LIST OF FIGURES
Figure page
3-1 Path PXPj connects the node Pi to the node Pj ... 19
3-2 Directed graph, G(M), for a tridiagonal matrix M with nonzero en-
tries on its diagonal, superdiagonal, and subdiagonal. 21
3-3 Electrical conductivity a and corresponding relaxation time T = Ea-1,
where E = 8.85-12 F m-1, versus altitude under a variety of geo-
physical conditions. LL, low latitude, "wavy"; MLPS, mid-latitude
typical night (high-latitude, quite); AZTDN, auroral zone, typical
disturbed night; MLD, mid-latitude day, quite; MHL, mid-high-
latitude, typical of ~ 100 measurements; REP, relativistic electron
(energy from a few MeV to 10 MeV) precipitation event (unusual);
PCA, polar cap absorption event (an unusually large flux of ener-
getic, ~ 100 MeV) solar protons within the polar cap). Adapted
from Hale [8]. (Source: reprinted with permission from Rakov and
Uman [21], published in 2003, copyright Vladimir A Rakov and
Martin A Uman, published by Cambridge University Press) 24
sin2
4-1 Graph of f(x) = sn+ )2, when a = -1.05. ........... 30
(a + cos X)2
sin x
4-2 Graph of f(x) = cosx)2, when a = -1. .............. 31
(a + cos X)2
6-1 Cylindrical shell of the volume integral f dV 60
6-2 Potentials (0(0, 0, z), 0 < z < 100 km) in two domains, Q1 and Q2 64
6-3 Potentials (0(0, 0, z), 4.6 km < z < 5.4 km) near the negative charge
(5 km) in two domains, Q1 and 2 . 64
6-4 Potentials (0(0, 0, z), 9.6 km < z < 10.4 km) near the positive charge
(10 km) in two domains, Q2 and 2 . 65
6-5 Potentials (O(x, 0, 5) and O(x, 0, 10), -25 km < x < 25 km) along the
x-axis at the altitude 5 km and 10 km .. ..... 65
6-6 Maximum norm of potential versus time, where At = 1/8 s and p = 0 68