Basic Linear Equations Research Articles

A semi-analytical method for frictional contact analysis between rock mass and concrete linings

The rock–lining interface typically exhibits a complex frictional contact behavior. Thus far, there has been no analytic method to analyze the frictional contact problems of arbitrary-shaped tunnels with concrete linings. In this work, we propose a novel analytic method to perform the frictional contact analysis of multiple lined tunnels based on the generalized complex variable method. Using two special composite analytic functions, the mechanical field in a multiply-connected domain can be accurately expressed, and the solution to the contact problem can thus be obtained in a closed mathematical form. In the present theoretical framework, the general contact condition is considered, where the contact mode is described using two complementary functions. The basic linear equations are obtained by satisfying the stress and contact boundary conditions at a finite number of discrete points. Since the contact analysis is a highly nonlinear problem, we propose an iterative scheme to determine the contact states at different positions on the rock–lining interface. Finally, a verification example and parametric investigation are performed to demonstrate the effectiveness and practicability of the proposed method.

Designing Regenerators of Thermoacoustic Engines for Automotive Waste Heat Recovery

<div class="section abstract"><div class="htmlview paragraph">Extraction and utilization of automotive waste exhaust heat is an effective way to save fuel and protect the environment. One promising technology for this purpose is the thermoacoustic engine, where thermal energy is converted to mechanical energy in terms of high amplitude oscillations. The core component in a travelling-wave thermoacoustic engine is its regenerator where the process of energy conversion is mainly realized. This paper introduces a strategy for the design of the regenerator for applications in typical light- and heavy-duty vehicles. Starting from 1-D linear thermoacoustic theory, the nonlinear effects (given by the high amplitude oscillations) are modelled as acoustic resistances and introduced into the basic linear equations to estimate the nonlinear dissipations in the regenerator. Then, a few dimensionless parameters are derived by normalizing these thermoacoustic equations. This yields a good overview of how different design parameters such as the geometrical dimensions, operating temperature, and thermal boundary conditions influence the performance of the regenerator. For the application of automotive waste heat recovery, the thermal properties of the actual exhaust gas are accepted to be the boundary condition for the heat matching. The results obtained in the current work show that the optimum designs for the regenerators in travelling-wave thermoacoustic engines aimed at light- and heavy-duty applications widely differ due to the different thermal properties of their exhaust gas. Finally, two possible optimal designs of the regenerators in travelling-wave thermoacoustic engines for the typical light- and heavy-duty applications are presented. The designs are based on heat matching between the required heat by the regenerators and the available heat from the exhaust gases.</div></div>

Monetary Equivalent Value (MEV) of a Published Article in Psychology.

Publishing one’s research in peer-reviewed journals is generally acknowledged to be a valuable enterprise. This is particularly the case for academic and research psychologists who rely on publications for career status, stability, and advancement. Psychological researchers can devote extensive amounts of time to planning, conducting, writing up, and getting their research published in respected psychology journals, yet their work efforts in this regard have heretofore never been quantified monetarily. This article introduces the concept of a monetary equivalent value (MEV) of a published article in psychology. An initial basic linear equation is introduced that sets the dollar (or Euro) value of an article based on the median number of hours involved in publishing an article, the mean hourly wage of psychologists, and the 5-year Impact Factor (IF) of the journal in which the article is published. MEVs were calculated for the full range of journals published by the American Psychological Association (APA) that have IF ratings. MEV values varied widely, from a low of $4,562 for an article published in the journal "Dreaming", to a high of $131,613 for an article appearing in "Psychological Bulletin". This article represents the first to explore the MEV as an additional metric to understand the impact of published articles, and as such this exploratory study has numerous limitations. Chief among these is the study’s reliance on the controversial Journal Citation Reports (JCR) journal impact factor metric, as well as its extrapolation from a limited medical literature on the average number of hours involved in publishing a study.

A Case Study Examining Links between Fractional Knowledge and Linear Equation Writing of Seventh-Grade Students and Whether to Introduce Linear Equations in an Earlier Grade

As a part of the larger study, a case study of two seventh grade students, Peter and Willa, was conducted. To examine links between their fractional knowledge and algebraic reasoning, the students were interviewed twice, once for their fractional knowledge and once for their algebraic knowledge in writing linear equations that required explicit use of unknowns. Peter and Willa’s fractional knowledge influenced the linear equations they wrote to represent quantitative situations. In particular, the findings showed that a reversible iterative fraction scheme is important to understand reciprocal relationships between two quantities in writing a basic linear equation of the form ax=b. Also, considering fractions as multipliers on unknowns is important to write linear equations. Implications for the possibility of introducing linear equations in an earlier grade and how to support the introduction are suggested.

