相关论文: Global Optimization on an Evolving Energy Landscap…

The global minima of clusters bound by a Dzugutov potential form non-compact polytetrahedral clusters mainly composed of interpenetrating and face-sharing 13-atom icosahedra. As the size increases, these icosahedral units first form linear…

As the world is transitioning towards highly renewable energy systems, advanced tools are needed to analyze such complex networks. Energy system design is, however, challenged by real-world objective functions consisting of a blurry mix of…

In the dynamic field of materials science, the quest to find optimal structures with low potential energy is of great significance. Over the past two decades, the minima hopping algorithm has emerged as a successful tool in this pursuit. We…

We investigate a novel stochastic technique for the global optimization of complex potential energy surfaces (PES) that avoids the freezing problem of simulated annealing by allowing the dynamical process to tunnel energetically…

We study the likelihood which relative minima of random polynomial potentials support the slow-roll conditions for inflation. Consistent with renormalizability and boundedness, the coefficients that appear in the potential are chosen to be…

In practice, objective functions of real-time control systems can have multiple local minimums or can dramatically change over the function space, making them hard to optimize. To efficiently optimize such systems, in this paper, we develop…

Solving large polynomial systems with coefficient parameters are ubiquitous and constitute an important class of problems. We demonstrate the computational power of two methods--a symbolic one called the Comprehensive Gr\"obner basis and a…

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…

Machine learning potentials (MLPs) have become indispensable for conducting accurate large-scale atomistic simulations and for the efficient prediction of crystal structures. Polynomial MLPs, defined by polynomial rotational invariants,…

We analyze the properties of a Lennard-Jones system at the level of the potential energy landscape. After an exhaustive investigation of the topological features of the landscape of the systems, obtained studying small size sample, we…

We study the energy levels of a single particle in a homogeneous magnetic field and in an axially symmetric external potential. For potentials that are superharmonic off the central axis, we find a general ``pseudoconcave'' ordering of the…

Determination of \emph{optimal} arrangements of $N$ particles on a sphere is a well-known problem in physics. A famous example of such is the Thomson problem of finding equilibrium configurations of electrical charges on a sphere. More…

Unit-vector fields $\nvec$ on a convex polyhedron $P$ subject to tangent boundary conditions provide a simple model of nematic liquid crystals in prototype bistable displays. The equilibrium and metastable configurations correspond to…

We have performed a detailed exploration of the energy landscape for configurations of points on the sphere, interacting via the logarithmic potential, and corresponding to local minima of the total energy, up to $N = 160$. The growth of…

In this work we introduce a procedure to find localized structures with finite energy. We start dealing with global monopoles, and add a new contribution to the potential of the scalar fields, to balance the contribution of the angular…

In principle, all of the dynamical complexities of many-body systems are encapsulated in the potential energy landscapes on which the atoms move - an observation that suggests that the essentials of the dynamics ought to be determined by…

Placement is crucial in the physical design, as it greatly affects power, performance, and area metrics. Recent advancements in analytical methods, such as DREAMPlace, have demonstrated impressive performance in global placement. However,…

We consider the minimisation of power-law repulsive-attractive interaction energies which occur in many biological and physical situations. We show existence of global minimizers in the discrete setting and get bounds for their supports…

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…

This paper proposes an automated method to detect, group and rectify arbitrarily-arranged coplanar repeated elements via energy minimization. The proposed energy functional combines several features that model how planes with coplanar…