Related papers: Computer-Assisted Proofs for Geometric Optimizatio…
We study the possibility for constraining the topology of the Universe by means of the matched circles statistic applied to polarised cosmic microwave background (CMB) anisotropy maps. The advantages of using the CMB polarisation maps in…
This report presents three proofs showing that idealized architectures capable of navigation guided by allocentric maps with landmark structure can be computationally universal. The navigation may occur either online (in the environment) or…
In this review, we present our recent computational work on carbon-based nanostructured composites. These materials consist of carbon crystallites embedded in an amorphous carbon matrix and are modeled here through classical and…
An efficient machine-learning-based method combined with a conventional local optimization technique has been proposed for exploring local energy minima of interstitial species in a crystal. In the proposed method, an effective initial…
Carbon fiber and graphene-based nanostructures such as carbon nanotubes (CNTs) and defective structures have extraordinary potential as strong and lightweight materials. A longstanding bottleneck has been lack of understanding and…
Symmetric minima of surface potential energy of a nanocatalyst act as nucleation sites for chirally selective initial growth of single walled carbon tubes at low temperatures. The nucleation sites are sites of maximum coordination number of…
Numerical simulations of crystal defects are necessarily restricted to finite computational domains, supplying artificial boundary conditions that emulate the effect of embedding the defect in an effectively infinite crystalline…
The purpose of this paper is to explore the question "to what extent could we produce formal, machine-verifiable, proofs in real algebraic geometry?" The question has been asked before but as yet the leading algorithms for answering such…
We present a novel application of neural networks to design improved mixing elements for single-screw extruders. Specifically, we propose to use neural networks in numerical shape optimization to parameterize geometries. Geometry…
The electric polarizability and the spread of the total position tensors are used to characterize the metallic vs insulator nature of large (finite) systems. Finite clusters are usually treated within the open boundary condition formalism.…
We derive and analyze the low-energy theory of superconductivity in carbon nanotube ropes. A rope is modelled as an array of metallic nanotubes, taking into account phonon-mediated as well as Coulomb interactions, and arbitrary Cooper pair…
We have developed and characterized an atom-guiding technique that loads $3\times10^6$ cold rubidium atoms into hollow-core optical fibre, an order-of-magnitude larger than previously reported results. This result was possible because it…
We introduce a universal sparse preconditioner that accelerates geometry optimisation and saddle point search tasks that are common in the atomic scale simulation of materials. Our preconditioner is based on the neighbourhood structure and…
Many mathematical imaging problems are posed as non-convex optimization problems. When numerically tractable global optimization procedures are not available, one is often interested in testing ex post facto whether or not a locally…
It is often the case that the computed optimal solution of an optimization problem cannot be implemented directly, irrespective of data accuracy, due to either (i) technological limitations (such as physical tolerances of machines or…
Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…
We study property prediction for crystal materials. A crystal structure consists of a minimal unit cell that is repeated infinitely in 3D space. How to accurately represent such repetitive structures in machine learning models remains…
We consider the steady heat conduction problem within a thermal isotropic and homogeneous infinite strip composite reinforced by uniformly and randomly distributed non-overlapping carbon nanotubes (CNTs) and containing voids. We treat the…
The cutting of single-walled carbon nanotubes by an 80 keV electron beam catalyzed by nickel clusters is imaged in situ using aberration-corrected high-resolution transmission electron microscopy. Extensive molecular dynamics simulations…
We present a comprehensive first-principles study of the ballistic transport properties of low dimensional nanostructures such as linear chains of atoms (Al, C) and carbon nanotubes in presence of defects. A novel approach is introduced…