On stratifiable locally convex spaces

In the present paper we prove several results on the stratifiability of locally convex spaces. In particular, we show that a free locally convex sum of an arbitrary set of stratifiable LCS is a stratifiable LCS, and that all locally convex F'-spaces whose bounded subsets are metrizable are stratifiable. Moreover, we prove that a strict inductive limit of metrizable LCS is stratifiable and establish the stratifiability of many important general and specific spaces used in functional analysis. We also construct some examples that clarify the relationship between the stratifiability and other properties.

The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.

Time operators and shift representation of dynamical systems

We introduce and characterise time operators for unilateral shifts and exact endomorphisms. The associated shift representation of evolution is related to the spectral representation by a generalized Fourier transform. We illustrate the results for a simple exact system, namely the Renyi map.

Non-trivial stably free modules over crossed products

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre's problem, was extensively studied before. It turns out that the method of lifting of non-trivial stably free modules from simple Ore extensions can be applied to crossed products after an appropriate choice of filtration. The motivating examples of crossed products are provided by the class of RIT algebras, originating in non-equilibrium physics.

Self-affine crossover length in a layered silicate deposit

Self-affine dehydrated colloidal deposits on fresh mica surfaces of the synthetic layered silicate 2:1 smectite clay laponite have been studied by means of atomic force microscopy (AFM). AFM images of these prepared assemblies of sol and gel aggregates have been analyzed both by means of standard AFM Fourier software and a wavelet method. The deposited surfaces show a persistence to antipersistent crossover with a clay concentration dependent crossover length. It is concluded that the crossover length is associated with aggregate size, and further that the persistent roughness at small length scales signals near compact clusters of fractal dimension three, whereas the antipersistent roughness at large length scales signals a sedimentation process.

Correction of dielectric losses in practical leaky-wave antenna designs

In this paper, the leaky-mode theory is applied to take into account for the dielectric losses in millimetre waveband inhomogeneous leaky-wave antennas. A practical dielectric-filled cosine-tapered periodic leaky-wave antenna working in the 45GHz band is studied, showing how the desired sidelobes level and directivity are spoilt due to the effect of the losses. An iterative procedure is used to correct the negative effects of the losses in the radiation patterns of the leaky-wave structure. It is also shown the practical limits of the proposed correction approach. The leaky-mode theory is applied for the first time to compensate the losses in a practical leaky-wave antenna in hybrid waveguide printed circuit technology. This leaky-mode theory is validated with full-wave three-dimensional finite element method simulations of the designed antenna.

Electromagnetic beam profile dynamics in collisional plasmas

The compression of a finite extent Gaussian laser pulse in collisional plasma is investigated. An analytical model is employed to describe the spatiotemporal evolution of a laser pulse propagating through the plasma medium. The pulse geometry is modeled via an appropriate ansatz which takes into account both beam radius (in space) and pulse width (in time). Compression and self-focusing are taken into account via appropriated group velocity dispersion and nonlinearity terms. The competition among the collisional nonlinearity in the plasma and the effect of divergence due to diffraction is pointed out and investigated numerically. Our results suggest that laser pulse compression and intensity localization is enhanced by plasma collisionality. In specific, a pulse width compression by an order of magnitude approximately is observed, for typical collisional laser plasma parameters, along with a significant increase in the intensity.

Observation of stable phase jump lines in convection of a twisted nematic liquid crystal

We report observations of stable, localized, linelike structures in the spatially periodic pattern formed by nematic electroconvection, along which the phase of the pattern jumps by pi. With increasing electric voltage, these lines form a gridlike structure that goes over into a structure indistinguishable from the well-known grid pattern. We present theoretical arguments that suggest that the twisted cell geometry we are using is indirectly stabilizing the phase jump lines, and that the phase jump lines lattice is caused by an interaction of phase jump lines and a zig-zag instability of the surrounding pattern.

Data-driven optimal filtering for phase and frequency of noisy oscillations: Application to vortex flow metering

A method for measuring the phase of oscillations from noisy time series is proposed. To obtain the phase, the signal is filtered in such a way that the filter output has minimal relative variation in the amplitude over all filters with complex-valued impulse response. The argument of the filter output yields the phase. Implementation of the algorithm and interpretation of the result are discussed. We argue that the phase obtained by the proposed method has a low susceptibility to measurement noise and a low rate of artificial phase slips. The method is applied for the detection and classification of mode locking in vortex flow meters. A measure for the strength of mode locking is proposed.

Magnetic field effect on the thresholds of a sequence of transitions in the electroconvection of a homeotropic nematic liquid crystal

We present a detailed analysis of the characteristics of electroconvection patterns in a homeotropic nematic liquid crystal under the influence of a variable magnetic field. An unambiguous observation of low frequency

Three-dimensional pattern formation, multiple homogeneous soft modes, and nonlinear dielectric electroconvection

Patterns forming spontaneously in extended, three-dimensional, dissipative systems are likely to excite several homogeneous soft modes (approximate to hydrodynamic modes) of the underlying physical system, much more than quasi-one- (1D) and two-dimensional (2D) patterns are. The reason is the lack of damping boundaries. This paper compares two analytic techniques to derive the pattern dynamics from hydrodynamics, which are usually equivalent but lead to different results when applied to multiple homogeneous soft modes. Dielectric electroconvection in nematic liquid crystals is introduced as a model for 3D pattern formation. The 3D pattern dynamics including soft modes are derived. For slabs of large but finite thickness the description is reduced further to a 2D one. It is argued that the range of validity of 2D descriptions is limited to a very small region above threshold. The transition from 2D to 3D pattern dynamics is discussed. Experimentally testable predictions for the stable range of ideal patterns and the electric Nusselt numbers are made. For most results analytic approximations in terms of material parameters are given. [S1063-651X(00)09512-X].

Twist localizes three-dimensional patterns

A mechanism or the localization of spatially periodic,self-oganized patterns in anisotropic media which requires systems extended in all three spatial dimensions is presented: When the anisotropy axis is twisted, the pattern becomes localized in planes parallel to the anisotropy axis. An analytical description of the effect is developed, and used to interpret recent experiments in the high-frequency regime of electroconvection by Bohatsch and Stannarius [Phys. Rev. E 60, 5591 (1999)]. The localization width is found to be of the order of magnitude of the geometrical average of the pattern wavelength and the inverse twist.

Pattern formation of chevrons in the conduction regime in homeotropically aligned liquid crystals

We report on chevrons (herringbonelike patterns) observed in homeotropically aligned liquid crystals with high electric conductivity. We focus our attention on two types of chevrons observed in the conduction regime. The threshold voltage and the characteristic double periodicity of chevrons (i.e., the short wavelength lambda(1) of the striated rolls and the long wavelength lambda(2) Of the chevron bands) have been measured as functions of the applied electric frequency f. With the aid of a crossed polarizer set, we have, in addition, determined the director field which shows a periodic in-plane rotation for our chevrons (with a wavelength lambda(2)) We arrived at the types of chevrons after qualitatively different bifurcation sequences with increasing voltage. The frequency dependence of lambda(2) also shows a qualitatively different behavior with respect to the two types of chevrons. The experimental results are discussed in terms of recent theoretical investigations.