Adhesion hysteresis in dynamic atomic force microscopy

The effects of adhesion hysteresis in the dynamic‐dissipation curves measured in amplitude‐modulation atomic force microscopy are discussed. Hysteresis in the interaction forces is shown to modify the dynamics of the cantilever leading to different power dissipation curves in the repulsive and attractive regimes. Experimental results together with numerical simulations show that power dissipation, as measured in force microscopy, is not always proportional to the energy dissipated in the tip–sample interaction process. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inclusion of Enantiomeric Carvones in β-Cyclodextrin: a Variable Temperature 1H NMR Study in Aqueous Solution

In aqueous solution, the apparent association constant at room temperature for the 1 : 1 inclusion of S-(+)-carvone in - cyclodextrin is double of that for R-(-)-carvone, whereas, at 45 °C, both enantiomers have association constants two orders of magnitude smaller, with the S-(+) inclusion being then slightly weaker than the R-(-) encapsulation. Calculations carried out at the molecular mechanics, AM1 and STO-3G levels confirm the preferential inclusion of the S-enantiomer and provide important clues for understanding chiral discrimination by -cyclodextrin.     

Waveform interactions and the segregation of concurrent vowels

Two experiments investigated the effects of small values of fundamental frequency difference (delta F0) on the identification of concurrent vowels. As delta F0's get smaller, mechanisms that exploit them must necessarily fail, and the pattern of breakdown may tell which mechanisms are used by the auditory system. Small delta F0's also present a methodological difficulty. If the stimulus is shorter than the beat period, its spectrum depends on which part of the beat pattern is sampled. A different starting phase might produce a different experimental outcome, and the experiment may lack generality. The first experiment explored the effects of delta F0's as small as 0.4%. The smallest delta F0 conditions were synthesized with several starting phases obtained by gating successive segments of the beat pattern. An improvement in identification was demonstrated for delta F0's as small as 0.4% for all segments. Differences between segments (or starting phase) were also observed, but when averaged over vowel pairs they were of small magnitude compared to delta F0 effects. The nature of delta F0-induced waveform interactions and the factors that affect them are discussed in detail in a tutorial section, and the hypothesis that the improvement in identification is the result of such interactions (beat hypothesis) is examined. It is unlikely that this hypothesis can account for the effects observed. The reduced benefit of delta F0 for identification at smaller delta F0's more likely reflects the breakdown of the same F0-guided segregation mechanism that operates at larger delta F0's.     

On Percolation with Fibers or Layers

We consider site percolation on Z ^d, directed edges going from any sZ ^d to s+A ₁,..., s+A _n, where A ₁,..., A _n are the same for all sites and at least two of them are noncollinear. A site is closed if it belongs to p+Block, where p is a point in a Poisson distribution in R ^dZ ^d with a density and Block={sL: |s|M}+{sR ^d: |s|}, where L is a linear subspace of R ^d, |·| is the Euclidean norm, =max(|A ₁|,..., |A _n|) and M is a parameter. We study the behavior of *, the critical value, and P _closed*, corresponding critical percentage of closed sites, when M. Denote R ^d/L the factor space. Call two nonzero vectors U, V codirected if U=kV, where k>0. Theorem. If there are A _i and A _j whose projections to R ^d/L are not codirected, then *1/M ^dim(L) and P _closed* remains separated both from 0 and 1 when M. If projections of all A ₁,..., A _n to R ^d/L are codirected, then *1/M ^dim(L)+1 and P _closed*1/M when M.     

Time-domain Fresnel-to-Fraunhofer diffraction with photon echoes

A photon echo experiment in Tm(3+):YAG is reported that shows, for the first time to the authors' knowledge, the time-domain equivalent of the transition from near- to far-field diffraction, including Talbot self-imaging effects. The experiment demonstrates the huge dispersion capability of photon echoes and opens the way to further exploration of space-time duality.     

Phase Retrieval for Probability Distributions on Quantum Groups and Braided Groups

For nilpotent quantum groups [as introduced by Franz et al. ⁽⁷⁾], we show that (in sharp contrast to the classical case) the symmetrization of a probability distribution and the first moments of together determine uniquely the original distribution .     

Atomlessr-maximal sets

We focus on % MathType!End!2!1!(A), the filter of supersets ofA in the structure of the computably enumerable sets under the inclusion relation, whereA is an atomlessr-maximal set. We answer a long-standing question by showing that there are infinitely many pairwise non-isomorphic filters of this type. Research partially supported NSF Grants DMS-96-3465 (Cholak) and DMS-95-00983 (Nies). The authors would like to thank Mike Stob for his help and interest.     

CP-MAS 207Pb with 19F decoupling NMR spectroscopy: medium range investigation in fluoride materials

The isotropic chemical shift of 207Pb is used to perform structural investigations of crystalline fluoride compounds (PbF2, Pb2ZnF6, PbGaF5, Pb3Ga2F12 and Pb9Ga2F24) and transition metal fluoride glasses (TMFG) of the PZG family (PbF2-ZnF2-GaF3). Using 207Pb Cross Polarisation Magic Angle Spinning (CP-MAS) NMR with 19F decoupling, it is shown that the isotropic chemical shift of 207Pb varies on a large scale (1000 ppm) and that the main changes of its value are not due to the nearest neighbour fluorines but may be related to the number of next nearest neighbour (nnn) Pb2+ ions. In this way, it is demonstrated that 207Pb chemical shift is an interesting probe to investigate medium range order in either crystalline or glassy fluoride systems. The 207Pb delta(iso) parameter has been linearly correlated to the number of nnn Pb2+ ions.     

Xuv resonant transition radiations from periodic stratified media

General formulation of the xuv intensity emitted when relativistic electrons cross through any periodic stratified medium is presented in the framework of electromagnetism in continuous media. Application is made to the resonant transition radiation emitted in the geometries of both normal and oblique incidence. In the first case, agreement is found between our calculated results and published values. Intensity emitted by a periodic multilayer stack used in the Bragg conditions is determined and the practical interest of a such a radiation source is discussed.     

Bifurcation of degenerate homoclinics

We analyze the continuation and bifurcation of homoclinic orbits near a given degenerate homoclinic orbit. We show that the existence of such degenerate homoclinic orbit is a codimension three phenomenon, and that generically the set of parametervalues at which a nearby homoclinic exists forms a codimension one surface which shows a singularity of Whitney umbrella type at the critical parametervalue. The line of self-intersecting points of such surface corresponds to systems which have two nearby homoclinics.