Entropy generation and induced magnetic field in pseudoplastic nanofluid flow near a stagnant point

In this present article the entropy generation, induced magnetic field, and mixed convection stagnant point flow of pseudoplastic nano liquid over an elastic surface is investigated. The Buongiorno model is employed in modeling. Through the use of the boundary layer idea, flow equations are transformed from compact to component form. The system of equations is solved numerically. The Induced magnetic spectrum falls near the boundary and grows further away as the reciprocal of the magnetic Prandtl number improves. The fluctuation of induced magnetic rises while expanding the values of mixed convection, thermophoresis, and magnetic parameters, whereas it declines for increment in the Brownian and stretching parameters. The velocity amplitude ascends and temperature descends for the rise in magnetic parameter. The mass transfer patterns degrade for the higher amount of buoyancy ratio while it boosts by the magnification of mixed convection and stretching parameters. Streamlines behavior is also taken into account against the different amounts of mixed convection and magnetic parameters. The pseudoplastic nanofluids are applicable in all electronic devices for increasing the heating or cooling rate in them. Further, pseudoplastic nanofluids are also applicable in reducing skin friction coefficient.

Ternary Mathematics and 3D Placement of Logical Elements Justification

Aims/ Objectives: The research presented in the following application aims to prove use of Ternary Maths for calculating machines and to simplify the process of calculating In it we will try to justify the use of triplets and describe how it works. An earlier research presented in “Logical Principles in Ternary Mathematics” [1,2,3] shows that we can transit from one expression of a number such as a "component form" to another, e.g a decimal, or still another, that is it’s vector form [4]. The aim of our further research is to explain why we associate Triplets of numbers in such choice {-1,0,1} and not the numbers 1,2,3 for example, or a set {1,2,3} The explanation seems obvious as a set of decimal numbers consists of 10 entries not 3 At the same time we have to prove that the mentioned set of triplets is a unique and the only one to be used as a Ternary Set or a base, as we might call it, for our calculating machines.

Organizing the mathematical proof process with the help of basic Components in teaching proof: Abstract algebra example

The aim of this study is to identify the basic components of the mathematical proof process in abstract algebra and to organize the proof process into phases with the help of these basic components. A basic component form was prepared by arranging a draft basic component form, which was created as a result of a document analysis in accordance with the opinions of three academicians, who were experts in algebra. The data obtained as a result of both document analysis and expert examination were analyzed by the descriptive analysis method and are explained here in a detailed manner. It is believed that this basic component form will facilitate the step-by-step addressing of such a complex process as proofs in a non-compulsory and non-hierarchical order.

Optical solitons and other soluions for Radhakrishnan–Kundu–Lakshmanan equation in birefringent fibers by an efficient computational technique

In this article, we are interested to discuss the exact optical soiltons and other solutions in birefringent fibers modeled by Radhakrishnan-Kundu-Lakshmanan equation in two component form for vector solitons. We extract the solutions in the form of hyperbolic, trigonometric and exponential functions including solitary wave solutions like multiple-optical soliton, mixed complex soliton solutions. The strategy that is used to explain the dynamics of soliton is known as generalized exponential rational function method. Moreover, singular periodic wave solutions are recovered and the constraint conditions for the existence of soliton solutions are also reported. Besides, the physical action of the solution attained are recorded in terms of 3D, 2D and contour plots for distinct parameters. The achieved outcomes show that the applied computational strategy is direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations. The primary benefit of this technique is to develop a significant relationships between NLPDEs and others simple NLODEs and we have succeeded in a single move to get and organize various types of new solutions. The obtained outcomes show that the applied method is concise, direct, elementary and can be imposed in more complex phenomena with the assistant of symbolic computations

Improvement of a Truss-Reinforced, Half-Concrete Slab Floor System for Construction Sustainability

The truss-reinforced half-concrete slab has been widely used in prefabricated construction all over the world. It has become the most widely used prefabricated component form in China. However, its construction cost is higher than using the conventional construction method. To improve the half slab floor system, it is essential to have a comprehensive understanding of the truss-reinforced half slab’s structural performance over its complete loading history. Six experimental tests on such slabs were carried out. Three of them were reinforced with a steel bar truss (SBT) and the other three with a steel tube/bar truss (STBT). The steel tube in an STBT was grouted. The results show that when the specimen is damaged, the grouted steel tube does not undergo out-of-plane or in-plane buckling, and its force performance is good when compared to the steel bar in SBT. Compared with the SBT-reinforced slab specimens, the load characteristic values of the STBT-reinforced slabs were significantly improved, and the slabs had greater initial stiffness and resistance to deformation. Due to the fact that good structural performance of the steel tube was observed, after having studied the half slab component design, a dry, prefabricated, STBT-reinforced half slab system that can reduce the volume of concrete and amount of steel used in the present slab system is proposed. The proposed system has the advantages of allowing easier construction, cost reduction, and reuse of the components afterward to make the prefabrication construction more sustainable.

