Related papers: Cyclic Bonds in Branched Polymers
Clustering is a fundamental property of complex networks and it is the mathematical expression of a ubiquitous phenomenon that arises in various types of self-organized networks such as biological networks, computer networks or social…
Given a real analytic function $f$ from $\mathbb{R}^4$ to $\mathbb{R}^2$ with isolated critical point at the origin, the link $L_f$ of the singularity is a real fibred knot in $\mathbb{S}^{3}$. From this singularities, we construct a family…
The formation, movement and gluing of clusters can be described through a system of non local balance laws. Here, the well posedness of this system is obtained, as well as various stability estimates. Remarkably, qualitative properties of…
We introduce a simple geometric model for a double-stranded and double-helical polymer. We study the statistical mechanics of such polymers using both analytical techniques and simulation. Our model has a single energy-scale which…
We propose a general theory to describe the distribution of protein-folding transition paths. We show that transition paths follow a predictable sequence of high-free-energy transient states that are separated by free-energy barriers. Each…
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…
Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…
The number of subgroups and the number of cyclic subgroups are natural combinatorial invariants of a finite group. We investigate how restrictions on these quantities, together with the number of distinct prime divisors of $|G|$, enforce…
We generalize a recently investigated lattice model of semiflexible polymers formed under equilibrium polymerization in a solution and conduct a comprehensive investigation of its melting properties. The model is characterized by six…
We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical…
Hydrogen bonds are typically treated as sufficiently localized directional intermolecular bonds, in which dispersion and electrostatic contributions can be distinguished. However, being formed chiefly due to the overlapping of p orbitals of…
Colloids that attractively bond to only a few neighbors (e.g., patchy particles) can form equilibrium gels with distinctive dynamic properties that are stable in time. Here, we use a coarse-grained model to explore the dynamics of linked…
The size of rings (also called cyclic polymers) in bidisperse blends of chemically identical rings is analyzed by computer simulations. Data of entangled ring blends and blends of interpenetrating rings are compared and it is shown that the…
We study the unfolding of a single polymer chain due to an external force. We use a simplified model which allows to perform all calculations in closed form without assuming a Boltzmann-Gibbs form for the equilibrium distribution.…
A fundamental theory is presented for the mechanical response of polymer networks undergoing large deformation which seamlessly integrates statistical mechanical principles with macroscopic thermodynamic constitutive theory. Our formulation…
The cluster algorithm in the fully frustrated Ising model on the square lattice is essentially different from the ones used in other systems. Thus its better understanding is particularly important for finding new lines of development.…
We study Bernoulli bond percolation on a random recursive tree of size $n$ with percolation parameter $p(n)$ converging to $1$ as $n$ tends to infinity. The sizes of the percolation clusters are naturally stored in a tree. We prove…
Under special conditions bacteria excrete an attractant and aggregate. The high density regions initially collapse into cylindrical structures, which subsequently destabilize and break up into spherical aggregates. This paper presents a…
We introduce and study the concept of cyclicity degree of a finite group $G$. This quantity measures the probability of a random subgroup of $G$ to be cyclic. Explicit formulas are obtained for some particular classes of finite groups. An…
Computer simulations were used to study the gel transition occurring in colloidal systems with short range attractions. A colloid-polymer mixture was modelled and the results were compared with mode coupling theory expectations and with the…