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].

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.

Spontaneous spin polarization and charge localization in metal nanowires: the role of a geometric constriction

An idealized jellium model of conducting nanowires with a geometric constriction is investigated by density functional theory (DFT) in the local spin density (LSD) approximation. The results reveal a fascinating variety of spin and charge patterns arising in wires of sufficiently low (r(s) >= 15) average electron density, pinned at the indentation by an apparent attractive interaction with the constriction. The spin-resolved frequency-dependent conductivity shows a marked asymmetry in the two spin channels, reflecting the spontaneous spin polarization around the wire neck. The relevance of the computational results is discussed in relation to the so-called 0.7 anomaly found by experiments in the low-frequency conductivity of nanowires at near-breaking conditions (see 2008 J. Phys.: Condens Matter 20, special issue on the 0.7 anomaly). Although our mean-field approach cannot account for the intrinsic many-body effects underlying the 0.7 anomaly, it still provides a diagnostic tool to predict impending transitions in the electronic structure.

A Description of the Stationary Wave Pattern of a Marine Craft in Shallow and Intermediate Water Depths

A stationary phase model is used to study supercritical waves generated by high speed ferries. Some general relationships in terms of wave angle, propagation direction, dispersion relationship and depth wavelength relationship are explored and discussed. In particular, it is shown that the wave pattern generated by high speed craft at supercritical speeds depends mainly on the relationship of water depth and ship speed and that the wave patterns are similar in terms of location of crests and troughs for a given depth Froude number. In addition it is found that the far field wave pattern can be described adequately using a single moving point source. The theoretical model compares well with towing tank measurements and full scale data over a range of parameters and hull shapes. The paper also demonstrates that the far field wave pattern at supercritical speeds should be non-dimensionalised by water depth and not hull length unlike it is usually done for subcritical speeds.

A geometric analysis of the effects of noise on Berry phase

In this work we describe the effect of classical and quantum noise on the Berry phase. It is not a topical review article but rather an overview of our work in this field aiming at giving a simple pictorial intuition of our results.

Patterns of hospitalisation before and following initiation of haemodialysis: a 5 year single centre study

Background: The utilisation of healthcare resources by prevalent haemodialysis patients has been robustly evaluated with regard to the provision of outpatient haemodialysis; however, the impact of hospitalisation among such patients is poorly defined. Minimal information is available in the UK to estimate the health and economic burden associated with the inpatient management of prevalent haemodialysis patients. The aim of this study was to assess the pattern of hospitalisation among a cohort of haemodialysis patients, before and following their initiation of haemodialysis. In addition the study sought to assess the impact of their admissions on bed occupancy in a large tertiary referral hospital in a single region in the UK.

Methods: All admission episodes were reviewed and those receiving dialysis with the Belfast City Hospital Programme were identified over a 5 year period from January 2001 to December 2005. This tertiary referral centre provides dialysis services for a population of approximately 700?000 and additional specialist renal services for the remainder of Northern Ireland. The frequency and duration of hospitalisation, and contribution to bed day occupancy of haemodialysis patients, was determined and compared to other common conditions which are known to be associated with high bed occupancy. In addition, the pattern and timing of admissions in dialysis patients in relation to their dialysis initiation date was assessed.

Results: Over the 5 year study period, 798 haemodialysis patients were admitted a total of 2882 times. These accounted for 2.5% of all admissions episodes; the median number of admissions for these patients was 3 (2–5) which compared with 1 (1–2) for non-dialysis patients. The majority of first hospitalisations (54%) were within 100 days before or after commencement of maintenance dialysis therapy. In all clinical specialties the median length of stay for haemodialysis patients was significantly longer than for patients not on haemodialysis (p=0.004). In multivariate analysis with adjustment for age, gender, and other clinically relevant diagnostic codes, maintenance haemodialysis patients stayed on average 3.75 times longer than other patient groups (ratio of geometric means 3.75, IQR 3.46–4.06).

Conclusions: Maintenance haemodialysis therapy is an important risk factor for prolonged hospitalisation regardless of the primary reason for admission. Such patients require admission more frequently than the general hospital population, particularly within 100 days before and after initiation of their first dialysis treatment.