Numerical study of inertial effects on permeability of porous media utilizing the Lattice Boltzmann Method

The Darcy law provides the basic linear equation for single-phase fluid flow in porous media in ideally simplified conditions. The Darcy equation has been shown to be valid in flow processes happening in sufficiently low Reynolds number regimes. At higher Reynolds numbers, inertial effects cause extra hydrodynamic head loss and Darcy's law becomes invalid. The Forchheimer equation is a semi-empirical relationship which accounts for the effect of the inertial effects on apparent permeability reduction.In this research, the apparent permeability reduction due to inertial effects is studied in simple and complex porous structures. For this purpose a Lattice Boltzmann based simulator was developed to model single-phase fluid flow in porous media. The simulator was verified by experimental and analytical solution tests and then was implemented to study high Reynolds number flow processes in three dimensional regular and irregular shaped porous structures. The effects of inertial on the onset and extent of non-Darcy flow in different geometries was studied. It was also shown that the Forchheimer equation does not accurately fit the high Reynolds number flow in simple and complex porous media. It was observed that a quadratic relationship exists between the introduced “scaled permeability” and the mass flow rate in the range of moderate Reynolds numbers. A new empirical correlation was proposed that fits the scaled permeability and mass flow rate relationship results very well. The proposed correlation predicts the scaled permeability change due to inertial effects more accurate than the Forchheimer equation.

NUMERICAL STUDY OF THE EULERIAN CORRELATIONS AND LAGRANGIAN VELOCITY IN STABLY STRATIFIED HOMOGENEOUS TURBULENCE

This study is based on a linear analysis in spectral space. To express the correlation double speed using Lagrangian Dual Eulerian correlations, we use the Corrsin assumption and then we compute the components of the tensor of the square displacements means. We begin by rewriting the basic linear equations governing the evolution of double correlations spectra. Subsequently, we analyze the numerical results.

Étude numérique de la diffusion turbulente dʼune turbulence homogène stablement stratifie à lʼaide dʼune analyse linéaire

In this Note, we study numerically turbulent diffusion in the case of homogeneous stably stratified turbulence. This study is based on a linear analysis in spectral space. To express the Lagrangian velocity correlations using Eulerian correlations, we adapt the Corrsin assumption and then we calculate the tensor components of the mean square displacement. We begin by writing the basic linear equations governing the evolution of the spectra of double correlations then we present the Corrsin hypothesis as a model of turbulent diffusion. Subsequently, we describe the numerical method used and analyze the numerical results. Clearly, the Corrsin assumption can give the proper behavior, at large times, of the horizontal diffusion and improves the prediction of vertical diffusion. As an application of the numerical code elaborated, we study the influence of Prandtl number on the vertical diffusion which results in an accentuation of the suppression of vertical diffusion when the Prandtl number (less than 1) diminishes.

Solving Some Linear Equations Over Alternative Rings

One of the fundamental research problems in algebra theory is to solve equations over the given algebraic structures. The purpose of this note is to solve some basic linear equations over alternative rings. In particular, we derive necessary and sufficient conditions for the equations ax = b, xa = b and axa = b to be solvable over an alternative ring, respectively, and give general solutions of these equations. In addition, we solve the three linear equations ax − ya = b, ax − xa = b and x − axa = b over alternative rings, respectively, where the coefficient element a is idempotent or involutory.

A Theory of Equatorial Deep Jets*

Abstract A simple linear theory of the circulation in a meridionally bounded equatorial ocean driven by density mixing localized near the eastern boundary is used to model the subthermocline circulation of the equatorial oceans. The mixing is modeled by a specified, spatially limited source term in the density equation. The theory is for a steady circulation, and the model, which is continuously stratified, contains simple linear drag laws for frictional dissipation and a similar, linear damping for density anomalies. The model employs Gill's formulation of the basic linear equations near the equator. The satisfaction of the condition of zero zonal flow at both bounding meridians requires the determination of the amplitude of the Kelvin component (or its steady counterpart) by an integral condition over the domain of the flow. When that condition is satisfied, the solution, for reasonable settings of the parameters, naturally yields an alternating array of zonal currents localized within a deformation rad...

