One-dimensional Linear Model Research Articles

Evaluation and Prediction of Blade-Passing Frequency Noise Generated by a Centrifugal Blower

The blade-passing frequency noise, abbreviated to BPF noise, of a low-specific-speed centrifugal blower is analyzed by separating the frequency response of the transmission passage and the intensity of the noise source. Frequency response has previously been evaluated by the authors using a one-dimensional linear wave model, and the results have agreed well with the experimental response in a practical range of the blower speed. In the present study, the intensity of the noise source is estimated by introducing the quasi-steady model of the blade wake impingement on the scroll surface. The effective location of the noise source is determined by analyzing the cross-correlation between measured data of the blower suction noise and pressure fluctuation on the scroll surface. Then, the surface density distribution of a dipole noise source is determined from pressure fluctuation expressed in terms of quasi-steady dynamic pressure of the traveling blade wake. Finally, the free-field noise level is predicted by integrating the density spectrum of the noise source over the effective source area. The sound pressure level of the blower suction noise is easily predicted by multiplying the free-field noise level by the frequency-response characteristics of the noise transmission passage.

Normal mode initialization for simple models

The normal mode initialization procedures of Phillips (1960) and Temperton (1988) are re-examined and applied to one-dimensional linear and non-linear primitive equations models. The linear method is obtained by setting the first and second substantial time derivatives of the divergence to zero. The resulting state is free of gravity waves. In the non-linear procedure, the substantial time derivatives calculated from the model equations of the gravitational modes are set to zero by implicitly adjusting these modes only. Five-day numerical integrations are performed using both models. The results clearly show the importance of proper initialization. Analytical solutions support the numerical results.

Phonon dispersion in quasiperiodic semiconductor superlattices

The phonon spectra of unstrained and strained quasiperiodic semiconductor superlattices (QSSL) have been calculated using one-dimensional linear chain model. We consider two types of quasiperiodic systems, namely cantor triadic bar (CTB) and Fibonacci sequences (FS), constituting of AlAs, GaAs and GaSb of which the latter two have a lattice mismatch of about 7%. The calculations have been made using transfer matrix method and also with and without the inclusion of strain. We present the results on phonon spectra of two component CTB and two as well as three component FS semiconductor superlattices (SSL), thickness and order dependence on LO mode of GaAs, effect of strain on LO frequency of GaAs. The calculated results show that the strain generated due to lattice mismatch reduces significantly the magnitudes of the confined optical phonon frequency of GaAs.

One-Dimensional Analytical Constant Parameter Linear Electromagnetic-Magnetomechanical Models of a Cylindrical Magnetostrictive (Terfenol-D) Transducer

A method is presented for including motional and eddy current effects when analytically modeling electrical impedance functions of cylindrical magnetostrictive transducers. To approximate eddy current effects, onedimensional analytical constant parameter linear electromagnetic models of a cylindrical magnetostrictive transducer are developed. Maxwell's equations are solved for the magnetic field strength as a function of radial position. Closed form expressions for magnetic flux as a function of radial position are then derived, from which transducer electrical impedance functions are formulated. Two different physical models of the transducer are considered. The first model results in the classic eddy current solution for a rod in a wound wire solenoid. The second physical model includes the effects of a conducting external cylindrical housing. Motional effects are incorporated into the electromagnetic models via the magnetomechanical model, which is a frequency and load dependent, complex valued expression for the "dynamic magnetic permeability" of the magnetostrictive material within the transducer. The functional form for this dynamic magnetic permeability is derived by comparing the transduction equations for the magnetostrictive material with those for the transducer containing the material. Electrical impedance functions for both physical models are compared with an experimental measurement for a particular magnetostrictive transducer (using Terfenol-D) in its low signal linear range of operation. The second physical model was found to offer the better simulation of the experimental measurement of the transducer's electrical impedance, with errors in magnitude or phase of less than + 5% for excitation frequencies between 100 and 10,000 Hz (the asrun mechanical resonant frequency was 8800 Hz). Experience has shown that measured material parameters typically yield simulations of electrical impedance functions within i 10%. Predictions of electrical impedance functions for Terfenol-D transducers, calculated based on estimated or published Terfenol-D parameters, can be in error by well over 40%. Thus, the accuracy of model results seem to be controlled primarily by the accuracy with which magnetostrictive material parameters are known.

