This paper reviews the current progress in mathematical modeling of anti-reflective subwavelength structures. Methods covered include effective medium theory (EMT), finite-difference time-domain (FDTD), transfer matrix method (TMM), the Fourier modal method (FMM)/rigorous coupled-wave analysis (RCWA) and the finite element method (FEM). Time-based solutions to Maxwell’s equations, such as FDTD, have the benefits of calculating reflectance for multiple wavelengths of light per simulation, but are computationally intensive. Space-discretized methods such as FDTD and FEM output field strength results over the whole geometry and are capable of modeling arbitrary shapes. Frequency-based solutions such as RCWA/FMM and FEM model one wavelength per simulation and are thus able to handle dispersion for regular geometries. Analytical approaches such as TMM are appropriate for very simple thin films. Initial disadvantages such as neglect of dispersion (FDTD), inaccuracy in TM polarization (RCWA), inability to model aperiodic gratings (RCWA), and inaccuracy with metallic materials (FDTD) have been overcome by most modern software. All rigorous numerical methods have accurately predicted the broadband reflection of ideal, graded-index anti-reflective subwavelength structures; ideal structures are tapered nanostructures with periods smaller than the wavelengths of light of interest and lengths that are at least a large portion of the wavelengths considered.

Summary We studied the effects on plant growth from insertion of five cisgenes that encode proteins involved in gibberellin metabolism or signalling. Intact genomic copies of PtGA20ox7, PtGA2ox2,Pt RGL1_1, PtRGL1_2 and PtGAI1 genes from the genome‐sequenced Populus trichocarpa clone Nisqually‐1 were transformed into Populus tremula × alba (clone INRA 717‐1B4), and growth, morphology and xylem cell size characterized in the greenhouse. Each cisgene encompassed 1–2 kb of 5′ and 1 kb of 3′ flanking DNA, as well as all native exons and introns. Large numbers of independent insertion events per cisgene (19–38), including empty vector controls, were studied. Three of the cisgenic modifications had significant effects on plant growth rate, morphology or wood properties. The PtGA20ox7 cisgene increased rate of shoot regeneration in vitro, accelerated early growth, and variation in growth rate was correlated with PtGA20ox7 gene expression. PtRGL1_1 and PtGA2ox2 caused reduced growth, while PtRGL1_2 gave rise to plants that grew normally but had significantly longer xylem fibres. RT‐PCR studies suggested that the lack of growth inhibition observed in PtRGL1_2 cisgenic plants was a result of co‐suppression. PtGAI1 slowed regeneration rate and both PtGAI1 and PtGA20ox7 gave rise to increased variance among events for early diameter and volume index, respectively. Our work suggests that cisgenic insertion of additional copies of native genes involved in growth regulation may provide tools to help modify plant architecture, expand the genetic variance in plant architecture available to breeders and accelerate transfer of alleles between difficult‐to‐cross species.

Purpose. To examine the surgical outcomes and graft conditions in patients receiving micropulse transscleral cyclophotocoagulation (MP-TSCPC) to treat post-keratoplasty ocular hypertension. Methods. This retrospective observational study included 30 eyes of 28 consecutive glaucoma patients with a history of penetrating keratoplasty (PKP) or Descemet’s stripping automated endothelial keratoplasty (DSAEK) who underwent MP-TSCPC at the University of California, San Francisco from 09/2015 to 08/2018. Using the Wilcoxon signed-rank test, we compared preoperative and postoperative intraocular pressure (IOP), number of glaucoma medications, visual acuity, and central corneal thickness at 1, 3, 6, and 12 months. Postoperative complications, additional surgeries, and graft failures were also recorded at these follow-up times. Linear regression model was used to study whether PKP vs. DSAEK affects the effectiveness of MP-TSCPC. Results. Thirty eyes from 28 patients were followed for 12 months. IOP was significantly decreased from preop at all follow-up points (P<0.001). There was no significant change in the number of glaucoma drops, visual acuity, or CCT. At 12 months, 21 of the 30 eyes met the definition of success, and only one underwent repeat PKP due to graft rejection. The type of corneal transplant was not a significant factor for IOP reduction at the last follow-up. Conclusions. MP-TSCPC achieved desirable IOP control and success rates for postkeratoplasty patients while resulting in minimal complications and graft failure. It appears to be a safe and effective procedure in patients who received corneal transplant with one-year follow-up.

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Sprinting on a curve is slower than sprinting on a straight lane. To explain this phenomenon, various models based on a combination of biological and physical assumptions have been developed. These models depend on detailed parameters that significantly differ for each individual athlete. Here, we propose a general model solely based on kinetic theory of physics that can be universally applied to all athletes. By solving the force and torque equations for the running speed of the athletes on a curved track, we analyzed sprinting speeds between the inner and outer curves. Applying the data from the classic works into our models, we find that our results and conclusions are mostly aligned with the previous works while our approach is built on the accurate physics principles and contains no uncontrollable parameters. Further we show how runners can alleviate the centrifugal effect of curved track by tilting their bodies and we quantitatively determine the optimal tilting angle for a given curvature.