Inferring suspended sediment carbon content and particle size at high frequency from the optical response of a submerged spectrometer

<p>Manual and unattended sampling in the field and laboratory analysis are common practices to measure suspended sediment (SS) carbon content and particle size. However, one of the major drawbacks of these ex-situ methods is that they make high frequency measurements challenging. This includes restricted data collection due to limited access to the sampling locations during turbulent conditions or high flows, when the largest amount of sediments is transported downstream, introducing uncertainty in quantification of SS properties (particle size and carbon content) and sediment loads. Knowledge on SS carbon content and particle size is also important to better understand the multi-component form of suspended sediments (i.e. flocs) that directly affect sediment transport and other sediment properties (e.g. settling velocity and density). Moreover, SS carbon content and particle size exert an impact on the optical sensor readings that are traditionally used to measure turbidity. In that respect, high frequency measurements of SS carbon content and particle size could eventually help us to move from ‘local’ calibrations towards ‘global’ dependencies based on in-situ SS characterization.</p><p>In this study, we propose to use a submerged UV-VIS spectrometer to infer SS carbon content and particle size. The sensor measures the entire light absorption spectrum of water between 200 nm and 750 nm at sampling intervals as short as 2-minutes. To this end, we first test our approach under controlled conditions with an experimental laboratory setup consisting of a cylindrical tank (40-L) with an open top. An UV-VIS spectrometer and a LISST-200X sensor (to measure particle size distribution) are installed horizontally. A stirrer facilitates the homogeneous mixing of SS and prevents the settling of heavy particles at the bottom. We use the sediments sampled from 6 sites in Luxembourg with contrasting composition and representing different land use types and geological settings. The sampled sediments were wet sieved into 3 size classes to clearly recognize the effect of particle size on absorption. In our investigation, we use specific wavelengths, chemometric techniques and carbon content specific absorbance indices to infer SS composition and particle size from the absorption spectrum. Results are then validated using in-situ field data from two instrumented field sites in Luxembourg. Amid the challenge of associating laboratory and field results, the preliminary results indicate that the absorption spectrum measured with a submerged UV-VIS spectrometer can be used to estimate SS particle size and carbon content.</p>

Two basic systems of maxwell’s equations in a rotating frame: application in theory of ring laser gyro

In the paper, using a linear in angular velocity approximation, two basic well-known systems of Maxwell’s equations in a uniformly rotating frame of reference are considered. The first system of equations was first obtained in the work [L. I. Schiff, Proc. Natl. Acad. Sci. USA 25, 391 (1939)] on the base of use of the formalism of the theory of general relativity, and the second one – in the work [W. M. Irvine, Physica 30, 1160 (1964)] on the base of use of the method of orthonormal tetrad in this theory. In the paper, in the approximation of plane waves, these two vectorial systems of Maxwell’s equations are simplified and rewritten in cylindrical coordinates in scalar component form in order to find the lows of propagation of transversal components of electromagnetic waves in a circular resonator of ring laser gyro in the case of its rotation about sensitivity axis. On the base of these two simplified systems of Maxwell’s equations, the well-known wave equation and its analytical solutions for the named transversal components are obtained. As a result of substitution of these solutions into the first and second simplified systems of Maxwell’s equations, it is revealed that they satisfy only the second one. On this basis, the conclusion is made that the second system of Maxwell’s equations is more suitable for application in the theory of ring laser gyro than the first one.

Spectral action in matrix form

Quantization of the noncommutative geometric spectral action has so far been performed on the final component form of the action where all traces over the Dirac matrices and symmetry algebra are carried out. In this work, in order to preserve the noncommutative geometric structure of the formalism, we derive the quantization rules for propagators and vertices in matrix form. We show that the results in the case of a product of a four-dimensional Euclidean manifold by a finite space, could be cast in the form of that of a Yang–Mills theory. We illustrate the procedure for the toy electroweak model.

Vectors and tensors: Algebra

This chapter introduces vectors and second-order tensors, and presents the fundamental rules and standard results of vector and tensor algebra. It briefly discusses fourth-order tensors. The most important results for vectors and tensors are presented in both direct and component form.