Related papers: Universal features of polymer shapes in crowded en…
These lecture notes are a guided tour through the fascinating world of polymer chains interacting with themselves and/or with their environment. The focus is on the mathematical description of a number of physical and chemical phenomena,…
We evaluate averages involving characteristic polynomials, inverse characteristic polynomials and ratios of characteristic polynomials for a $N\times N$ random matrix taken from a $L$-deformed Chiral Gaussian Unitary Ensemble with an…
In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles is beyond a critical density. Starting with a reduced model for collective motion,…
We present an overview of the Density Matrix Renormalization Group and its connections to Quantum Groups, Matrix Products and Conformal Field Theory. We emphasize some common formal structures in all these theories. We also propose…
We study the dynamics of an ideal polymer chain in a crowded, viscoelastic medium and in the presence of active forces. The motion of the centre of mass and of individual monomers is calculated. On time scales that are comparable to the…
We present simulations on a binary blend of bead-spring polymer chains. The introduction of monomer size disparity yields very different relaxation times for each component of the blend. Competition between two different arrest mechanisms,…
We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure with which the symmetry groups of physics are usually endowed…
The statistical mechanics of a linear non-interacting polymer chain with a large number of monomers is considered with fixed angular momentum. The radius of gyration for a linear polymer is derived exactly by functional integration. This…
Systems undergoing an equilibrium phase transition from a liquid state to an amorphous solid state exhibit certain universal characteristics. Chief among these are the fraction of particles that are randomly localized and the scaling…
A single semiflexible polymer chain folds into a toroidal object under poor solvent conditions. In this study, we examined the morphological change in such a toroidal state as a function of the width and stiffness of the chain together with…
In this paper, we study a model of directed polymers in random environment, where the environment is restricted to a time-space tube whose spatial width grows polynomially with time. It can be viewed as an interpolation between the…
We obtain several new characterizations of ultrametric spaces in terms of roundness, generalized roundness, strict p-negative type, and p-polygonal equalities (p > 0). This allows new insight into the isometric embedding of ultrametric…
Abstract polymer models are systems of weighted objects, called polymers, equipped with an incompatibility relation. An important quantity associated with such models is the partition function, which is the weighted sum over all sets of…
A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0,1]^2. The topological properties of the…
Field-theoretical method is efficient in predicting the assembling structures of polymeric systems. However, for the polymer/nanoparticle mixture, the continuous density description is not suitable to capture the realistic assembly of…
I am showing how the ideas behind the renormalisation group can be generalised in order to produce the desired reduction in the degrees of freedom other that the ones considered up to now. Instead of looking only at the renormalisation…
Bead packs of up to 150,000 mono-sized spheres with packing densities ranging from 0.58 to 0.64 have been studied by means of X-ray Computed Tomography. These studies represent the largest and the most accurate description of the structure…
The looping of polymers such as DNA is a fundamental process in the molecular biology of living cells, whose interior is characterised by a high degree of molecular crowding. We here investigate in detail the looping dynamics of flexible…
Modeling of polymer chains has received a lot of attention in mathematics. In fact, probabilistic models that naturally arise in statistical mechanics have been widely studied by mathematicians for the very challenging and novel problems…
We present a new approach to study measures on ensembles of contours, polymers or other objects interacting by some sort of exclusion condition. For concreteness we develop it here for the case of Peierls contours. Unlike existing methods,…