Analytical Study of Light Propagation in Highly Nonlinear Media

The present dissertation is devoted to the construction of exact and approximate analytical solutions of the problem of light propagation in highly nonlinear media. It is demonstrated that for many experimental conditions, the problem can be studied under the geometrical optics approximation with a sufficient accuracy. Based on the renormalization group symmetry analysis, exact analytical solutions of the eikonal equations with a higher order refractive index are constructed. A new analytical approach to the construction of approximate solutions is suggested. Based on it, approximate solutions for various boundary conditions, nonlinear refractive indices and dimensions are constructed. Exact analytical expressions for the nonlinear self-focusing positions are deduced. On the basis of the obtained solutions a general rule for the single filament intensity is derived; it is demonstrated that the scaling law (the functional dependence of the self-focusing position on the peak beam intensity) is defined by a form of the nonlinear refractive index but not the beam shape at the boundary. Comparisons of the obtained solutions with results of experiments and numerical simulations are discussed.

Resource use pattern and agroecosystem functioning in Rawanganga micro-watershed in Garhwal Himalaya, India

Agro-ecological resource use pattern in a traditional hill agricultural watershed in Garhwal Himalaya was analysed along an altitudinal transect. Thirty one food crops were found, although only 0.5% agriculture land is under irrigation in the area. Fifteen different tree species within agroforestry systems were located and their density varied from 30-90 trees/ha. Grain yield, fodder from agroforest trees and crop residue were observed to be highest between 1200 and 1600 m a.s.l. Also the annual energy input- output ratio per hectare was highest between 1200 and 1600 m a.s.l. (1.46). This higher input- output ratio between 1200-1600 m a.s.l. was attributed to the fact that green fodder, obtained from agroforestry trees, was considered as farm produce. The energy budget across altitudinal zones revealed 95% contribution of the farmyard manure and the maximum output was in terms of either crop residue (35%) or fodder (55%) from the agroforestry component. Presently on average 23%, 29% and 41% cattle were dependent on stall feeding in villages located at higher, lower and middle altitudes respectively. Similarly, fuel wood consumption was greatly influenced by altitude and family size. The efficiency and sustainability of the hill agroecosystem can be restored by strengthening of the agroforestry component. The approach will be appreciated by the local communities and will readily find their acceptance and can ensure their effective participation in the programme.

Development of mechanical methods for cell-tray propagation and field transplanting of dwarf napiergrass (Pennisetum purpureum Schumach.)

Since dwarf napiergrass (Pennisetum purpureum Schumach.) must be propagated vegetatively due to lack of viable seeds, root splitting and stem cuttings are generally used to obtain true-to-type plant populations. These ordinary methods are laborious and costly, and are the greatest barriers for expanding the cultivation area of this crop. The objectives of this research were to develop nursery production of dwarf napiergrass in cell trays and to compare the efficiency of mechanical versus manual methods for cell-tray propagation and field transplanting. After defoliation of herbage either by a sickle (manually) or hand-mowing machine, every potential aerial tiller bud was cut to a single one for transplanting into cell trays as stem cuttings and placed in a glasshouse over winter. The following June, nursery plants were trimmed to a 25–cm length and transplanted in an experimental field (sandy soil) with 20,000 plants ha^(−1) either by shovel (manually) or Welsh onion planter. Labour time was recorded for each process. The manual defoliation of plants required 44% more labour time for preparing the stem cuttings (0.73 person-min. stemcutting^(−1)) compared to using hand-mowing machinery (0.51 person-min. stem-cutting^(−1)). In contrast, labour time for transplanting required an extra 0.30 person-min. m^(−2) (14%) using the machinery compared to manual transplanting, possibly due to the limited plot size for machinery operation. The transplanting method had no significant effect on plant establishment or plant growth, except for herbage yield 110 days after planting. Defoliation of herbage by machinery, production using a cell-tray nursery and mechanical transplanting reduced the labour intensity of dwarf napiergrass propagation.