Wet Removal of Pollutants from Gaussian Plumes: Basic Linear Equations and Computational Approaches

Abstract Over the past several years, a number of Gaussian plume–based computer codes have been produced. These codes describe transport, transformation, and deposition of air pollutants under a variety of atmospheric conditions. For a number of reasons, there is increasing interest in simulating wet-deposition processes in such codes, and several approaches have been applied to this end. Some of these approaches involve elaborate solubility and chemistry characterizations, but many of them resort to a diversity of approximate techniques. This paper presents a procedure that can be used as a practical guide to improve many of these formulations, especially for the case of pollutant gases. The approach takes the form of a set of analytical equations that correspond to five kinds of Gaussian plume formulations: standard bivariate-normal point-source plumes, line-source plumes, unrestricted instantaneous puffs, and point-source plumes and puffs that experience reflection from inversion layers aloft. These eq...

Universal Equations for Linear Adiabatic Pulses and Characterization of Partial Adiabaticity

A numerical analysis of the sech/tanh (or hyperbolic secant) and tanh/tan adiabatic inversion pulses provides a set of master equations for each type of pulse that guarantee their optimal implementation over a wide range of practical conditions without needing to further simulate the inversion profiles of the pulses. These simple equations determine the necessary maximum RF amplitude (RFmax) required for a preselected degree of inversion across a chosen effective bandwidth (bweff) and for a chosen pulse length (Tp). The two types of pulse function differently: The sech/tanh pulse provides a rectangular inversion profile with bweff being a large fraction of the adiabatic frequency sweep (bwdth), whereas for tanh/tan bweff is ≤bwdth/20. If the quality of inversion is defined as the minimum allowable extent of inversion, ιbw, at the boundaries of bweff, two basic linear equations are found for both types of pulse and these are of the form (RFmaxTp)2=m1Tpbwdth+c1 and Tpbwdth=m3Tpbweff+c3. The different behavior of the two pulses is expressed as different dependencies of the slopes mn and intercepts cn on ιbw and allowances are made for second order effects within these equations. The availability of these master relationships enables a direct comparison of the two types of adiabatic pulse and it is found that tanh/tan requires about half the pulse length of an equivalent sech/tanh pulse and also has the advantage of being less sensitive to the effects of scalar coupling. In contrast sech/tanh delivers about half the total RF power of an equivalent tanh/tan pulse. It is expected that the forms of these two basic linear equations are generally applicable to adiabatic inversion pulses and thus define the concept of “linear adiabaticity.” At low values of Tpbwdth or Tpbweff the linear equations no longer apply, defining a region of “partial adiabaticity.” Normal adiabatic pulses in the middle of this partial region are more efficient in terms of RFmax or Tp but are moderately less tolerant to RF inhomogeneity. A class of numerically optimized pulses has recently been developed that specifically trades adiabaticity in an attempt to gain RFmax or Tp efficiency. In comparison to normal adiabatic pulses implemented under optimal conditions, these new partially adiabatic pulses show only marginal improvements; they are restricted to single values of Tpbweff, and they are vastly less tolerant to RF inhomogeneity. These comparisons, and direct comparisons between any types of inversion pulse, adiabatic or otherwise, can be made using plots of (RFmaxTp)2 or (Total Power) Tp versus Tpbweff.

Electric drive system for a steerable aerial at a satellite-communication Earth station

The paper describes the control and motor-drive system for the steerable aerial located at the Post Office Earth station, Goonhilly Downs, Cornwall. Specification, performance and control racilities are detailed for the purpose of establishing the general design considerations involved. The arrangement of the principal items of the closed-loop Ward Leonard drive is given briefly, and particular attention is then directed in the remaining sections of the paper to the design and performance of the servosystem. The basic linear equations of the system are developed for the major components, and the nonlinear restrictions are then introduced to establish the complete analogue network for the computer analysis. The simulation of the nonlinear elements is detailed for the particular cases of saturation limits, `dead band? and backlash; a useful method of derivative-network simulation is also outlined. The introduction of appropriate stabilising networks, to counteract system instabilities demonstrated by the computer study, is considered, and linear networks are employed in this application. The paper concludes with a brief review of the commissioning procedure and with an example of operational performance data.