Clustering, Chaos and Crisis in a Bailout Embedding Map

We study the dynamics of inertial particles in two dimensional incompressible flows. The particle dynamics is modelled by four dimensional dissipative bailout embedding maps of the base flow which is represented by 2-d area preserving maps. The phase diagram of the embedded map is rich and interesting both in the aerosol regime, where the density of the particle is larger than that of the base flow, as well as the bubble regime, where the particle density is less than that of the base flow. The embedding map shows three types of dynamic behaviour, periodic orbits, chaotic structures and mixed regions. Thus, the embedding map can target periodic orbits as well as chaotic structures in both the aerosol and bubble regimes at certain values of the dissipation parameter. The bifurcation diagram of the 4-d map is useful for the identification of regimes where such structures can be found. An attractor merging and widening crisis is seen for a special region for the aerosols. At the crisis, two period-10 attractors merge and widen simultaneously into a single chaotic attractor. Crisis induced intermittency is seen at some points in the phase diagram. The characteristic times before bursts at the crisis show power law behaviour as functions of the dissipation parameter. Although the bifurcation diagram for the bubbles looks similar to that of aerosols, no such crisis regime is seen for the bubbles. Our results can have implications for the dynamics of impurities in diverse application contexts.Comment: 16 pages, 9 figures, submitted for publicatio

Metamorphism of cordierite gneisses from Eastern Ghat Granulite Terrain, Andhra Pradesh, South India

Cordierite-bearing metapelites of the Eastern Ghat granulite terrain occur in close association of Khondalites, quartzites, calc-silicate rocks and charnockites. Rocks occurring between Bobbili in the north and Guntur in the south of Andhra Pradesh are studied. The association of the mineral and textural relationships suggest the following metamorphic reactions: Garnet + sillimanite + quartz = cordierite, hypersthene + sillimanite + quartz = cordierite, sillimanite + spinel = cordierite + corundum, and biotite + quartz + sillimanite = cordierite + K=feldspar. Generally the minerals are not chemically zoned except garnet-biotite showing zoning when they come in close contact with one another. The potential thermometers are provided by the Fe-Mg distribution of coexisting biotite-garnet and cordierite-garnet. Conflicting interpretation of the P/T dependence of these reactions involving cordierite are due to H2O in the cordierite. The presence of alkali feldspar-quartz assemblage which is common in these gneisses will be constrained from melting only if H2O activity is less than 0.5. The piezometric array inferred is convex towards the temperature array, indicating a rapid and isothermal crustal uplift probably aided by thrust tectonics

Energy Usage and Benefit-Cost Analysis of Castor Production in Haryana

The study used farm level data collected from rain-fed and irrigated castor seed cultivators from three purposively selected districts namely Rewari, Sirsa and Hisar of Haryana on the basis of highest acreage under castor crop. From each selected district, two villages were selected purposively having large number of castor cultivators. Sixty castor cultivators were interacted to extract relevant information related to various energy utilized in castor seed production using survey method. The aim of this research is to determine the energy input and output involved in castor production in the Haryana. The average energy consumption of the farms investigated in this study is 11064.18 MJha-1 of the total energy, 23.67 per cent is direct and 56.56 per centwas indirect. Renewable energy accounts for 3.49% and energy usage efficiency is found to be 5.92. The total energy input into the production of one kilogram of average castor was estimated to be 8.55 MJ. The dominant contribution to input is energy in the form of nitrogen fertiliser (32.86%), followed by water for diesel- oil (20.61%) and irrigation (19.77%). The cost of castor production per hectare is found to be ` 97412ha-1 in the region, with 52.70% of this beingfixed costs. It can be concluded that intensive castor farms are being operated in the area since the fixed cost was quite high. As a result of benefit-cost ratio (1.48) analysis, castor production was found to be economically efficient

Magnetic properties of Mn-doped Ge46 and Ba8Ge46 clathrates

We present a detailed study of the magnetic properties of unique cluster assembled solids namely Mn doped Ge46 and Ba8Ge46 clathrates using density functional theory. We find that ferromagnetic (FM) ground states may be realized in both the compounds when doped with Mn. In Mn2Ge44, ferromagnetism is driven by hybridization induced negative exchange splitting, a generic mechanism operating in many diluted magnetic semiconductors. However, for Mn-doped Ba8Ge46 clathrates incorporation of conduction electrons via Ba encapsulation results in RKKY-like magnetic interactions between the Mn ions. We show that our results are consistent with the major experimental observations for this system.Comment: 6 pages, 4 figure

Transport and diffusion in the embedding map

We study the transport properties of passive inertial particles in a $2-d$ incompressible flows. Here the particle dynamics is represented by the $4-d$ dissipative embedding map of $2-d$ area-preserving standard map which models the incompressible flow. The system is a model for impurity dynamics in a fluid and is characterized by two parameters, the inertia parameter $\alpha$, and the dissipation parameter $\gamma$. We obtain the statistical characterisers of transport for this system in these dynamical regimes. These are, the recurrence time statistics, the diffusion constant, and the distribution of jump lengths. The recurrence time distribution shows a power law tail in the dynamical regimes where there is preferential concentration of particles in sticky regions of the phase space, and an exponential decay in mixing regimes. The diffusion constant shows behaviour of three types - normal, subdiffusive and superdiffusive, depending on the parameter regimes. Phase diagrams of the system are constructed to differentiate different types of diffusion behaviour, as well as the behaviour of the absolute drift. We correlate the dynamical regimes seen for the system at different parameter values with the transport properties observed at these regimes, and in the behaviour of the transients. This system also shows the existence of a crisis and unstable dimension variability at certain parameter values. The signature of the unstable dimension variability is seen in the statistical characterisers of transport. We discuss the implications of our results for realistic systems.Comment: 28 pages, 14 figures, To Appear in Phys. Rev. E; Vol. 79 (2009

Optimal corrosive behaviour on the weldment of AA6063 aluminum alloy by tungsten inert gas (TIG) welding process with backing plates

Pertaining on the present work on improving the corrosion resistance of AA 6063 aluminum alloy is found to weld with many backing plate materials like stainless steel, copper, marble and brass in accordance to the welding process that inherits itself with TIG. Utilizing the Orthogonal array L16, experiments were carried out. The corrosion resistance was improved by optimizing the pulsed TIG welding process parameters like current (A), gas flow rate (B), backing material (C) and backing thickness (D) using Genetic Algorithm (GA). Results proved that the GA shows a better corrosion resistance rate that was obtained to about 0,0408 mm/year with the backing material as copper