Random Copolymers of 1,5-Dioxepan-2-one

ABSTRACT

Copolymers of 1,5-dioxepan-2-one (DXO) and e-caprolactone (?-CL), δ-valerolactone (δ-VL) or L-lactide (LLA) have been synthesized and characterized. High molecular weight copolymers were obtained using stannous-2-ethyl hexanoate as catalyst in bulk. Reactivity ratios for the copolymerization of DXO and δ-VL were determined at 110°C as r_VL=0.5 and r_DXO=2.3. At high conversion, depolymerization of δ-VL occurred, resulting in lower molecular weight and variations in the copolymer composition.

Physical properties, such as crystallinity and melting temperature of the DXO-copolymers proved to be strongly dependent on the choice of comonomer and on the molar composition of the copolymers. DXO appears to be incorporated into the poly-?-caprolactone (PCL) crystals and to some extent into the poly-δ-valerolactone (PVL) crystals, resulting in a more gradual decrease in crystallinity with increasing amount of DXO.     

A fibrous dynamic continuum model of the tympanic membrane

The geometry and anisotropic ultrastructure of the tympanic membrane are used in combination with curvilinear shell equations to formulate a general continuum model describing its dynamic behavior. Primary terms appearing in the model are associated with shell membrane restoring forces, bending-type structural damping, and transverse inertia. Since the model is based extensively on the physical characteristics of the membrane, it is relatively easy to account for differences between species as well as pathological conditions. The fibrous structure and cone-shaped geometry, readily apparent in mammalian eardrums, introduce several small parameters into the model that are exploited in order to construct a closed-form asymptotic solution. The solution includes the coupling to the three-dimensional motion of the ossicular chain and it includes the frequency-dependent pressure distribution in the auditory canal. When applied to the cat eardrum, this asymptotic solution is shown to reproduce a large manifold of experimentally observed frequency and excitation-dependent vibrational shapes. In addition to the shapes, transient amplitude and phase data for the cat are reproduced.     

High-frequency plane waves in the ear canal: application of a simple asymptotic theory

An asymptotic theory describing the propagation of plane waves in a variable cross-section ear canal is combined with pressure measurements in order to determine the energy reflection coefficient at the eardrum and the standing wave patterns along the length of the canal. The relative phase of the reflected wave, and the cross-sectional area function of the ear canal, are also determined from the noninvasive pressure measurements. The theory is based on a high-frequency multiscale solution of the one-dimensional horn equation and is shown to agree well with the phase and amplitude of experimental measurements in human replica ear canals.     

Secondary ion yields produced by keV atomic and polyatomic ion impacts on a self-assembled monolayer surface

A suite of keV polyatomic or 'cluster' projectiles was used to bombard unoxidized and oxidized self-assembled monolayer surfaces. Negative secondary ion yields, collected at the limit of single ion impacts, were measured and compared for both molecular and fragment ions. In contrast to targets that are orders of magnitude thicker than the penetration range of the primary ions, secondary ion yields from polyatomic projectile impacts on self-assembled monolayers show little to no enhancement when compared with monatomic projectiles at the same velocity. This unusual trend is most likely due to the structural arrangement and bonding characteristics of the monolayer molecules with the Au(111). Copyright 1999 John Wiley & Sons, Ltd.     

Fusion around the barrier for 7Li+12C

Fusion cross-sections for the ⁷Li + ¹²C reaction have been measured at energies above the Coulomb barrier by the direct detection of evaporation residues. The heavy evaporation residues with energies below 3 MeV could not be separated out from the α-particles in the spectrum and hence their contribution was estimated using statistical model calculations. The present work indicates that suppression of fusion cross-sections due to the breakup of ⁷Li may not be significant for ⁷Li + ¹²C reaction at energies around the barrier.     

Essential oil of Nepeta x faassenii Bergmans ex Stearn (N. mussinii Spreng. x N. nepetella L.): a comparison study

