Nonionic diethanolamide amphiphiles with isoprenoid-type hydrocarbon chains: thermotropic and lyotropic liquid crystalline phase behaviour

The thermotropic and lyotropic liquid crystalline phase behaviour of a series of diethanolamide amphiphiles with isoprenoid-type hydrocarbon chains (geranoyl, H-farnesoyl, and phytanoyl) has been investigated. When neat, both H-farnesoyl and phytanoyl diethanolamide form a smectic liquid crystalline structure at sub-zero temperatures. In addition, all three diethanolamides exhibit a glass transition temperature at around -73 °C. Geranoyl diethanolamide forms a lamellar crystalline phase with a lattice parameter of 17.4 ? following long term storage accompanied by the loss of the glass transition. In the presence of water, H-farnesoyl and phytanoyl diethanolamide form lyotropic liquid crystalline phases, whilst geranoyl diethanolamide forms an L(2) phase. H-farnesoyl diethanolamide forms a fluid lamellar phase (L(α)) at room temperature and up to ～ 40 °C. Phytanoyl diethanolamide displays a rich mesomorphism forming the inverse diamond (Q(II)(D)) and gyroid (Q(II)(G)) bicontinuous cubic phases in addition to an L(α) phase.     

Single dibenzoterrylene molecules in naphthalene and 2,3-dimethylnaphthalene crystals: vibronic spectra

Fluorescence excitation spectra of single dibenzoterrylene (DBT) molecules embedded in naphthalene (N) and 2,3-dimethylnaphthalene (2,3-DMN) crystals were studied at 5 K. The frequencies characterizing the vibronic structure of single DBT molecules in an N crystal agree with the theoretical prediction for the isolated DBT molecule. The 'dipolar' disorder encountered in 2,3-DMN crystals leads to a broad distribution of frequencies of the (0,0) lines of single DBT molecules. Moreover, the observed vibronic frequencies and intensities in the spectrum of DBT in 2,3-DMN crystals are slightly different to those in an N crystal. We conclude that the structure of DBT molecules in a 2,3-DMN crystal is disturbed in comparison with isolated DBT and the main change concerns its central tetracene moiety.     

Nonionic diethanolamide amphiphiles with unsaturated C18 hydrocarbon chains: thermotropic and lyotropic liquid crystalline phase behavior

The neat and lyotropic liquid crystalline phase behavior of three nonionic diethanolamide amphiphiles with C18 hydrocarbon chains containing one, two or three unsaturated bonds has been examined. This has allowed the effect of degree of unsaturation on the phase behavior of diethanolamide amphiphiles to be investigated. Neat linoleoyl and linolenoyl diethanolamide undergo a transition from a glassy liquid crystal to a liquid crystal at ～-85 °C, while neat oleoyl diethanolamide undergoes a transition at ～-60 °C to a liquid crystalline material before re-crystallizing at -34 °C. Oleoyl diethanolamide then undergoes a third transition from a crystalline phase to a smectic liquid crystalline phase at ～5 °C. In the absence of water, the transition temperature from a smectic liquid crystal to an isotropic liquid decreases with increasing unsaturation. The addition of water results in the formation of a lamellar phase (L(α)) for all three amphiphiles. The lamellar phase is stable under excess water conditions up to temperatures of at least 70 °C. Approximate partial binary amphiphile-water phase diagrams generated for the three unsaturated C18 amphiphiles indicate that the excess water point for each amphiphile occurs at ～60% (w/w) amphiphile.     

On the number of eigenvalues for parameter‐dependent diffusion problem on time scales

In this study, we consider parameter‐dependent diffusion eigenvalue problem on time scales. An upper bound on the number of eigenvalues for this problem on a finite time scale is given.     

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)     

Inertial Manifolds for von Karman Plate Equations

Inertial manifolds associated with nonlinear plate models governed by dynamical von Karman equations are considered. Three different dissipative mechanisms are discussed: viscous, structural and thermal damping. Though the systems considered are subject to some dissipation, the overall dynamics may not be dissipative. This means that the energy may not be decreasing. The main result of the paper establishes the existence of an inertial manifold subject to the spectral gap condition for linearized problems. The validity of the spectral gap condition depends on the geometry of the domain and the type of damping. It is shown that the spectral gap condition holds for plates of rectangular shape. In the case of viscous damping, which is associated with hyperbolic-like dynamics, it is also required that the damping parameter be sufficiently large. This last requirement is not needed for other types of dissipation considered in the paper.     

Global existence to a three‐dimensional non‐linear thermoelasticity system arising in shape memory materials

This paper is concerned with the unique global solvability of a three‐dimensional (3‐D) non‐linear thermoelasticity system arising from the study of shape memory materials. The system consists of the coupled evolutionary problems of viscoelasticity with non‐convex elastic energy and non‐linear heat conduction with mechanical dissipation. The present paper extends the previous 2‐D existence result of the authors Reference [1] to 3‐D case. This goal is achieved by means of the Leray–Schauder fixed point theorem using technique based on energy arguments and DeGiorgi method. Copyright © 2004 John Wiley & Sons, Ltd.     

The minimal free resolution of a Borel ideal

We consider the Eliahou–Kervaire minimal free resolution of a 0-Borel ideal and its applications.