scholarly journals The mysterious story of square ice, piles of cubes, and bijections

2020 ◽  
Vol 117 (38) ◽  
pp. 23460-23466
Author(s):  
Ilse Fischer ◽  
Matjaž Konvalinka

When combinatorialists discover two different types of objects that are counted by the same numbers, they usually want to prove this by constructing an explicit bijective correspondence. Such proofs frequently reveal many more details about the relation between the two types of objects than just equinumerosity. A famous set of problems that has resisted various attempts to find bijective proofs for almost 40 y is concerned with alternating sign matrices (which are equivalent to a well-known physics model for two-dimensional ice) and their relations to certain classes of plane partitions. In this paper we tell the story of how the bijections were found.

In this work, bifurcation characteristics of unsteady, viscous, Newtonian laminar flow in two-dimensional sudden expansion and sudden contraction-expansion channels have been studied for different values of expansion ratio. The governing equations have been solved using finite volume method and FLUENT software has been employed to visualize the simulation results. Three different mesh studies have been performed to calculate critical Reynolds number (Recr) for different types of bifurcation phenomena. It is found that Recr decreases with the increase in expansion ratio (ER).


Author(s):  
Hao Li

Traditional mural repair methods only observe the texture of murals when segmenting the repair area, but ignore the extraction of a mural damage data, resulting in incomplete damage crack information. For this reason, the method of repairing the damaged murals based on machine vision is studied. Using machine vision, it can get two-dimensional image of a mural, preprocess the image, extract the damaged data of a mural, and then divide the repair area and repair degree index. According to different types of damage, it can choose the corresponding repair methods to achieve the repair of damaged mural. The results show: Compared with the reference [1] method and reference [2] method, the number of repair points and repair cracks extracted by the proposed method is more than that of the two traditional methods, which can more accurately and comprehensively extract the repair information of murals.


2021 ◽  
Vol 91 (8) ◽  
pp. 887-911
Author(s):  
Manuel F. Isla ◽  
Ernesto Schwarz ◽  
Gonzalo D. Veiga ◽  
Jerónimo J. Zuazo ◽  
Mariano N. Remirez

ABSTRACT The intra-parasequence scale is still relatively unexplored territory in high-resolution sequence stratigraphy. The analysis of internal genetic units of parasequences has commonly been simplified to the definition of bedsets. Such simplification is insufficient to cover the complexity involved in the building of individual parasequences. Different types of intra-parasequence units have been previously identified and characterized in successive wave-dominated shoreface–shelf parasequences in the Lower Cretaceous Pilmatué Member of the Agrio Formation in central Neuquén Basin. Sedimentary and stratigraphic attributes such as the number of intra-parasequence units, their thickness, the proportions of facies associations in the regressive interval, the lateral extent of bounding surfaces, the degree of deepening recorded across these boundaries, and the type and lateral extent of associated transgressive deposits are quantitatively analyzed in this paper. Based on the analysis of these quantified attributes, three different scales of genetic units in parasequences are identified. 1) Bedset complexes are 10–40 m thick, basin to upper-shoreface successions, bounded by 5 to 16 km-long surfaces with a degree of deepening of one to three facies belts. These stratigraphic units represent the highest hierarchy of intra-parasequence stratigraphic units, and the vertical stacking of two or three of them typically forms an individual parasequence. 2) Bedsets are 2–20 m thick, offshore to upper-shoreface successions, bounded by up to 10 km long surfaces with a degree of deepening of zero to one facies belt. Two or three bedsets stack vertically build a bedset complex. 3) Sub-bedsets are 0.5–5 m thick, offshore transition to upper-shoreface successions, bounded by 0.5 to 2 km long surfaces with a degree of deepening of zero to one facies belt. Two or three sub-bedsets commonly stack to form bedsets. The proposed methodology indicates that the combination of thickness with the proportion of facies associations in the regressive interval of stratigraphic units can be used to discriminate between bedsets and sub-bedsets, whereas for higher ranks (bedsets and bedset complexes) the degree of deepening, lateral extent of bounding surfaces, and the characteristics of associated shell-bed deposits become more effective. Finally, the results for the Pilmatué Member are compared with other ancient and Holocene examples to improve understanding of the high-frequency evolution of wave-dominated shoreface–shelf systems.


