Propagation of a curved shock is governed by a system of shock ray equations which is coupled to an infinite system of transport equations along these rays. For a two-dimensional weak shock, it has been suggested that this system can be approximated by a hyperbolic system of four partial differential equations in a ray coordinate system, which consists of two independent variables (ζ, t) where the curves t = constant give successive positions of the shock and ζ = constant give rays. The equations show that shock rays not only stretch longitudinally due to finite amplitude on a shock front but also turn due to a non-uniform distribution of the shock strength on it. These changes finally lead to a modification of the amplitude of the shock strength. Since discontinuities in the form of kinks appear on the shock, it is necessary to study the problem by using the correct conservation form of these equations. We use such a system of equations in conservation form to construct a total-variation-bounded finite difference scheme. The numerical solution captures converging shock fronts with a pair of kinks on them – the shock front emerges without the usual folds in the caustic region. The shock strength, even when the shock passes through the caustic region, remains so small that the small-amplitude theory remains valid. The shock strength ultimately decays with a well-defined geometrical shape of the shock front – a pair of kinks which separate a central disc from a pair of wings on the two sides. We also study the ultimate shape and decay of shocks of initially periodic shapes and plane shocks with a dent and a bulge.

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This paper presents an enhanced approach for capacitor placement in radial distribution feeders to reduce the real power loss and to improve the voltage profile. The capacitor placement approach involves the identification of location for capacitor placement and the size of the capacitor to be installed at the identified location. The location of the nodes where the capacitors should be placed is decided by a set of rules given by the Fuzzy Expert System (FES). Capacitor location problem is a highly nonlinear problem and hence FES method is chosen. Then the sizing of the capacitors is modeled as an optimization problem and the objective function (loss minimization) is solved using Hybrid Particle Swarm Optimization (HPSO) technique. A case study with an IEEE 34 bus distribution feeder is presented to illustrate the applicability of the algorithm. A comparison is made between the proposed HPSO approach and the classical Particle Swarm Optimization (PSO) algorithm in terms of convergence and economic savings achieved to study the performance of both the optimization algorithms. The proposed HPSO algorithm is proven to give better results in terms of greater economic saving than the existing techniques.

VANET means vehicular ad-hoc network. The routing protocol ant colony optimization (ACO) is a swarm intelligence which is based on the behavior of the ant, the ACO algorithm includes the cooperation and adaption and it produces an optimal solution.ACOalgorithm depends upon the amount of pheromone deposit. The particle swarm optimization is also swarm intelligence, the PSO algorithm is population based and depends upon the movement and the intelligence of the swarm. The pheromone value is used for the decision purpose. The benefit of particle swarm optimization technique is that the particle moves always in the same direction with the same velocity and it also selects the position that is better than the previous position thus the best path is followed by each particle. In PSO the set of potential solutions evolves to approach a convenient solution for a problem. This algorithm produces Global best (Gbest) and Personal best (Pbest) solution. The benefits of the ACO and PSO protocols are combine have a hybridACO-PSOalgorithm to have an optimal solution to a multicast network and thus it helps in clustering.

In Recent Scenario, scarcity of energy source, ever growing Power demand, increasing in generation cost necessitate optimal economic dispatch. This paper includes Biogeography Algorithm to compute Economic Load Dispatch Problem for Thermal generator of power system. Biogeography Describes how the species arise, migrates from one habitat another and gets wipes out.In BGA model, problem solutions are represents as islands and sharing of features between solution is represented as immigration and emigration which searches for the global optimum mainly through two steps :migration and mutation. BGA has features in common with other biology-based optimization methods, such as GAs and particle swarm optimization (PSO). This makes BGA applicable to many of the same types of problems that GAs and PSO are used for, namely, high-dimension problems with multiple local optimal. To show the advantages of the proposed algorithm, it has been applied to two different test systems for solving ELD problems. First, a 3-generators system then a 6 generators system with simple quadratic cost function considering operating limit constraints is considered.