Third-order Uranus-Neptune theory by Hori's method

We construct a U-N secular canonical planetary theory of the third order with respect to planetary masses. The Hori-Lie procedure is adopted to solve the problem. Expansions have been carried out by hand, neglecting powers higher than the second with respect to the eccentricity-inclination. We take into account the principal as well as the indirect part of the planetary disturbing function. The theory is expressed in terms of the Poincaré canonical variables, referring to the Jacobi-Radau set of origins. We assume that the 1:2 U-N critical terms and its multiples are the only periodic terms.     

The expansion of negative powers of the mutual distance between two planets

An outline of a new method is given to obtain the expansion of ^–S by the method of W. M. Smart, using Taylor theorem and neglecting powers higher than the fourth in the eccentricity and inclination.     

Determination of secular terms in general planetary theory

A method to calculate secular terms of the two parts of the planetary disturbing function— when it is expressed in terms of the true anomalies or the eccentric anomalies instead of the mean anomalies - is described. Also an alternative method is outlined.     

Second order secular planetary theory for the four major planets

We generalize our results of a second order Jupiter-Saturn planetary theory to be applicable for the case of the four major planets.We use the Von Zeipel method and we neglect powers higher than the third with respect to the eccentricities and sines of the inclinations in our expansions. We consider the critical terms as the only periodic terms.     

On the elimination of the critical term in a general first-order Uranus-Neptune theory

A solution of the Uranus-Neptune planetary canonical equations of motion through the Von Zeipel technique is presented. A unique determinging function which depends upon mixed canonical variables, reduces the 12 critical terms of the Hamiltonian to the set of its secular terms. The Poincaré canonical variables are used. We refer to a common fixed plane, and apply the Jacobi-Radau set of origins. In our expansion we neglected terms of power higher than the fourth with respect to the eccentricities and sines of the inclinations.     

The expansion of negative powers of mutual distance between two planets

In this part we obtain the expression for ^–s by the application of Smart's method, which involves Taylor's theorem for functions of several variables. We neglected terms of power higher than the fourth with respect to eccentricities and tangents of inclinations.     

Regional fracture analysis south Latitude 29° N of Egypt and their influence on earthquakes

Egypt had been subjected to earthquakes of various degrees but earthquake observation in this country started only in 1899. Earthquakes were found in the locations where fractures have relatives high densities.The Fracture pattern of Egypt south Latitude at 29° N was studied regionally based on Landsat images and aerial photomosaics. Fractures in the Eastern Desert have the prominent trends, NW, EW, NNW and ENE, showing high density in the northern and southern parts. These fractures control the distribution of mineral deposits and radioactivity in the basement rocks.Fractures in Western Desert are less remarkable with the main trend NNW, E-W, N-S and NW, showing high density in the central part. The NNW trending fractures have the same direction of sand dunes which cover larger areas in the northwestern part of Western Desert.Based on the geographical distribution of earthquakes in the seismic maps and centers of high fractures density on the structural contour maps, the area south of latitude 29° N of Egypt was divided into three regions: The Red Sea, Western Desert and Aswan Environs. This correlation led to the conclusion that the fractures have an effect on earthquake activity, are trending ENE and WNW in the Red Sea, NW and N-S in the Western Desert and E-W and NNW in Aswan Environs.It should be emphasized that fractures with higher density are more susceptible to earthquakes in the locations characterized by two dominant sets of fractures especially at their intersections.     

Seismic damage to segmented buried pipelines

Seismic damage to segmented buried pipelines is investigated in this paper. Information on their performance during past earthquakes is reviewed briefly. An analytical model for evaluating the response of long straight runs of segmented buried pipelines to seismic wave propagation is presented. It takes into account the non-linearity as well as the variability of the system characteristics. Also, results from laboratory tests by others are used to establish the relative joint displacement which leads to leakage. These two elements are combined to predict the damage ratio (number of leaks per kilometre) for cast iron pipes with lead caulked joints subject to a joint pull-out failure mode.     

Vegetation-groundwater dynamics at a former uranium mill site following invasion of a biocontrol agent: A time series analysis of Landsat normalized difference vegetation index data

Because groundwater recharge in dry regions is generally low, arid and semiarid environments have been considered well-suited for long-term isolation of hazardous materials (e.g., radioactive waste). In these dry regions, water lost (transpired) by plants and evaporated from the soil surface, collectively termed evapotranspiration (ET), is usually the primary discharge component in the water balance. Therefore, vegetation can potentially affect groundwater flow and contaminant transport at waste disposal sites. We studied vegetation health and ET dynamics at a Uranium Mill Tailings Radiation Control Act (UMTRCA) disposal site in Shiprock, New Mexico, where a floodplain alluvial aquifer was contaminated by mill effluent. Vegetation on the floodplain was predominantly deep-rooted, non-native tamarisk shrubs (Tamarix sp.). After the introduction of the tamarisk beetle (Diorhabda sp.) as a biocontrol agent, the health of the invasive tamarisk on the Shiprock floodplain declined. We used Landsat normalized difference vegetation index (NDVI) data to measure greenness and a remote sensing algorithm to estimate landscape-scale ET along the floodplain of the UMTRCA site in Shiprock prior to (2000–2009) and after (2010–2018) beetle establishment. Using groundwater level data collected from 2011 to 2014, we also assessed the role of ET in explaining seasonal variations in depth to water of the floodplain. Growing season scaled NDVI decreased 30% (p < .001), while ET decreased 26% from the pre- to post-beetle period and seasonal ET estimates were significantly correlated with groundwater levels from 2011 to 2014 (r² = .71; p = .009). Tamarisk greenness (a proxy for health) was significantly affected by Diorhabda but has partially recovered since 2012. Despite this, increased ET demand in the summer/fall period might reduce contaminant transport to the San Juan River during this period.     

The elimination of the 1:2 critical terms of a first order theory of Uranus perturbed by Neptune through Von Zeipel method

In this paper we eliminate in a first order U-N theory the 1 : 2 critical terms up to the third degree with respect to eccentricity — inclination in both parts, main and indirect of the U-N planetary Hamiltonian. We operate the Von Zeipel technique. We adopt, in this theory, the Jacobi-Radau coordinates, and the Poincaré canonical variables. We neglect powers higher than the third in the eccentricity-inclination. This paper is related to the two previous articles (Kamel, 1982; 1983).