The Frobenius formalism in Galois quantum systems

Quantum systems in which the position and momentum take values in the ring ${\cal Z}_d$ and which are described with $d$-dimensional Hilbert space, are considered. When $d$ is the power of a prime, the position and momentum take values in the Galois field $GF(p^ \ell)$, the position-momentum phase space is a finite geometry and the corresponding `Galois quantum systems' have stronger properties. The study of these systems uses ideas from the subject of field extension in the context of quantum mechanics. The Frobenius automorphism in Galois fields leads to Frobenius subspaces and Frobenius transformations in Galois quantum systems. Links between the Frobenius formalism and Riemann surfaces, are discussed

Drop impact upon micro- and nanostructured superhydrophobic surfaces

We experimentally investigate drop impact dynamics onto different superhydrophobic surfaces, consisting of regular polymeric micropatterns and rough carbon nanofibers, with similar static contact angles. The main control parameters are the Weber number \We and the roughness of the surface. At small \We, i.e. small impact velocity, the impact evolutions are similar for both types of substrates, exhibiting Fakir state, complete bouncing, partial rebouncing, trapping of an air bubble, jetting, and sticky vibrating water balls. At large \We, splashing impacts emerge forming several satellite droplets, which are more pronounced for the multiscale rough carbon nanofiber jungles. The results imply that the multiscale surface roughness at nanoscale plays a minor role in the impact events for small \We \apprle 120 but an important one for large \We \apprge 120. Finally, we find the effect of ambient air pressure to be negligible in the explored parameter regime \We \apprle 150Comment: 8 pages, 7 figure

Mechanical tuning of the evaporation rate of liquid on crossed fibers

We investigate experimentally the drying of a small volume of perfectly wetting liquid on two crossed fibers. We characterize the drying dynamics for the three liquid morphologies that are encountered in this geometry: drop, column and a mixed morphology, in which a drop and a column coexist. For each morphology, we rationalize our findings with theoretical models that capture the drying kinetics. We find that the evaporation rate depends significantly on the liquid morphology and that the drying of liquid column is faster than the evaporation of the drop and the mixed morphology for a given liquid volume. Finally, we illustrate that shearing a network of fibers reduces the angle between them, changes the morphology towards the column state, and so enhances the drying rate of a volatile liquid deposited on it

Shape programming for narrow ribbons of nematic elastomers

Using the theory of Γ-convergence, we derive from three-dimensional elasticity new one-dimensional models for non-Euclidean elastic ribbons, i.e., ribbons exhibiting spontaneous curvature and twist. We apply the models to shape-selection problems for thin films of nematic elastomers with twist and splay-bend texture of the nematic director. For the former, we discuss the possibility of helicoid-like shapes as an alternative to spiral ribbons

Pine cone scale-inspired motile origami

Stimuli-sensitive hydrogels have received attention because of their potential applications in various fields. Stimuli-directed motion offers many practical applications, such as in drug delivery systems and actuators. Directed motion of asymmetric hydrogels has long been designed; however, few studies have investigated the motion control of symmetric hydrogels. We designed a pine cone scale-inspired movable temperature-sensitive symmetric hydrogel that contains Fe3O4. Alignment of Fe3O4 along the magnetic force is key in motion control in which Fe3O4 acts like fibers in a pine cone scale. Although a homogeneous temperature-sensitive hydrogel cannot respond to a temperature gradient, the Fe3O4-containing hydrogel demonstrates considerable bending motion. Varying degrees and directions of motion are easily facilitated by controlling the amount and alignment angle of the Fe3O4. The shape of the hydrogel layer also influences the morphological structure. This study introduced facile and low-cost methods to control various bending motions. These results can be applied to many fields of engineering, including industrial engineering.111Ysciescopu

Improving the dielectric properties of ethylene-glycol alkanethiol self-assembled monolayers.

Self-assembled monolayers (SAMs) can be formed at the interface between solids and fluids, and are often used to modify the surface properties of the solid. One of the most widely employed SAM systems is exploiting thiol-gold chemistry, which, together with alkane-chain-based molecules, provides a reliable way of SAM formation to modify the surface properties of electrodes. Oligo ethylene-glycol (OEG) terminated alkanethiol monolayers have shown excellent antifouling properties and have been used extensively for the coating of biosensor electrodes to minimize nonspecific binding. Here, we report the investigation of the dielectric properties of COOH-capped OEG monolayers and demonstrate a strategy to improve the dielectric properties significantly by mixing the OEG SAM with small concentrations of 11-mercaptoundecanol (MUD). The monolayer properties and composition were characterized by means of impedance spectroscopy, water contact angle, ellipsometry and X-ray photoelectron spectroscopy. An equivalent circuit model is proposed to interpret the EIS data and to determine the conductivity of the monolayer. We find that for increasing MUD concentrations up to about 5% the resistivity of the SAM steadily increases, which together with a considerable decrease of the phase of the impedance, demonstrates significantly improved dielectric properties of the monolayer. Such monolayers will find widespread use in applications which depend critically on good dielectric properties such as capacitive biosensor

Breaking the diffusion limit with super-hydrophobic delivery of molecules to plasmonic nanofocusing SERS structures

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