Related papers: Shearless barriers in the conservative Ikeda map

In this paper we study dynamical aspects of the two-dimensional gonihedric spin model using both numerical and analytical methods. This spin model has vanishing microscopic surface tension and it actually describes an ensemble of loops…

We theoretically examine the inertial migration of a neutrally buoyant spheroid of aspect ratio $\kappa$ in wall-bounded plane Poiseuille flow at small particle Reynolds number ($Re_p$) and small confinement ratio ($\lambda$), with channel…

We consider a one-parameter family of invertible maps of a two-dimensional lattice, obtained by applying round-off to planar rotations. All orbits of these maps are conjectured to be periodic. We let the angle of rotation approach pi/2, and…

The motion of a freely rotating prolate spheroid in a simple shear flow of a dilute polymeric solution is examined in the limit of large particle aspect ratio, $\kappa$. A regular perturbation expansion in the polymer concentration, $c$, a…

Multistable coupled map lattices typically support travelling fronts, separating two adjacent stable phases. We show how the existence of an invariant function describing the front profile, allows a reduction of the infinitely-dimensional…

In this paper we give an elementary treatment of the dynamics of skew tent maps. We divide the two-parameter space into six regions. Two of these regions are further subdivided into infinitely many regions. All of the regions are given…

The hydrodynamic response of the inviscid small shearing box model of a midplane section of a rotationally supported astrophysical disk is examined. An energy functional ${\cal E}$ is formulated for the general nonlinear problem. It is…

This paper studies the behavior under iteration of the maps T_{ab}(x,y)=(F_{ab}(x)-y,x) of the plane R^2, in which F_{ab}(x)=ax if x>=0 and bx if x<0. The orbits under iteration correspond to solutions of the nonlinear difference equation…

It is well known that inertia-free shearing flows of a viscoelastic fluid with curved streamlines, such as the torsional flow between a rotating cone and plate, or the flow in a Taylor-Couette geometry, can become unstable to a…

Spontaneous growth of long-wavelength deformations is a defining feature of active fluids with orientational order. We investigate the effect of biaxial rectangular confinement on the instability of initially shear-aligned 3D isotropic…

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…

This paper concerns piecewise-smooth maps on $\mathbb{R}^d$ that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The stability of fixed points on switching manifolds is…

Bifurcation cascades in conservative systems are shown to exhibit a generalized diagram, which contains all relevant informations regarding the location of periodic orbits (resonances), their width (island size), irrational tori and the…

Simple mathematical models have been unable to predict the conditions leading to instabilities in a tuneable ring laser. Here, we propose a nonlinear iterative map model for tuneable ring lasers. Solving a reduced nonlinear Schr\"odinger…

We consider a one-dimensional, time-reversal-invariant system with attractive interactions and spin-orbit coupling. Such a system is gapless due to the strong quantum fluctuations of the superconducting order parameter. However, we show…

The dynamics of microcapsules in steady shear flow was studied using a theoretical approach based on three variables: The Taylor deformation parameter $\alpha_{\rm D}$, the inclination angle $\theta$, and the phase angle $\phi$ of the…

We consider the moduli space of isotropic maps from a closed surface $\Sigma$ to a symplectic affine space and construct a K\"ahler moment map geometry, on a space of differential forms on $\Sigma$, such that the isotropic maps correspond…

In this paper we consider random dynamical systems formed by concatenating maps acting on the unit interval $[0,1]$ in an iid fashion. Considered as a stationary Markov process, the random dynamical system possesses a unique stationary…

We devise a geometric description of bounded systems at criticality in any dimension $d$. This is achieved by altering the flat metric with a space dependent scale factor $\gamma(x)$, $x$ belonging to a general bounded domain $\Omega$.…

This study considers the stability of a non-inflectional elastica under a conservative end force subject to the Dirichlet, mixed, and Neumann boundary conditions. It is demonstrated that the non-inflectional elastica subject to the…