Related papers: Computer-Assisted Proofs for Geometric Optimizatio…
The electron transport through the nanotube junctions which connect the different metallic nanotubes by a pair of a pentagonal defect and a heptagonal defect is investigated by Landauer's formula and the effective mass approximation. From…
Finding the optimal solution to a complex optimization problem is of great importance in practically all fields of science, technology, technical design and econometrics. We demonstrate that a modified Grover's quantum algorithm can be…
We have investigated atom-nanotube van der Waals (vdW) coupling in atomically doped carbon nanotubes (CNs). Our approach is based on the perturbation theory for degenerated atomic levels, thus accounting for both weak and strong…
We study a geometric variational problem arising from modeling two-dimensional charged drops of a perfectly conducting liquid in the presence of an external potential. We characterize the semicontinuous envelope of the energy in terms of a…
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…
Recent work has explored using the stabilizer formalism to classically simulate quantum circuits containing a few non-Clifford gates. The computational cost of such methods is directly related to the notion of stabilizer rank, which for a…
In this paper, we study a shape optimization problem for the torsional energy associated with a domain contained in an infinite cylinder, under a volume constraint. We prove that a minimizer exists for all fixed volumes and show some of its…
We propose a numerical method to find the optimal transport map between a measure supported on a lower-dimensional subset of R^d and a finitely supported measure. More precisely, the source measure is assumed to be supported on a simplex…
The analytical expressions for the van der Waals potential energy and force between two crossed carbon nanotubes are presented. The Lennard-Jones potential for two carbon atoms and the method of the smeared out approximation suggested by…
We combine ab initio density functional theory with transport calculations to provide a microscopic basis for distinguishing between good and poor metal contacts to nanotubes. Comparing Ti and Pd as examples of different contact metals, we…
The characterization of nanostructued materials under reactive environments is challenging due to the complexity of the structural motifs involved and their chemical transformations. Global optimization approaches allow predicting stable…
In this study, we describe a procedure of topology optimization in the framework of the linear Boltzmann equation, implemented using a reference Monte-Carlo particle transport code. This procedure can design complex structures that optimize…
By combining ab initio all-electron localized orbital and pseudopotential plane-wave approaches we report on calculations of the electron affinity (EA) and the ionization potential (IP) of (5, 5) and (7, 0) single-wall carbon nanotubes. The…
We consider the problem of finding optimal shapes of fluid domains. The fluid obeys the Navier--Stokes equations. Inside a holdall container we use a phase field approach using diffuse interfaces to describe the domain of free flow. We…
Finding appropriate interatomic potentials which can accurately describe the crystal structure of material is one of important topics in material science. In this paper, several interatomic potentials which comprise of Lennard-Jones (LJ)…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
Since electrons in a ballistic regime perceive a carbon nanotube or a graphene layer structure as a continuous medium, we can use the study of the quantum dynamics of one electron constrained to a curve or surface to obtain a qualitative…
Geometric image transformations that arise in the real world, such as scaling and rotation, have been shown to easily deceive deep neural networks (DNNs). Hence, training DNNs to be certifiably robust to these perturbations is critical.…
We have investigated the thermal rectification phenomenon in a single-wall mass graded carbon nanotube by molecular dynamics simulation. Second generation Brenner potential has been used to model the inter atomic carbon interaction. Fixed…
We devise a new technique to prove two-dimensional crystallization results in the square lattice for finite particle systems. We apply this strategy to energy minimizers of configurational energies featuring two-body short-ranged particle…