Related papers: Calculating Voronoi diagrams using simple chemical…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
We propose a general method for constructing system-dependent basis functions for correlated quantum chemical calculations. Our construction combines features from several traditional approaches: plane waves, localized basis functions, and…
In this paper we are concerned with finding the vertices of the Voronoi cell of a Euclidean lattice. Given a basis of a lattice, we prove that computing the number of vertices is a #P-hard problem. On the other hand we describe an algorithm…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
In this paper, we study a generalization of the classical Voronoi diagram, called clustering induced Voronoi diagram (CIVD). Different from the traditional model, CIVD takes as its sites the power set $U$ of an input set $P$ of objects. For…
We discuss the parallelization of algorithms for solving polynomial systems symbolically by way of triangular decomposition. Algorithms for solving polynomial systems combine low-level routines for performing arithmetic operations on…
VORO++ is a software library written in C++ for computing the Voronoi tessellation, a technique in computational geometry that is widely used for analyzing systems of particles. VORO++ was released in 2009 and is based on computing the…
Atomic nuclei are composite systems, and they may be dynamically excited during nuclear reactions. Such excitations are not only relevant to inelastic scattering but they also affect other reaction processes such as elastic scattering and…
We study the geodesic Voronoi diagram of a set $S$ of $n$ linearly moving sites inside a static simple polygon $P$ with $m$ vertices. We identify all events where the structure of the Voronoi diagram changes, bound the number of such…
This chapter discusses geometric models of biomolecules and geometric constructs, including the union of ball model, the weigthed Voronoi diagram, the weighted Delaunay triangulation, and the alpha shapes. These geometric constructs enable…
Perturbed lattices provide simple models for studying many physical systems. In this paper we study the distribution of Voronoi chains, blocks, and clusters with prescribed combinatorial features in the perturbed square lattice,…
The Voronoi diagram is a geometric object which is widely used in many areas. Recently it has been shown that under mild conditions Voronoi diagrams have a certain continuity property: small perturbations of the sites yield small…
Cellular structures manifest their outstanding mechanical properties in many biological systems. One key challenge for designing and optimizing these geometrically complicated structures lies in devising an effective geometric…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
Machine learning (ML) strategies are opening the door to faster computer simulations, allowing us to simulate more realistic colloidal systems. Since the interactions in colloidal systems are often highly many-body, stemming from e.g.…
We discuss existing and new computational analysis techniques to classify local atomic arrangements in large-scale atomistic computer simulations of crystalline solids. This article includes a performance comparison of typical analysis…
We suggest a geometric approach to modeling biochemical processes, aiming at those processes that occur in humans with food sensitivities or chemical sensitivities.
Graph transformation systems have the potential to be realistic models of chemistry, provided a comprehensive collection of reaction rules can be extracted from the body of chemical knowledge. A first key step for rule learning is the…
Computational chemistry allows researchers to experiment in sillico: by running a computer simulations of a biological or chemical processes of interest. Molecular dynamics with molecular mechanics model of interactions simulates N-body…
Solving for detailed chemical kinetics remains one of the major bottlenecks for computational fluid dynamics simulations of reacting flows using a finite-rate-chemistry approach. This has motivated the use of fully connected artificial…