Related papers: Topological Data Analysis for Particulate Gels
The aggregation of protein-stabilised emulsions leads to the formation of emulsion gels. These soft solids are classically envisioned as droplet-filled matrices. Here however, it is assumed that protein-coated sub-micron droplets contribute…
On microscopic scales, the crystallinity of flexible tethered or cross linked membranes determines their mechanical response. We show that by controlling the type, number and distribution of defects on a spherical elastic shell, it is…
Topological Data Analysis (TDA) studies the shape of data. A common topological descriptor is the persistence diagram, which encodes topological features in a topological space at different scales. Turner, Mukeherjee, and Boyer showed that…
Supercooled liquids exhibit complicated dynamical behaviors: At the microscopic level, the dynamics is heterogeneous spatially, known as dynamic heterogeneity. At the macroscopic level, the shear viscosity $\eta$ decreases as shear rate…
Colloidal gels constitute an important class of materials found in many contexts and with a wide range of applications. Yet as matter far from equilibrium, gels exhibit a variety of time-dependent behaviours, which can be perplexing, such…
In this paper we study the role of topology in DNA gel electrophoresis experiments via molecular dynamics simulations. The gel is modelled as a 3D array of obstacles from which half edges are removed at random with probability p, thereby…
Topological data analysis is an emerging field that applies the study of topological invariants to data. Perhaps the simplest of these invariants is the number of connected components or clusters. In this work, we explore a topological…
Thermosensitive microgels are widely studied hybrid systems combining properties of polymers and colloidal particles in a unique way. Due to their complex morphology their interactions and packing, and consequentially the viscoelastcity of…
Shape analysis and classification are popular methods for biologists, biophysicists and mathematicians investigating relationships between object function and form. Classic shape descriptors, such as sphericity, can be powerful but may be…
By their nature it is difficult to differentiate chaotic dynamical systems through measurement. In recent years, work has begun on using methods of Topological Data Analysis (TDA) to qualitatively type dynamical data by approximating the…
Motivated by the unique physical properties of {\em biological active matter}, e.g., cytoskeletal dynamics in eukaryotic cells, we set up {\em effective} two-dimensional (2d) coarse-grained hydrodynamic equations for the dynamics of thin…
Persistent homology is a widely-used tool in topological data analysis (TDA) for understanding the underlying shape of complex data. By constructing a filtration of simplicial complexes from data points, it captures topological features…
We explicitly build a generalized local-density approximation (GLDA) correlation functional based on one-dimensional (1D) uniform electron gases (UEGs). The fundamental parameters of the GLDA \textemdash a generalization of the widely-known…
Topological Data Analysis has grown in popularity in recent years as a way to apply tools from algebraic topology to large data sets. One of the main tools in topological data analysis is persistent homology. This paper uses undergraduate…
The potential energy landscape (PEL) formalism is a statistical mechanical approach to describe supercooled liquids and glasses. Here we use the PEL formalism to study the pressure-induced transformations between low-density amorphous ice…
Childhood maltreatment may adversely affect brain development and consequently influence behavioral, emotional, and psychological patterns during adulthood. In this study, we propose an analytical pipeline for modeling the altered…
We investigate bulk structural properties of tetravalent associating particles within the framework of classical density functional theory, building upon Wertheim's thermodynamic perturbation theory. To this end, we calculate density…
The Delta-variance analysis is an efficient tool for measuring the structural scaling behaviour of interstellar turbulence in astronomical maps. In paper I we proposed essential improvements to the Delta-variance analysis. In this paper we…
Topological data analysis (TDA) approaches are becoming increasingly popular for studying the dependence patterns in multivariate time series data. In particular, various dependence patterns in brain networks may be linked to specific tasks…
Understanding the topological characteristics of data is important to many areas of research. Recent work has demonstrated that synthetic 4D image-type data can be useful to train 4D convolutional neural network models to see topological…