Sharma, Puneet

We study the dynamics of a general non-autonomous dynamical system generated by a family of continuous self-maps on a compact space X. We derive necessary and sufficient conditions for the system to exhibit complex dynamical behavior. In the process we discuss properties like transitivity, weakly mixing, topologically mixing, minimality, sensitivity, topological entropy, and Li-Yorke chaoticity for the non-autonomous system. We also give examples to prove that the dynamical behavior of the nonautonomous system in general cannot be characterized in terms of the dynamical behavior of its generating functions.

In this paper, we discuss the dynamics of alterations and rearrangements of a non-autonomous dynamical system generated by the family F. We prove that while insertion/deletion of a map in the family F can disturb the dynamics of a system, the dynamics of the system does not change if the map inserted/deleted is feeble open. In the process, we prove that if the inserted/deleted map is feeble open, the altered system exhibits any form of mixing/sensitivity if and only if the original system exhibits the same. We extend our investigations to properties like equicontinuity, minimality, and proximality for the two systems. We prove that any finite rearrangement of a non-autonomous dynamical system preserves the dynamics of original system if the family F is feeble open. We also give examples to show that the dynamical behavior of a system need be not be preserved under infinite rearrangement.

In this paper, we study the dynamics induced by finite commutative relation. We prove that the dynamics generated by such a non-trivial collection cannot be transitive/super-transitive and hence cannot exhibit higher degrees of mixing. As a consequence we establish that the dynamics induced by such a collection on the hyperspace endowed with any admissible hit and miss topology cannot be transitive and hence cannot exhibit any form of mixing. We also prove that if the system is generated by such a commutative collection, under suitable conditions the induced system cannot have dense set of periodic points. In the end we give example to show that the induced dynamics in this case may or may not be sensitive.

Electrical energy is employed for processing operations of material, such as, smelting, soaking and heat treatment. During this process, fossil, coal, and nuclear as a fuel is employed. Extraction and use of these fuel sources have serious environmental implications. Moreover, the employed process involves conversion of fuel to heat and then to electricity. Double conversion process can be avoided by directly introducing hot air provided by a solar tower equipped with a volumetric air receiver into a retrofitted furnace. This is a clean, green alternative for generating high temperatures required for metals processing operations. Initially a system would be developed for the heat treatment of aluminum, which requires temperature between 290 and 400°C. A survey of the literature shows that quantitative design basis of individual volumetric air receiver components is conspicuous by its absence. Hence the objective of this investigation has been to use principles of fluid flow and heat transfer to design individual components of an Open Volumetric Air Receiver (OVAR) system. Experiments on a 2kWth Solar Air Tower Simulator system (SATS) validate the process used in designing individual components of the OVAR. The ultimate aim of this research is to develop a system that can be used for heat treatment of steels and other possible extractive metallurgy operations such as the smelting of metals from its ores.

We discuss conditions under which an affine automorphism of a compact nilmanifold is almost automorphic, and the structure of such automorphisms from dynamical as well as algebraic points of view.

Abstract: A numerical visualization study of wetlands is detailed in this article using finite volume methods. The aim of this study is to model treatment efficiency of the wetlands in terms of the residence time distribution function. Shape and depth of wetlands are critically analysed to find the optimal flow requirement for effective treatment. Laminar three-dimensional flow dynamics is used to simulate the slow water flows that occur in treatment wetlands. Slow inlet flows are assumed. Dye is used as the tracer to characterize the hydrodynamics within the wetlands. Three different geometrical configurations, namely square, square with two islands, and triangle, respectively, are simulated. The variation in the tracer concentration is studied as a function of recirculation volumes, flow rates, time and depth of the wetland for each of the wetland shapes. The change in the variation of tracer concentration at inlet and exit helps to assess treatment effectiveness. In another case, glycerine is used to simulate sewage flow. Plug flow is prominent in sewage-laden wetlands. The results obtained from the above-illustrated case studies are compared with each other to assess the reproducibility of the optimal flow model. Multi-parameter regression models for residence time distribution functions are derived to characterize flow through constructed wetlands of different shapes.