Dimensional System Of Equations Research Articles

Role of electromagnetic analysis in radiative immiscible Newtonian and non‐Newtonian fluids through a microchannel with chemical reactions

AbstractThe study of an immiscible fluid plays a significant role in the field of petroleum extraction, blood flow in arteries, hydrology, manufacturing process, and reservoir mechanics. These phenomena include immiscible fluids of different densities and viscosities in the same channel. Due to the various practical applications, in the current study, the generalized Couette flow of two immiscible fluids (Newtonian and non‐Newtonian fluids) of different viscosities between two infinite parallel plates under the presence of constant pressure gradient and electroosmosis is addressed. The effects such as electromagnetohydrodynamics, zeta potential, Joule heating, thermal radiation, modified Darcy's law, and chemical reaction have been also considered into account. The dimensional system of equations has been nondenationalized with suitable dimensionless quantities. The resulting nondimensional system of coupled flow equations has been solved analytically. The solutions for the velocity, temperature, and concentration have been presented. The effect of various pertinent fluid flow parameters has been displayed graphically. The current study concludes that both the velocity and temperature profiles decrease with the increase in Hartmann number and radiation parameter, whereas an increase in chemical reaction parameter uplifts the concentration of both fluids.

Exact Solutions and Conservation Laws of a Generalized (1 + 1) Dimensional System of Equations via Symbolic Computation

The aim of this paper is to compute the exact solutions and conservation of a generalized (1 + 1) dimensional system. This can be achieved by employing symbolic manipulation software such as Maple, Mathematica, or MATLAB. In theoretical physics and in many scientific applications, the mentioned system naturally arises. Time, space, and scaling transformation symmetries lead to novel similarity reductions and new exact solutions. The solutions obtained include solitary waves and cnoidal and snoidal waves. The familiarity of closed-form solutions of nonlinear ordinary and partial differential equations enables numerical solvers and supports stability analysis. Although many efforts have been dedicated to solving nonlinear evolution equations, there is no unified method. To the best of our knowledge, this is the first time that Lie point symmetry analysis in conjunction with an ansatz method has been applied on this underlying equation. It should also be noted that the methods applied in this paper give a unique solution set that differs from the newly reported solutions. In addition, we derive the conservation laws of the underlying system. It is also worth mentioning that this is the first time that the conservation laws for the equation under study are derived.

Perturbation based analytical solutions of non‐Newtonian differential equation with heat and mass transportation between horizontal permeable channel

AbstractA mathematical model is constructed in this investigation to examine the effects of heat and mass transfer in tangent‐hyperbolic fluid bounded within horizontal channel. The lower‐wall of channel is taken as heated. The dimensional momentum, energy and concentration equations are determined by defining a stress‐tensor of undertaken fluid (Tangent‐hyperbolic fluid). To calculate the solution, the system of dimensional equations is transformed into nondimensional system by using normalized variables and then solved by applying perturbation technique. The impacts of several dimensionless parameters that is, power‐law index parameter , pressure gradient parameter , Reynolds number (Re), time constant parameter (Γ), Peclet number (λ4), viscous heating parameter (λ5), Schmidt number (Sc), thermophoresis parameter (NT), and Brownian motion (NB) parameter are sketched and also physically discussed. The results reveal that power‐law index parameter and pressure gradient cause increment in velocity and temperature fields and decrement in concentration field. Further, the variations in skin‐friction coefficient, Nusselt number and Sherwood number via emerging parameters are also expressed in form of table in this exploration.

Разработка математической модели управления железнодорожными грузовыми перевозками в мультимодальном сообщении

Objective: To develop a mathematical model of the functioning of the freight traffic subsystem interconnected with the general freight transportation model on the basis of the accepted basic assumptions and conditions, since the main type of interaction of the general system with a particular system (subsystem) is the application of constraints on the particular model parameters imposed by the requirements for the quality of the general model functioning according to the nomenclature, service level, and time characteristics of customer service, which are external to the modeled transportation subsystem. Methods: Analysis, synthesis, abstraction, comparison, and mathematical modeling methods were used. Results: A mathematical model of the functioning of a transportation subsystem has been created, taking into account the necessary restrictions imposed by the Russian Railways general functioning model. The complete package of source data required for the practical implementation of this mathematical model as applied to railway transportation is available in the data stores of the main data processing center of Russian Railways. Existing numerical methods for solving such higher dimensional systems of equations make it possible to obtain a numerical implementation of such a model. The proposed model can serve the purposes of assessing the efficiency of the transportation subsystem, since it makes it possible to assess the mathematical expectations of the numbers of each of this system's states at any given time. Practical importance: The practical result of applying the developed model should be quantitatively substantiated recommendations for solving the main problems of choosing a transportation provider when planning multimodal transportation process, as well as for current and future transportation management under given conditions

Effects of g-jitter and radiation on three-dimensional double diffusion stagnation point nanofluid flow

The unsteady double diffusion of the boundary layer with the nanofluid flow near a three-dimensional (3D) stagnation point body is studied under a microgravity environment. The effects of g-jitter and thermal radiation exist under the microgravity environment, where there is a gravitational field with fluctuations. The flow problem is mathematically formulated into a system of equations derived from the physical laws and principles under the no-slip boundary condition. With the semi-similar transformation technique, the dimensional system of equations is reduced into a dimensionless system of equations, where the dependent variables of the problem are lessened. A numerical solution for the flow problem derived from the system of dimensionless partial differential equations is obtained with the Keller box method, which is an implicit finite difference approach. The effects studied are analyzed in terms of the physical quantities of principle interest with the fluid behavior characteristics, the heat transfer properties, and the concentration distributions. The results show that the value of the curvature ratio parameter represents the geometrical shape of the boundary body, where the stagnation point is located. The increased modulation amplitude parameter produces a fluctuating behavior on all physical quantities studied, where the fluctuating range becomes smaller when the oscillation frequency increases. Moreover, the addition of Cu nanoparticles enhances the thermal conductivity of the heat flux, and the thermal radiation could increase the heat transfer properties.

