Related papers: The length of excitable knots
Twisted torus knots and links are given by twisting adjacent strands of a torus link. They are geometrically simple and contain many examples of the smallest volume hyperbolic knots. Many are also Lorenz links. We study the geometry of…
Many multicellular communities propagate signals in a directed manner via excitable waves. Cell-to-cell heterogeneity is a ubiquitous feature of multicellular communities, but the effects of heterogeneity on wave propagation are still…
In the loop representation the quantum constraints of gravity can be solved. This fact allowed significant progress in the understanding of the space of states of the theory. The analysis of the constraints over loop dependent wavefunctions…
The Skyrme-Faddeev model is a modified sigma model in three-dimensional space, which has string-like topological solitons classified by the integer-valued Hopf charge. Numerical simulations are performed to compute soliton solutions for…
We present new computations of approximately length-minimizing polygons with fixed thickness. These curves model the centerlines of "tight" knotted tubes with minimal length and fixed circular cross-section. Our curves approximately…
Knotted and tangled structures frequently appear in physical fields, but so do mechanisms for untying them. To understand how this untying works, we simulate the behavior of 1,458 superfluid vortex knots of varying complexity and scale in…
A new type of knot energy is presented via real life experiments involving a thin resilient metallic tube. Knotted in different ways, the device mechanically acquires a uniquely determined (up to isometry) normal form at least when the…
We construct two distinct yet related M-theory models that provide suitable frameworks for the study of knot invariants. We then focus on the four-dimensional gauge theory that follows from appropriately compactifying one of these M-theory…
The bidomain model is the standard model for cardiac electrophysiology. In this paper, we investigate the instability and asymptotic behavior of planar fronts and planar pulses of the bidomain Allen-Cahn equation and the bidomain…
We study steady vortex sheet solutions of the Navier-Stokes in the limit of vanishing viscosity at fixed energy flow. We refer to this as the turbulent limit. These steady flows correspond to a minimum of the Euler Hamiltonian as a…
In this article, we are interested in the behavior of a fully connected network of $N$ neurons, where $N$ tends to infinity. We assume that the neurons follow the stochastic FitzHugh-Nagumo model, whose specificity is the non-linearity with…
We construct a family of exact solutions to Maxwell's equations in which the points of zero intensity form knotted lines topologically equivalent to a given but arbitrary algebraic link. These lines of zero intensity, more commonly referred…
We extend the entanglement bootstrap approach to (3+1)-dimensions. We study knotted excitations of (3+1)-dimensional liquid topological orders and exotic fusion processes of loops. As in previous work in (2+1)-dimensions, we define a…
The existence of a random attractor for the stochastic FitzHugh-Nagumo system defined on an unbounded domain is established. The pullback asymptotic compactness of the stochastic system is proved by uniform estimates on solutions for large…
I consider the quantum interference of electrons moving along knotted trajectories under external magnetic field. The induced persistent current is formulated in terms of characteristic parameters that classify the torus knot geometry. The…
A model is developed describing the approach to a finite-time singularity of the Navier-Stokes equations for two interacting vortices. The model is derived from a combination of the Biot-Savart law and an equation describing the evolution…
We study vortex knotting in the Faddeev-Skyrme model. Starting with a straight vortex line twisted around its axis we follow its evolution under dissipative energy minimization dynamics. With low twist per unit length the vortex forms a…
In math.GT/0002110 the author's Theorems 1.1 and 1.2, combined, implied that iterated torus knots are transversally simple. This result is in error and this erratum pin points the error. In "An addendum on iterated torus knots" a more…
Recent experiments showed that the last, single channel conductance step in monatomic gold contacts exhibits significant fluctuations as a function of stretching. From simulations of a stretched gold nanowire linked to deformable tips, we…
We use geometric singular perturbation techniques combined with an action functional approach to study traveling pulse solutions in a three-component FitzHugh--Nagumo model. First, we derive the profile of traveling $1$-pulse solutions with…