Encontrados 5 documentos, a visualizar página 1 de 1
Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-c...
Costa, Fernando Pestana da; Gartland Jr, Eugene C.; Grinfeld, Michael; Pinto, João TeixeiraMotivated by a recent investigation of Millar and McKay [Director orientation of a twisted nematic under the influence of an in-plane magnetic field. Mol. Cryst. Liq. Cryst 435, 277/[937]–286/[946] (2005)], we study the magnetic field twist-Fréedericksz transition for a nematic liquid crystal of positive diamagnetic anisotropy with strong anchoring and pre-twist boundary conditions. Despite the pre-twist, the s...
Uniqueness in the Freedericksz transition with weak anchoring
Costa, Fernando Pestana da; Grinfeld, Michael; Mottram, Nigel J.; Pinto, João TeixeiraIn this paper we consider a boundary value problem for a quasilinear pendulum equation with non-linear boundary conditions that arises in a classical liquid crystals setup, the Freedericksz transition, which is the simplest opto-electronic switch, the result of competition between reorienting effects of an applied electric field and the anchoring to the bounding surfaces. A change of variables transforms the pr...
A mathematical study of a bistable nematic liquid crystal device
Costa, Fernando Pestana da; Grinfeld, Michael; Mottram, Nigel J.; Pinto, João TeixeiraElectronic version of an article published as Mathematical Models and Methods in Applied Sciences Vol. 17, No. 12 (2007). p. 2009–2034. Article DOI No: 10.1142/S0218202507002546. Copyright World Scientific Publishing Company http://www.worldscientific.com/ ; We consider a model of a bistable nematic liquid crystal device based on the Ericksen– Leslie theory. The resulting mathematical object is a parabolic PD...
A hierarchical cluster system based on Horton-Strahler rules for river networks
Costa, Fernando Pestana da; Grinfeld, Michael; Wattis, Jonathan A. D.We consider a cluster system in which each cluster is characterized by two parameters: an \order" i; following Horton-Strahler's rules, and a \mass" j following the usual additive rule. Denoting by ci;j (t) the concen- tration of clusters of order i and mass j at time t; we derive a coagulation- like ordinary di erential system for the time dynamics of these clusters. Results about existence and the behaviour o...
Unimodality of steady size distributions of growing cell populations
Costa, Fernando Pestana da; Grinfeld, Michael; McLeod, J. B.We consider an equation for the evolution of growing and dividing cells, and show, using a result of Kato and McLeod, that the probability density function for the stationary size distribution is necessarily unimodal.
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