Department of Mathematics

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Mathematics

Consideration is given to the problem of steady axisymmetric creeping flow of a micropolar fluid around the spherical drop of non-Newtonian liquid shell covered with permeable medium. The field equations of micropolar fluids are presented in terms of velocity vector and microrotation vector. External liquid permeates into the porous layer, but it is not mixed with the liquid located in the internal cavity of a capsule. The flow inside the permeable medium is described by the Brinkman equation. The stream function solution for the external flow field is derived in terms of modified Bessel's function and Gegenbauer's polynomial. The solution is determined by dilating the stream function in terms of the dimensionless parameter S for the internal flow field (Reiner-Rivlin liquid sphere). Analytical expressions for the pressure field, coupling number, microrotation component, viscosity ratio, permeability parameter, and drag force are calculated. The effect of various parameters on the drag force is presented graphically and discussed. It is observed that the drag on a micropolar fluid sphere is more than that on a permeable sphere. Different limiting cases are also considered. © 2020 by Begell House, Inc.

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School of Advanced Sciences

Chennai Campus

Journal of Porous Media

Drag on a reiner-rivlin liquid sphere embedded in a porous region placed in a micropolar fluid

Abstract: Flow around a Reiner–Rivlin non-Newtonian liquid particle, which is surrounded with a Newtonian liquid shell and placed into a permeable medium, is studied. This formulation of the problem is typical for, e.g., studying the motion of an oil droplet surrounded with an aqueous medium (oil-in-water emulsion) in a porous collector under the action of an external pressure drop. An analogous problem is encountered when lymph penetrates into human or animal tissues. The flows inside of the permeable layer, in the region between the Reiner–Rivlin liquid and a porous medium, and inside of the spherical region are described by the Brinkman, Stokes, and Reiner–Rivlin equations, respectively. The general solution for the stream function in the external porous region is written in terms of the modified Bessel function and Gegenbauer polynomials. For the Reiner–Rivlin liquid sphere, the solution is found by expanding the stream function into a power series in terms of small dimensionless parameter S. The boundary problem is solved by conjugating the boundary conditions for all regions. The drag force applied to the Reiner–Rivlin liquid particle placed into the permeable medium is determined. The effects of permeability parameter α, viscosity ratio λ, and dimensionless parameter S on the drag coefficient are studied. Corresponding dependences are represented graphically and discussed. Known particular cases are described using passages to the limits. © 2020, Pleiades Publishing, Ltd.

Colloid Journal

Flow around a Liquid Sphere Filled with a Non-Newtonian Liquid and Placed into a Porous Medium

A effective coloring of the vertices of a graph G starts with an initial subset S of colored vertices, with all residual vertices being uncolored. At each various time interval, a colored vertex with exactly one uncolored adjacent vertex forces this uncolored vertex to be colored. The initial set S is called a forcing set (zero forcing set) of G if, by iteratively applying the forcing process, every vertex in G becomes colored. If the set S has the added property that the subgraph induced by S is a perfect matching or 1-factor, then S is called a 1-factor forcing set of G. The 1-factor forcing number of G, denoted (equation presented), is the minimum cardinality of a 1-factor forcing set of G. In this paper, we introduce this new parameter namely the 1-factor forcing number and obtain the same for certain interconnection networks. © 2020 The Authors. Published by Elsevier B.V.

Fulltext

Procedia Computer Science

1-factor forcing in certain interconnection networks

In this paper, a novel technique is proposed to solve fuzzy fractional delay differential equations (FFDDEs) with initial condition and source function, which are fuzzy triangular functions. The obtained solution is a fuzzy set of real functions. Each real function satisfies an FFDDE with a specific membership degree. A detailed algorithm is provided to solve the FFDDE. The proposed method has been elucidated in detail through numerical illustrations. Graphs are plotted using MATLAB. © 2010 2020

International Journal of Fuzzy Logic and Intelligent Systems

Numerical Solutions of Fuzzy Fractional Delay Differential Equations

In this research contribution we have considered two subclasses of bi-univalent functions defined using subordination and studied about the bounds for the pre-Schwarzian norm. Initially Shalini et al. have handled this problem. We have made a remark on the proofs and bounds by Shalini et al. © 2020, Research Publication. All rights reserved.

