AbstractCapsules with a thin aerogel shell were prepared by the OO/W/OIemulsion process. (Phloroglucinol carboxylic acid)/formaldehyde (PF) was used as the water phase (W) solution to form the shell of the capsule. PF is a linear polymer prepared from phloroglucinol carboxylic acid. The viscosity of the PF solution can reach a high level of 9×10−5m2/s without gelation while resorcinol/formaldehyde (RF) gelates at ~3–4×10−5m2/s. Using the viscous PF solution, capsule with a 17 µm gel shell was fabricated. This thickness satisfies the specification of the first phase of Fast Ignition Realization Experiment (FIREX-I) at Osaka University. When PF gel was extracted to remove the organic solvent, shrinkage of 9% occurred. The final density of the PF aerogel was 145 mg/cm3. Both the shell thickness and density can satisfy the specification of FIREX-I. The pore size of the PF aerogel was less than 100 nm while that of RF was 200–500 nm. The SEM showed that PF had particle-like foam structure while RF had fibrous-like foam structure.
AbstractIt is a well-known fact – which can be shown by elementary calculus – that the volume of the unit ball in \mathbb{R}^{n} decays to zero and simultaneously gets concentrated on the thin shell near the boundary sphere as n\nearrow\infty.
Many rigorous proofs and heuristic arguments are provided for this fact from different viewpoints, including Euclidean geometry, convex geometry, Banach space theory, combinatorics, probability, discrete geometry, etc.
In this note, we give yet another two proofs via the regularity theory of elliptic partial differential equations and calculus of variations.
AbstractAutomatic craniomaxillofacial (CMF) three dimensional (3D) dense phenotyping promises quantification of the complete CMF shape compared to the limiting use of sparse landmarks in classical phenotyping. This study assesses the accuracy and reliability of this new approach on the human mandible. Classic and automatic phenotyping techniques were applied on 30 unaltered and 20 operated human mandibles. Seven observers indicated 26 anatomical landmarks on each mandible three times. All mandibles were subjected to three rounds of automatic phenotyping using Meshmonk. The toolbox performed non-rigid surface registration of a template mandibular mesh consisting of 17,415 quasi landmarks on each target mandible and the quasi landmarks corresponding to the 26 anatomical locations of interest were identified. Repeated-measures reliability was assessed using root mean square (RMS) distances of repeated landmark indications to their centroid. Automatic phenotyping showed very low RMS distances confirming excellent repeated-measures reliability. The average Euclidean distance between manual and corresponding automatic landmarks was 1.40 mm for the unaltered and 1.76 mm for the operated sample. Centroid sizes from the automatic and manual shape configurations were highly similar with intraclass correlation coefficients (ICC) of > 0.99. Reproducibility coefficients for centroid size were < 2 mm, accounting for < 1% of the total variability of the centroid size of the mandibles in this sample. ICC’s for the multivariate set of 325 interlandmark distances were all > 0.90 indicating again high similarity between shapes quantified by classic or automatic phenotyping. Combined, these findings established high accuracy and repeated-measures reliability of the automatic approach. 3D dense CMF phenotyping of the human mandible using the Meshmonk toolbox introduces a novel improvement in quantifying CMF shape.
Thin shell aerogel fabrication for FIREX-I targets using high viscosity (phloroglucinol carboxylic acid)/formaldehyde solution
