Related papers: Topological versus rheological entanglement length…
The classical rheological theories of entangled polymeric liquids are built upon two pillars: Gaussian statistics of entanglement strands and the assumption that the stress arises exclusively from the change of intramolecular configuration…
Significant challenges exist in the nonlinear extensional rheology of entangled polymers. With simulations, we show that the key to understanding this problem is to recognize the existence and importance of a strain-induced crossover from…
The path integral is not typically utilized for analyzing entanglement experiments, in part because there is no standard toolbox for converting an arbitrary experiment into a form allowing a simple sum-over-history calculation. After…
Although the behavior of entangled polymers in startup shear flows with constant shear rates has been thoroughly investigated, the response under creep has not been frequently considered. In this study, primitive chain network simulations,…
Projected Entangled Pair States (PEPS) are a promising ansatz for the study of strongly correlated quantum many-body systems in two dimensions. But due to their high computational cost, developing and improving PEPS algorithms is necessary…
The spatial correlations of entangled polymer dynamics are examined by molecular dynamics simulations and neutron spin-echo spectroscopy. Due to the soft nature of topological constraints, the initial spatial decays of intermediate…
We briefly review the recent advances in the rheology of entangled polymers and identify emerging research trends and outstanding challenges, especially with respect to branched polymers. Emphasis is placed on the role of well-characterized…
In this paper, we explore how to use topological tools to compare dimension reduction methods. We first make a brief overview of some of the methods often used dimension reduction such as Isometric Feature Mapping, Laplacian Eigenmaps, Fast…
In this work a new strategy is proposed in order to build analytic and microscopic models of fluctuating polymer rings subjected to topological constraints. The topological invariants used to fix these constraints belong to a wide class of…
By combining molecular dynamics simulations and topological analyses with scaling arguments, we obtain analytic expressions that quantitatively predict the entanglement length $N_e$, the plateau modulus $G$, and the tube diameter $a$ in…
The study of multipartite entanglement is much less developed than the bipartite scenario. Recently, a string of results have proposed using tools from Topological Data Analysis (TDA) to attach topological quantities to multipartite states.…
A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via persistent homology, which encodes features of interest as…
Topological entanglement entropy has been regarded as a smoking-gun signature of topological order in two dimensions, capturing the total quantum dimension of the topological particle content. An extrapolation method on cylinders has been…
Topological Data Analysis (TDA) uses insights from topology to create representations of data able to capture global and local geometric and topological properties. Its methods have successfully been used to develop estimations of fractal…
Studies of the degrees of freedom or "synergies" in musculoskeletal systems rely critically on algorithms to estimate the "dimension" of kinematic or neural data. Linear algorithms such as principal component analysis (PCA) are used almost…
The statistical mechanics of polymer loops entangled in the two-dimensional array of randomly distributed obstacles of infinite length is discussed. The area of the loop projected to the plane perpendicular to the obstacles is used as a…
Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time -- commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena,…
The conformational statistics of ring polymers in melts or dense solutions is strongly affected by their quenched microscopic topological state. The effect is particularly strong for untangled (i.e. non-concatenated and unknotted) rings,…
We present an algorithm to compute path homology for simple digraphs, and use it to topologically analyze various small digraphs en route to an analysis of complex temporal networks which exhibit such digraphs as underlying motifs. The…
Current theories on the conformation and dynamics of unknotted and non-concatenated ring polymers in melt conditions describe each ring as a tree-like double-folded object. While evidence from simulations supports this picture on a single…