Effect of strain on vibrational modes in strained layer superlattices

We have investigated the lattice vibrational properties of a two-component strained layer semiconductor superlattice (GaAs)n1 (GaSb)n2 using a one-dimensional linear chain model and transfer matrix method [1]. Effect of strain, arising due to the lattice mismatch (∼ 7%) has been considered explicitly in the equation of motion. We show for the first time that the optical vibrational frequency increases (in the case of (GaAs)4 (GaSb)n) or decreases (in the case of (GaAs)n(GaSb)4) with increase of layer thicknessn, in either type of superlattices. Raman scattering measurements on some other similar systems support our findings.

The Lagged Innovation Covariance: A Performance Diagnostic for Atmospheric Data Assimilation

Abstract The goal of atmospheric data assimilation is to determine the most accurate representation of the signal from the available observations. The optimality of a data assimilation scheme measures how much information has been extracted from the observations. It is possible to quantify the optimality of the scheme using on-line performance diagnostics. Such a diagnostic is the proposed lagged innovation covariance procedure. This diagnostic has been developed from Kalman filter theory. Its characteristics are examined using a simple scalar model, a univariate one-dimensional linear advection model, and a linear quasigeostrophic model. The model results are compared with actual lagged innovation covariances derived from the innovation sequences of an operational data assimilation system.

Waterflood simulation of stratified sandstone reservoirs using dynamic pseudo curves

Many studies have shown that pseudo relative permeability curves can be used in one-dimensional (1-D) linear models to successfully match simulation performance of two-dimensional (2-D) cross-sectional models. Additional studies have shown that pseudo relative permeability curves can be used in 2-D areal models to match 3-D model performance. The techniques, however, used in the latter studies were laborious and complex and often required multiple sets of pseudo relative permeability curves. This study shows that a 2-D areal model that uses only one set of pseudo relative permeability curves (generated from a cross-sectional model) allows accurate simulation of waterflood performance for highly stratified reservoirs that would otherwise require 3-D simulation or 2-D simulation with multiple sets of curves. The cases examined are waterfloods in reservoirs with repeating 5-spot patterns for several sandstone stratifications from beach, fluvial channel, and delta margin environments of deposition. Reservoir simulation in this study makes use of lab-derived capillary pressure curves and the method of Jacks et al. to compute pseudo relative permeability curves. Gravity numbers were developed to characterize cross-sectional and 5-spot (areal) displacements. These gravity numbers were correlated for several geological stratifications to minimize the need for iterative simulations of each particular cross-sectional model to obtain pseudo relative permeability curves. Two of these correlations were applied to field cases to demonstrate their utility.

Linear and nonlinear one-dimensional models of pulse wave transmission at high Womersley numbers

The accuracy of nonlinear and linear one-dimensional models in describing pulse wave propagation in a uniform cylindrical viscoelastic tube, with Womersley's parameter α equal to 7.6 at 1 Hz, was evaluated. To this end calculations of wave propagation using these models were compared with the experimentally determined propagation of the pressure wave in the tube. The experimentally generated pressure pulse had an amplitude of 9.0 kPa and caused a relative radius change of about 17%. The static pressure vs cross-sectional area relation was found to be nonlinear for these pressure changes. Maximum fluid velocity was about 2.9 m s −1, while the phase velocity was about 5.4 m s −1. The radius change and the ratio of fluid and phase velocities violated the linear model assumptions. The nonlinear model with viscous fluid friction modelled on the basis of Poiseuille's law and treating the tube wall as purely elastic, underestimated the damping of the pulse wave and predicted the formation of shock waves, which were not found experimentally. In the linear models, the viscous friction of the blood was modelled according to either Poiseuille's law or Womersley's theory and the tube wall was treated as either linearly elastic or linearly viscoelastic. A description of the viscous friction of the blood based on Poiseuille's law underestimated damping. Disregarding the viscoelasticity of the tube wall resulted in an underestimation of both phase velocity and damping. In spite of the nonlinearity of the system, the linear viscoelastic Womersley model described the pulse wave propagation satisfactorily.

