[1] A compiled empirical global Joule heating (CEJH) model is described in this study. This model can be used to study Joule heating patterns, Joule heating power, potential drop, and polar potential size in the high-latitude ionosphere and thermosphere, and their variations with solar wind conditions, geomagnetic activities, the solar EUV radiation, and the neutral wind. It is shown that the interplanetary magnetic field (IMF) orientation and its magnitude, the solar wind speed, AL index, geomagnetic K p index, and solar radio flux F 10.7 index are important parameters that control Joule heating patterns, Joule heating power, potential drop, and polar potential size. Other parameters, such as the solar wind number density (N sw ) and Earth's dipole tilt, do not significantly affect these quantities. It is also shown that the neutral wind can increase or reduce the Joule heating production, and its effectiveness mainly depends on the IMF orientation and its magnitude, the solar wind speed, AL index, K p index, and F 10.7 index. Our results indicate that for less disturbed solar wind conditions, the increase or reduction of the neutral wind contribution to the Joule heating is not significant compared to the convection Joule heating, whereas under extreme solar wind conditions, the neutral wind can significantly contribute to the Joule heating. Application of the CEJH model to the 16 July 2000 storm implies that the model outputs are basically consistent with the results from the AMIE mapping procedure. The CEJH model can be used to examine large-scale energy deposition during disturbed solar wind conditions and to study the dependence of the hemispheric Joule heating on the level of geomagnetic activities and the intensity of solar EUV radiation. This investigation enables us to predict global Joule heating patterns for other models in the high-latitude ionosphere and thermosphere in the sense of space weather forecasting.

Analysis of observations from both space-borne (LASCO/SOHO, Skylab and Solar Maximum Mission) and ground-based (Mauna Loa Observatory) instruments show that there are two types of coronal mass ejections (CMEs), fast CMEs and slow CMEs. Fast CMEs start with a high initial speed, which remains more or less constant, while slow CMEs start with a low initial speed, but show a gradual acceleration. To explain the difference between the two types of CMEs, Low and Zhang (2002) proposed that it resulted from a difference in the initial topology of the magnetic fields associated with the underlying quiescent prominences, i.e., a normal prominence configuration will lead to a fast CME, while an inverse quiescent prominence results in a slow CME. In this paper we explore a different scenario to explain the existence of fast and slow CMEs. Postulating only an inverse topology for the quiescent prominences, we show that fast and slow CMEs result from different physical processes responsible for the destabilization of the coronal magnetic field and for the initiation and launching of the CME. We use a 2.5-D, time-dependent streamer and flux-rope magnetohydrodynamic (MHD) model (Wu and Guo, 1997) and investigate three initiation processes, viz. (1) injecting of magnetic flux into the flux-rope, thereby causing an additional Lorentz force that will destabilize the streamer and launch a CME (Wu et al., 1997(Wu et al., , 1999; (2) draining of plasma from the flux-rope and triggering a magnetic buoyancy force that causes the flux-rope to lift and launch a CME; and (3) introducing additional heating into the flux-rope, thereby simulating an active-region flux-rope accompanied by a flare to launch a CME. We present 12 numerical tests using these three driving mechanisms either alone or in various combinations. The results show that both fast and slow CMEs can be obtained from an inverse prominence configuration subjected to one or more of these three different initiation processes.

An older approach to the problem of projectile motion with quadratic drag force is presented with the fly ball as an example. In this approach, analytical solutions for the velocity, curvature, and arc length are obtained as functions of the slope angle. It is shown that the velocity and curvature do not have their extrema at the top of the trajectory but during the early phase of descent. The entire problem is reduced to simple integrations over the slope angle.

[1] From a simple theoretical consideration, we obtained two coupling functions linking upstream solar wind parameters to geomagnetic activity. We took into account (1) a scaling factor related to polar cap expansion while increasing the reconnected magnetic flux in the dayside magnetosphere, and (2) a modified Akasofu function for the reconnected flux for combined IMF B z and B y components. One of these coupling functions may be written as F a = aV sw B yz 1/2 sin a (q/2), where V sw is the solar wind speed, B yz is the magnitude of the IMF vector in the Y-Z plane, q is the clock angle between the Z axis and IMF vector in the Y-Z plane, a is a coefficient, and the exponent, a, is derived from the experimental data and equals approximately to 2. The F a function is proportional to the square root of B yz , which makes it significantly different from the coupling functions proposed earlier. Nevertheless, the statistical data analysis supports this dependence. For testing the found coupling function, we used the solar wind and IMF data for four years. We computed 2-D diagrams showing the correlation coefficients for the dependence of the polar cap PC geomagnetic activity index on different combinations of solar wind/IMF parameters. The obtained diagrams showed very good agreement with the theoretical coupling function. The correlation coefficient for the dependence of the PC index on the coupling function is about 0.8-0.85, which is significantly higher that that for other commonly used coupling functions for the same time intervals.

By considering heat flux as ‘‘rays,’’ a law of refraction for heat conduction through an interface is obtained from the boundary conditions. This law is analogous to but different from Snell’s law, with the tangents of the angles of incidence and refraction replacing the sines and the reciprocal of the thermal conductivity taking the place of the refractive index. The deviation of the refracted ray departs from that predicted by Snell’s law as the angle of incidence increases and is zero for both normal and grazing incidences. The tangent law of refraction is also derived from a minimal principle similar to Fermat’s. Finally, a variational principle of heat conduction is postulated and illustrated with a simple example.