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The Redner - Ben-Avraham - Kahng cluster system
Costa, Fernando Pestana da; Pinto, João Teixeira; Sasportes, RafaelWe consider a coagulation model first introduced by Redner, Ben-Avraham and Kahng in [11], the main feature of which is that the reaction between a j-cluster and a k-cluster results in the creation of a ; j − k; -cluster, and not, as in Smoluchowski’s model, of a (j + k)-cluster. In this paper we prove existence and uniqueness of solutions under reasonably general conditions on the coagulation coefficients, and...
Scaling behaviour in a coagulation-annihilation model and Lotka-Volterra compet...
Costa, Fernando Pestana da; Pinto, João Teixeira; Sasportes, Rafael; Roessel, Henry J. vanIn a recent paper, Laurencot and van Roessel (2010 J. Phys. A: Math. Theor., 43, 455210) studied the scaling behaviour of solutions to a two-species coagulation–annihilation system with total annihilation and equal strength coagulation, and identified cases where self-similar behaviour occurs, and others where it does not. In this paper, we proceed with the study of this kind of system by assuming that the coag...
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...
Convergence to self-similarity in an addition model with power-like time-depend...
Costa, Fernando Pestana da; Sasportes, Rafael; Pinto, João TeixeiraIn this note we extend the results published in Ref. 1 to a coagulation system with Becker-Doring type interactions and time-dependent input of monomers $J_{1}(t)$ of power–like type: $J_{1}(t)/(\alpha t^{\omega }) \rightarrow 1$ as $t \rightarrow \infty$, with $\alpha > 0$ and $\omega > − \frac{1}{2}$. The general framework of the proof follows Ref. 1 but a different strategy is needed at a number of points.
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