Elliptical Perimeter Research Articles

Geometric form changes of soil quartz minerals under Freeze-thaw weathering

Freeze-thaw weathering can alter the geometry of soil minerals and severely damage the Earth's surface. This has significant implications for the global geological environment. To investigate the process of morphological development and show the morphological trends and evolution of quartz minerals under freeze-thaw cycle (FTC) action, researchers conducted many freeze-thaw weathering experiments. We collected the surface morphology of quartz under different freeze-thaw cycles (FTCs) using a particle image processor. The results showed that: (1) Grain-size morphology became increasingly heterogeneous geometrically as the number of FTCs increased. (2) Freeze-thaw weathering caused the breakage of soil minerals. For longer FTCs, the ratio of the corresponding elliptical axis to the rectangular axis fluctuated. The fluctuation in the equivalent elliptical perimeter exhibited the same trend as the texture and angle values of the particles. (3) During freeze-thaw weathering, the surface geometrical characteristics of quartz minerals resembled those of quartz crystals. Extensive morphological characterization data played a crucial role in determining the morphological evolution of quartz mineral grains during freeze-thaw weathering. Researchers made a novel discovery of self-similarity between the macro- and micro-morphology of quartz minerals during weathering denudation, which has significant implications for advancing our understanding of underlying geomorphological changes.

Active Optics in Astronomy: Freeform Mirror for the MESSIER Telescope Proposal

Active optics techniques in astronomy provide high imaging quality. This paper is dedicated to highly deformable active optics that can generate non-axisymmetric aspheric surfaces—or freeform surfaces—by use of a minimum number of actuators. The aspheric mirror is obtained from a single uniform load that acts over the surface of a closed-form substrate whilst under axial reaction to its elliptical perimeter ring during spherical polishing. MESSIER space proposal is a wide-field low-central-obstruction folded-two-mirror-anastigmat or here called briefly three-mirror-anastigmat (TMA) telescope. The optical design is a folded reflective Schmidt. Basic telescope features are 36 cm aperture, f/2.5, with 1.6° × 2.6° field of view and a curved field detector allowing null distortion aberration for drift-scan observations. The freeform mirror is generated by spherical stress polishing that provides super-polished freeform surfaces after elastic relaxation. Preliminary analysis required use of the optics theory of 3rd-order aberrations and elasticity theory of thin elliptical plates. Final cross-optimizations were carried out with Zemax raytracing code and Nastran FEA elasticity code in order to determine the complete geometry of a glass ceramic Zerodur deformable substrate.

Active optics in astronomy – modeling of deformable substrates: freeform surfaces for FIREBall and MESSIER

Abstract Active optics techniques on large telescopes and astronomical instrumentations provide high imaging quality. For ground-based astronomy, the co-addition of adaptive optics again increases angular resolution up to providing diffraction-limited imaging at least in the infrared. Active and adaptive optics marked milestone progress in the detection of exoplanets, super-massive black holes, and large-scale structure of galaxies. This paper is dedicated to highly deformable active optics that can generate non-axisymmetric aspheric surfaces – or freeform surfaces – by use of a minimum number of actuators: a single uniform load acts over the surface of a vase-form substrate whilst under reaction to its elliptical perimeter ring. Two such instruments are presented: (1) the Faint Intergalactic Redshifted Emission Balloon (FIREBall) telescope and multi object spectrograph (MOS) where the freeform reflective diffraction grating is generated by replication of a deformable master grating, and (2) the MESSIER wide-field low-central-obstruction three-mirror-anastigmat (TMA) telescope proposal where the freeform mirror is generated by stress figuring and elastic relaxation. Freeform surfaces were obtained by plane super-polishing. Preliminary analysis required use of the optics theory of 3rd-order aberrations and elasticity theory of thin elliptical plates. Final cross-optimizations were carried out with Zemax raytracing code and Nastran FEA elasticity code in order to determine geometry of the deformable substrates.

