Individual and collective behavior of vibrating motors interacting through a resonant plate

We report on experiments of many small motors—cell phone vibrators—glued to and interacting through a resonant elastic plate. We find that the motors tend to avoid frequencies that are just higher than the resonances of a plate, preferring instead frequencies just below those resonances. As a result, motors interacting through a resonant plate exhibit hysteresis in their frequency versus driving voltage. We also find that the stability of a single motor near a resonance is different from the stability of a group of motors near a resonance. When the driving voltage is constant and the transient behavior of the system has passed, we find that the average frequency of all the motors is constant.     

Gasanalyse

Ohne Zusammenfassung     

From finitary to infinitary second‐order logic

A back and forth condition on interpretations for those second‐order languages without functional variables whose non‐logical vocabulary is finite and excludes functional constants is presented. It is shown that this condition is necessary and sufficient for the interpretations to be equivalent in the language. When applied to second‐order languages with an infinite non‐logical vocabulary, excluding functional constants, the back and forth condition is sufficient but not necessary. It is shown that there is a class of infinitary second‐order languages whose non‐logical vocabulary is infinite for which the back and forth condition is both necessary and sufficient. It is also shown that some applications of the back and forth construction for second‐order languages can be extended to the infinitary second‐order languages. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electrosorptive detection in liquid chromatography of simple charged organic compounds

Summary The applicability of electrosorptive (ES) detection in liquid chromatography to charged organic species, specifically amines, alkanolamines, and alkylsulfonates is demonstrated. Separations can be carried out using ion-pair chromatography, and detection acieved by measuring changes in differential double-layer capacitance (DLC), C_d, brought about by analyte adsorption at potentials either well negative or positive of the potential of zero charge (pzc), depending on whether cationic or anionic forms, respectively, are being determined. The C_d-analyte concentration response curves are linear over a limited range. A welcome feature of the technique is that organic modifiers may be used in the mobile phase without deleterious consequence to the detection. Attempts were also made to detect these charged species as ion pairs by DLC at potentials close to the pzc. This approach, however, appears to have less practical utility.     

Limited field of view spin echo MR imaging

Several groups have reported using a method of limiting the field of view (FOV) where the slices excited by the 90 and 180 degree pulses are perpendicular. However, only one slice can be excited during each repetition time, so multislice imaging is not possible. We present a modification of this method that allows multislice imaging. The slices excited by the 90 degrees and 180 degrees pulses are at a small angle; the field of view is limited and multislice imaging is possible. The modifications also allow the center of the FOV to be offset to any position. We describe the conditions that yield optimal images for the given FOV, slice thickness, and interslice gap. Representative images demonstrating the features of the technique are presented. The technique can be used to reduce the number of phase-encoding steps resulting in reduced imaging time, or it can be used to increase the spatial resolution without increasing the imaging time.     

Temperature and volume dependence of some magnetic properties of Pr-pnictides

Several experiments relating to the volume dependence of crystal field interactions in rare earth pnictides have been carried out. These experiments include measurements of 1) the temperature dependence of the susceptibility of PrN, 2) the room temperature compressibilities of PrN and PrAs, 3) the NMR frequency shifts for ¹⁴¹Pr in PrN and PrSb, and 4) the low-temperature pressure dependence of the ¹⁴¹Pr frequency shift in PrN and PrSb. Although electrostatic screening effects on crystal field interactions in PrN are smaller than in the heavier Pr- pnictides, the anomalous volume dependence of the ¹⁴¹Pr NMR shift is essentially the same in all these compounds.     

Electronic structure of C84 and KxC84: Comparison to C60 and graphite

X ray photoemission spectra show ～10 valence band features in C₆₀ and C₈₄ films, although they are less distinct in C₈₄ because of the increased number of valence electrons and the decreased molecular symmetry. The presence of inequivalent carbon atoms in C₈₄ is reflected by the fact that the C 1s main line is ～0.2 eV wider than in C₆₀. The C 1s satellite region of C₈₄ exhibits four features within 15 eV of the main line and shows that the HOMO-LUMO π-π* excitation energy of C₈₄ is ～0.5 eV smaller than in C₆₀. Potassium 2p spectra for K-doped C₈₄ films suggest the formation of a phase with composition K₃C₈₄ with two spectroscopically-distinguishable K sites. A new spectral feature emerges when the K content is increased beyond K₃C₈₄, suggesting a phase transition and a saturated composition of K₆C₈₄, as for K_xC₆₀. These similarities are intriguing since K_xC₈₄ is insulating for all x while K₃C₆₀ is metallic and superconducting.     

Nuclear rotational-vibrational collective motion with nonvanishing vortex-spin

The theory of linear collective motion is developed by the method of canonical transformations, recovering, as special cases, the earlier results of Casimir, Bohr-Mottelson, and Villars. In the approximation of constant Eckart-frame vectors, the kinetic energy Hamiltonian is shown to commute with the invariant operators of the collective motion symmetry group CM(3). The collective motion approach of Tomonaga, and the symmetry approach of Gell-Mann, are discussed and shown to be essentially equivalent, and to be properly contained in the CM(3) structure. The invariant operators of CM(3) are determined and shown to imply two invariants for nuclear collective motion: the volume Λ and the vortex-spin v. Representations of CM(3) are obtained and related to wavefunctions of the generator-coordinate form.