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Modeling electronic systems is an important application for quantum computers. In the context of materials science, an important open problem is the computational description of chemical reactions on surfaces. In this work, we outline a…
Designing large-scale geological carbon capture and storage projects and ensuring safe long-term CO2 containment - as a climate change mitigation strategy - requires fast and accurate numerical simulations. These simulations involve solving…
To predict liquid-gas two-phase flow phenomena, accurate tracking and prediction of the evolving liquid-gas interface is required. Volume-of-Fluid or VoF method has been used in the literature for computationally modeling of such flows. In…
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is…
In this paper, we focus on the numerical analysis of quantitative photoacoustic tomography. Our goal is to reconstruct the optical coefficients, i.e., the diffusion and absorption coefficients, using multiple internal observational data.…
In this article, we aim at obtaining the analytical expression ({\bf not previously found and recorded in the literature}) for the exact curved surface area of a hyperboloid of one sheet in terms of Srivastava-Daoust triple hypergeometric…
Quantum computers are special purpose machines that are expected to be particularly useful in simulating strongly correlated chemical systems. The quantum computer excels at treating a moderate number of orbitals within an active space in a…
As convolution has empowered many smart applications, dynamic convolution further equips it with the ability to adapt to diverse inputs. However, the static and dynamic convolutions are either layout-agnostic or computation-heavy, making it…
In this paper, we address the challenge of accurately calculating droplet/bubble properties (e.g., volume, number) in diffuse-interface two-phase flow simulations. Currently, flood-fill algorithms can truncate a significant portion of the…
Computational fluid dynamics (CFD) can be used for evaluation of hemodynamics. However, its routine use is limited by labor-intensive manual segmentation, CFD mesh creation, and time-consuming simulation. This study aims to train a deep…
Piecewise Linear Interface Construction (PLIC) is frequently used to geometrically reconstruct fluid interfaces in Computational Fluid Dynamics (CFD) modeling of two-phase flows. PLIC reconstructs interfaces from a scalar field that…
Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in…
An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained…
The Convex Hull algorithm is one of the most important algorithms in computational geometry, with many applications such as in computer graphics, robotics, and data mining. Despite the advances in the new algorithms in this area, it is…
Computing offsets of curves on parametric surfaces is a fundamental yet challenging operation in computer aided design and manufacturing. Traditional analytical approaches suffer from time-consuming geodesic distance queries and complex…
A procedure for defining virtual spaces, and the periodic one-electron and two-electron integrals, for plane-wave second quantized Hamiltonians has been developed and demonstrated using full configuration interaction (FCI) simulations and…
We fully generalize a previously-developed computational geometry tool [1] to perform large-scale simulations of arbitrary two-dimensional faceted surfaces $z = h(x,y)$. Our method uses a three-component facet/edge/junction storage model,…
Every surface that is intrinsically polyhedral can be represented by a portalgon: a collection of polygons in the Euclidean plane with some pairs of equally long edges abstractly identified. While this representation is arguably simpler…
In a companion study \cite{patterson2020computing2D}, we present a numerical method for simulating 2D viscous flow through an open compliant closed channel, drive by pressure gradient. We consider the highly viscous regime, where fluid…
The permeability of complex porous materials can be obtained via direct flow simulation, which provides the most accurate results, but is very computationally expensive. In particular, the simulation convergence time scales poorly as…