Study of third-order non-linear systems- Variation of parameters approach

In this paper, the transient response of a third-order non-linear system is obtained by first reducing the given third-order equation to three first-order equations by applying the method of variation of parameters. On the assumption that the variations of amplitude and phase are small, the functions are expanded in ultraspherical polynomials. The expansion is restricted to the constant term. The resulting equations are solved to obtain the response of the given third-order system. A numerical example is considered to illustrate the method. The results show that the agreement between the approximate and digital solution is good thus vindicating the approximation.

Geographical Information System Approach for Regional Biogas Potential Assessment

The economic prosperity and quality of life in a region are closely linked to the level of its per capita energy consumption. In India more than 70% of the total population inhabits rural areas and 85-90% of energy requirement is being met by bioresources. With dwindling resources, attention of planners is diverted to viable energy alternatives to meet the rural energy demand. Biogas as fuel is one such alternative, which can be obtained by anaerobic digestion of animal residues and domestic and farm wastes, abundantly available in the countryside. Study presents the techniques to assess biogas potential spatially using GIS in Kolar district, Karnataka State, India. This would help decision makers in selecting villages for implementing biogas programmes based on resource availability. Analyses reveal that the domestic energy requirement of more than 60% population can be met by biogas option. This is based on the estimation of the per capita requirement of gas for domestic purposes and availability of livestock residues.

Flux Partitioning of Species Approach in Binary Interdiffusion Process

Validation of the flux partitioning of species model has been illustrated. Various combinations of inequality expression for the fluxes of species A and B in two successively grown hypothetical intermetallic phases in the interdiffusion zone have been considered within the constraints of this concept. Furthermore, ratio of intrinsic diffusivities of the species A and B in those two phases has been correlated in four different cases. Moreover, complete and or partial validation or invalidation of this model with respect to both the species, has been proven theoretically and also discussed with the Co-Si system as an example.