Related papers: Models for polymer dynamics from dimensionality re…
Dimensionality reduction techniques have found great success in a wide range of fields requiring analysis of high-dimensional datasets. Time-lagged independent components analysis (TICA), which finds independent components (TICs) with…
In this chapter we review concepts and theories of polymer dynamics. We think of it as an introduction to the topic for scientists specializing in other subfields of statistical mechanics and condensed matter theory, so, for the readers…
The theory of the dynamics of polymers in solution is developed coming from the hydrodynamic theory of the Brownian motion (BM) and the Rouse-Zimm (RZ) model. It is shown that the time correlation functions describing the polymer motion…
We study the dynamics of a polymer that is pulled by a constant force through a viscoelastic medium. This is a model for a polymer being pulled through a cell by an external force, or for an active biopolymer moving due to a self generated…
Dynamics of a discrete polymer in time-dependent external potentials is studied with the master equation approach. We consider both stochastic and deterministic switching mechanisms for the potential states and give the essential equations…
The Rouse model can be regarded as the standard model to describe the dynamics of a short polymer chain under melt conditions. In this contribution, we explicitly check one of the fundamental assumptions of this model, namely that of a…
A simple one-dimensional model is constructed for polymer motion. It exhibits the crossover from reptation to Rouse dynamics through gradually allowing hernia creation and annihilation. The model is treated by the density matrix technique…
We extend the Rouse model of polymer dynamics to situations of non-stationary chain growth. For a dragged polymer chain of length $N(t) = t^\alpha$, we find two transitions in conformational dynamics. At $\alpha= 1/2$, the propagation of…
The local dynamical features of a PEO melt studied by MD simulations are compared to two model chain systems, namely the well-known Rouse model as well as the semiflexible chain model (SFCM) that additionally incorporates chain stiffness.…
We propose a theory of the dynamics of polymers in dilute solution, in which the popular Zimm and Rouse models are limiting cases of infinitely large and small draining parameter. The equation of motion for the polymer segments beads) is…
We introduce a new model of random layered media, extending the Matheron-de Marsily model: Here we allow for the flows to change in time. For such layered structures, we solve exactly the equations of motion for single particles, and also…
Some recent results on the rotational dynamics of polymers are reviewed and extended. We focus here on the relaxation of a polymer, either flexible or semiflexible, initially wrapped around a rigid rod. We also study the steady polymer…
The long time dynamics of polymeric materials has been extensively studied in the past through various experimental techniques and computer simulations. While computer simulations typically treat generic, simplified models, experiments deal…
The self-consistent field theory is a popular and highly successful theoretical framework for studying equilibrium (co)polymer systems at the mesoscopic level. Dynamic density functionals allow one to use this framework for studying…
By means of computer simulations, we investigate the relaxation of the Rouse modes in a simple bead-spring model for non-entangled polymer blends. Two different models are used for the fast component, namely fully-flexible and semiflexible…
Traditional models of wormlike chains in shear flows at finite temperature approximate the equation of motion via finite difference discretization (bead and rod models). We introduce here a new method based on a spectral representation in…
Dimensionality reduction is a fundamental technique in machine learning and data analysis, enabling efficient representation and visualization of high-dimensional data. This paper explores five key methods: Principal Component Analysis…
In many reacting flow systems, the thermo-chemical state-space is known or assumed to evolve close to a low-dimensional manifold (LDM). Various approaches are available to obtain those manifolds and subsequently express the original…
Machine learning (ML) methods provide advanced means for understanding inherent patterns within large and complex datasets. Here, we employ the principal component analysis (PCA) and the diffusion map (DM) techniques to evaluate the glass…
A theoretic framework for dynamics is obtained by transferring dynamics from state space to its dual space. As a result, the linear structure where dynamics are analytically decomposed to subcomponents and invariant subspaces decomposition…