Advances in Mathematics: Scientific Journal

Optimal estimation for the norm of pre-schwarzian derivative

A word is a finite sequence of symbols. Parikh matrix of a word is an upper triangular matrix with ones in the main diagonal and nonnegative integers above the main diagonal which are counts of certain scattered subwords in the word. On the other hand, a picture array, which is a rectangular arrangement of symbols, is an extension of the notion of a word to two dimensions. Parikh matrices associated with a picture array have been introduced, and their properties have been studied. Here, we obtain certain algebraic properties of Parikh matrices of binary picture arrays based on the notions of power, fairness, and a restricted shuffle operator extending the corresponding notions studied in the case of words. We also obtain properties of Parikh matrices of arrays formed by certain geometric operations. © 2020 Somnath Bera et al.

Journal of Mathematics

Algebraic Properties of Parikh Matrices of Binary Picture Arrays

The Parikh matrix mapping plays an important role in the study of words through numerical properties. The Parikh q-matrix mapping, introduced by Egecioglu and Ibarra (2004) as an extension of the Parikh matrix mapping, maps words to matrices with polynomial entries in q. A word w over an ordered alphabet ς is said to be q-ambiguous if there exists another word v over ς such that both the words have same Parikh q-matrix. Here we derive several properties of q-ambiguous words, in particular, for a binary alphabet. © 2020 World Scientific Publishing Company.

International Journal of Foundations of Computer Science

Parikh q-Matrices and q-Ambiguous Words

Scanners are a special class of automata and considered as computational models which accept local information. A local language is defined by the factors of its words of length two and can be generalized by Locally Testable Languages. A natural computation on sequential tasks is concatenation; it models a system finishing one task and then starting another one. We have adopted parallelism to model the tasks of a sequential system because this methodology enables computational tasks to be completed using various types of multiple resources simultaneously. Parallel computing has become an important concept in computer architecture. The classification of parallel computers is based on the level at which parallelism is supported by the hardware. We have introduced parallelisable string-based SP-languages as the collection of series parallel languages and parallel series languages. Parallelisable string-based SP-local language has been defined and their acceptance or recognition on parallelisable string-based SP-regular grammar has been proved. © 2020. All Rights Reserved.

International Journal of Mathematics and Computer Science

Parallelisable String-Based SP-Local Languages and their properties

Cosmological models with time dependent displacement field in the cosmological theory based on Lyra’s geometry have been discussed. Exact solutions have been obtained for a spatially flat FRW model by considering a particular form for the time dependent displacement field. We have also obtained conditions under which the matter-dominated, flat universe undergoes decelerated or accelerated expansions. Accelerated expansion of the Universe is of particular interest in view of the recent observations. © 2020

African Review of Physics

Cosmological Models in Lyra Geometry with Time-varying Displacement Field

The study of nanofluid flow in porous media is of great interest because of enhanced heat transfer rates of these fluids. In this paper we present a study of mixed convection in a nanofluid flow in a porous medium along a vertical plate. The flow field is subjected to magnetic effects and nonlinear thermal radiation. The study further assumes the effects of heat generation within the boundary layer flow. The transport equations are solved numerically using the fifth-order Runge-Kutta-Fehlberg scheme with a shooting technique and appropriate boundary conditions for different values of physical parameters. The model for the nanofluid flow in the porous medium incorporates the effects of buoyancy ratio parameter and Darcy number. The effects of various physical parameters on the dimensionless velocity, temperature and concentration profiles is investigated. It is observed among other findings that an increase in the Darcy number leads to increase in the velocity profiles. © 2020 by Begell House, Inc.