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Within the Landau-de Gennes theory of liquid crystals, we study the equilibrium configurations of a nematic cell with twist boundary conditions. Under the assumption that the order tensor Q be uniaxial on both bounding plates, we find three separate classes of solutions, one of which contains the absolute energy minimizer, a twistlike solution that exists(More)
We study the static, long-range interactions of inclusions embedded in lipid membranes. By using a two-dimensional model, we are able to determine explicitly the closed equilibrium shape of the membrane for any value of the distance between the inclusions; our results show that these shapes cannot be obtained by linearizing the equilibrium equations near a(More)
Inclusions embedded in lipid membranes undergo a mediated force, due to the tendency of the membrane to relax its excess of elastic energy. In this paper we determine the exact shape of a two-dimensional vesicle hosting two different inclusions, and we analyse how the inclusion conformation influences the mediated interaction. We find non-trivial(More)
Over the last few years, renewed interest has been raised by the simplified general interaction models proposed by Straley for mesogenic molecules possessing the D{2h} symmetry and capable of producing biaxial nematic order. It has already been shown that, in the presence of certain special symmetries, just two out of the four order parameters that are in(More)
We study a class of quadratic Hamiltonians which describe both fully attractive and partly repulsive molecular interactions, characteristic of biaxial liquid crystal molecules. To treat the partly repulsive interactions we establish a minimax principle for the associated mean-field free energy. We show that the phase diagram described by Sonnet [Phys. Rev.(More)
Within the general quadrupolar model for biaxial nematic liquid crystals, whose potential of mean torque extends that in the Maier-Saupe theory with two extra interaction terms, we propose a quantitative criterion to identify the dominant biaxial interaction. We show that the ratio of the biaxial-to-uniaxial and uniaxial-to-isotropic transition temperatures(More)
We consider here a classical model, consisting of D_{2h}-symmetric particles in a three-dimensional simple-cubic lattice; the pair potential is isotropic in orientation space, and restricted to nearest neighbors. The simplest potential model is written in terms of the squares of the scalar products between unit vectors describing the three interacting arms(More)
Temporal patterns of masting in conifer species are intriguing phenomena that have cascading effects on different trophic levels in ecosystems. Many studies suggest that meteorological cues (changes in temperature and precipitation) affect variation in seed-crop size over years. We monitored cone crops of six conifer species in the Italian Alps (1999–2013)(More)
The existence of uniaxial liquid crystals comprising polar molecules, with all the dipoles aligned in a parallel pattern, is classically ruled out. Generally, there are two different avenues to a mean-field theory for liquid crystals: one is based on short-range, repulsive, steric forces, and the other is based on long-range, globally attractive, dispersion(More)
We employ a continuum model to compute both torque and force transmitted through a thin twist cell filled with a nematic liquid crystal and bounded by flat plates with anchorings at right angles. The transmitted torque vanishes at the order reconstruction threshold when the cell thickness is comparable with the biaxial coherence length. At the same point,(More)