Related papers: Average Structures of a Single Knotted Ring Polyme…
In this document, we study the interaction between different geometric structures that can be defined as morphisms of sections of the generalized tangent bundle $\mathbb TM:= TM\oplus T^*M\to M$. In particular, we show the behaviour of…
Multiple resolution analysis of two dimensional structures composed of randomly adsorbed penetrable rods, for densities below the percolation threshold, has been carried out using box-counting functions. It is found that at relevant…
We propose and solve a simple model describing secondary structure formation in random hetero-polymers. It describes monomers with a combination of one-dimensional short-range interactions (representing steric forces and hydrogen bonds) and…
The structural properties of a linear polymer and its evolution in time have a strong bearing on its anisotropic stress response. The mean-square bond length and mean bond angle are the critical parameters that influence the time-varying…
We have studied structure formation in a confined block copolymer melt by means of dynamic density functional theory (DDFT). The confinement is two-dimensional, and the confined geometry is that of a cylindrical nanopore. Although the…
Contact can be conceptualized as a set of constraints imposed on two bodies that are interacting with one another in some way. The nature of a contact, whether a point, line, or surface, dictates how these bodies are able to move with…
Knitted and woven textile structures are examples of doubly periodic structures in a thickened plane made out of intertwining strands of yarn. Factoring out the group of translation symmetries of such a structure gives rise to a link…
For a given convex body K in $R^d$, a random polytope $K^{(n)}$ is defined (essentially) as the intersection of $n$ independent closed halfspaces containing $K$ and having an isotropic and (in a specified sense) uniform distribution. We…
We consider flexible branched polymer, with quenched branch structure, and show that its conformational entropy as a function of its gyration radius $R$, at large $R$, obeys, in the scaling sense, $\Delta S \sim R^2/(a^2L)$, with $a$ bond…
The rapid collapse of a polymer, due to external forces or changes in solvent, yields a long-lived `crumpled globule.' The conjectured fractal structure shaped by hierarchical collapse dynamics has proved difficult to establish, even with…
We have examined the behaviors of a knotted linear polymer in narrow tubes using Langevin dynamics simulation to investigate the knot localization property in one-dimensional (1D) geometry. We have found that the knot is strongly localized…
Ring polymers remain a major challenge to our current understanding of polymer dynamics. Experimental results are difficult to interpret because of the uncertainty in the purity and dispersity of the sample. Using both equilibrium and…
Studies of random close packing of spheres have advanced our knowledge about the structure of systems such as liquids, glasses, emulsions, granular media, and amorphous solids. When these systems are confined their structural properties…
Compact polymers are self-avoiding random walks which visit every site on a lattice. This polymer model is used widely for studying statistical problems inspired by protein folding. One difficulty with using compact polymers to perform…
Polymer models are used to describe chromatin, which can be folded at different spatial scales by binding molecules. By folding, chromatin generates loops of various sizes. We present here a randomly cross-linked (RCL) polymer model, where…
Symmetries and their anomalies are powerful tools for understanding quantum systems. However, realistic systems are often subject to disorders, dissipation and decoherence. In many circumstances, symmetries are not exact but only on…
Topologically constrained genome-like polymers often double-fold into tree-like configurations, which can be modelled on the level of folded (ring) polymers or on the level of the underlying random trees. For both descriptions, we have…
The determinant method in the conformal bootstrap is applied for the critical phenomena of a single polymer in arbitrary $D$ dimensions. The scale dimensions (critical exponents) of the polymer ($2< D \le 4$) and the branched polymer ($3 <…
The conformational complexity of linear polymers far exceeds that of point-like atoms and molecules. Polymers can bend, twist, even become knotted. Thus they may also display a much richer phase structure than point particles. But it is not…
A random matrix model to describe the coupling of m-fold symmetry in constructed. The particular threefold case is used to analyze data on eigenfrequencies of elastomechanical vibration of an anisotropic quartz block. It is suggested that…