Resonances and Twist in Volume-Preserving Mappings

The phase space of an integrable, volume-preserving map with one action and $d$ angles is foliated by a one-parameter family of $d$-dimensional invariant tori. Perturbations of such a system may lead to chaotic dynamics and transport. We show that near a rank-one, resonant torus these mappings can be reduced to volume-preserving "standard maps." These have twist only when the image of the frequency map crosses the resonance curve transversely. We show that these maps can be approximated---using averaging theory---by the usual area-preserving twist or nontwist standard maps. The twist condition appropriate for the volume-preserving setting is shown to be distinct from the nondegeneracy condition used in (volume-preserving) KAM theory.Comment: Many typos fixed and notation simplified. New $n^{th}$ order averaging theorem and volume-preserving variant. Numerical comparison with averaging adde

Resonances in a spring-pendulum: algorithms for equivariant singularity theory

A spring-pendulum in resonance is a time-independent Hamiltonian model system for formal reduction to one degree of freedom, where some symmetry (reversibility) is maintained. The reduction is handled by equivariant singularity theory with a distinguished parameter, yielding an integrable approximation of the Poincaré map. This makes a concise description of certain bifurcations possible. The computation of reparametrizations from normal form to the actual system is performed by Gröbner basis techniques.

Circular dichroism of cholesteric polymers and the orbital angular momentum of light

We explore experimentally if the light's orbital angular momentum (OAM) interacts with chiral nematic polymer films. Specifically, we measure the circular dichroism of such a material using light beams with different OAM. We investigate the case of strongly focussed, non-paraxial light beams, where the spatial and polarization degrees of freedom are coupled. Within the experimental accuracy, we cannot find any influence of the OAM on the circular dichroism of the cholesteric polymer.Comment: 3 pages, 4 figure

Collective versus individual pension schemes: a welfare-theoretical perspective

Collective pension contracts allow for intergenerational risk sharing with the unborn. They therefore imply a higher level of social welfare than individual accounts. Collective pension contracts also imply a sub-optimal allocation of consumption across time periods and states of nature however. Hence, collective pension contracts also reduce social welfare. This paper explores the welfare effects of a number of collective pension contracts, distinguishing between the two welfare effects. We find that collective schemes can be either superior or inferior to individual schemes

A Cantor set of tori with monodromy near a focus-focus singularity

We write down an asymptotic expression for action coordinates in an integrable Hamiltonian system with a focus-focus equilibrium. From the singularity in the actions we deduce that the Arnol'd determinant grows infinitely large near the pinched torus. Moreover, we prove that it is possible to globally parametrise the Liouville tori by their frequencies. If one perturbs this integrable system, then the KAM tori form a Whitney smooth family: they can be smoothly interpolated by a torus bundle that is diffeomorphic to the bundle of Liouville tori of the unperturbed integrable system. As is well-known, this bundle of Liouville tori is not trivial. Our result implies that the KAM tori have monodromy. In semi-classical quantum mechanics, quantisation rules select sequences of KAM tori that correspond to quantum levels. Hence a global labeling of quantum levels by two quantum numbers is not possible.Comment: 11 pages, 2 figure

Functional Liquid Crystal Polymer Surfaces with Switchable Topographies

Surface coatings, as interfaces between functional devices and targeted objects, are critical in the performance of functional devices. Switchable topographies bring opportunities to regulate the functionality of surfaces, ranging from morphing and controllable friction to object lifting and debris removal. Various responsive materials have been investigated to develop switchable surfaces, among which liquid crystal (LC) polymers are attractive candidates due to their anisotropic properties. Herein, focus is put on recent reports of switchable surfaces made of LC polymers. The principle of actuation of LC polymer–based switchable surfaces is introduced, with following exemplary applications derived from these responsive surfaces in the field of surface morphing, switchable surface friction, and moving/lifting of objects. Finally, future possible applications of and challenges in using dynamic coatings with switchable surface topographies are discussed.</p

Facilitating Interskin Communication in Artificial Polymer Systems through Liquid Transfer

Chemical communication is a ubiquitous process in nature, and it has sparked interest in the development of electric-sense-based robotic perception systems with chemical components. Here, a novel liquid crystal polymer is introduced that combines the transferring, receiving, and sensing of chemical signals, providing a new principle to achieve chemical communication in robotic systems. This approach allows for the transfer of cargo between two polymer coatings, and the transfer can be monitored through an electrical signal. Additionally, cascade transfer can be achieved through this approach, as the transfer of cargo is not limited to only two coatings, but can continue from the second to a third coating. Furthermore, the two coatings can be infused with different reagents, and upon exchange, a reaction takes place to generate the desired species. The novel method of chemical communication that is developed presents a notable improvement in embodied perception. This advancement facilitates human–robot and robot–robot interactions and enhances the ability of robots to efficiently and accurately perform complex tasks in their environment.</p