Choosing sheep (Ovis aries) as animal model for temporomandibular joint research: Morphological, histological and biomechanical characterization of the joint disc

Preclinical trials are essential to the development of scientific technologies. Remarkable molecular and cellular research has been done using small animal models. However, significant differences exist regarding the articular behavior between these models and humans. Thus, large animal models may be more appropriate to perform trials involving the temporomandibular joint (TMJ). The aim of this work was to make a morphological (anatomic dissection and white light 3D scanning system), histological (TMJ in bloc was removed for histologic analysis) and biomechanical characterization (tension and compression tests) of sheep TMJ comparing the obtained results with human data. Results showed that sheep processus condylaris and fossa mandibularis are anatomically similar to the same human structures. TMJ disc has an elliptical perimeter, thinner in the center than in periphery. Peripheral area acts as a ring structure supporting the central zone. The disc cells display both fibroblast and chondrocyte-like morphology. Marginal area is formed by loose connective tissue, with some chondrocyte-like cells and collagen fibers in diverse orientations. Discs obtained a tensile modulus of 3.97±0.73MPa and 9.39±1.67MPa, for anteroposterior and mediolateral assessment. The TMJ discs presented a compressive modulus (E) of 446.41±5.16MPa and their maximum stress value (σmax) was 18.87±1.33MPa. Obtained results suggest that these animals should be considered as a prime model for TMJ research and procedural training. Further investigations in the field of oromaxillofacial surgery involving TMJ should consider sheep as a good animal model due to its resemblance of the same joint in humans.

Geometric-attributes-based segmentation of cortical bone slides using optimized neural networks.

In cortical bone, solid (lamellar and interstitial) matrix occupies space left over by porous microfeatures such as Haversian canals, lacunae, and canaliculi-containing clusters. In this work, pulse-coupled neural networks (PCNN) were used to automatically distinguish the microfeatures present in histology slides of cortical bone. The networks' parameters were optimized using particle swarm optimization (PSO). When forming the fitness functions for the PSO, we considered the microfeatures' geometric attributes-namely, their size (based on measures of elliptical perimeter or area), shape (based on measures of compactness or the ratio of minor axis length to major axis length), and a two-way combination of these two geometric attributes. This hybrid PCNN-PSO method was further enhanced for pulse evaluation by combination with yet another method, adaptive threshold (AT), where the PCNN algorithm is repeated until the best threshold is found corresponding to the maximum variance between two segmented regions. Together, this framework of using PCNN-PSO-AT constitutes, we believe, a novel framework in biomedical imaging. Using this framework and extracting microfeatures from only one training image, we successfully extracted microfeatures from other test images. The high fidelity of all resultant segments was established using quantitative metrics such as precision, specificity, and Dice indices.

Discussion of “Learning from Failure of a Long Curved Veneer Wall: Structural Analysis and Repair” by Paulo B. Lourenço and Pedro Medeiros

Discussion of “Learning from Failure of a Long Curved Veneer Wall: Structural Analysis and Repair” by Paulo B. Lourenço and Pedro Medeiros

The shape of Sennacherib's camps: Strategic functions and ideological space

Sennacherib's representations of military events on the reliefs which decorate his residence in Nineveh offer some of the most remarkable images of camps. Their iconographic aspect deserves to be explored, especially considering their role in the visual narrative. Unfortunately, many drawings of lost slabs with representations of camps are totally isolated and unrelated to the narrative episodes; the reconstruction of their role in the dynamics of the story is possible only when a nearly complete cycle is preserved.The spatial shape of Sennacherib's camps is exclusively an elliptical line which encloses a space in which there are various items. The items are arranged either together or as alternatives, and consist of representations of the king sitting on the throne, two priests celebrating a ritual (Collon 1999: 24–5), tents, accommodation for the soldiers and the people that followed the Assyrian army when on campaign (Postgate 2000: 89–93). Sennacherib's sculptors defined the Assyrian type of camp by a curved enclosing line, partially reproducing earlier visual modules. A broad band, which could be either a road or a wall, is found inside it. In addition, the band divides the military camp into an upper and a lower part, and the internal space is sometimes divided into rows which are superimposed and aligned. The rows serve to arrange the distribution inside the elliptical perimeter; similar way to the way slabs are subdivided into registers, the rows inside the camps contribute to organising and setting each item in a fixed and precise place. The structural skeleton, formed by the curving perimeter and internal division into two or more departments (registers) is the foundation of the shape of Assyrian military camps, a well-defined and unchanged icon, always clearly recognizable, especially in Sennacherib's sculptures.