Periodic Néel skyrmion transport

In this work, we have used the MuMax3 software to simulate devices consisting of a ferromagnetic thin film placed over a heavy metal thin film. The devices are two interconnected partial-disks where a Néel domain wall is formed in the disks junction. In our simulations we investigate devices with disk radius $r=50$ nm and different distance d between the disks centers (from $d=12$ nm to $d=2R=100$ nm). By applying strong sinusoidal external magnetic fields, we find a mechanism able to create, annihilate and even manipulate a skyrmion in each side of the device. This mechanism is discussed in terms of interactions between skyrmion and domain wall. The Néel domain wall formed in the center of the device interacts with the Néel skyrmion, leading to a process of transporting a skyrmion from one disk to the other periodically. Our results have relevance for potential applications in spintronics such as logical devices.     

Bounds for rectilinear crossing numbers

A rectilinear drawing of a graph is one where each edge is drawn as a straight-line segment, and the rectilinear crossing number of a graph is the minimum number of crossings over all rectilinear drawings. We describe, for every integer k ≥ 4, a class of graphs of crossing number k, but unbounded rectilinear crossing number. This is best possible since the rectilinear crossing number is equal to the crossing number whenever the latter is at most 3. Further, if we consider drawings where each edge is drawn as a polygonal line segment with at most one break point, then the resulting crossing number is at most quadratic in the regular crossing number. © 1993 John Wiley & Sons, Inc.     

Influence of the sulfonate countercation on the thermal stability of nafion perfluorosulfonate membranes

We report a strong dependence of the thermal stability of Nafion® perfluorosulfonate ionomer on the nature of the counterion associated with the fixed sulfonate site. These results were obtained using thermal gravimetric analysis on a series of alkali metal and alkyl ammonium cation-exchanged Nafion films. We have found that the temperature of decomposition of Nafion is inversely dependent on the size of the exchanged cation; i.e., Nafion films show improved thermal stability as the size of the counter cation decreases. We attribute this inverse relationship of thermal stability with counterion size to an initial decomposition reaction which is strongly influenced by the strength of the sulfonate-coun-terion interaction. © 1993 John Wiley & Sons, Inc.     

Large Water-Soluble Cyclophanes with Convergent Intracavity Functionality

New tricyclic spacers, readily available through fourfold Mannich reaction of substituted dibenzyl ketones, were introduced into a series of ten H₂O-soluble cyclophanes with spacious preorganized cavity binding sites. These spacers provide H₂O-solubility with amine or crown-ether functionality remote from the cyclophane cavity while directing functional groups such as keto or OH groups in a precise geometrical array inside the cavity. The cyclophanes were designed to include organic substrates via a combination of apolar and specific polar functional group interactions. The X-ray crystal-structure analysis of the tritopic receptor 18 with one potential neutral-molecule and two cation-binding sites showed a large rectangular open cavity with dimensions of roughly 9 × 14 Å and a spacing of 9.7 Å between the O-atoms of two convergent C?O groups. Despite the binding-site preorganization, cyclophanes incorporating two of the new spacers did not show any substrate binding in aqueous solutions. The failure of these systems to function as receptors is mainly due to steric hindrance to important cyclophane aromatic ring-guest interactions. Also, the favorable solvation of the intracavity functionality may prevent the formation of complexes. Hybrid receptors constructed from the novel spacers and diphenylmethane units were found to bind flat aromatic substrates as well as bulky [4.2]paracyclophanes. The observed large differences in stability (ΔΔG°> 2 kcal mol^?1) of the complexes formed by three structurally closely related hybrid receptors with convergent C?O, OH or CH₂ groups and 6-hydroxynaphthalene-2-carbonitrile as guest can be explained by a strong solvation effect of the convergent functional groups on apolar inclusion complexation.     

Heisenberg-limited Measurements and Sub-Planck Structures in Phase Space

It is shown how sub-Planck phase-space structures can be used to achieve Heisenberg-limited sensitivity in weak force measurements. Nonclassical states of harmonic oscillators, such as superpositions of coherent states, are shown to be useful for the measurement of weak forces that cause translations or rotations in phase space, which is done by entangling the quantum oscillator with a two-level system. This method is closely related to the Loschmidt echo techniques employed in nuclear magnetic resonance experiments. Implementations of this strategy in cavity QED and ion traps are described.     

A detailed study of the generation of optically detectable watermarks using the logistic map

A digital watermark is a visible, or preferably invisible, identification code that is permanently embedded in digital media, to prove owner authentication and provide protection for documents. Given the interest in watermark generation using chaotic functions a detailed study of one chaotic function for this purpose is performed. In this paper, we present an approach for the generation of watermarks using the logistic map. Using this function, in conjunction with seed management, it is possible to generate chaotic sequences that may be used to create highpass or lowpass digital watermarks. In this paper we provide a detailed study on the generation of optically detectable watermarks and we provide some guidelines on successful chaotic watermark generation using the logistic map, and show using a recently published scheme, how care must be taken in the selection of the function seed.