Abstract: The shape of leaf laminae exhibits considerable diversity and complexity that reflects adaptations to environmental factors such as ambient light and precipitation as well as phyletic legacy. Many leaves appear to be elliptical which may represent a ‘default’ developmental condition. However, whether their geometry truly conforms to the ellipse equation (EE), i.e., (x/a)2 + (y/b)2 = 1, remains conjectural. One alternative is described by the superellipse equation (SE), a generalized version of EE, i.e., |x/a|n +|y/b|n = 1. To test the efficacy of EE versus SE to describe leaf geometry, the leaf shapes of two Michelia species (i.e., M. cavaleriei var. platypetala, and M. maudiae), were investigated using 60 leaves from each species. Analysis shows that the majority of leaves (118 out of 120) had adjusted root-mean-square errors of < 0.05 for the nonlinear fitting of SE to leaf geometry, i.e., the mean absolute deviation from the polar point to leaf marginal points was smaller than 5% of the radius of a hypothesized circle with its area equaling leaf area. The estimates of n for the two species were ˂ 2, indicating that all sampled leaves conformed to SE and not to EE. This study confirms the existence of SE in leaves, linking this to its potential functional advantages, particularly the possible influence of leaf shape on hydraulic conductance.

Abstract: In this work, the effect of geometry and orientation of food cans on the heating characteristics of processed liquid foods and the resulting lethality target values as a function of the processing times have been investigated. For this purpose, the governing differential equations have been solved numerically for elliptical and cylindrical cans of varying aspect ratios in different orientations in order to delineate their effect on the heating rate (especially of the slowest heating zone [SHZ]) and lethality values over wide ranges of rheological features including shear thinning (n < 1), Newtonian (n = 1), and shear thickening (n > 1) behaviors. The flow and heat transfer characteristics were analyzed with the help of velocity vectors, isotherm contours, average Nusselt number, SHZ temperature and heat penetration parameters, and lethality target values. Also, comparisons were made in terms of the sterilization time and heat penetration parameters to identify the preferable geometries and orientations of food cans for effective heating of non-Newtonian foodstuffs. Finally, favorable conditions in terms of the shape and orientation of the can and the rheological properties have been delineated which lead to superior heating characteristics. Practical Applications Processed foodstuffs are produced in various forms ranging from that in solid, liquid, or as heterogeneous mixtures. Often such liquid and heterogeneous suspensions products are viscous non-Newtonian in character and their thermal processing (including pasteurization, sterilization, etc.) tends to be much more challenging than that of their Newtonian counterparts like air and water. This work explores heating of non-Newtonian liquid foodstuffs in cans of various shapes, geometries and in different orientations in the free convection regime. The results show that depending upon the rheological properties of the products, some orientations and/or geometries offer potential advantages in terms of shorter processing times and lethality values. This information can be of great potential in customizing the design of containers for different food products as well as of different rheological properties.

Abstract: Nano-width martensite plates in a fully martensitic Ni50Ti50 alloy are indexed successfully by using the off-axis transmission Kikuchi diffraction in scanning electron microscope (i.e., SEM-based TKD). The data obtained by SEM-TKD are effectively interpreted using an improved approach based on the framework of the theoretical groupoid structure method, where the equivalent variants transformed from the monoclinic variants are introduced to calculate all theoretical axis/angle pairs of rotation, and to formulate a complete list of source martensite to target martensite pairs. Consequently, B19' monoclinic martensite variants in NiTi alloys are identified unambiguously, by using numerical comparison between the experimental and theoretical rotation components, without the reference of retained parent phase. (C) 2020 Elsevier B.V. All rights reserved.