A Parallel Programming for Robust Chaotic Map Generation Based on Two Dimensional Equation System

A Parallel Programming for Robust Chaotic Map Generation Based on Two Dimensional Equation System

Observable for a Large System of Globally Coupled Excitable Units

The study of large arrays of coupled excitable systems has largely benefited from a technique proposed by Ott and Antonsen, which results in a low dimensional system of equations for the system’s order parameter. In this work, we show how to explicitly introduce a variable describing the global synaptic activation of the network into these family of models. This global variable is built by adding realistic synaptic time traces. We propose that this variable can, under certain conditions, be a good proxy for the local field potential of the network. We report experimental, in vivo, electrophysiology data supporting this claim.

A dynamic model of the piezoelectric traveling wave rotary ultrasonic motor stator with the finite volume method

This manuscript presents a method to model in detail the piezoelectric traveling wave rotary ultrasonic motor (PTRUSM) stator response under the action of DC and AC voltages. The stator is modeled with a discrete two dimensional system of equations using the finite volume method (FVM). In order to obtain accurate results, a model of the stator bridge is included into the stator model. The model of the stator under the action of DC voltage is presented first, and the results of the model are compared versus a similar model using the commercial finite element software COMSOL Multiphysics. One can observe that there is a difference of less than 5% between the displacements of the stator using the proposed model and the one with COMSOL Multiphysics. After that, the model of the stator under the action of AC voltages is presented. The time domain analysis shows the generation of the traveling wave in the stator surface. One can use this model to accurately calculate the stator surface velocities, elliptical motion of the stator surface and the amplitude and shape of the stator traveling wave. A system of equations discretized with the finite volume method can easily be transformed into electrical circuits, because of that, FVM may be a better choice to develop a model-based control strategy for the PTRUSM.

Existence and Smoothness of the Navier-Stokes Equation in Two and Three-Dimensional Euclidean Space

A solution to this problem has been unknown for years and the fact that it hasn’t been solved yet leaves a lot of unanswered questions regarding Engineering and Pure Mathematics. Turbulence is a specific topic in fluid mechanics which is a vital part of the course when it comes to real life situations. In two and three dimensional systems of equations and some initial conditions, if the smooth solutions exist, they have bounded kinetic energy. In three space dimensions and time, given an initial velocity vector, there exists a velocity field and scalar pressure field which are both smooth and globally defined that solve the Navier-Stokes equations. There are difficulties in two-dimensions and three dimensions in a possible solution and which have been unsolved for a long time and our goal is to propose a solution in three-dimensions. Lets see if we can relate a couple of courses of pure mathematics to come up with an implication.

Computer aided dimensional analysis for knowledge management in chemical engineering processes

An algorithmic procedure has been designed/developed for computer aided Dimensional Analysis (DA) of chemical engineering processes. The main purpose of this software is to construct/select the best combination of dimensionless groups describing adequately a process under certain criteria. The creation/operation of an Ontological Knowledge Base (OKB) plays a central role in this procedure as it provides, inter alia, the means for filtering/reducing the dimensionless groups obtained by solving the system of dimensional equations according to the Buckingham Π Theorem. The successful implementation of this software is thoroughly presented step by step in a case of mass transfer (liquid drops moving in immiscible liquids).

Geometric Interpretation of Discrete Approaches to Solving Magnetostatic Problems

The finite-element approach can be considered as a tool for constructing finite dimensional systems of equations that approximate to field problems on the discrete level. Although the finite-element technique is explained typically in terms of variational or weighted-residual approaches, another, less familiar way is available to introduce the same ideas geometrically. Using magnetostatics as an example, we will show how finite-element-type system matrices can be developed by exploiting the geometric properties of so-called Whitney elements. The simple interpretation we gain thereby enables us to view also the convergence properties of finite-element-type schemes in an intuitive way.

Extending Newton'S Method For Finding The Roots Of An Arbitrary System Of Equations

The author presents a new technique for determining the roots of an arbitrary system of equations iteratively, where the equations can be nonlinear algebraic or transcendental, and the number of equations of the system can be greater than, less than or equal to the number of variables. When the number of equations is equal to the number of variables, the method is similar to Newton's method. The method is a hybrid symbolic-numerical method, in that it uses symbolic techniques to transform a system of algebraic equations into a regular form whenever the system has some redundant parts or does not have a full-rank Jacobian matrix. The method has a wide range of applicability. It is especially useful for applications in which we need to find some particular roots from a nonzero dimensional system of equations, i.e., a system whose set of zeroes is nonzero dimensional. Some conditions for convergence of the method are considered, with the convergence of the method claimed to still be quadratic. Several examples are presented to show that the method works nicely.

On the Modulations and Nonlinear Interactions of Waves and the Nonlinear Stability of a Near‐Critical System

The nonlinear interactions and modulations of an n‐dimensional wave and of a disturbance to a near‐critical system governed by a general (n + 1)‐dimensional system of equations are studied by perturbation methods. It is found that these modulations are governed by an evolution equation which is either by itself or coupled to a second equation, depending on the nature of the long wave solutions of the corresponding linearized system. When a single evolution equation exists, its leading terms are shown to give the nonlinear Schrödinger equation. Water waves and near‐critical plane Poiseuille flow are discussed as examples.