shape models
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2021 ◽  
Vol 2 (6) ◽  
pp. 229
Author(s):  
Xiangyu Li ◽  
Daniel J. Scheeres

Abstract In this paper, the structural stability of a fast-spinning small body is investigated. In particular, a nonlinear yield condition in tensile stress is applied to estimate the required cohesion in a fast-spinning small body. The least upper bound of required cohesion is investigated for both ellipsoid and irregular shape models. The stress state of a fast-spinning ellipsoid is discussed analytically, and the effects of spin rates and size ratios are analyzed. For an irregularly shaped body, an element average stress method is developed to estimate the range of stress of any element in the body, where only self-gravity and centrifugal force are considered. The maximum tensile stress in the whole body is used to solve the required cohesion. Finally, the proposed methods are applied to different asteroid shape models. The result shows that the least upper bound of cohesion is mainly determined by the spin rate and length of the major axis, but an irregular shape will change the stress distribution and cause a stressed surface. The required cohesion of a fast-spinning small body varies between tens to 1000 Pa. The methods developed in this paper can rapidly provide a conservative lower bound on the cohesion in a fast-spinning body and qualitatively show the distribution of stress, which provides an effective way to study the structural stability of fast-spinning bodies of those bodies.


Author(s):  
Meletios Liaskos ◽  
Michalis A. Savelonas ◽  
Pantelis A. Asvestas ◽  
Dimitrios Papageorgiou ◽  
George K. Matsopoulos

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Christina Boukouvala ◽  
Joshua Daniel ◽  
Emilie Ringe

AbstractUnlike in the bulk, at the nanoscale shape dictates properties. The imperative to understand and predict nanocrystal shape led to the development, over several decades, of a large number of mathematical models and, later, their software implementations. In this review, the various mathematical approaches used to model crystal shapes are first overviewed, from the century-old Wulff construction to the year-old (2020) approach to describe supported twinned nanocrystals, together with a discussion and disambiguation of the terminology. Then, the multitude of published software implementations of these Wulff-based shape models are described in detail, describing their technical aspects, advantages and limitations. Finally, a discussion of the scientific applications of shape models to either predict shape or use shape to deduce thermodynamic and/or kinetic parameters is offered, followed by a conclusion. This review provides a guide for scientists looking to model crystal shape in a field where ever-increasingly complex crystal shapes and compositions are required to fulfil the exciting promises of nanotechnology.


Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1524
Author(s):  
Peijian Shi ◽  
Kexin Yu ◽  
Karl J. Niklas ◽  
Julian Schrader ◽  
Yu Song ◽  
...  

Many plant species produce ovate leaves, but there is no general parametric model for describing this shape. Here, we used two empirical nonlinear equations, the beta and Lobry–Rosso–Flandrois (LRF) equations, and their modified forms (referred to as the Mbeta and MLRF equations for convenience), to generate bilaterally symmetrical curves along the x-axis to form ovate leaf shapes. In order to evaluate which of these four equations best describes the ovate leaf shape, we used 14 leaves from 7 Neocinnamomum species (Lauraceae) and 72 leaves from Chimonanthus praecox (Calycanthaceae). Using the AIC and adjusted root mean square error to compare the fitted results, the modified equations fitted the leaf shapes better than the unmodified equations. However, the MLRF equation provided the best overall fit. As the parameters of the MLRF equation represent leaf length, maximum leaf width, and the distance from leaf apex to the point associated with the maximum leaf width along the leaf length axis, these findings are potentially valuable for studying the influence of environmental factors on leaf shape, differences in leaf shape among closely related plant species with ovate leaf shapes, and the extent to which leaves are bilaterally symmetrical. This is the first work in which temperature-dependent developmental equations to describe the ovate leaf shape have been employed, as previous studies lacked similar leaf shape models. In addition, prior work seldom attempted to describe real ovate leaf shapes. Our work bridges the gap between theoretical leaf shape models and empirical leaf shape indices that cannot predict leaf shape profiles.


2021 ◽  
Author(s):  
Volodymyr Troianskyi ◽  
Dagmara Oszkiewicz ◽  
Anna Marciniak ◽  
Pawel Kankiewicz ◽  
Dora Fohring ◽  
...  

