Monocrystals of the cubic lyotropic liquid crystal phase V1 are studied in droplets of the mixture C12EO6/water surrounded by water vapor of controlled pressure p. Shapes of monocrystals are found to depend on the conditions of growth from the lamellar phase and on the nature of the substrate. After the growth, when the lamellar phase is exhausted and crystals are in equilibrium with water vapors, their shapes are shown to depend on the pressure p. Thermodynamic aspects of these phenomena are discussed.
PACS. 64.70.Md Phase transitions in liquid crystals -82.65.Dp Thermodynamics of surfaces and interfaces
Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the parameters. However, some systems do not obey power-law scaling, instead there is numerical evidence for a logarithmic scaling form, in which the scaling function depends on ratios of the logarithms of the parameters. Based on previous ideas by Tang we propose that this type of logarithmic scaling can be explained by a concept of local scaling invariance with continuously varying exponents. The functional dependence of the exponents is constrained by a homomorphism which can be expressed as a set of partial differential equations. Solving these equations we obtain logarithmic scaling as a special case. The other solutions lead to scaling forms where logarithmic and power-law scaling are mixed.
We study a contact process on a two-dimensional square lattice which is diluted by randomly removing bonds with probability p. For p < 1/2 and varying birth rate λ the model was shown to exhibit a continuous phase transition which belongs to the universality class of strongly disordered directed percolation. The phase transition line terminates in a multicritical point at p = 1/2 and λ = λ * = 3.55( 1), where the model can be interpreted as a critical directed percolation process running on a critical isotropic percolation cluster. In the present work we study the multicritical point and its neighboorhood by numerical simulations, discussing possible scaling forms which could describe the critical behavior at the transition.
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