The Quartic Trigonometric Bézier Curve with Two Shape Parameters

AbstractThe production of 2D material flakes in large quantities is a rapidly evolving field and a cornerstone for their industrial applicability. Although flake production has advanced in a fast pace, its statistical characterization is somewhat slower, with few examples in the literature which may lack either modelling uniformity and/or physical equivalence to actual flake dimensions. The present work brings a methodology for 2D material flake characterization with a threefold target: (i) propose a set of morphological shape parameters that correctly map to actual and relevant flake dimensions; (ii) find a single distribution function that efficiently describes all these parameter distributions; and (iii) suggest a representation system—topological vectors—that uniquely characterizes the statistical flake morphology within a given distribution. The applicability of such methodology is illustrated via the analysis of tens of thousands flakes of graphene/graphite and talc, which were submitted to different production protocols. The richness of information unveiled by this universal methodology may help the development of necessary standardization procedures for the imminent 2D-materials industry.

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Predicting the Characteristics of Defect Transitions on Curved Surfaces

Soft Matter ◽

10.1039/d0sm02197k ◽

2021 ◽

Author(s):

Siddhansh Agarwal ◽

Sascha Hilgenfeldt

Keyword(s):

Critical Size ◽

Complex Function ◽

Lattice Defects ◽

Curved Surfaces ◽

Simple Condition ◽

Shape Parameters ◽

Optimal Position

The energetically optimal position of lattice defects on intrinsically curved surfaces is a complex function of shape parameters. For open surfaces, a simple condition predicts the critical size for which...

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Stochastic comparison of parallel systems with Pareto components

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964821000176 ◽

2021 ◽

pp. 1-13

Author(s):

Sameen Naqvi ◽

Weiyong Ding ◽

Peng Zhao

Keyword(s):

Order Statistics ◽

Extreme Value Theory ◽

Pareto Distribution ◽

Parallel Systems ◽

Value Theory ◽

Extreme Value ◽

Stochastic Comparison ◽

Shape Parameters ◽

Scale Parameters ◽

Dispersive Ordering

Abstract Pareto distribution is an important distribution in extreme value theory. In this paper, we consider parallel systems with Pareto components and study the effect of heterogeneity on skewness of such systems. It is shown that, when the lifetimes of components have different shape parameters, the parallel system with heterogeneous Pareto component lifetimes is more skewed than the system with independent and identically distributed Pareto components. However, for the case when the lifetimes of components have different scale parameters, the result gets reversed in the sense of star ordering. We also establish the relation between star ordering and dispersive ordering by extending the result of Deshpande and Kochar [(1983). Dispersive ordering is the same as tail ordering. Advances in Applied Probability 15(3): 686–687] from support $(0, \infty )$ to general supports $(a, \infty )$ , $a > 0$ . As a consequence, we obtain some new results on dispersion of order statistics from heterogeneous Pareto samples with respect to dispersive ordering.

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Asteroid collisions as origin of debris disks: Asteroid shape reconstruction from BNAO Rozhen photometry

Proceedings of the International Astronomical Union ◽

10.1017/s1743921319009426 ◽

2019 ◽

Vol 15 (S350) ◽

pp. 451-453

Author(s):

G. Apostolovska ◽

E. Vchkova Bebekovska ◽

A. Kostov ◽

Z. Donchev

Keyword(s):

Laboratory Experiments ◽

Extrasolar Planets ◽

Shape Reconstruction ◽

Inversion Method ◽

Debris Disks ◽

Shape Parameters ◽

Zodiacal Cloud ◽

Photometric Observations ◽

Different Shapes ◽

Asteroid Surface

AbstractAs a result of collisions during their lifetimes, asteroids have a large variety of different shapes. It is believed that high velocity collisions or rotational spin-up of asteroids continuously replenish the Sun’s zodiacal cloud and debris disks around extrasolar planets (Jewitt (2010)). Knowledge of the spin and shape parameters of the asteroids is very important for understanding collision asteroid processes. Lately photometric observations of asteroids showed that variations in brightness are not accompanied by variations in colour index which indicate that the shape of the lightcurve is caused by varying illuminations of the asteroid surface rather than albedo variations over the surface. This conclusion became possible when photometric investigations were combined with laboratory experiments (Dunlap (1971)). In this article using the convex lightcurve inversion method we obtained the sense of rotation, pole solutions and preliminary shape of 901 Brunsia.

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