Related papers: Computer-Assisted Proofs for Geometric Optimizatio…
For smooth bounded pseudoconvex domains in $mathbb{C}^{2}$, we provide geometric conditions on (the points of infinite type in) the boundary which imply compactness of the $\bar{\partial}$-Neumann operator. It is noteworthy that the proof…
Measurements of optical properties at nanometre-level are of central importance for characterization of optoelectronic device. It was, however, hardly possible for the conventional light-probe measurements to determine the local optical…
We consider a version of Gamow's liquid drop model with a short range attractive perimeter-penalizing potential and a long-range Coulomb interaction of a uniformly charged mass in $\R^3$. Here we constrain ourselves to minimizing among the…
A simulation study demonstrates that localization can arise as the result of the breakdown of stable quasi-crystal-like atomic configurations. Samples produced at elevated quench rates and via more energetic processes contain a lower…
This article is intended to an introductory lecture in material physics, in which the modern computational group theory and the electronic structure calculation are in collaboration. The effort of mathematicians in field of the group…
Topology optimization has matured to become a powerful engineering design tool that is capable of designing extraordinary structures and materials taking into account various physical phenomena. Despite the method's great advancements in…
This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…
A predictive control barrier function (PCBF) based safety filter is a modular framework to verify safety of a control input by predicting a future trajectory. The approach relies on the solution of two optimization problems, first computing…
The ability to design and dynamically control chiroptical responses in solid-state matter at wafer scale enables new opportunities in various areas. Here we present a full stack of computer-aided designs and experimental implementations of…
An important new trend in additive manufacturing is the use of optimization to automatically design industrial objects, such as beams, rudders or wings. Topology optimization, as it is often called, computes the best configuration of…
We use scanning photocurrent microscopy (SPCM) to investigate individual suspended semiconducting carbon nanotube devices where the potential profile is engineered by means of local gates. In situ tunable p-n junctions can be generated at…
Numerical and symbolic methods for optimization are used extensively in engineering, industry, and finance. Various methods are used to reduce problems of interest to ones that are amenable to solution by such software. We develop a…
Availability of affordable and widely applicable interatomic potentials is the key needed to unlock the riches of modern materials modelling. Artificial neural network based approaches for generating potentials are promising; however neural…
We address in this work the problem of minimizing quantum entropies under local constraints. We suppose macroscopic quantities such as the particle density, current, and kinetic energy are fixed at each point of $\Rm^d$, and look for a…
We demonstrate that it is possible to construct operators that stabilize the constraint-satisfying subspaces of computational problems in their Ising representations. We provide an explicit recipe to construct unitaries and associated…
We investigate the problem of safety verification of infinite-state parameterized programs that are formed based on a rich class of topologies. We introduce a new proof system, called parametric proof spaces, which exploits the underlying…
We use electrostatic force microscopy and scanned gate microscopy to probe the conducting properties of carbon nanotubes at room temperature. Multi-walled carbon nanotubes are shown to be diffusive conductors, while metallic single-walled…
We study numerically nonlinear dynamics of several types of molecular systems composed of hydrogen-bonded chains placed inside carbon nanotubes with open edges. We demonstrate that carbon nanotubes provide a stabilization mechanism for…
Carbon nanotubes bridge the molecular and crystalline quantum worlds, and their extraordinary electronic, mechanical and optical properties have attracted enormous attention from a broad scientific community. We review the basic principles…
We show how lattice Quantum Monte Carlo simulations can be used to calculate electronic properties of carbon nanotubes in the presence of strong electron-electron correlations. We employ the path integral formalism and use methods developed…