Related papers: Skyrmion Vibration Modes within the Rational Map A…
We analyze the mechanism of condensation of orientational moduli (as introduced in [25]) on multi-Skyrmionic configurations of the four-dimensional Skyrme model. The present analysis reveals interesting novel features. First of all, the…
A quantization of a breathing motion of a rotating chiral soliton on $S^3$ is performed in terms of a family of trial functions for a profile function of the hegdehog ansatz. We determine eigenenergies of the quantized $S^3$ skyrmion by…
We consider the real dynamics of a two parameter family of plane birational maps, focusing especially on an open subset of parameter space on which the real and complex dynamics are in close agreement. On the complex side, we find a…
We consider multishell configurations in the Skyrme model within the rational map ansatz. We show that equations for the Skyrme field are linearized in the limit of large number of shells, thus allowing for a simple analytic solution.…
Classically spinning B=1 Skyrmions can be regarded as approximations to nucleons with quantised spin. Here, we investigate nucleon-nucleon scattering through numerical collisions of spinning Skyrmions. We identify the dineutron/diproton and…
We report an experimental study of the statistical properties of vibrated granular rings. In this system, a linked rod and bead metallic chain in the form of a ring is collisionally excited by a vertically oscillating plate. The dynamics…
We develop a simple continuum model to analyze the vibrational modes of a nanomechanical multi-element structure. In this model, arrays of sub-micron cantilevers located symmetrically on both sides of the central clamped-clamped nanobeam…
Skyrmions are topological solitons in two-dimensional systems and have been observed in various physical systems. Generating and controlling skyrmions in artificial resonator arrays lead to novel acoustic, photonic, and electric devices,…
In a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents…
In this work we consider the higher dimensional Skyrme model, with spatial dimension $d > 3$, focusing on its BPS submodels and their corresponding features. To accommodate the cases with a higher topological degree, \(B\geq 1\), a modified…
Magnetic skyrmion bags are composite topological spin textures with arbitrary topological charges. Here, we computationally study the transient rotational motion of skyrmion bags, which is characterized by a global rotation of the inner…
The kinetic energy of the Skyrmion-Skyrmion system is calculated in the product ansatz. The energy is expanded in a set of rotationally invariant quadratic functions of translational and iso-rotational velocities in the product ansatz and…
Using a recently introduced mapping between a scalar elastic network tethered at its boundaries and a diffusion problem with permanent traps, we study various vibrational properties of progressively tethered disordered fractals. Different…
In this note, we generalize biharmonic equation for rotationally symmetric maps ([4], [16], [10]) to equivariant maps between model spaces and use it to give a complete classification of rotationally symmetric conformal biharmonic maps from…
We give formulas and effective sharp bounds for the degree of multi-graded rational maps and provide some effective and computable criteria for birationality in terms of their algebraic and geometric properties. We also extend the Jacobian…
We consider a rational map f:S->S of a complex projective surface together with an invariant meromorphic two form. Under a mild topological assumption on the map, we show that the zeroes of the invariant form can be eliminated by birational…
A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map which contains one fast and one slow variable. The mechanisms behind generation…
This survey article is concerned with the study of bifurcations of piecewise-smooth maps. We review the literature in circle maps and quasi-contractions and provide paths through this literature to prove sufficient conditions for the…
Vibrational motions in electronically excited states can be observed by either time and frequency resolved infrared absorption or by off resonant stimulated Raman techniques. Multipoint correlation function expressions are derived for both…
The unstable manifold of the B=2 sector of the Skyrme model is constructed numerically using the gradient-flow method. Following paths of steepest descent from the B=2 hedgehog, we apply a collective coordinate description for the motion on…