characterize how difficult it is to solve complex problems. Here it is shown that the parameters of a specific model…

Several commonly observed physical and biological systems are arranged in shapes that closely resemble an honeycomb cluster, that is, a tessellation of the plane by regular hexagons. Although these shapes are not always the direct product…

Computing an optimal cycle in a given homology class, also referred to as the homology localization problem, is known to be an NP-hard problem in general. Furthermore, there is currently no known optimality criterion that localizes classes…

We have located the global minimum for all lead clusters with up to 160 atoms using a glue potential to model the interatomic interactions. The lowest-energy structures are not face-centred cubic as suggested previously. Rather, for N<40…

Global minimum potential energy state can be very challenging to locate in a relatively large atomistic system. Our present work investigates this problem using an example of gold nanoclusters, Au10, Au20, Au30, Au50. Nanoscale gold…

Understanding the substructure of atomic nuclei, particularly the clustering of nucleons inside them, is essential for comprehending nuclear dynamics. Various cluster configurations can emerge depending on excitation energy, the number and…

We present a method for reliably determining the lowest energy structure of an atomic cluster in an arbitrary model potential. The method is based on a genetic algorithm, which operates on a population of candidate structures to produce new…

We present a novel approach for finding and evaluating structural models of small metallic nanoparticles. Rather than fitting a single model with many degrees of freedom, the approach algorithmically builds libraries of nanoparticle…

Product states, unentangled tensor products of single qubits, are a ubiquitous ansatz in quantum computation, including for state-of-the-art Hamiltonian approximation algorithms. A natural question is whether we should expect to efficiently…

Simple generic aspects of nuclear pairing in homogeneous medium as well as in finite nuclei are discussed. It is argued that low-energy nuclear structure is not sensitive enough to resolve fine details of nuclear nucleon-nucleon (NN)…

Density functional and quantum Monte Carlo calculations challenge the existence of a unique ground state structure for certain Si clusters. For Si clusters with more than a dozen atoms the lowest ten isomers are close in energy and for some…

In nuclear cluster systems, a rigorous structural forbiddenness of virtual nuclear division into unexcited fragments is obtained. We re-analyze the concept of forbiddenness, introduced in Ref. 1 for the understanding of structural effects…