Rectification of Circular Arcs by Linkages

2019 ◽  
Vol 42 (1) ◽  
pp. 18-23
Author(s):  
Robert Dawson ◽  
Pietro Milici
Keyword(s):  
2021 ◽  
pp. 1-35
Author(s):  
FERENC BENCS ◽  
PJOTR BUYS ◽  
LORENZO GUERINI ◽  
HAN PETERS

Abstract We investigate the location of zeros for the partition function of the anti-ferromagnetic Ising model, focusing on the zeros lying on the unit circle. We give a precise characterization for the class of rooted Cayley trees, showing that the zeros are nowhere dense on the most interesting circular arcs. In contrast, we prove that when considering all graphs with a given degree bound, the zeros are dense in a circular sub-arc, implying that Cayley trees are in this sense not extremal. The proofs rely on describing the rational dynamical systems arising when considering ratios of partition functions on recursively defined trees.


1997 ◽  
Vol 67 (3) ◽  
pp. 311-317 ◽  
Author(s):  
Bjørn Lillekjendlie
Keyword(s):  

2012 ◽  
Vol 219 (3) ◽  
pp. 1306-1311 ◽  
Author(s):  
Zhi Liu ◽  
Jie-qing Tan ◽  
Xiao-yan Chen ◽  
Li Zhang

1967 ◽  
Vol 50 (6) ◽  
pp. 241-258 ◽  
Author(s):  
Peter Satir

In Elliptio complanatus lateral cilia, two distinct patterns of filament termination can be discerned. In one case, all nine filaments are present and all are single; in the second, at least one filament is missing but doublets are still present. These probably represent different configurations within one cilium in different stroke positions; to get from one to the other, some peripheral filaments must move with respect to others. The data are consistent with the hypothesis that the filaments themselves do not change length, but rather slide past one another to accommodate increasing curvature. The bent regions of the cilium are in the form of circular arcs. In a few cases, apparent displacement of filaments at the tip (Δl) can be shown to be accounted for if we assume that all differences are generated within these arcs. The displacement per degree of bend is 35 A. Regions of bent arc are initially confined to the base of the cilium but move up the shaft as straight regions appear below them. From the relationship between arc length and radius of curvature, a shaft length that is the unit that initially bends and slides may be defined. Quantal displacements of the length of one 14S dynein may perhaps occur at sites between filaments at opposite sides of such a unit as sliding occurs.


1974 ◽  
Vol 41 (2) ◽  
pp. 355-359 ◽  
Author(s):  
J. L. Hill ◽  
C. G. Davis

The effect of initial forces on the vibration and stability of curved, clamped, fluid conveying tubes is analyzed by the finite-element technique. The tubes are initially planar with general center-line shapes approximated by constant curvature arcs. The effect of internal pressure is included. Numerical results are presented with, and without, the effects of the initial in-plane forces, for circular arcs S, L, and spiral configurations. Neglecting initial forces results in out-of-plane buckling, while including these forces prevents buckling within the elastic limit, in all configurations studied.


Author(s):  
H Fessler ◽  
C J Moore

This paper describes an alternative to splines for connecting turbine discs to shafts. The trilobe shape consists of six smoothly blending 60° circular arcs of two alternating radii; it is between a circle (both radii equal) and a triangle (smaller radius zero, larger radius infinite). Frozen-stress, photoelastic models of a realistic disc and a tubular shaft have been designed, made and loaded centrifugally, under static torsion and under combined torsion and rotation. The results show that the greatest centrifugal stresses in the disc occur in the bore at the tips of the trilobe and the greatest contact stresses occur near the transition from the larger to the smaller radius. The centrifugal stress concentrations due to the trilobe were small. Bore deformation and backlash due to differential centrifugal expansion were measured and found to be acceptable for a similar ceramic or nickel alloy disc.


2021 ◽  
Vol 922 (2) ◽  
pp. 182
Author(s):  
Robin Hanson ◽  
Daniel Martin ◽  
Calvin McCarter ◽  
Jonathan Paulson

Abstract If life on Earth had to achieve n “hard steps“ to reach humanity's level, then the chance of this event rose as time to the nth power. Integrating this over habitable star formation and planet lifetime distributions predicts >99% of advanced life appears after today, unless n < 3 and max planet duration <50 Gyr. That is, we seem early. We offer this explanation: a deadline is set by loud aliens who are born according to a hard steps power law, expand at a common rate, change their volume appearances, and prevent advanced life like us from appearing in their volumes. Quiet aliens, in contrast, are much harder to see. We fit this three-parameter model of loud aliens to data: (1) birth power from the number of hard steps seen in Earth’s history, (2) birth constant by assuming a inform distribution over our rank among loud alien birth dates, and (3) expansion speed from our not seeing alien volumes in our sky. We estimate that loud alien civilizations now control 40%–50% of universe volume, each will later control ∼ 105–3 × 107 galaxies, and we could meet them in ∼200 Myr–2 Gyr. If loud aliens arise from quiet ones, a depressingly low transition chance (<∼10−4 ) is required to expect that even one other quiet alien civilization has ever been active in our galaxy. Which seems to be bad news for the Search for Extraterrestrial Intelligence. But perhaps alien volume appearances are subtle, and their expansion speed lower, in which case we predict many long circular arcs to find in our sky.


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