<p>Through numerical modeling, Nesvorny et al. (2008) showed that asteroids can migrate due to Yarkovsky drift and resonances to outside of the boundaries of the Vesta family. In particular, they found that objects which end up in the scattered resonances region (so-called Cell I, defined by orbital elements 2.2 AU < a < 2.3 AU, 0.05 < e < 0.2, 0 < i deg < 10 deg) typically have retrograde rotations and thermal parameters that maximize Yarkovsky drift rates. These autors also showed, that asteroids migrating to the low inclination region (Cell II defined by 2.32 AU < a < 2.48 AU, 0.05 < e < 0.2, 2 deg < i < 6 deg) should be predominantly prograde rotators.</p> <p>We performe photometric observations and determine spins and shapes of V-type objects in Cell I and Cell II in order to characterize the dynamical properties of these asteroids more accurately. The results of dynamical modelling show that some asteroids may have migrated to their current location from the Vesta family within ~2 Gy. There are objects, however, whose origin in another parent body may also be plausible. This may support the hypothesis that the number of differentiated basaltic objects in the inner and middle Main Belt should be much higher than previously assumed. We will present preliminary results for the first ~10 asteroids in Cell I and Cell II.</p>


2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Shayan Naseri Nia ◽  
Faranak Rabiei ◽  
M. M. Rashidi

Purpose This paper aims to use the Lattice Boltzmann method (LBM) to numerically simulate the natural convection heat transfer of Cu-water nanofluid in an L-shaped enclosure with curved boundaries. Design/methodology/approach LBM on three different models of curved L-shape cavity using staircase approach is applied to perform a comparative investigation for the effects of curved boundary on fluid flow and heat transfer. The staircase approximation is a straightforward and efficient approach to simulating curved boundaries in LBM. Findings The effect of curved boundary on natural convection in different parameter ranges of Rayleigh number and nanoparticle volume fraction is investigated. The curved L-shape results are also compared to the rectangular L-shape results that were also achieved in this study. The curved boundary LBM simulation is also validated with existing studies, which shows great accuracy in this study. The results show that the top curved boundary in curved L-shape models causes a notable increase in the Nusselt number values. Originality/value Based on existing literature, there is a lack of comparative studies which would specifically examine the effects of curved boundaries on natural convection in closed cavities. Particularly, the application of curved boundaries to an L-shape cavity has not been examined. In this study, curved boundaries are applied to the sharp corners of the bending section in the L-shape and the results of the curved L-shape models are compared to the simple rectangular L-shape model. Hence, a comparative evaluation is performed for the effect of curved boundaries on fluid flow in the L-shape enclosure.


2021 ◽  
Vol 14 (1) ◽  
pp. 67-77
Author(s):  
Arief Ruslan ◽  
Arif Nur Hidayat ◽  
Archita Desia Logiana

People with tunagrahita are generally categorized as mental retardation. Several studies have seen that one of the effective learning concepts is through visual and audio-visual forms. But in drawing education, mentally retarded persons have different patterns in response to visual meaning. Visual perception is built on coarse motor concepts in processing images which are not always done easily. This research is developed with a descriptive qualitative methodology to see and describe what forms and image models are easy to difficult the draw process. Retrieval of the research data was through mentally retarded children from the Extraordinary School of the Amal Mulia Foundation by processing images in three forms, namely lines, shape models, and combinations of shapes. The preliminary findings in this study were that students with mental retardation had difficulties in drawing shapes that were not straight or solid, such as curves and circles, even though the students were still able to process according to directions in not too long. Keywords: mental retardation; drawing; visual perception; shape models; education.


2021 ◽  
Vol 11 (11) ◽  
pp. 5204
Author(s):  
Giulia Pascoletti ◽  
Alessandra Aldieri ◽  
Mara Terzini ◽  
Pinaki Bhattacharya ◽  
Michele Calì ◽  
...  

Principal components analysis is a powerful technique which can be used to reduce data dimensionality. With reference to three-dimensional bone shape models, it can be used to generate an unlimited number of models, defined by thousands of nodes, from a limited (less than twenty) number of scalars. The full procedure has been here described in detail and tested. Two databases were used as input data: the first database comprised 40 mandibles, while the second one comprised 98 proximal femurs. The “average shape” and principal components that were required to cover at least 90% of the whole variance were identified for both bones, as well as the statistical distributions of the respective principal components weights. Fifteen principal components sufficed to describe the mandibular shape, while nine components sufficed to describe the proximal femur morphology. A routine has been set up to generate any number of mandible or proximal femur geometries, according to the actual statistical shape distributions. The set-up procedure can be generalized to any bone shape given a sufficiently large database of the respective 3D shapes.


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