Related papers: Computer-Assisted Proofs for Geometric Optimizatio…
Optimization problems with both control variables and environmental variables arise in many fields. This paper introduces a framework of personalized optimization to han- dle such problems. Unlike traditional robust optimization,…
We study a family of local depth-based corrections to maxmin landmark selection for lazy witness persistence. Starting from maxmin seeds, we partition the cloud into nearest-seed cells and replace or move each seed toward a deep…
We systematically investigate the relationships between structural and electronic effects of finite size zigzag or armchair carbon nanotubes of various diameters and lengths, starting from a molecular template of varying shape and diameter,…
State-of-the-art classical optimization solvers set a high bar for quantum computers to deliver utility in this domain. Here, we introduce a quantum preconditioning approach based on the quantum approximate optimization algorithm. It…
In Machine-Assisted Theorem Proving, a theorem proving agent searches for a sequence of expressions and tactics that can prove a conjecture in a proof assistant. In this work, we introduce several novel concepts and capabilities to address…
The ancient Gamow liquid drop model of nuclear energies has had a renewed life as an interesting problem in the calculus of variations: Find a set $\Omega \subset \mathbb R^3$ with given volume A that minimizes the sum of its surface area…
This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…
This short note describes the tentative form of a finite-dimensional optimization problem that may be of use in a second-generation proof of the Kepler conjecture. In the original 1998 proof of the Kepler conjecture, the form of the…
We investigate the mechanical and adsorption properties of single-walled carbon nanotubes (SWCNTs) filled with greenhouse gases through Grand Canonical Monte Carlo (GCMC) and Molecular Dynamics (MD) simulations using a recently developed…
The nucleation and growth of single wall carbon nanotubes from a carbon-saturated catalytic particle surrounded by a single sheet of graphene is described qualitatively by using a very restricted number of elementary processes, namely…
Trapped, laser-cooled atoms and ions are quantum systems which can be experimentally controlled with an as yet unmatched degree of precision. Due to the control of the motion and the internal degrees of freedom, these quantum systems can be…
The fully atomistic modeling of real-size plasmonic nanostructures is computationally demanding, therefore most calculations are limited to small-to-medium sized systems. However, plasmonic properties strongly depend on the actual shape and…
A local optimization method based on Bayesian Gaussian Processes is developed and applied to atomic structures. The method is applied to a variety of systems including molecules, clusters, bulk materials, and molecules at surfaces. The…
We present an effective medium theory in order to analyze the reported optical properties of aligned carbon nanotube films (W.A. de Heer et al., Science 268, 845 (1995)). This methodology is based on photonic band structure calculations and…
Carbon nanotubes (CNTs) are critical building blocks in nanotechnology, yet the characterization of their dynamic growth is limited by the experimental challenges in nanoscale motion measurement using scanning electron microscopy (SEM)…
A generalization of the Anderson model that includes pseudo-Jahn-Teller impurity coupling is proposed to describe distortions of an endohedral impurity in a carbon nanotube. Treating the distortion within mean-field theory, spontaneous…
We show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to stationarity of order $1$),…
We present an accurate machine learning (ML) model for atomistic simulations of carbon, constructed using the Gaussian approximation potential (GAP) methodology. The potential, named GAP-20, describes the properties of the bulk crystalline…
Optimization is finding the best solution, which mathematically amounts to locating the global minimum of some cost function. Optimization is traditionally automated with digital or quantum computers, each having their limitations and none…
The stability of a single-walled carbon nanotube placed on top of a catalytic nickel nanoparticle is investigated by means of molecular dynamics simulations. As a case study, we consider the $(12,0)$ nanotube consisting of 720 carbon atoms…