An Energy-Minimization Finite-Element Approach for the Frank-Oseen Model of Nematic Liquid Crystals: Continuum and Discrete Analysis

This paper outlines an energy-minimization finite-element approach to the computational modeling of equilibrium configurations for nematic liquid crystals under free elastic effects. The method targets minimization of the system free energy based on the Frank-Oseen free-energy model. Solutions to the intermediate discretized free elastic linearizations are shown to exist generally and are unique under certain assumptions. This requires proving continuity, coercivity, and weak coercivity for the accompanying appropriate bilinear forms within a mixed finite-element framework. Error analysis demonstrates that the method constitutes a convergent scheme. Numerical experiments are performed for problems with a range of physical parameters as well as simple and patterned boundary conditions. The resulting algorithm accurately handles heterogeneous constant coefficients and effectively resolves configurations resulting from complicated boundary conditions relevant in ongoing research.Comment: 31 pages, 3 figures, 3 table

Orientational transition in a nematic liquid crystal at a patterned surface

T. J. Atherton and J. Roy Sambles, Physical Review E, Vol. 74, article 022701 (2006) "Copyright © 2006 by the American Physical Society."We consider a semi-infinite nematic in contact with a periodic patterned surface with alternate planar and homeotropic stripes. Extending the work of Barbero et al., we find the free energy (assuming K1=K3) for the situations where the easy direction on the planar stripe is either perpendicular or parallel to the length of the stripes. We find the bulk free energy difference between the structures to be proportional to √ K2/K1 and so we consider the possibility of a spontaneous transition between the two states if the azimuthal anchoring energy is sufficiently weak and K1≠K2. We compute the critical azimuthal anchoring energy for such a transition in terms of the relative width of the stripes and the period of the pattern and find it to be ~10−6 J m−2, comparable to experimental values

Onset of photosynthesis in spring speeds up monoterpene synthesis and leads to emission bursts

Emissions of biogenic volatile organic compounds (BVOC) by boreal evergreen trees have strong seasonality, with low emission rates during photosynthetically inactive winter and increasing rates towards summer. Yet, the regulation of this seasonality remains unclear. We measured in situ monoterpene emissions from Scots pine shoots during several spring periods and analysed their dynamics in connection with the spring recovery of photosynthesis. We found high emission peaks caused by enhanced monoterpene synthesis consistently during every spring period (monoterpene emission bursts, MEB). The timing of the MEBs varied relatively little between the spring periods. The timing of the MEBs showed good agreement with the photosynthetic spring recovery, which was studied with simultaneous measurements of chlorophyll fluorescence, CO2 exchange and a simple, temperature history-based proxy for state of photosynthetic acclimation, S. We conclude that the MEBs were related to the early stages of photosynthetic recovery, when the efficiency of photosynthetic carbon reactions is still low whereas the light harvesting machinery actively absorbs light energy. This suggests that the MEBs may serve a protective functional role for the foliage during this critical transitory state and that these high emission peaks may contribute to atmospheric chemistry in the boreal forest in springtime. Emissions of biogenic volatile organic compounds (BVOC) by boreal evergreen trees have strong seasonality. We measured high emission peaks from Scots pine shoots caused by enhanced monoterpene synthesis taking place simultaneously with the photosynthetic spring recovery. We conclude that the increased emissions were related to the photosynthetic recovery, when the efficiency of photosynthetic carbon reactions is low whereas the light harvesting machinery actively absorbs light energy. Increased emissions may serve a protective functional role for the foliage during the transitory state, and these high emission peaks may contribute to atmospheric chemistry in the boreal forest in springtime.Peer reviewe

Independent control of polar and azimuthal anchoring

Monte Carlo simulation, experiment and continuum theory are used to examine the anchoring exhibited by a nematic liquid crystal at a patterned substrate comprising a periodic array of rectangles that, respectively, promote vertical and planar alignment. It is shown that the easy axis and effective anchoring energy promoted by such surfaces can be readily controlled by adjusting the design of the pattern. The calculations reveal rich behavior: for strong anchoring, as exhibited by the simulated system, for rectangle ratios $\geq 2$ the nematic aligns in the direction of the long edge of the rectangles, the azimuthal anchoring coefficient changing with pattern shape. In weak anchoring scenarios, however, including our experimental systems, preferential anchoring is degenerate between the two rectangle diagonals. Bistability between diagonally-aligned and edge-aligned arrangement is predicted for intermediate combinations of anchoring coefficient and system length-scale.Comment: 12 pages, 12 figure

Calculation Of Secondary Particles In Atmosphere And Hadronic Interactions

Calculation of secondary particles produced by the interaction of cosmic rays with the nuclei of Earth's atmosphere pose important requirements to particle production models. Here we summarize the important features of hadronic simulations, stressing the importance of the so called ``microscopic'' approach, making explicit reference to the case of the FLUKA code. Some benchmarks are also presented.Comment: 10 pages, 4 figures. Extended version of report given at the IInd Workshop on Matter and anti-Matter, Trento, Oct. 200