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Fujiyabu et al. have experimentally reported that mixing of 3-arm star prepolymers into 4-arm analog improves the toughness of the resultant polymer networks compared to the base network composed of 4-arm star polymers only. For the…
Semiflexible polymers such as filamentous actin play a vital role in the mechanical behavior of cells, yet the basic properties of cross-linked F-actin networks remain poorly understood. To address this issue, we have performed numerical…
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,…
The non-linear stress-strain relation for crosslinked polymer networks is studied using molecular dynamics simulations. Previously we demonstrated the importance of trapped entanglements in determining the elastic and relaxational…
Tanglegrams are drawings of two rooted binary phylogenetic trees and a matching between their leaf sets. The trees are drawn crossing-free on opposite sides with their leaf sets facing each other on two vertical lines. Instead of minimizing…
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…
We study interaction-induced broken symmetry phases that can arise in metallic or semimetallic band structures with two nested Weyl or Dirac loops. The odered phases can be of the charge or (pseudo)spin density wave type, or…
We study transformers' in-context learning of variable-length Markov chains (VOMCs), focusing on the finite-sample accuracy as the number of in-context examples increases. Compared to fixed-order Markov chains (FOMCs), learning VOMCs is…
In this paper, we employ Molecular Dynamics computer simulations to study and compare the statics and dynamics of linear and circular (ring) polymer chains in entangled solutions of different densities. While we confirm that linear chain…
The interplay of topological constraints, excluded volume interactions, persistence length and dynamical entanglement length in solutions and melts of linear chains and ring polymers is investigated by means of kinetic Monte Carlo…
We numerically investigate critically delocalized wavefunctions in models of 2D Dirac fermions, subject to vector potential disorder. These describe the surface states of 3D topological superconductors, and can also be realized through…
We show that for any fixed dense graph G and bounded-degree tree T on the same number of vertices, a modest random perturbation of G will typically contain a copy of T . This combines the viewpoints of the well-studied problems of embedding…
Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length N_e which operate on results for a single chain…
We study the interaction problem of a linear polymer chain, floating in fractal containers that belong to the three-dimensional Sierpinski gasket (3D SG) family of fractals, with a surface-adsorbed linear polymer chain. Each member of the…
We develop a model for charge trapping on conjugated polymer chains using a continuous representation of the polymer. By constraining the motion to along the chain, we find that kinks along the chain serve as points of attraction and can…
We consider the problem of undirected polymers (tied at the endpoints) in random environment, also known as the unoriented first passage percolation on the hypercube, in the limit of large dimensions. By means of the multiscale refinement…
We study the energy structure and the coherent transfer of an extra electron or hole along aperiodic polymers made of $N$ monomers, with fixed boundaries, using B-DNA as our prototype system. We use a Tight-Binding wire model, where a site…
In the first part of the paper we show that the constraining potentials introduced to mimic entanglement effects in Edwards' tube model and Flory's constrained junction model are diagonal in the generalized Rouse modes of the corresponding…
We present a unified scaling theory for the structural behavior of polymers embedded in a disordered energy substrate. An optimal polymer configuration is defined as the polymer configuration that minimizes the sum of interacting energies…
Matroids, particularly linear ones, have been a powerful tool in parameterized complexity for algorithms and kernelization. They have sped up or replaced dynamic programming. Delta-matroids generalize matroids by encapsulating structures…