scholarly journals The polar curve of a foliation on \mathbb{P}^2

2010 ◽  
Vol 19 (3-4) ◽  
pp. 849-863 ◽  
Author(s):  
Rogério S. Mol
Keyword(s):  
Polar Curve

Drifting along with a wandering polar curve

Geology ◽  
1983 ◽  
Vol 11 (11) ◽  
pp. 672
Author(s):  
Chester B. Beaty
Keyword(s):  
Polar Curve

scholarly journals Relativity Research of Total Pressure and Regulating Valve in Continuous Wind Tunnel and Its Application

2020 ◽  
Vol 38 (2) ◽  
pp. 325-332
Author(s):  
Dan Chen ◽  
Xiaosong Yang ◽  
Gang Li ◽  
Shouchun Guo ◽  
Tianyi Chen
Keyword(s):  
Wind Tunnel ◽  
Flow Field ◽  
Total Pressure ◽  
Position Control ◽  
Flow Characteristics ◽  
Field Performance ◽  
Pressure Control ◽  
Static Test ◽  
Polar Curve ◽  
Transonic Wind Tunnel

As the main adjusting means of the total pressure for the continuous transonic wind tunnel, the characteristics of regulating valve directly affect the flow field performance of the wind tunnel, therefore, it is important to analyze and establish the correlation between the regulating valve and the total pressure, and it is necessary to select the appropriate regulating valve and its combination accordingly. Firstly, in terms of the pressure regulation principle of the wind tunnel pressure regulating system, combining with the flow characteristics of the regulating valve, the correlation between the position control of the regulating valve and the total pressure control of the wind tunnel is established, then the static test is conducted to verify the relationship. In order to shorten the flow field stability time under the negative pressure of 0.6m continuous transonic wind tunnel, based on the established theory, the valve system is optimized and reformed, and the blowing test is carried out. The results show that the time of optimized Mach number polar curve decreases by 40%~50%, which greatly improves the test efficiency, which further proves that the present analysis is correct and effective, and can provide reference for the design of pressure regulating system in continuous transonic wind tunnel.

scholarly journals Factorization of the polar curve and the Newton polygon

2003 ◽  
Vol 26 (3) ◽  
pp. 288-303 ◽  
Author(s):  
Andrzej Lenarcik ◽  
Mateusz Masternak ◽  
Arkadiusz Płoski
Keyword(s):  
Newton Polygon ◽  
Polar Curve

AERODYNAMICS OF GLIDING FLIGHT IN A HARRIS' HAWK, PARABUTEO UNICINCTUS

1990 ◽  
Vol 149 (1) ◽  
pp. 469-489 ◽  
Author(s):  
VANCE A. TUCKER ◽  
CARLTON HEINE
Keyword(s):  
Wind Tunnel ◽  
Lift Coefficient ◽  
Drag Coefficients ◽  
Polar Curve ◽  
Wing Span ◽  
Gliding Flight ◽  
Black Vulture ◽  
Polar Area ◽  
Air Speed ◽  
Parabuteo Unicinctus

1. A Harris' hawk with a mass of 0.702 kg and a maximum wing span of 1.02 m glided freely in a wind tunnel at air speeds between 6.1 and 16.2ms−1. The glide angle varied from 8.5% at the slowest speed to a minimum of 5% at speeds between 8.0 and 14.7 ms−1. The maximum ratio of lift to drag was 10.9 and the minimum sinking speed was 0.81ms−1 2. Wing span decreased when either air speed or glide angle increased. Wing area was a parabolic function of wing span 3. Lift and profile drag coefficients of the wings fell in a polar area similar to that for a laggar falcon (Falco jugger) and a black vulture (Coragyps atratus). A single polar curve relating lift coefficients to minimum profile drag coefficients can predict the maximum gliding performance of all three birds when used with a mathematical model for gliding flight 4. The parasite drag values that have been used with the model are probably too high. Thus, the profile drag coefficients determined from the polar curve mentioned above are too low, and the predicted wing spans for gliding at maximum performance are too large. The predicted curve for maximum gliding performance is relatively unaffected 5. The maximum lift coefficient for the Harris' hawk in the wind tunnel was 1.6. This value is probably less than the maximum attainable, since the hawk's wings never appeared to stall. The best estimate of the minimum profile drag coefficient is 0.026 at a lift coefficient of 0.60.

