Polyazapodands Derived from Biphenyl. Study of their Behaviour as Conformationally Regulated Fluorescent Sensors

Eight new polyazapodands containing a 4,4′-substituted biphenyl moiety have been synthesised. Four (7, 8, 9 and 11) are functionalised on positions 4 and 4′ with a nitro group and four (1, 2, 3 and 10) with a dimethylamino substituent. Comparison of the emission behaviour of 1, 2, 3 with that of the reference compounds 10 and tetramthylbenzidine, clearly suggests that a modification in the dihedral angle between the biphenyl rings is an important factor in determining the fluorescent response of the molecule. The fluorescence is pH dependent, due to the formation of intramolecular hydrogen bonds between protonated aliphatic nitrogens and a carbonyl oxygen, which influences the aforementioned dihedral angle. A crystal structure resolved by X-ray diffraction of 7·2HCl has been determined, and confirms the dependence of the angle and the rigidity on the hydrogen bonding. The complexation properties of these ligands have been studied with Zn²⁺, Cd²⁺, Ni²⁺, Cu²⁺ and Pb²⁺, which show that the number of amino groups within the pendants has a strong influence on the nature of the complexation and the fluorescent response of each ligand.     

A substructure-based SAR model for odor perception in humans relevant to health risk assessments

The ability of humans to perceive odors is a very complex phenomenon involving the selective binding of molecules to approximately 1000 olfactory receptors. Accordingly, the derivation of a substructure-based SAR model can be expected to be problematic. Yet, based upon published data on odor thresholds of volatile organic chemicals, we were able to derive such an SAR model. An examination of the structural determinants and related modulators indicates that lipophilicity is a major contributor to olfactory perception. The availability of a substructure-based SAR model permits an examination of the relationship between the presence in the environment of odorous chemicals and public health risks.     

A quadratic convergence scheme for determining families of periodic solutions

Global and local boundedness results for the solutions of a certain class of A₂-degenerate parabolic equations are proved.     

Further observations on the anharmonic motion equation

Peters [1] discussed some theoretical aspects of the ‘ringing’ sound associated with barbershop quartet singing. These combination tones were first investigated theoretically by Helmholtz [2] who showed that the transient displacement of the ear membrane is governed by the anharmonic motion equation. Rayleigh [3] modelled the situation as an initial value problem and this is now referred to as the Rayleigh problem. Following [1] there has been a renewed interest in the problem (see [4‐8]). The intention of the present paper is to:

• illustrate the qualitative behaviour of the solutions of the Rayleigh problem by a phase plane analysis;

• describe how the method of multiple scales provides a framework within which previous analyses can be seen;

• describe an improvement to the method of multiple scales, which may also prove useful in other applications.

     

Asymptotic behavior of the potential and existence of a periodic solution for a second order differential equation

We establish the existence of a 2π-periodic solution for a second order semilinear equation in terms of the asymptotic behavior of the potential of the nonlinearity. Our condition includes the case in which the nonlinearity is asymptotically linear with slopes at infinity of the jumping nonlinearity between the positive axes and the first Fucik spectrum curve (see [S. Fucik (1976 Fucik, S. 1976. Boundary value problems with jumping nonlinearities. Casopis Pest. Mat., 101: 69–87.  [Google Scholar]). Boundary value problems with jumping nonlinearities. Casopis Pest. Mat., 101, 69–87.]). Our results extend those of [L. Fernandez and F. Zanolin (1988 Fernandez, L. and Zanolin, F. 1988. Periodic solutions of a second order differential equation with one-sided growth restriction on the restoning term. Arch. Math., 51: 151–163.  [Google Scholar]). Periodic solutions of a second order differential equation with one-sided growth restriction on the restoning term. Arch. Math., 51, 151–163.].     

Unambiguous evidence for extended s-wave pairing symmetry in hole-doped high-temperature superconductors

We have analysed data from angle-resolved photo-emission spectroscopy, Fourier transform scanning tunneling spectroscopy, and low-temperature thermal conductivity for optimally doped Bi₂Sr₂CaCu₂ O _8+y in order to discriminate between d-wave and extended s-wave pairing symmetry. The combined data are inconsistent with d-wave symmetry, but quantitatively consistent with extended s-wave symmetry with eight line nodes. We also explain all phase-sensitive experiments in a consistent manner.     

A discussion of the structure and behaviour of dipole walls in cyclic plasticity

Assuming that cross-slip by thermally activated migration of jogs can cause annihilation of screw dislocation dipoles without macroscopic crystallographic confinement of cross-slip to the cross-slip plane, an attempt is made to re-derive earlier equations for the saturation stress and the plastic strain amplitude in persistent slip bands. These equations had been based on the assumption that cross-slip could occur only on a cross-slip plane making an obtuse angle with the slip plane, an assumption which limits the mean free path of screw dislocations. The key new assumption is that the walls of edge dislocation dipoles which dominate the structure of persistent slip bands are penetrable obstacles, which increases the mean free paths of the mobile dislocations. Agreement with experiment is obtained if the penetration probability in cyclic saturation is on average one third, a value for which there is a simple rationalization. Estimates can be made of the wall width, which is independent of temperature, in agreement with recent observations by Tippelt et al. However, the main unresolved difficulty is the role of the very fine dipoles, particularly the faulted dipoles, in the walls. A further weakness in the theory is that it ignores the cutting of dipoles by the cross-slipping screw dislocations. Despite these problems, the distribution of dipole heights can be worked out and is found to be in reasonable agreeement with experiment.     

Negative stiffness-induced extreme viscoelastic mechanical properties: stability and dynamics

Use of negative stiffness inclusions allows one to exceed the classic bounds upon overall mechanical properties of composite materials. We here analyse discrete viscoelastic ‘spring’ systems with negative stiffness elements to demonstrate the origin of extreme properties, and analyse the stability and dynamics of the systems. Two different models are analysed: one requires geometrical nonlinear analysis with pre-load as a negative stiffness source and the other is a linearized model with a direct application of negative stiffness. Material linearity is assumed for both models. The metastability is controlled by a viscous element. In the stable regime, extreme high mechanical damping tan?δ can be obtained at low frequency. In the metastable regime, singular resonance-like responses occur in tan?δ. The pre-stressed viscoelastic system is stable at the equilibrium point with maximal overall compliance and is metastable when tuned for maximal overall stiffness. A reversal in the relationship between the magnitude of complex modulus and frequency is also observed. The experimental observability of the singularities in tan?δ is discussed in the context of designed composites and polycrystalline solids with metastable grain boundaries.