相关论文: Topological Analysis of Linear Polymer Melts
The formation of chain-folded structures from the melt is observed in molecular dynamics simulations resembling the lamellae of polymer crystals. Crystallization and subsequent melting temperatures are related linearly to the inverse…
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…
We develop intuitive metrics for quantifying complex nucleating systems under confinement. These are shown to arise naturally from the analysis of the topological ring network, and are amenable for use as order parameters for such systems.…
Several methods for preparing well equilibrated melts of long chains polymers are studied. We show that the standard method in which one starts with an ensemble of chains with the correct end-to-end distance arranged randomly in the…
We consider the statistical mechanics of a system of topologically linked polymers, such as for instance a dense solution of polymer rings. If the possible topological states of the system are distinguished using the Gauss linking number as…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
A ring polymer is a random walk whose steps obey a single linear condition; their sum vanishes. Factoring the graph Laplacian into the product of the incidence matrix and its transpose allows us to show that for a more complicated network,…
Symmetric edge polytopes are a recent and well-studied family of centrally symmetric polytopes arising from graphs. In this paper, we introduce a generalization of this family to arbitrary simplicial complexes. We show how topological…
Using group theoretic and topological concepts, together with tunneling phenomena, we geometrically design interfacial wave networks that contain splitters which partition energy in 2, 3, 4 or 5 directions. This enriches the valleytronics…
Multilevel self-assembly involving small structured groups of nano-particles provides new routes to development of functional materials with a sophisticated architecture. Apart from the inter-particle forces, the geometrical shapes and…
We demonstrate that nascent polymer crystals (i.e., nuclei) are anisotropic entities, with neither spherical nor cylindrical geometry, in contrast to previous assumptions. In fact, cylindrical, spherical, and other high symmetry geometries…
A multilayered particle is illuminated by plane acoustic or electromagnetic waves of one or several frequencies. We consider the inverse scattering problem for the identification of the layers and of the refraction coefficients of the…
A machine learning approach is presented to accelerate the computation of block polymer morphology evolution for large domains over long timescales. The strategy exploits the separation of characteristic times between coarse-grained…
We visualize entanglements in polymer melts using molecular dynamics simulation. A bead at an entanglement interacts persistently for long times with the non-bonded beads (those excluding the adjacent ones in the same chain). The…
The central goal of this thesis is to develop methods to experimentally study topological phases. We do so by applying the powerful toolbox of quantum simulation techniques with cold atoms in optical lattices. To this day, a complete…
Entangled networks are ubiquitous in tissues, polymers, and fabrics. However, their mechanics remain insufficiently understood due to the complexity of the topological constraints at the network level. Here, we develop a mathematical…
This paper proposes a machine learning (ML) method to predict stable molecular geometries from their chemical composition. The method is useful for generating molecular conformations which may serve as initial geometries for saving time…
Complex networks are a powerful modeling tool, allowing the study of countless real-world systems. They have been used in very different domains such as computer science, biology, sociology, management, etc. Authors have been trying to…
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 slow dynamics of topological solitons in the CP^1 sigma-model, known as lumps, can be approximated by the geodesic flow of the L^2 metric on certain moduli spaces of holomorphic maps. In the present work, we consider the dynamics of…