Related papers: Computer-Assisted Proofs for Geometric Optimizatio…
Carbon nanotubes are modeled as point configurations and investigated by minimizing configurational energies including two-and three-body interactions. Optimal configurations are identified with local minima and their fine geometry is fully…
Carbon nanotubes are modeled as point particle configurations in the framework of Molecular Mechanics, where interactions are described by means of short range attractive-repulsive potentials. The identification of local energy minimizers…
Nanotruss structures made of carbon nanotubes are investigated in two conceptual applications: either as building blocks of metamaterials or for nanostructural applications. The nanotrusses are optimized for different purposes, including…
The efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in safety critical roles. There is a considerable body of mathematical…
We propose an experimentally viable setup for the realization of one-dimensional ultracold atom gases in a nanoscale magnetic waveguide formed by single doubly-clamped suspended carbon nanotubes. We show that all common decoherence and atom…
This paper proposes a computer-assisted solution existence verification method for the stationary Navier-Stokes equation over general 3D domains. The proposed method verifies that the exact solution as the fixed point of the Newton…
We present a formally verified global optimization framework. Given a semialgebraic or transcendental function $f$ and a compact semialgebraic domain $K$, we use the nonlinear maxplus template approximation algorithm to provide a certified…
Coiled Carbon Nanotubes (CCNTs) are increasingly set to become a vital factor in the new generation of nanodevices and energy-absorbing materials due to their outstanding properties. In the following work, the multi-objective optimization…
Amorphous carbon nanotubes (a-CNT) with up to four walls and sizes ranging from 200 to 3200 atoms have been simulated, starting from initial random configurations and using the Gaussian Approximation Potential [Phys. Rev. B 95, 094203…
Understanding NP-complete problems is a central topic in computer science. This is why adiabatic quantum optimization has attracted so much attention, as it provided a new approach to tackle NP-complete problems using a quantum computer.…
The Cahn-Hilliard energy landscape on the torus is explored in the critical regime of large system size and mean value close to $-1$. Existence and properties of a "droplet-shaped" local energy minimizer are established. A standard mountain…
We show that quantum confinement in the valence and conduction bands of semiconducting single-walled carbon nanotubes can be engineered by means of artificial defects. This ability holds potential for designing future nanotube-based quantum…
We address the problem of verifying neural networks against geometric transformations of the input image, including rotation, scaling, shearing, and translation. The proposed method computes provably sound piecewise linear constraints for…
A combination of ab initio simulations and linear-scaling Green's functions techniques is used to analyze the transport properties of long (up to one micron) carbon nanotubes with realistic disorder. The energetics and the influence of…
Optimizations of atomic positions belong to the most commonly performed tasks in electronic structure calculations. Many simulations like global minimum searches or characterizations of chemical reactions require performing hundreds or…
The interaction of electromagnetic waves with pairs of nanotubes having arbitrary-shaped cross sections is investigated. The study starts by thoroughly examining nanotube couples with circular boundaries to identify the structural, textural…
Atomistic-to-Continuum (AtC) coupling methods are a novel means of computing the properties of a discrete crystal structure, such as those containing defects, that combine the accuracy of an atomistic (fully discrete) model with the…
It is highly desirable for a numerical approximation of a stationary point for a potential energy landscape to lie in the quadratic convergence basin of that stationary point. However, it is possible that an approximation may lie only in…
The O(N) and parallelization techniques have been successfully applied in tight-binding molecular-dynamics simulations of single-walled carbon nanotubes (SWNTs) of various chiralities. The accuracy of the O(N) description is found to be…
Classical atomistic simulations based on interatomic potentials resolve lattice instabilities, defect nucleation, and microstructure evolution with high fidelity, but their accessible system sizes remain far below those required for…