Magic™ Mouse Anti-ENG monoclonal antibody, clone 4I6

Motivated by recent mathematical studies of Freedericksz transitions in twist cells and helix unwinding in cholesteric liquid crystal cells [(da Costa et al. in Eur J Appl Math 20:269-287, 2009), (da Costa et al. in Eur J Appl Math 28:243-260, 2017), (McKay in J Eng Math 87:19-28, 2014), (Millar and McKay in Mol Cryst Liq Cryst 435:277/[937]-286/[946], 2005)], we consider a model for the director configuration obtained within the framework of the Frank-Oseen theory and consisting of a nonlinear ordinary differential equation in a bounded interval with non-homogeneous mixed boundary conditions (Dirichlet at one end of the interval, Neumann at the other). We study the structure of the solution set using the depth of the sample as a bifurcation parameter. Employing phase space analysis techniques, time maps, and asymptotic methods to estimate integrals, together with appropriate numerical evidence, we obtain the corresponding novel bifurcation diagram and discuss its implications for liquid crystal display technology. Numerical simulations of the corresponding dynamic problem also provide suggestive evidence about stability of some solution branches, pointing to a promising avenue of further analytical, numerical, and experimental studies.

Longshore sediment transport (LST) acts on beach morphodynamics on distinct temporal scales, being fundamental over sediment budget, and, so over the dynamic balance of coastlines. This study determined the most adequate methodology to estimate rates of non-cohesive sediments (from fine sand to gravel) transported by longshore currents, in the surf zone, under different meteoceanographic conditions, at the southern coast of Rio Grande do Sul (RS), Brazil. The methods proposed by CERC (Shore Protection Manual, Coastal Engineering Research Center (CERC), US Army Corps of Engineers Research and Development Center, Coastal and Hydraulics Laboratory, Vicksburg, 1984), Kamphuis (J Waterw Port Coast Ocean Eng 117(6):624-640, 1991), Bayramet al.(Coast Eng 54:700-710, 2007) and Van Rijn (Coast Eng 90:23-33, 2014) were tested through the comparison with data collected with streamer traps, as well as through statistical tests. Van Rijn (2014) was elected the most suitable approach for all beaches studied, followed by CERC (1984). The other two did not perform well for the study area. All models resulted in underestimated rates during high-energy scenarios, and this is attributed to wind negligence or insufficient weight factor in model's calculations, besides the lack of sampled data during very energetic conditions. Wave characteristics, median grain size and beach slope were proven to strongly influence LST, in accordance with the choice of best model overall. LST behavioural response and model's effectiveness will be different for each specific region, especially in what concerns the beach morphodynamic stage. Hence, the method prediction accuracy depends greatly on the suitability of the dataset with respect to the analytical model being used.