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Summary The majority of plant colours are produced by anthocyanin and carotenoid pigments, but colouration obtained by nanostructured materials (i.e. structural colours) is increasingly reported in plants. Here, we identify a multilayer photonic structure in the fruits of
Lantana strigocamara and compare it with a similar structure inViburnum tinus fruits.We used a combination of transmission electron microscopy (EM), serial EM tomography, scanning force microscopy and optical simulations to characterise the photonic structure in
L. strigocamara . We also examine the development of the structure during maturation.We found that the structural colour derives from a disordered, multilayered reflector consisting of lipid droplets of
c. 105 nm that form a plate‐like structure in 3D. This structure begins to form early in development and reflects blue wavelengths of light with increasing intensity over time as the structure develops. The materials used are likely to be lipid polymers.Lantana strigocamara is the second origin of a lipid‐based photonic structure, convergently evolved with the structure inViburnum tinus . Chemical differences between the lipids inL. strigocamara and those ofV. tinus suggest a distinct evolutionary trajectory with implications for the signalling function of structural colours in fruits. -
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Abstract To advance the MXene field, it is crucial to optimize each step of the synthesis process and create a detailed, systematic guide for synthesizing high‐quality MXene that can be consistently reproduced. In this study, a detailed guide is provided for an optimized synthesis of titanium carbide (Ti3C2T
x ) MXene using a mixture of hydrofluoric and hydrochloric acids for the selective etching of the stoichimetric‐Ti3AlC2MAX phase and delamination of the etched multilayered Ti3C2Tx MXene using lithium chloride at 65 °C for 1 h with argon bubbling. The effect of different synthesis variables is investigated, including the stoichiometry of the mixed powders to synthesize Ti3AlC2, pre‐etch impurity removal conditions, selective etching, storage, and drying of MXene multilayer powder, and the subsequent delamination conditions. The synthesis yield and the MXene film electrical conductivity are used as the two parameters to evaluate the MXene quality. Also the MXenes are characterized with scanning electron microscopy, x‐ray diffraction, atomic force microscopy, and ellipsometry. The Ti3C2Tx film made via the optimized method shows electrical conductivity as high as ≈21,000 S/cm with a synthesis yield of up to 38 %. A detailed protocol is also provided for the Ti3C2Tx MXene synthesis as the supporting information for this study. -
Abstract We present the first a priori error analysis of a new method proposed in Cockburn & Wang (2017, Adjoint-based, superconvergent Galerkin approximations of linear functionals. J. Comput. Sci., 73, 644–666), for computing adjoint-based, super-convergent Galerkin approximations of linear functionals. If $J(u)$ is a smooth linear functional, where $u$ is the solution of a steady-state diffusion problem, the standard approximation $J(u_h)$ converges with order $h^{2k+1}$, where $u_h$ is the Hybridizable Discontinuous Galerkin approximation to $u$ with polynomials of degree $k>0$. In contrast, numerical experiments show that the new method provides an approximation that converges with order $h^{4k}$, and can be computed by only using twice the computational effort needed to compute $J(u_h)$. Here, we put these experimental results in firm mathematical ground. We also display numerical experiments devised to explore the convergence properties of the method in cases not covered by the theory, in particular, when the solution $u$ or the functional $J(\cdot )$ are not very smooth. We end by indicating how to extend these results to the case of general Galerkin methods.more » « less
