Synthesis and preliminary results on the characterization of liquid-crystalline polyacrylates with truns-1,3-dioxane-2,5-diyl group in the side chain are presented. A stabilization of the mesophases occurs when two phenyl groups are present in the mesogenic moiety. All polymers with three rings exhibit S , mesophases except for poly(6-[truns-2-(4-(4-methoxybenzoyloxy)phenyl)l,3-dioxane-S-yl]hexyl acrylate) which presents a nematic phase over 200 O C and is potentially useful as host matrix for applications in non-linear optics. 0 1990, HUthig & Wepf Verlag, Basel CCC 0025-1 16X/90/%03.00
The synthesis of a series of side-chain liquid-crystalline polyacrylates having mesogenic groups containing the trans-2-(4-cyanopheny1)-1.3-dioxan-5-y1 moiety is reported. Methylenic spacer groups of different lengths have been used. Polymers were prepared by radical polymerization of the corresponding acrylates. The liquid-crystalline nature of these polymers has been established by calorimetric measurements and optical texture observations. The phase behaviour is strongly dependent on the length of the spacer group. With (CH&, the unusual I-N-S,-N, sequence is observed. =) Part 1: cf. 1). b,
The purpose of this article is to study the convergence of a low order finite element approximation for a natural convection problem. We prove that the discretization based on P1 polynomials for every variable (velocity, pressure and temperature) is well-posed if used with a penalty term in the divergence equation, to compensate the loss of an inf-sup condition. With mild assumptions on the pressure regularity, we recover convergence for the Navier-Stokes-Boussinesq system, provided the penalty term is chosen in accordance with the mesh size. We express conditions to obtain optimal order of convergence. We illustrate theoretical convergence results with extensive examples. The computational cost that can be saved by this approach is also assessed.
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