Complicated Systems Of Equations Research Articles

Flow and heat transfer of Al2O3 and γ-Al2O3 through a channel with non-parallel walls: a numerical study.

Nanofluids are referred to as nanometer suspensions in standard nanometer-sized fluid transfer. In this study, our focus was to examine the flow and transmission of heat through a non-parallel walled channel of nanofluids. For this purpose, we used the thermal transport in H2O composed of Al2O3 and γ-Al2O3 nanomaterials within the convergent/divergent channel for stretching/shrinking parameters. The flow was considered two-dimensional and unsteady. As a result, the flow of an unstable fluid, including various nanoparticles, was modeled within the convergent/divergent channel. A suitable similarity transformation was used to convert the complicated coupled system of differential equations into a non-dimensional form. For numerical solutions, the complicated system of equations was first transformed into a set of first-order differential equations using the shooting method. The Runge-Kutta (RK-4) method was then used to solve the reduced first-order equations. To comprehend the flow pattern and temperature and velocity profile deviations caused by dimensionless parameters, a graphical investigation was performed. Graphs were also used to investigate the variation in the velocity and temperature profiles for various emerging factors.

A Geometric Algebra Based Higher Dimensional Approximation Method for Statics and Kinematics of Robotic Manipulators

Evaluation of a robotic (serial or parallel) manipulator’s static and kinematics performance requires the solution of closed and complicated non-closed form systems of equations for both the forward and inverse problem types. In this work, a robotic system or manipulator is represented as a network whose motion generating kinematic pairs are represented as the network’s inter-connected nodes. Within this network theoretic context, we develop a formulation employing higher dimensional multivectors defined in Clifford Algebra that approximates the computational outcomes of such complicated systems of equations, for both inverse and forward problem types. The statics and kinematics performance of these mechanical networks (serial and parallel robots) are rapidly evaluated without the need to solve their respective traditional systems of equations using what we call ‘screw hypervolumes’, which capture the algebro-geometric structures generated by a robot’s physical design parameters and end-effector position in terms of kinematics and statics. These dimensionless hypervolume functions enable the specialist to produce a very computationally efficient function/index that approximates the kinematic and static output spaces of robots. We find that this formulation inadvertently presents a curious mathematical analogue to these systems of equations. A 6R serial robot, the Delta robot and the 3-RRR manipulator are analysed using the hypervolume methods for the case studies. This approach can be adapted and applied to other multi-agent physical systems displaying non-commutative interactions as well.

Analytical approximation schemes for solving exact renormalization group equations. II Conformal mappings

We present a new efficient analytical approximation scheme to two-point boundary value problems of ordinary differential equations (ODEs) adapted to the study of the derivative expansion of the exact renormalization group equations. It is based on a compactification of the complex plane of the independent variable using a mapping of an angular sector onto a unit disc. We explicitly treat, for the scalar field, the local potential approximations of the Wegner–Houghton equation in the dimension d = 3 and of the Wilson–Polchinski equation for some values of d ∈ ] 2 , 3 ] . We then consider, for d = 3 , the coupled ODEs obtained by Morris at the second order of the derivative expansion. In both cases the fixed points and the eigenvalues attached to them are estimated. Comparisons of the results obtained are made with the shooting method and with the other analytical methods available. The best accuracy is reached with our new method which presents also the advantage of being very fast. Thus, it is well adapted to the study of more complicated systems of equations.

Genetic programming model of solid oxide fuel cell stack: first results

Models that predict performance are important tools in understanding and designing solid oxide fuel cells (SOFCs). Modelling of SOFC stack-based systems is a powerful approach that can provide useful insights into the nonlinear dynamics of the system without the need for formulating complicated systems of equations describing the electrochemical and thermal properties. Several algorithmic approaches have already been reported for the modelling of solid oxide fuel cell stack-based systems. This paper presents a new, genetic programming approach to SOFC modelling. Initial simulation results obtained with the proposed approach outperform the state-of-the-art radial basis function neural network method for this task.

Weak Solutions to the Equations of Motion of Viscous Compressible Reacting Binary Mixtures: Uniqueness and Lipschitz-Continuous Dependence on Data

1. An extensive literature is devoted to systems of quasilinear equations of motion of viscous compressible media (see [1, 2]). One of the problems of current interest is the development of the theory of global (with respect to time and data) weak solutions, including questions of their existence, uniqueness, and continuous dependence on data (such as initial data, the coefficients of the equations, the constant terms, etc.). For the system of equations of one-dimensional motion of a viscous heat-conducting gas, the last two questions were studied in [3–6] (see also [7, 8]). For more complicated systems of equations for reacting gases (in other words, in combustion problems) weak solutions were studied in [9, 10]. Quite recently, in [11], the existence of weak solutions was obtained for an even more complicated system of equations, namely, for a reacting binary gas mixture. Note that regular solutions of problems concerning binary mixtures were studied earlier in [12, 13]. The present paper is devoted to the questions of uniqueness of these weak solutions and of their continuous dependence on data. The system of quasilinear equations of one-dimensional motion of a viscous compressible reacting binary gas mixture is of the form

New statistical investigations of the ornstein-uhlenbeck process

An asymptotic analysis is presented for estimation in the three-parameter Ornstein-Uhlenbeck process, where the parameters are the local mean, the drift, and the variance. We are interested in the case when the damping parameter (λ, or λ T = κ) is nearly zero. The asymptotic sufficient statistics can be related to noncentral χ 1 2 distribution. The maximum likelihood estimate of the parameter vector is a solution of a rather complicated system of equations. We describe the methods for solving maximum-likelihood equations. Classical and robust estimators are determined for parameters. It is shown that the lower confidence limit of the drift (or damping) parameter is equal to zero with positive probability when it is near to zero.

Carrier diffusion inCd1−xMnxTe

Carrier diffusion and electron-hole recombination are shown to be considerably slowed down in ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Te}$ semimagnetic semiconductors due to the efficient trapping of electrons on manganese sites. The theoretical interpretation is based on population dynamics, charge continuity equations, and Poisson's law. A simple analytical solution of this complicated system of equations is in very good agreement with the numerical one for a large range of durations of the write pulses (from 100 ps to 1 \ensuremath{\mu}s). Both calculations predict a reduction of electron mobility by a factor of 6000. These theoretical predictions are confirmed by the results of an experimental study performed by using the simple grating technique: We observe the temporal evolution of the diffracted signal when a continuous read beam is used to read gratings of different wavelengths encoded in the material by interfering write laser pulses. An effective ambipolar mobility of $0.54{\mathrm{cm}}^{2}/\mathrm{V}\mathrm{}\mathrm{s}$ is measured, which provides a value of $3400{\mathrm{cm}}^{2}/\mathrm{V}\mathrm{}\mathrm{s}$ for the intrinsic mobility in ${\mathrm{Cd}}_{0.7}{\mathrm{Mn}}_{0.3}\mathrm{Te}.$ This low ambipolar mobility could make this efficient material potentially interesting for parallel optical processing in the microsecond range.