On the role of organic adlayers in the anomalous water sorptivity of Lépine limestone

Sorptivity data are reported for the capillary absorption of water, ethanol, propan-2-ol, and n-heptane by the calcitic limestone Lépine (Lavoux à grain). The data confirm that the water sorptivity is anomalously low, an indication of partial wetting by water. Results are expressed in terms of a wetting index. The water sorptivity increases after heat treatment and chemical oxidation by hydrogen peroxide bleaching, while the sorptivity with organic liquids is unchanged. These treatments, therefore, increase the water wetting index. The results provide strong evidence that the presence of a natural organic adlayer is responsible for the anomalously low water sorptivity of this particular limestone. This natural water repellency effect may be exploited in developing chemical treatments to modify the water transport properties of stone.     

Functionalized spiro- and fused-ring heterocycles via oxidative demetalation of cyclohexadienyl ruthenium complexes

Electron-rich alkoxy- and chloro-substituted azaspirocyclic cyclohexadienyl Ru(II) complexes have been converted to either azaspiro[4.5]decane derivatives or functionalized tetrahydroisoquinolines by treatment with suitable oxidizing agents. Copper(II) chloride was found to provide demetalated products in high yield relative to the other oxidants examined (FeCl(3), DDQ, CAN, [Cp(2)Fe][PF(6)], phenyliodine diacetate, IBX). In certain instances, the efficiency of oxidative demetalation was enhanced by the inclusion of chloride ion additives in the reaction. Pyridinium dichromate (PDC) was also found to effect the demetalation of a wide range of cyclohexadienyl Ru complexes; however, isolated yields of metal-free products were exceedingly low. The cyclohexadienyl ruthenium complexes used in this study were prepared from (arene)Ru(II) precursors; thus, the isolation of alicyclic cyclohexadienone derivatives upon demetalation constitutes completion of a Ru-mediated dearomatization process.     

Lead and thallium tetrakis(imidazolyl)borates: modifying structure by varying metal and anion

We are using the coordinating anions tetrakis(imidazolyl)borate and tetrakis(4-methylimidazolyl)borate to construct new metal-organic framework structures. In this report, we are exploring materials similar in composition to the previously reported layered network structure Pb[B(Im)(4)](NO(3))(nH(2)O). The metal in this compound can be replaced with isoelectronic Tl(I), affording Tl[B(Im)(4)], and the borate can be modified by using 4-methylimidazole, resulting in Pb[B(4-MeIm)(4)](NO(3)) and Tl[B(4-MeIm)(4)]. Like the parent Pb[B(Im)(4)](NO(3))(nH(2)O), Tl[B(Im)(4)] and Tl[B(4-MeIm)(4)] are layered network structures but both lack anions or solvent molecules in the interlayer spacing. The material Pb[B(4-MeIm)(4)](NO(3)), however, exhibits a 3D network structure that lacks an open topology, resulting from the increased stereochemical activity (greater steric bulk toward other ligands) of the 4-methylimidazole ring. Both of the Tl(I) solids display longer M-N bonds than observed in the analogous Pb(II) compounds; these lengths account for the decreased effect of the stereochemical activity of the 4-methylimidazole ring in Tl[B(4-MeIm)(4)].     

Linearized stability analysis of discrete Volterra equations

Various different types of stability are defined, in a unified framework, for discrete Volterra equations of the type x(n)=f(n)+∑ⁿ_j=0K(n,j,x(n)) (n?0). Under appropriate assumptions, stability results are obtainable from those valid in the linear case (K(n,j,x(n))=B(n,j)x(j)), and a linearized stability theory is studied here by using the fundamental and resolvent matrices. Several necessary and sufficient conditions for stability are obtained for solutions of the linear equation by considering the equations in various choices of Banach space , the elements of which are sequences of vectors (, , n,j?0, etc.). We show that the theory, including a number of new results as well as results already known, can be presented in a systematic framework, in which results parallel corresponding results for classical Volterra integral equations of the second kind.     

Logarithmic derivatives of solutions to linear differential equations

Given an ordinary differential field of characteristic zero, it is known that if and satisfy linear differential equations with coefficients in , then is algebraic over . We present a new short proof of this fact using Gröbner basis techniques and give a direct method for finding a polynomial over that satisfies. Moreover, we provide explicit degree bounds and extend the result to fields with positive characteristic. Finally, we give an application of our method to a class of nonlinear differential equations.

     

Almost global existence for quasilinear wave equations in three space dimensions

We prove almost global existence for multiple speed quasilinear wave equations with quadratic nonlinearities in three spatial dimensions. We prove new results both for Minkowski space and also for nonlinear Dirichlet-wave equations outside of star shaped obstacles. The results for Minkowski space generalize a classical theorem of John and Klainerman. Our techniques only use the classical invariance of the wave operator under translations, spatial rotations, and scaling. We exploit the decay of solutions of the wave equation as much as the decay. Accordingly, a key step in our approach is to prove a pointwise estimate of solutions of the wave equation that gives decay of solutions of the inhomogeneous linear wave equation in terms of a -weighted norm on the forcing term. A weighted space-time estimate for inhomogeneous wave equations is also important in making the spatial decay useful for the long-term existence argument.

