Related papers: Topological methods for searching barriers and rea…
Persistent homology is a topological feature used in a variety of applications such as generating features for data analysis and penalizing optimization problems. We develop an approach to accelerate persistent homology computations…
The kinetics of ordering and concurrent ordering and clustering is analyzed with an equation of motion initially developed to account for dissipative processes in quantum systems. A simplified energy eigenstructure, or…
Molecular Dynamics simulations are essential tools for understanding the dynamic behavior of biomolecules, yet extracting meaningful molecular pathways from these simulations remains challenging due to the vast amount of generated data. In…
Near equilibrium, thermodynamic intuition suggests that fast, irreversible processes will dissipate more energy and entropy than slow, quasistatic processes connecting the same initial and final states. Here, we test the hypothesis that…
Accurately modeling chemical reactions in molecular dynamics simulations requires detailed pre- and post-reaction templates, often created through labor-intensive manual workflows. This work introduces a Python-based algorithm that…
A thorough in situ characterization of materials at extreme conditions is challenging, and computational tools such as crystal structural search methods in combination with ab initio calculations are widely used to guide experiments by…
Topological techniques are used to study the motions of systems of point vortices in the infinite plane, in singly-periodic arrays, and in doubly-periodic lattices. The reduction of each system using its symmetries is described in detail.…
An anisotropic random barrier model is presented, in which the transition probabilities in different directions have different probability density functions. At low temperatures, the anisotropic long--time diffusion coefficients, obtained…
After collecting data from observations or experiments, the next step is to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the models. In this article, the…
Using the entropy $S$ as a reaction coordinate, we determine the free energy barrier associated with the formation of a liquid droplet from a supersaturated vapor for atomic and molecular fluids. For this purpose, we develop the $\mu VT-S$…
Within the context of topological data analysis, the problems of identifying topological significance and matching signals across datasets are important and useful inferential tasks in many applications. The limitation of existing solutions…
We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the phase field variable. Two main applications of our method are…
Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by…
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…
I discuss methods for identifying and quantifying phase transitions in particle collisions, concentrating on two techniques for use in ultra-relativistic nuclear collisions. The first technique is to use rapidity correlation measurements to…
We present a novel approach to the parallelization of the parabolic fast multipole method for a space-time boundary element method for the heat equation. We exploit the special temporal structure of the involved operators to provide an…
Normal molecular dynamics simulations are usually unable to simulate chemical reactions due to the low probability of forming the transition state. Therefore, enhanced sampling methods are implemented to accelerate the occurrence of…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
The search for pathways that optimize the formation of a particular target molecule in a reaction network is a key problem in many settings, including reactor systems. Chemical reaction networks are mathematically well represented as…
Phase separation of multicomponent liquid mixtures plays an integral part in many processes ranging from industry to cellular biology. In many cases the morphology of coexisting phases is crucially linked to the function of the separated…