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Concept# North Pole

Summary

The North Pole, also known as the Geographic North Pole, Terrestrial North Pole or 90th Parallel North, is the point in the Northern Hemisphere where the Earth's axis of rotation meets its surface. It is called the True North Pole to distinguish from the Magnetic North Pole.
The North Pole is by definition the northernmost point on the Earth, lying antipodally to the South Pole. It defines geodetic latitude 90° North, as well as the direction of true north. At the North Pole all directions point south; all lines of longitude converge there, so its longitude can be defined as any degree value. No time zone has been assigned to the North Pole, so any time can be used as the local time. Along tight latitude circles, counterclockwise is east and clockwise is west. The North Pole is at the center of the Northern Hemisphere. The nearest land is usually said to be Kaffeklubben Island, off the northern coast of Greenland about away, though some perhaps semi-permanent gravel banks lie sli

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We construct a one parameter family of nite time blow ups to the co-rotational wave maps problem from $S^2\times R$ to $S^2$ parameterized by $\nu \epsilon (\frac{1}{2},1]$. The longitudinal function $u(t,\alpha)$ which is the main object of study will be obtained as a perturbation of a rescaled harmonic map of rotation index one from $\mathbb{R}^2$ to $S^2$. The domain of this harmonic map is identied with a neighborhood of the north pole in the domain $S^2$ via the exponential coordinates $(\alpha ,\theta)$. In these coordinates $u(t,\alpha) = Q(\lambda(t)\alpha) + R(t,\alpha)$, where $Q(r) = 2\,arctan\,r$ is the standard co-rotational harmonic map to the sphere, $\lambda (t) = t^{-1-\nu}$, and $R(t,\alpha)$ is the error with local energy going to zero as t ! 0: Blow up will occur at $(t,\alpha) = (0,0)$ due to energy concentration, and up to this point the solution will have regularity $H^{1+\nu-}$.

2016We construct a one parameter family of finite time blow-ups to the co-rotational wave maps problem from S-2 x R to S-2, parameterized by nu is an element of (1/2, 1]. The longitudinal function u(t, alpha) which is the main object of study will be obtained as a perturbation of a rescaled harmonic map of rotation index one from R-2 to S-2. The domain of this harmonic map is identified with a neighborhood of the north pole in the domain S-2 via the exponential coordinates (alpha, theta). In these coordinates u(t, alpha) = Q(lambda(t)alpha) + R(t, alpha), where Q(r) = 2arctan r is the standard co-rotational harmonic map to the sphere, lambda(t) = t(-1-nu), and R(t, alpha) is the error with local energy going to zero as t -> 0. Blow-up will occur at (t, alpha) = (0, 0) due to energy concentration, and up to this point the solution will have regularity H1+nu-.

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Current from nearby rocket-triggered lightning that flowed through the soil and into an unenergized test power distribution line was studied based on experimental data acquired in 2003 at the International Center for Lightning Research and Testing in Florida. The 15-pole, three-phase line was 812 m long, was equipped with four arrester stations, at poles 2, 6, 10, and 14, and was terminated in its characteristic impedance at poles I and 15. The neutral conductor of the line was grounded at each arrester station and at both line terminations. Measurements suggest that a significant fraction of the lightning current injected into the earth a distance of 11 in from pole 15 entered the line through the grounding system of pole 15. The peak value of the microsecond-scale return stroke current entering the line through the pole 15 line ground was 7% of the peak value of the return stroke current injected into the earth. The peak value of the millisecond-scale triggered lightning initial stage current and the millisecond-scale return-stroke and initial-stage charge transfer to the line through the pole 15 line ground was between 12% and 19% of the lightning peak current/charge transfer, indicating that the percentage values for the injected peak currents are dependent on the current waveshape: for microsecond-scale return stroke currents, possibly due to electromagnetic coupling effects, a smaller fraction of the current peak enters the line compared to millisecond-scale initial stage currents. In the latter case, any influence of electromagnetic coupling to the line on ground currents is expected to be negligible.

2009Lightning Currents Flowing in the Soil and Entering a Test Power Distribution Line Via Its Grounding

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