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For exact area-preserving twist maps, curves were constructed through the gaps of cantori in \cite{MMP84}, which were conjectured to have minimal flux subject to passing through the points of the cantorus. It was pointed out by \cite{Pol}…
Chiral particles are experimentally investigated while settling inwater with various turbulence intensity levels. The locations and orientations of the particles are tracked over time, allowing the close investigation of the particles'…
We consider the outer billiards map with contraction outside polygons. We construct a 1-parameter family of systems such that each system has an open set in which the dynamics is reduced to that of a piecewise contraction on the interval.…
We study a parametric family of piecewise rotations of the torus, in the limit in which the rotation number approaches the rational value 1/4. There is a region of positive measure where the discontinuity set becomes dense in the limit; we…
Here we report a surface curvature-induced directional movement phenomenon, based on molecular dynamics simulations, that a nanoscale water droplet at the outer surface of a graphene cone always spontaneously moves toward the larger end of…
We study a quasi-one-dimensional fluid of hard dumbbells with continuous orientational degrees of freedom using an exact transfer-matrix formulation. The model allows for a complete analytical characterization of thermodynamic properties,…
We investigate the motion of point vortices on the Mobius band and Klein bottle. Since these are non-orientable surfaces, the standard Hamiltonian approach does not apply. We therefore begin by establishing a modified Hamiltonian approach…
The morphology of adiabatic accretion flows with small non-zero specific angular momentum has been investigated in the axisymmetric and nonviscous limit. For an initial state characterized by a Bondi flow with the specific angular momentum…
New observable integer-valued numbers of the topological origin were revealed by the present authors studying the conductivity theory of single crystal 3D normal metals in the reasonably strong magnetic field ($B \leq 10^{3} Tl$). Our…
Let $f$ be an $R$-closed homeomorphism on a connected orientable closed surface $M$. In this paper, we show that If $M$ has genus more than one, then each minimal set is either a periodic orbit or an extension of a Cantor set. If $M =…
We show that the discrete approximate volume preserving mean curvature flow in the flat torus $\mathbb{T}^N$ starting near a strictly stable critical set $E$ of the perimeter converges in the long time to a translate of $E$ exponentially…
We study transport across a time-dependent magnetic barrier present on the surface of a three-dimensional topological insulator. We show that such a barrier can be implemented for Dirac electrons on the surface of a three-dimensional…
We study by simulation the physics of two colloidal particles in a cholesteric liquid crystal with tangential order parameter alignment at the particle surface. The effective force between the pair is attractive at short range and favors…
The paper is devoted to the applications of the theory of dynamical systems to the theory of transport phenomena in metals in the presence of strong magnetic fields. More precisely, we consider the connection between the geometry of the…
In this paper we consider a Ricci de Turck flow of spaces with isolated conical singularities, which preserves the conical structure along the flow. We establish that a given initial regularity of Ricci curvature is preserved along the…
We prove that on the typical translation surface the flow in almost every pair of directions are not isomorphic to each other and are in fact disjoint. It was not known if there were any translation surfaces other than torus covers with…
We investigate vortex dipoles on surfaces of variable negative curvature, focusing on a catenoid of arbitrary throat radius as a concrete example. We construct the effective dynamical system including mutual and geometric self-interaction…
Flexible mechanical structures can undergo large deformations under small loads, enabling large, complex, and nonlinear wave responses under finite-frequency driving. Here, we study a dynamically driven canonical flexible mechanical…
Models of monodisperse particle flow in partially filled three-dimensional tumblers often assume that flow along the axis of rotation is negligible. We test this assumption, for spherical and double cone tumblers, using experiments and…
In this paper we study the Ricci flow on surfaces homeomorphic to a cylinder (that is, a product of the circle with a compact interval). We prove longtime existence results, results on the asymptotic behavior of the flow, and we report on…