Perturbed iterative solution of nonlinear equations with applications to fluid dynamics

AbstractIn this work a technique has been developed to solve a set of nonlinear equations with the assumption that a solution exists. The algorithm involves nonlinear Gauss-Seidel iteractions and at each iteration the value of the iterate is added to a predetermined perturbation parameter which is computed in terms of quantities already known. This perturbation parameter has two properties: (i) it determines the mode of convergence, that means it shows how many more computations are required so that convergence may be achieved, and (ii) it accelerates the rate of convergence. The algorithm is computationally simple. Several nonlinear equations have been studied. The results seem to be encouraging

High density planting - an option for higher productivity of Hevea brasiliensis in north eastern region of India

The effect of planting density in rubber (Hevea brasiliensis) was studied in an experiment conducted with three densities viz., 420, 620, 824 trees ha-1. It was observed that lower density had higher percentage of trees ready for tapping during initial years, due to better growth. However, higher density achieved required girth in subsequent years. In spite of decrease in plant number over the years, the highest density had always lower girth even after 24 years of planting. Higher density also has higher percentage of too small trees, not suitable for harvesting latex. The higher plant densities resulted taller plants, increased crotch height and decreased the number of branches and thereby plant density affected yield per tree and yield per unit area. Though the yield per hectare increased with increased plant density during initial years, however declined later period. High yield per tree per tap was observed in the lowest density with lower yield per unit area. Yield increased in all densities with application of stimulant. Percentage of yield increase due to application of stimulant was higher (40%) in medium density (620 trees ha-1) compared to other plant densities. Percentage of wind damage was lower in high density planting during initial years. Total timber volume per hectare was high in higher planting density and lower per tree volume of log compared to lower density. Maintaining a density of 620 trees per hectare appears to be most suitable for north eastern region of India

A single period inventory model of a deteriorating item sold from two shops with shortage via genetic algorithm

Inventory of differential units of a deteriorating item purchased in a lot and sold separately from two shops under a single management is considered. Here deterioration increases with time and demands are time- and price-dependent for fresh and deteriorated units respectively. For the fresh units, shortages are allowed and later partially-backlogged. For the deteriorated units, there are two scenarios depending upon whether initial rate of replenishment of deteriorated units is less or more than the demand of these items. Under each scenario, five sub-scenarios are depicted depending upon the time periods of the two-shops. For each sub scenarios, profit maximization problem has been formulated and solved for optimum order quantity and corresponding time period using genetic Algorithm (GA) with Roulette wheel selection, arithmetic crossover and uniform mutation and Generalized Reduced Gradient method (GRG). All sub-scenarios are illustrated numerically and results from two methods are compared.

Pathology of mixed infections of saprolegniasis-myxosporidiosis in Indian major carp (Catla catla Ham.)

An outbreak of saprolegniasis in Catla catla in composite carp culture ponds were recorded during winter season. The typical cotton wool growths were observed on whole body surfaces of catla along with sporadic mortality. The fungal invasion was only restricted to skin and no fungal elements were visible in any internal organs after periodic acid schiff staining. On histology, periportal accumulation of mononuclear cells in liver, presence of myxosporidean cysts in antieror kidney, eosinophilic granular cells reaction in submucosa of stomach and intestine, dilated and engorged blood vessels of brain along with sloughing of epidermis and hyperplasia at gill lamellar base were pronounced changes. The possible role of release of Saprolegnia toxin in producing internal organs pathology has been discussed

Synthesis of Corrosion-resistant Nanocrystalline Nickle-copper Alloy Coatings by Pulse-plating Technique

Bright and smooth nanocrystalline Monel-type Ni-Cu alloy gets deposited from complex citrate electrolyte by pulse electrolysis. Transmission electron microscopy studies have revealedthat the deposited Ni-Cu alloy was nanocrystalline in nature and it comprised a two-phase (fcc+Ll,) mixture. The presence of twins could be seen in the nanocrystals. The Ni-Cu alloysprepared by pulse electrolysis were finer grained (- 2.5-28.5 nm) than those deposited by direct current method. Nelson-Riley function has been used to calculate the lattice parameters for both the pulse current-plated and direct current-plated alloys from x-ray diffraction analysis. The microhardness values for pulse current-plated alloys were higher than for the direct currentplated alloys. The internal stresses of both the pulse current-deposited and the direct currentdeposited alloys have also been measured; the values were lower for pulse current-plated alloys. Potentiodynamic polarisation studies were carried out in aerated and deaerated neutral 3.0 Wt per cent NaCl solution and instantaneous corrosion current density of the plated alloy was determined and compared with the Monel-400 alloy. It was found that nanocrystalline pulse current-N,-35 8 Wt p;r cent copper alloy uxh~bitedlo wer instantaneous value of corros~onc urrent densirv than that of soeclrnens with direct current method and Monel-400 allov The d~ssolut~on ~ ~~~~-~ behaviour ofthe deposited nanocrystalline material was found to be more like general corrosion rather than localised corrosion as in the case of Monel-400 alloy

