Related papers: Topologically Driven Swelling of a Polymer Loop
A flow generator is described in which homogeneous axisymmetric turbulent air flows with varying and fully controllable degrees of anisotropy, including the much studied isotropic case, are generated by the combined agitations produced by…
A notion of random walks for circle packings is introduced. The geometry behind this notion is discussed, together with some applications. In particular, we obtain a short proof of a result regarding the type problem for circle packings,…
Topological chaos relies on the periodic motion of obstacles in a two-dimensional flow in order to form nontrivial braids. This motion generates exponential stretching of material lines, and hence efficient mixing. Boyland et al. [P. L.…
We develop topological methods for characterizing the relationship between polymer chain entanglement and bulk viscoelastic responses. We introduce generalized Linking Number and Writhe characteristics that are applicable to open linear…
We construct a simple analytic model for wall-bounded turbulence, containing only four adjustable parameters. Two of these parameters characterize the viscous dissipation of the components of the Reynolds stress-tensor and other two…
Nodal loop semimetals are close descendants of Weyl semimetals and possess a topologically dressed band structure. We argue by combining the conventional theory of magnetic oscillation with topological arguments that nodal loop semimetals…
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…
We study the statistical mechanics of a closed random manifold of fixed area and fluctuating volume, encapsulating a fixed number of noninteracting particles. Scaling analysis yields a unified description of such swollen manifolds,…
Investigations into the effects of polymers on small-scale statistics and flow patterns were conducted in a turbulent von Karman swirling (VKS) flow. We employed the tomographic particle image velocimetry (Tomo-PIV) technique to obtain full…
Topologically nontrivial states are common in symmetry broken phases at macroscopic scales. Low dimensional systems bring them to a microscopic level where solitons emerge as single particles. The earliest and latest applications are…
We find a power law for the number of knot-monomers with an exponent $0.39 \pm0.13$ in agreement with previous simulations. For the average size of a knot we also obtain a power law $N_m=2.56\cdot N^{0.20\pm0.04}$. We further present data…
Coronal loops in active regions are often characterized by quasi-circular and helically twisted (sigmoidal) geometries, which are consistent with dipolar potential field models in the former case, and with nonlinear force-free field models…
We consider the set of solutions to $M$ random polynomial equations whose $N$ variables are restricted to the $(N-1)$-sphere. Each equation has independent Gaussian coefficients and a target value $V_0$. When solutions exist, they form a…
Entangled states are ubiquitous amongst fibrous materials, whether naturally occurring (keratin, collagen, DNA) or synthetic (nanotube assemblies, elastane). A key mechanical characteristic of these systems is their ability to reorganise in…
The relationship between the polymer orientation and the chaotic flow, in a dilute solution of rigid rodlike polymers at low Reynolds number, is investigated by means of direct numerical simulations. It is found that the rods tend to align…
We study nontrivial entropy invariants in the class of parabolic flows on homogeneous spaces, quasi-unipotent flows. We show that topological complexity (ie, slow entropy) can be computed directly from the Jordan block structure of the…
Generic dynamical systems have `typical' Lyapunov exponents, measuring the sensitivity to small perturbations of almost all trajectories. A generic system has also trajectories with exceptional values of the exponents, corresponding to…
Brownian motion and viscoelasticity of semiflexible polymers is a subject that has been studied for many years. Still, rigorous analysis has been hindered due to the difficulty in handling the constraint that polymer chains cannot be…
This review is an extended version of the Seoul ICM 2014 proceedings.It is a short overview of the "topological recursion", a relation appearing in the asymptotic expansion of many integrable systems and in enumerative problems. We recall…
We consider equilibrium statistics for high Reynolds number isotropic turbulence in an incompressible flow driven by steady forcing at the largest scale. Motivated by shell model observations, we develop a similarity theory for the inertial…