     

Determination of West Indian manatee vocalization levels and rate

The West Indian manatee (Trichechus manatus latirostris) has become endangered partly because of a growing number of collisions with boats. A system to warn boaters of the presence of manatees, based upon the vocalizations of manatees, could potentially reduce these boat collisions. The feasibility of this warning system would depend mainly upon two factors: the rate at which manatees vocalize and the distance in which the manatees can be detected. The research presented in this paper verifies that the average vocalization rate of the West Indian manatee is approximately one to two times per 5-min period. Several different manatee vocalization recordings were broadcast to the manatees and their response was observed. It was found that during the broadcast periods, the vocalization rates for the manatees increased substantially when compared with the average vocalization rates during nonbroadcast periods. An array of four hydrophones was used while recording the manatees. This allowed for position estimation techniques to be used to determine the location of the vocalizing manatee. Knowing the position of the manatee, the source level was determined and it was found that the mean source level of the manatee vocalizations is approximately 112 dB (re 1 microPa) @ 1 m.     

Inferred basilar-membrane response functions for listeners with mild to moderate sensorineural hearing loss

Psychophysical estimates of cochlear function suggest that normal-hearing listeners exhibit a compressive basilar-membrane (BM) response. Listeners with moderate to severe sensorineural hearing loss may exhibit a linearized BM response along with reduced gain, suggesting the loss of an active cochlear mechanism. This study investigated how the BM response changes with increasing hearing loss by comparing psychophysical measures of BM compression and gain for normal-hearing listeners with those for listeners who have mild to moderate sensorineural hearing loss. Data were collected from 16 normal-hearing listeners and 12 ears from 9 hearing-impaired listeners. The forward masker level required to mask a fixed low-level, 4000-Hz signal was measured as a function of the masker-signal interval using a masker frequency of either 2200 or 4000 Hz. These plots are known as temporal masking curves (TMCs). BM response functions derived from the TMCs showed a systematic reduction in gain with degree of hearing loss. Contrary to current thinking, however, no clear relationship was found between maximum compression and absolute threshold.     

Wave equations, dispersion relations, and van Hove singularities for applications of doublet mechanics to ultrasound propagation in bio- and nanomaterials

A fundamental mathematical framework for applications of Doublet Mechanics to ultrasound propagation in a discrete material is introduced. A multiscale wave equation, dispersion relation for longitudinal waves, and shear waves are derived. The van Hove singularities and corresponding highest frequency limits for the Mth-order wave equations of longitudinal and shear waves are determined for a widely used microbundle structure. Doublet Mechanics is applied to soft tissue and low-density polyethylene. The experimental dispersion data for soft tissue and low-density polyethylene are compared with results predicted by Doublet Mechanics and an attenuation model based on a Kramers-Kronig relation in classical continuum mechanics.     

Supramolecular assembly of strongly chemisorbed size- and shape-defined chiral clusters: S- and R-alanine on Cu(110)

The bonding and self-assembly of a chirally organized monolayer of alanine on the Cu(110) surface has been investigated using reflection-absorption infrared spectroscopy, low-energy electron diffraction (LEED), and scanning tunneling microscopy (STM). This multitechnique approach has enabled an in-depth understanding of the hierarchy of chirality transfer: from a single adsorbed molecule, to size-defined chiral clusters, and then to an overall chiral assembly. The data have indicated that the alanine is in its anionic form, bound to the copper surface through the oxygens of the ionized carboxylate group and the nitrogen of the neutral amino group. Importantly, the methyl group is held away from the surface, resulting in direct chirality transfer into the footprint of the adsorbed alanine molecules, with the local adsorption motif for S-alanine being the mirror image of that created for R-alanine. STM has shown that S-alanine molecules self-organize to form size-defined chiral clusters of six or eight molecules at the surface, interspersed with chiral channels of bare metal. Together, these clusters and channels further self-assemble into a chiral array with one unique chiral domain sustained across the entire surface. A similar chiral assembly, but with the mirror organization, has been observed for R-alanine. Structural models for the individual clusters are proposed, and in conjunction with LEED data, overall models for these chiral phases of both S- and R-alanine have been constructed. Overall, this adsorption system has been found to be both strongly chemisorbed and capable of extensive intermolecular H-bonding, causing stresses that lead not only to the chiral self-organization of molecules but also to a specific self-organization of the empty chiral channels and spaces that intersperse the structure which, in turn, chirally assemble across macroscopic length scales to give a surface with global organizational chirality.