Sharma, Puneet

Let X be a multi-dimensional subshift of finite type generated by a finite set of finite forbidden blocks. We give an algorithm for generating the elements of the shift space using a sequence of finite matrices (of increasing order). We prove that the sequence generated yields precisely the elements of the shift space X and hence characterizes the elements of the shift space X. In the process, we prove that elements of d-dimensional shift of finite type can be characterized by a sequence of finite matrices.

This paper deals with the time delayed SIR model with saturated treatment function under the effect of pollution. As the pollution rate has hiked in this era and the presence of toxicants are found in various resources, therefore it is important to study their effects on disease dynamic of population. Hence, we consider the populace affected by the pollution. As the effect of treatment is not immediate, rather involves time lag to show its effect, therefore we consider time that is taken by infective to recover as the time delay. Existence of equilibrium points and the boundedness of the system has been obtained. Stability analysis using reproduction number R0 has been done. Global stability of the endemic equilibrium point is established using Lyapunov Lasalles theorem. Considering time delay as the critical parameter, existence of hopf bifurcation has been proved. Also,the direction and stability of Hopf Bifurcation has been obtained. Numerical simulations are done in support of results obtained analytically. It is observed that as pollution increases, infective take more time to recover and we also note that recovered individuals decrease with increase in the pollution. Therefore, it important to reduce pollution and provide timely treatment to the patients. Thus, we prove that, pollution and time delay play a critical role in shaping the dynamics of the system.

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.

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.

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.

Let X ⊂ AZd be a 2-dimensional subshift of finite type. We prove that any 2-dimensional subshift of finite type can be characterized by a square matrix of infinite dimension. We extend our result to a general d-dimensional case. We prove that the multidimensional shift space is non-empty if and only if the matrix obtained is of positive dimension. In the process, we give an alternative view of the necessary and sufficient conditions obtained for the non-emptiness of the multidimensional shift space. We also give sufficient conditions for the shift space X to exhibit periodic points.

Polymer composites based on poly(vinylidene fluoride) (PVDF) filled with carbon nanotubes (CNT) decorated with metal nanoparticles (NP) of cobalt, nickel, platinum and palladium have been produced. The CNT nanofillers decorated with metal NP were synthesized by a modified wet impregnation method and their structural, morphological and thermal properties were evaluated. The metal NP ranging from 2 to 10 nm were found well dispersed on the CNT structure. The structural, optical, thermal and electrical properties of the metal/CNT/PVDF composite films demonstrate that the inclusion of the nanofillers leads to the nucleation of the γ-PVDF phase (up to 90%) and enhance the thermal properties (higher melting point) of the polymer. The nanofillers also proved to be suitability to tailor the optical properties of the polymer composite films and lead to an increase in the d.c. electrical conductivity (up to 10−13 S/cm). Thus, the reported metal/CNT nanofillers are suitable to tune PVDF polymer properties towards specific applications.

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.

Most of the real world scenes have a very high dynamic range (HDR). The mobile phone cameras and the digital cameras available in market are limited in their capability in both the range and spatial resolutions. Same argument can be posed about the limited dynamic range of display devices which further differ in spatial resolution and aspect ratio. In this paper, we address the problem of displaying the high contrast low dynamic range (LDR) image of a HDR scene in a display device which has different spatial resolution compared to that of the capturing device. We want to achieve this task while preserving the salient scene contents. The solution proposed in this work can be employed with any camera which has the ability to shoot multiple differently exposed images of a scene. Further, the proposed solutions provide the flexibility in the depiction of entire contrast of the HDR scene as an LDR image with user specified spatial resolution. This task is achieved through an optimized content aware retargeting framework which preserves the salient features apart from a novel algorithm to fuse multi-exposure images. We show that the proposed approach performs exceedingly well in the generation of high contrast LDR image of varying spatial resolutions.

In this paper, a prey-predator model in polluted environment with disease in prey has been proposed and studied. It is assumed that only prey population is prone to disease whereas, both the populations are affected by the pollutant. Boundedness of the solution of the system is discussed. Existence of all possible equilibrium points has been established. Using Routh Hurwitz criterion, local stability of all the possible equilibrium points has been obtained. Also, interior equilibrium point has been proved to be globally asymptotically stable using Lyapunov function. Then time delay has been introduced in the system making the model more realistic. Existence and direction of Hopf bifurcation in the delay model has been established using normal form theory and center manifold theorem. By taking a set of hypothetical and biologically feasible parameters, model has been studied numerically using MATLAB and the effect of pollutant on the system has been deduced.