Related papers: Critical exponents for random knots
A coarse-grained computational model is used to investigate how the bending rigidity of a polymer under tension affects the formation of a trefoil knot. Thermodynamic integration techniques are applied to demonstrate that the free-energy…
Studying the threshold of black hole formation via numerical evolution has led to the discovery of fascinating nonlinear phenomena. Power-law mass scaling, aspects of universality, and self-similarity have now been found for a large variety…
Many real-world networks exhibit the so-called small-world phenomenon: their typical distances are much smaller than their sizes. One mathematical model for this phenomenon is a long-range percolation graph on a $d$-dimensional box $\{0, 1,…
We probe the character of knotting in open, confined polymers, assigning knot types to open curves by identifying their projections as virtual knots. In this sense, virtual knots are transitional, lying in between classical knot types,…
Using canonical Monte Carlo simulations, we introduce a new numerical procedure for comparing the entropic exponents of polymers with different constraints and/or topologies. Setting up competitions between polymer segments which can…
We study the volume of rigid loop-$O(n)$ quadrangulations with a boundary of length $2p$ in the non-generic critical regime. We prove that, as the half-perimeter $p$ goes to infinity, the volume scales in distribution to an explicit random…
We use numerical simulations to study tangentially active flexible ring polymers with different knot topologies. Simple, unknotted active rings display a transition from an extended phase to a collapsed one upon increasing the degree of…
A physical interpretation of the rope simulated by the SONO algorithm is presented. Properties of the tight polygonal knots delivered by the algorithm are analyzed. An algorithm for bounding the ropelength of a smooth inscribed knot is…
The stretching of a polymer chain by a large scale chaotic flow is considered. The steady state which emerges as a balance of the turbulent stretching and anharmonic resistance of the chain is quantitatively described, i.e. the dependency…
Universal dimensionless quantities, such as Binder ratios and wrapping probabilities, play an important role in the study of critical phenomena. We study the finite-size scaling behavior of the wrapping probability for the Potts model in…
In this thesis we study in detail the self-intersection properties of Random Walks. Although notoriously hard to tackle, these properties are crucially related to the excluded-volume effect and other central features of real polymers. Our…
We present here computational work on the center-of-mass displacements in thin polymer films of finite width without topological constraints and without momentum conservation obtained using a well-known lattice Monte Carlo algorithm with…
An extended polymer collapses to form a globule when subjected to a quench below the collapse transition temperature. The process begins with the formation of clusters of monomers or ``pearls''. The nascent clusters merge, resulting in…
We imagine the strings on the stretched horizon of any $d$ space-time dimensional black hole to be bits of polymer. Then, proposing an interaction between these bits we obtain the size of the configuration, and thus of the black hole, using…
The ropelength of a knot or link is the minimal number of inches of 1-inch-thick rope that it takes to tie it. The relationship of this measurement to knot and link invariants has been studied by various authors. We give the first results…
The convex hull of N independent random points chosen on the boundary of a simple polytope in R^n is investigated. Asymptotic formulas for the expected number of vertices and facets, and for the expectation of the volume difference are…
Twist stiffness and an asymmetric bending stiffness of a polymer or a polymer bundle is captured by the elastic ribbon model. We investigate the effects a ring geometry induces to a thermally fluctuating ribbon, finding bend-bend coupling…
We consider an inextensible, semiflexible polymer or worm-like chain which is confined in the transverse direction by a parabolic potential and subject to a longitudinal force at the ends, so that the polymer is stretched out and…
We study the critical properties of three-dimensional O(N) models, for N=2,3,4. Parameterizing the leading corrections-to-scaling for the $\eta$ exponent, we obtain a reliable infinite volume extrapolation, incompatible with previous Monte…
The mean area of a two-dimensional Gaussian ring of $N$ monomers is known to diverge when the ring is subject to a critical pressure differential, $p_c \sim N^{-1}$. In a recent publication [Eur. Phys. J. E 19, 461 (2006)] we have shown…