Author(s):  
José Lages ◽  
Justin Loye ◽  
Célestin Coquidé ◽  
Guillaume Rollin

The worldwide football transfer market is analyzed as a directed complex network: the football clubs are the network nodes and the directed edges are weighted by the total amount of money transferred from a club to another. The Google matrix description allows to treat every club independently of their richness and allows to measure for a given club the efficiency of player sales and player acquisitions. The PageRank algorithm, developed initially for the World Wide Web, naturally characterizes the ability of a club to import players. The CheiRank algorithm, also developed to analyze large scale directed complex networks, characterizes the ability of a club to export players. The analysis in the two-dimensional PageRank-CheiRank plan permits to determine the transfer balance of the clubs in a more subtle manner than the traditional import-export scheme. We investigate the 2017-2018 mercato concerning 2296 clubs, 6698 player transfers, and 147 player nationalities. The transfer balance is determined globally for different types of player trades (defender, midfielder, forward, …) and for different national football leagues. Although, on average, the network transfer flows from and to clubs are balanced, the discrimination by player type draws a specific portrait of each football club.


1989 ◽  
Vol 120 ◽  
pp. 484-493 ◽  
Author(s):  
Carl Heiles

ABSTRACT.Recent developments, both observational and theoretical, require a reevaluation of the effects of clustered supernovae on the two-dimensional porosity parameter Q2D and the rates of mass injection into the halo Ṁ of both cold and hot gas. Clustered supernovae produce two types of bubble. Most clusters produce breakthrough bubbles, which do no more than break through the dense gas disk. But large clusters produce enough energy to make blowout bubbles, which blow gas up into the halo. We calculate area filling factors and mass injection rates into the halo for different types of galaxy. We relate our calculations to two observables, the area covered by H I ‘holes’ and the area covered by giant H II regions. We also reiterate the difficulty of producing the very largest supershells by clusered supernovae.


2014 ◽  
Vol 11 (03) ◽  
pp. 1450020 ◽  
Author(s):  
John Fasoulas ◽  
Michael Sfakiotakis

This paper presents a general dynamic model that describes the two-dimensional grasp by two robotic fingers with soft fingertips. We derive the system's kinematics and dynamics by incorporating rolling constraints that depend on the deformation and on the rolling distance characteristics of the fingertips' material. We analyze the grasp stability at equilibrium, and conclude that the rolling properties of the fingertips can play an important role in grasp stability, especially when the width of the grasped object is small compared to the radius of the tips. Subsequently, a controller, which is based on the fingertips' rolling properties, is proposed for stable grasping concurrent with object orientation control. We evaluate the dynamic model under the proposed control law by simulations and experiments that make use of two different types of soft fingertip materials, through which it is confirmed that the dynamic model can successfully capture the effect of the fingertips' deformation and their rolling distance characteristics. Finally, we use the dynamic model to demonstrate by simulations the significance of the fingertips' rolling properties in grasping thin objects.


1983 ◽  
Vol 30 (2) ◽  
pp. 321-344 ◽  
Author(s):  
V. S. Semenov ◽  
I. V. Kubyshkin ◽  
M. F. Heyn ◽  
H. K. Biernat

A detailed mathematical analysis of plane steady-state reconnexion is given for the case when the plasma parameters and the magnetic fields are not identical on both sides of the current sheet. Asymptotic solutions in the sense that the inflow velocity is much less than the local Alfvén velocity as well as the arrangement of shock waves are obtained. Rotational (Alfvén) waves, slow shock waves, rarefaction waves (expansion fans), and a contact discontinuity may occur. Four different types of solution, corresponding to different shock wave configurations, are possible. They depend on the parameters of the inflow regions in a unique way.


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