Related papers: Cyclic Bonds in Branched Polymers
Concentration invariance of cyclic species in the irreversible polymerization is examined. The simulation shows that the invariance theorem holds in good approximation for the irreversible process also. The physical soundness of the…
Different methods for creating Olympic gels are analyzed using computer simulations. First ideal reference samples are obtained from freely interpenetrating semi-dilute solutions and melts of cyclic polymers. The distribution of pairwise…
Biological molecules can form hydrogen bonds between nearby residues, leading to helical secondary structures. The associated reduction of configurational entropy leads to a temperature dependence of this effect: the "helix-coil…
Three-dimensional bond or site percolation theory on a lattice can be interpreted as a gauge theory in which the Wilson loops are viewed as counters of topological linking with random clusters. Beyond the percolation threshold large Wilson…
All crossed products of two cyclic groups are explicitly described using generators and relations. A necessary and sufficient condition for an extension of a group by a group to be a cyclic group is given.
We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the Configuration Model where nodes of different types are connected via…
We present some recent theory and simulation results addressing the phenomena of colloidal gelation at both high and low volume fractions, in the presence of short-range attractive interactions. We discuss the ability of mode-coupling…
This paper concerns the reliability of a pair of coupled oscillators in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations regardless of the network's initial…
Adding dynamic bonds in polymer networks enables reprocessing and recycling; however the full impact of reversible bonds on dynamic network mechanics remains unclear. We build model dynamic networks and observe substantial deviations from…
Structural properties of evolving random graphs are investigated. Treating linking as a dynamic aggregation process, rate equations for the distribution of node to node distances (paths) and of cycles are formulated and solved analytically.…
A lattice model is used to estimate the self-diffusivity of entangled cyclic and linear polymers in blends of varying compositions. To interpret simulation results, we suggest a minimal model based on the physical idea that constraints…
Dispersed colloidal particles within a suspension can aggregate and spontaneously self-organize into a robust, percolating structure known as a gel. These network-like structures are prevalent in nature and play a critical role in many…
Polymerization and formation of crosslinked polymer networks are important processes in manufacturing, materials fabrication, and in the case of hydrated polymer networks, synthesis of biomedical materials, drug delivery, and tissue…
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 use the fact that certain cosets of the stabilizer of points are pairwise conjugate in a symmetric group $S_n$ in order to construct recurrence relations for enumerating certain subsets of $S_n$. Occasionally one can find `closed form'…
Our curiosity-driven desire to "see" chemical bonds dates back at least one-hundred years, perhaps to antiquity. Sweeping improvements in the accuracy of measured and predicted electron charge densities, alongside our largely bondcentric…
This paper introduces a new representation method that is mainly based on chemical bonds among atoms in materials. Each chemical bond and its surrounded atoms are considered as a unified unit or a local structure that is expected to reflect…
The chemical bond is a central organizing concept in chemistry, yet it is absent from the molecular Hamiltonian and no "bond operator" exists. Bonding is therefore not a primitive physical entity but a derived descriptor emerging from the…
In recent times some interesting field theoretical descriptions of the statistical mechanics of entangling polymers have been proposed by various authors. In these approaches, a single test polymer fluctuating in a background of static…
Chemical bonding is a nonlocal phenomenon that binds atoms into molecules. Its ubiquitous presence in chemistry, however, stands in stark contrast to its ambiguous definition and the lack of a universal perspective for its understanding. In…