Related papers: Marginally compact hyperbranched polymer trees
We study a directed polymer model in a random environment on infinite binary trees. The model is characterized by a phase transition depending on the inverse temperature. We concentrate on the asymptotics of the partition function in the…
Based on experiments of the compaction of granular materials under periodic shear of a packing of glass beads, a minimal model for the dynamics of the packing density as a function of time is proposed. First, a random ``energy landscape''…
The mechanics of disordered fibrous networks such as those that make up the extracellular matrix are strongly dependent on the local connectivity or coordination number. For biopolymer networks this coordination number is typically between…
We propose a coarse-grained model for polymer chains and polymer networks based on the meso-scale dynamics. The model takes the internal degrees of freedom of the constituent polymer chains into account using memory functions and colored…
Dynamical properties of a long polymer ring in a melt of unknotted and unconcatenated rings are calculated. We re-examine and generalize the well known model of a ring confined to a lattice of topological obstacles in the light of the…
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…
We examine the thermally-induced fracture of an unstrained polymer chain of discrete segments coupled by an anharmonic potential by means of Molecular Dynamics simulation with a Langevin thermostat. Cases of both under- and over-damped…
The effect of excluded volume interactions on the structure of a polymer in shear flow is investigated by Brownian Dynamics simulations for chains with size $30\leq N\leq 300$. The main results concern the structure factor $S({\bf q})$ of…
This study focuses on comparing the individual polymer chain dynamics in an entangled polymeric liquid under different shear and extension rates. Polymer chains under various shear rates and extension rates were simulated using a…
We investigate the kinetics of loop formation in flexible ideal polymer chains (Rouse model), and polymers in good and poor solvents. We show for the Rouse model, using a modification of the theory of Szabo, Schulten, and Schulten, that the…
The non-linear response of entangled polymers to shear flow is complicated. Its current understanding is framed mainly as a rheological description in terms of the complex viscosity. However, the full picture requires an assessment of the…
The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established…
Rooted, weighted continuum random trees are used to describe limits of sequences of random discrete trees. Formally, they are random quadruples $(\mathcal{T},d,r,p)$, where $(\mathcal{T},d)$ is a tree-like metric space, $r\in\mathcal{T}$ is…
Here, we provide an overview of theoretical approaches to semiflexible polymers and their networks. Such semiflexible polymers have large bending rigidities that can compete with the entropic tendency of a chain to crumple up into a random…
The constraints imposed by nano- and microscale confinement on the conformational degrees of freedom of thermally fluctuating biopolymers are utilized in contemporary nano-devices to specifically elongate and manipulate single chains. A…
Recent developments of microscopic mechanical experiments allow the manipulation of individual polymer molecules in two main ways: \textit{uniform} stretching by external forces and \textit{non-uniform} stretching by external fields. Many…
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 consider edge effects in grafted polymer layers under compression. For a semi-infinite brush, the penetration depth of edge effects $\xi\propto h_0(h_0/h)^{1/2}$ is larger than the natural height $h_0$ and the actual height $h$. For a…
We study self avoiding random walks in an environment where sites are excluded randomly, in two and three dimensions. For a single polymer chain, we study the statistics of the time averaged monomer density and show that these are well…
Strain energy density is calculated for a network of flexible chains with weak excluded-volume interactions (whose energy is small compared with thermal energy). Constitutive equations are developed for an incompressible network of chains…