A comparative assessment of waste incinerators in the UK

The uptake in Europe of Energy from Waste (EfW) incinerator plants has increased rapidly in recent years. In the UK, 25 municipal waste incinerators with energy recovery are now in operation; however, their waste supply chains and business practices vary significantly. With over a hundred more plant developments being considered it is important to establish best business practices for ensuring efficient environmental and operational performance. By reviewing the 25 plants we identify four suitable case study plants to compare technologies (moving grate, fluidised bed and rotary kiln), plant economics and operations. Using data collected from annual reports and through interviews and site visits we provide recommendations for improving the supply chain for waste incinerators and highlight the current issues and challenges faced by the industry. We find that plants using moving grate have a high availability of 87-92%. However, compared to the fluidised bed and rotary kiln, quantities of bottom ash and emissions of hydrogen chloride and carbon monoxide are high. The uptake of integrated recycling practices, combined heat and power, and post incineration non-ferrous metal collections needs to be increased among EfW incinerators in the UK. We conclude that one of the major difficulties encountered by waste facilities is the appropriate selection of technology, capacity, site, waste suppliers and heat consumers. This study will be of particular value to EfW plant developers, government authorities and researchers working within the sector of waste management

Report on the socio-economic impact of Natural Rubber cultivation under the block planting scheme in Tripura

The study is a pioneering attempt to assess the socio-economic impact of the Block Planting Scheme (BPS) from the angle of the beneficiaries,implementing agencies and the policymakers.The report is based on the primary information gathered from 480 households drawn from Block Planting Units with mature (Mature BPUs)and immature (Immature BPUs) area under Natural Rubber (NR) as well as households attached to Group Processing Scheme (GPUs) with mature area under NR during the year 2008.The tripartite BPS involving the Rubber Board, the State Government of Tripura and the beneficiaries has been unique in its contents and mode of implementation since 1992.The average household income of mature BPUs was Rs.99168 compared to Rs.46824 of immature BPUs. Therefore, an annual income difference of Rs.52344 (112%) was observed between households with and without income from rubber (mature and immature BPUs).The compositions of income showed that rubber was the major source of income for GPUs (75%) and mature BPUs (66%). For immature BPUs,employment was the major source of income (77%).In the long-run, the concerned agencies of the state government may initiate skill oriented programmes for empowering the unemployed/underemployed youth along with improvements in the infrastructural facilities. Such policy initiatives will enable diversification of the sources of income and ensure sustainability of NR cultivation as observed in the case of Kerala and FELDA in Malaysia

Stochastic dynamic stability analysis of composite curved panels subjected to non-uniform partial edge loading

The stochastic dynamic stability analysis of laminated composite curved panels under non-uniform partial edge loading is studied using finite element analysis. The system input parameters are randomized to ascertain the stochastic first buckling load and zone of resonance. Considering the effects of transverse shear deformation and rotary inertia, first order shear deformation theory is used to model the composite doubly curved shells. The stochasticity is introduced in Love's and Donnell's theory considering dynamic and shear deformable theory according to the Sander's first approximation by tracers for doubly curved laminated shells. The moving least square method is employed as a surrogate of the actual finite element model to reduce the computational cost. The results are compared with those available in the literature. Statistical results are presented to show the effects of radius of curvatures, material properties, fibre parameters, and non-uniform load parameters on the stability boundaries

An Analytical Study on the Multi-critical Behaviour and Related Bifurcation Phenomena for Relativistic Black Hole Accretion

We apply the theory of algebraic polynomials to analytically study the transonic properties of general relativistic hydrodynamic axisymmetric accretion onto non-rotating astrophysical black holes. For such accretion phenomena, the conserved specific energy of the flow, which turns out to be one of the two first integrals of motion in the system studied, can be expressed as a 8$^{th}$ degree polynomial of the critical point of the flow configuration. We then construct the corresponding Sturm's chain algorithm to calculate the number of real roots lying within the astrophysically relevant domain of $\mathbb{R}$. This allows, for the first time in literature, to {\it analytically} find out the maximum number of physically acceptable solution an accretion flow with certain geometric configuration, space-time metric, and equation of state can have, and thus to investigate its multi-critical properties {\it completely analytically}, for accretion flow in which the location of the critical points can not be computed without taking recourse to the numerical scheme. This work can further be generalized to analytically calculate the maximal number of equilibrium points certain autonomous dynamical system can have in general. We also demonstrate how the transition from a mono-critical to multi-critical (or vice versa) flow configuration can be realized through the saddle-centre bifurcation phenomena using certain techniques of the catastrophe theory.Comment: 19 pages, 2 eps figures, to appear in "General Relativity and Gravitation