Analysis (GC and GC/MS) of an essential oil sample obtained from dry leaves of Nepeta x faassenii Bergmans ex Steam, a hybrid species produced by crossbreeding N. mussinii Spreng. with N. nepetella L., led to the identification of 109 constituents that represented 95.9% of the oil. The major constituents were 4aalpha,7alpha,7aalpha-nepetalactone (67.8%), 1,8-cineole (6.6%), germacrene D (4.8%), beta-pinene (2.7%), (E)-beta-ocimene (2.6%), 4aalpha,7beta,7aalpha-nepetalactone (2.3%) and (E)-beta-farnesene (1.0%). Chemical composition of the oil was compared, using multivariate statistical analyses (MVA) with those of the oils of other Nepeta taxa, in particular N. mussinii and N. nepetella. This was done in order to explore the mode of inheritance of the monoterpene biosynthetic apparatus of N. faassenii. Chemical composition of the volatiles of a Nepeta taxon (different populations) can be subject to variation due to environmental and geographical factors. To accommodate this fact in the MVAs, along side with N. faassenii essential oil, additional 6 oils (3 different populations of N. nuda L. and N. cataria L. from Serbia) were included in this study (isolated and analyzed (chemically and statistically)). The MVA analyses recognized N. faassenii as being closely related to both N. mussinii and N. nepetella. If the relative content of oil constituents per plant and not per chromatogram were used as variables in the MVA (this was done by simple multiplication of the yields and relative percentages of components) a higher degree of mutual similarity (in respect to the monoterpene biosynthesis) of N. faassenii to N. mussinii, than to the other parent species, was observed.     

Three-dimensional acoustic waves in the ear canal and their interaction with the tympanic membrane

The long and slender geometry of the ear canal supports an infinite number of cross-sectional acoustic modes. The lower mode(s) travel along the length of the ear canal, while the higher modes are trapped near the ends of the canal. Many of these waves are introduced as a result of the complex vibrational shape of the eardrum. A three-dimensional mathematical model of the ear canal is formulated that includes this acoustic interaction. The coupled system is solved using matched asymptotic expansions that take advantage of the small slenderness ratio. This solution in the ear canal is in the form of a series of modes, the first being the plane-wave solution. As an illustrative example, the analysis is applied to a geometry that partially represents the ear canal and eardrum of a cat. The results indicate that the plane-wave solution is supplemented by multidimensional trapped modes at low frequencies and by a limited number of traveling waves at high frequencies. The magnitude of these higher modes generally increases with frequency and can significantly influence the acoustic coupling of the ear.     

Real meromorphic functions and linear differential polynomials

We determine all real meromorphic functions f in the plane such that f has finitely many zeros, the poles of f have bounded multiplicities, and f and F have finitely many non-real zeros, where F is a linear differential polynomial given by F = f (k) +Σk-1j=0ajf(j) , in which k≥2 and the coefficients aj are real numbers with a0≠0.     

A hierarchy of examples illustrating the acoustic coupling of the eardrum

Basic principles underlying the acoustic coupling of the eardrum are illustrated in the form of a hierarchy of examples ranging from a simple piston coupled to a semi-infinite acoustic duct, to a flexible partition coupled to a variable cross-section duct, and to a closed cavity. The hierarchy illuminates some of the limitations of various simplified elements commonly used to model the middle ear and demonstrates the necessity of treating the acoustics and the eardrum as an integrated subsystem. Results show that the tympanic cavity and the secondary middle-ear air chambers contribute fundamental features to the acoustic coupling of the ear. The nature of the acoustic coupling limits the passive energy absorption and transmission properties of the eardrum. The magnitude and frequency dependence of the energy dissipation within the ultrastructure of the partition, due to bending and transverse deflection, is discussed in analogy to possible dissipation mechanisms within the eardrum itself. Examples are provided for several simple systems reproducing some of the gross anatomical characteristics of the cat eardrum.     

Ear canal cross-sectional pressure distributions: mathematical analysis and computation.

Cross-sectional pressure distributions, natural acoustic modes, and associated cutoff frequencies are determined for real ear-canal geometries using an asymptotic theory in combination with a numerical method. The technique is particularly well suited to obtain the higher modes, which are trapped near both ends of the ear canal. Results detail the influence of the canal geometry and frequency on the spatial distribution of the pressure. Adult ear-canal geometries are determined near the concha from ear-mold sections using a light microscope interfaced to a video-data-acquisition system. Computed results compare favorably to the exact solutions for circular and square acoustic waveguides. The cutoff frequency of the two adult ear canals studied averaged 20% less than the cutoff frequency of a circular tube of identical cross-sectional area. Inserting a probe microphone into the canal decreases the rate of decay of circumferential nonplanar modes while increasing the rate of decay of radial modes. Relative to the pressure beyond the tube, insertion increases the plane-wave component of the pressure around the tube by a multiplicative factor approximately equal to the square root of the original area divided by the occluded area. Eccentric placement of the probe tube has a relatively small influence on the cutoff frequency. The transition of the pressure distribution at the entrance to a simple plane wave in the core region of the canal is calculated and shown graphically for the actual geometry of two adult subjects.