The response of the nematic twist-bend (N TB ) phase to an applied field can provide important insight into structure of this liquid and may bring us closer to understanding mechanisms generating mirror symmetry breaking in a fluid of achiral molecules. Here we investigate theoretically how an external uniform field can affect structural properties and stability of N TB . Assuming that the driving force responsible for the formation of this phase is packing entropy we show, within Landau-de Gennes theory, that N TB can undergo a rich sequence of structural changes with field.For the systems with positive anisotropy of permittivity we first observe a decrease of the tilt angle of N TB until it transforms through a field-induced phase transition to the ordinary prolate uniaxial nematic phase (N ). Then, at very high fields this nematic phase develops polarization perpendicular to the field. For systems with negative anisotropy of permittivity the results reveal new modulated structures. Even an infinitesimally small field transforms N TB to its elliptical counterpart (N TBe ), where the circular base of the cone of the main director becomes elliptic.With stronger fields the ellipse degenerates to a line giving rise to a nonchiral periodic structure, the nematic splay-bend (N SB ), where the two nematic directors are restricted to a plane. The three structures, N TB , N TBe and N SB , with a modulated polar order are globally nonpolar. But further increase of the field induces phase transitions into globally polar structures with nonvanishing polarization along the field's direction. We found two such structures, one of which is a polar and chiral modification of N SB , where splay and bend deformations are accompanied by weak twist deformations (N * SBp ). Further increase of the field unwinds this structure into a polar nematic (N p ) of polarization parallel to the field.

The structure of a fluid of hard Gaussian overlap particles of elongation κ = 5, confined between two hard walls, has been calculated from density-functional theory and Monte Carlo simulations. By using the exact expression for the excluded volume kernel (Velasco E and Mederos L 1998 J. Chem. Phys. 109 2361) and solving the appropriate Euler-Lagrange equation entirely numerically, we have been able to extend our theoretical predictions into the nematic phase, which had up till now remained relatively unexplored due to the high computational cost. Simulation reveals a rich adsorption behaviour with increasing bulk density, which is described semi-quantitatively by the theory without any adjustable parameters.

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Outcrossed mating systems play a very important role in the persistence of endangered, selfincompatible plants such as shrub birch, Betula humilis Schrk. The goal of this study was to estimate, for the first time, the effectiveness of sexual reproduction in threatened edge and sub-central populations of shrub birch. The amplified fragment length polymorphism (AFLP) method revealed that all of the individuals at each locality had different genotypes. The matrix incompatibility count (MIC) suggested that the effectiveness of recombination was similar among all the populations of shrub birch under study. However, taking into account the greater germination ability of seeds in subcentral populations, we conclude that sexual reproduction in those populations can be more efficient. The germination capacity of seeds depends on their mass, which was significantly lower in dry or more shaded sites compared to wet or more exposed sites. Nonsignificant results of multiple regression models suggest that chemical parameters of the habitat (pH, EC, NH 4 + , PO 4 3− ) had no influence on the reproductive output of B. humilis. The discrepancy between the still quite substantial genetic diversity and the poor sexual reproduction in shrub birch populations can be explained by the production of a few phosphorus-rich seeds, insufficient time for a decrease in genetic variation in the disappearing part of the range or hybridization with close congeners.

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