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In chaotic deterministic systems, seemingly stochastic behavior is generated by relatively simple, though hidden, organizing rules and structures. Prominent among the tools used to characterize this complexity in 1D and 2D systems are…
We have studied the breakup and subsequent fluid flow in very thin films of partially wetting liquid on solid substrates, using molecular dynamics simulations. The liquid is made of short chain molecules interacting with Lennard-Jones…
We connect topological changes that can occur in $3$-space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena, including relationships between quantum entanglement and wormhole…
Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional…
Molecular dynamics simulations are a central computational methodology in materials design for relating atomic composition to mechanical properties. However, simulating materials with atomic-level resolution on a macroscopic scale is…
Topological physics opens up a plethora of exciting phenomena allowing to engineer disorder-robust unidirectional flows of light. Recent advances in topological protection of electromagnetic waves suggest that even richer functionalities…
Molecular dynamics simulations are used to study structure formation in simple model polymer chains that are subject to excluded volume and torsional interactions. The changing conformations exhibited by chains of different lengths under…
Molecular simulation technologies have afforded researchers a unique look into the nanoscale interactions driving physical processes. However, a limitation for molecular dynamics (MD) simulations is that they must be performed on…
A powerful technique is introduced for simulating mechanical and electromechanical properties of one-dimensional nanostructures under arbitrary combinations of bending, twisting, and stretching. The technique is based on a novel control of…
In this paper we present an implementation of a computer algorithm that automatically determines the topological structure of spacetime, using a branched covering space representation. This algorithm is applied to a few simple examples in…
A finite element simulation of the mechanical behaviour of woven textile materials at the scale of individual fibers is proposed in this paper. The aim of the simulation is to understand and identify phenomena involved at different scales…
Image acquisition techniques such as micro-computed tomography are nowadays widely available. Quantitative analysis of the resulting 3D image data enables geometric characterization of the micro-structure of materials. Stochastic geometry…
We study how to generate molecule conformations (i.e., 3D structures) from a molecular graph. Traditional methods, such as molecular dynamics, sample conformations via computationally expensive simulations. Recently, machine learning…
Cooperativity is a hallmark of proteins, many of which show a modular architecture comprising discrete structural domains. Detecting and describing dynamic couplings between structural regions is difficult in view of the many-body nature of…
Topological quantum computation is a promising technique to achieve large-scale, error-corrected computation. Quantum hardware is used to create a large, 3-dimensional lattice of entangled qubits while performing computation requires…
A quantum model of universe is constructed in which values of dimensionless coupling constants of the fundamental interactions (including the cosmological constant) are determined via certain topological invariants of manifolds forming…
Molecular Dynamics simulations are becoming a powerful tool for examining and predicting atomic and molecular processes in various environment. The present review shows how, in the fields of plasma physics, chemistry and interactions with…
We show that a topological quantum computer based on the evaluation of a Witten-Reshetikhin-Turaev TQFT invariant of knots can always be arranged so that the knot diagrams with which one computes are diagrams of hyperbolic knots. The…
Cryo-EM reconstruction algorithms seek to determine a molecule's 3D density map from a series of noisy, unlabeled 2D projection images captured with an electron microscope. Although reconstruction algorithms typically model the 3D volume as…
Molecular dynamics refers to the computer simulation of a material at the atomic level. An open problem in numerical analysis is to explain the apparent reliability of molecular dynamics simulations. The difficulty is that individual…