Bilayer-by-bilayer antiferroelectric ordering in freely suspended films of an achiral polymer-monomer liquid crystal mixture

Thin freely suspended films of a mixture of an achiral side-chain liquid crystal polymer and its monomer have been studied with depolarized reflected light microscopy. We observe that regions with an odd number of bilayers exhibit a net spontaneous polarization in the tilt plane of the molecules, while regions with an even number of bilayers have no net polarization. These odd-even effects are direct evidence that the tilted smectic bilayers are anticlinic at the polymer backbone and synclinic at bilayer interface and confirm that the phase is bilayer-by-bilayer antiferroelectric.     

Generating sensor signals in isotropic noise fields

Researchers in the signal processing community often require sensor signals that result from a spherically or cylindrically isotropic noise field for simulation purposes. Although it has been shown that these signals can be generated using a number of uncorrelated noise sources that are uniformly spaced on a sphere or cylinder, this method is seldom used in practice. In this paper algorithms that generate sensor signals of an arbitrary one- and three-dimensional array that result from a spherically or cylindrically isotropic noise field are developed. Furthermore, the influence of the number of noise sources on the accuracy of the generated sensor signals is investigated.     

Maximum likelihood estimation of direction of arrival using an acoustic vector-sensor

A vector-sensor consisting of a monopole sensor collocated with orthogonally oriented dipole sensors is used for direction of arrival (DOA) estimation in the presence of an isotropic noise-field or internal device noise. A maximum likelihood (ML) DOA estimator is derived and subsequently shown to be a special case of DOA estimation by means of a search for the direction of maximum steered response power (SRP). The problem of SRP maximization with respect to a vector-sensor can be solved with a computationally inexpensive algorithm. The ML estimator achieves asymptotic efficiency and thus outperforms existing estimators with respect to the mean square angular error (MSAE) measure. The beampattern associated with the ML estimator is shown to be identical to that used by the minimum power distortionless response beamformer for the purpose of signal enhancement.     

Classification of stability-like concepts and their study using vector Lyapunov functions

In the first section, stability-like definitions for ordinary differential equations are derived from a general qualitative concept. It is shown that the classical definitions of stability in the sense of Lyapunov, and their extensions can easily be deduced from this general formulation. A classification of all the definitions which may be derived is proposed.The second section contains the main results of this paper. It deals with the “comparison method” based upon one of T. Wazewski's theorems on differential inequalities. Several authors have used this method in order to investigate stability-like properties. We display the structure of this method, in order to state and prove some general comparison principles. These apply to the class of concepts considered earlier.In the last section some new results about stability and attractivity of sets are obtained as examples for the comparison principles. A theorem on stability in tube-like domains is proved in order to emphasize the generality and the flexibility of the comparison method.