scholarly journals Plane branches with Newton non-degenerate polars

2018 ◽  
Vol 29 (01) ◽  
pp. 1850001
Author(s):  
A. Hefez ◽  
M. E. Hernandes ◽  
M. F. H. Iglesias
Keyword(s):  
Complex Plane ◽  
Newton Polygon ◽  
Polar Curve ◽  
Characteristic Exponents ◽  
Complete Set ◽  
Multiplicity Formula ◽  
Associated Family ◽  
General Member

To an equisingularity class of complex plane branches, described by its multiplicity [Formula: see text] and characteristic exponents [Formula: see text], [Formula: see text], there is a naturally associated family [Formula: see text] of equations containing a complete set of analytic representatives for all branches of the class. We show in this paper that the general polar curve of any member of [Formula: see text] is Newton degenerate, except when [Formula: see text], in which case the general member of [Formula: see text] corresponds to a curve which has a Newton non-degenerate general polar curve with a fixed Newton polygon, or when [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], with [Formula: see text] and [Formula: see text] is odd, in which case [Formula: see text] has a subset containing a complete set of analytic representatives for all branches of the class whose general member has also a Newton non-degenerate general polar curve with a fixed Newton polygon. In both cases, we give explicit Zariski open sets the points of which represent branches with Newton non-degenerate polars and describe the topology of their general polars.

A Degree Formula for Secant Varieties of Curves

2013 ◽  
Vol 57 (2) ◽  
pp. 305-322 ◽  
Author(s):  
Rüdiger Achilles ◽  
Mirella Manaresi ◽  
Peter Schenzel
Keyword(s):  
Plane Curve ◽  
Natural Generalization ◽  
Singular Points ◽  
The Self ◽  
Hilbert Polynomial ◽  
Intersection Numbers ◽  
Secant Varieties ◽  
Secant Variety ◽  
Intersection Multiplicity ◽  
Polar Curve

AbstractUsing the Stückrad–Vogel self-intersection cycle of an irreducible and reduced curve in pro-jective space, we obtain a formula that relates the degree of the secant variety, the degree and the genus of the curve and the self-intersection numbers, the multiplicities and the number of branches of the curve at its singular points. From this formula we deduce an expression for the difference between the genera of the curve. This result shows that the self-intersection multiplicity of a curve in projectiveN-space at a singular point is a natural generalization of the intersection multiplicity of a plane curve with its generic polar curve. In this approach, the degree of the secant variety (up to a factor 2), the self-intersection numbers and the multiplicities of the singular points are leading coefficients of a bivariate Hilbert polynomial, which can be computed by computer algebra systems.

Magnetization of Pacific Seamounts: A preliminary polar curve for the northeastern Pacific

1970 ◽  
Vol 75 (11) ◽  
pp. 2035-2061 ◽  
Author(s):  
Jean Francheteau ◽  
C. G. A. Harrison ◽  
J. G. Sclater ◽  
M. L. Richards
Keyword(s):  
Polar Curve ◽  
Northeastern Pacific

scholarly journals On the Approximation of the Black Hole Shadow with a Simple Polar Curve

2020 ◽  
Vol 900 (1) ◽  
pp. 77 ◽  
Author(s):  
Joseph R. Farah ◽  
Dominic W. Pesce ◽  
Michael D. Johnson ◽  
Lindy Blackburn
Keyword(s):  
Black Hole ◽  
Polar Curve
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