Linear propagation of pulsatile waves in viscoelastic tubes

An experimental and theoretical analysis is made of pulsatile wave propagation in deformable latex tubes as a model of the propagation of pressure pulses in arteries. A quasi one-dimensional linear model is used in which, in particular, attention is paid to the viscous phenomena in fluid and tube wall. The agreement between experimental and theoretical results is satisfactory. It appeared that the viscoelastic behaviour of the tube wall dominates the damping of the pressure pulse. Several linear models are used to describe the wall behaviour. No significant differences between the results of these models were found.

The alternating group explicit (AGE) matrix iterative method

It is well known that iterative methods, utilizing the great speed of modern computers, are extensively used in large-scale computations for solving matrix equations which arise from finite difference approxmations to elliptic partial differential equations. The object of this paper is to introduce a new explicit iterative method suitable for parallel computation for the solution of the associated matrix equations and compare its performance with existing methods (Jacobi, successive over-relaxation). It is hoped that numerical experiments on the simple one-dimensional linear model and its extensions to multi-dimensional problems will serve as an indication of the power of the new (AGE) matrix iterative method.

Electrohydrodynamic instabilities in nematic liquid crystals under dichotomous parametric modulation

The onset of EHD instabilities in nematic liquid crystals driven by parametric modulation is investigated starting with the one-dimensional linear model of Dubois-Violette. The superposition of a constant electric field with a dichotomous (stochastic or periodic) field as well as the superposition of two dichotomous stochastic fields (pregaussian noise) are considered in detail. The experimentally observed discontinuous behaviour of the threshold (direct transition towards chaos) above a critical strength of the driving field and the dependence of the threshold curve on the correlation time of the noise can be explained qualitatively. Experiments to complete the phase diagram are proposed.

A spectral multidomain method for the solution of hyperbolic systems

A multidomain Chebyshev spectral collocation method for solving hyperbolic partial differential equations has been developed. Though spectral methods are global methods, an attractive idea is to break a computational domain into several subdomains, and a way to handle the interfaces is described. The multidomain approach offers advantages over the use of a single Chebyshev grid. It allows complex geometries to be covered, and local refinement can be used to resolve important features. For steady-state problems it reduces the stiffness associated with the use of explicit time integration as a relaxation scheme. Furthermore, the proposed method remains spectrally accurate. Results showing performance of the method on one-dimensional linear models and one- and two-dimensional nonlinear gas-dynamics problems are presented.

Stiffness characteristic and the applications of the method of lines on nonuniform grids

The method of lines is investigated for the numerical solution of the stream-function-and-vorticity form of the Navier-Stokes equations on nonuniform grids. Stiffness characteristics of a linear one-dimensional model equation are examined to establish the feasibility of applying the method to the vorticity equation in two dimensions. The governing equations are transformed from the physical domain with a highly variable grid to a computational domain with a uniform grid. The method of lines is used to solve only the vorticity equation, and the successive-over relaxation technique is used to solve the stream-function equation. It is observed that the transformed governing equations become stiffer with increased concentration of grid points and also as the number of grid points increases. It is also observed that the differencing technique affects the stiffness characteristics. The use of forward differencing is not feasible, and backward differencing is preferable to central differencing for high Reynolds numbers. The results of specific applications for the solution of flow in curved-wall diffusers and a driven cavity demonstrate that the method of lines under certain circumstances is feasible for the numerical solution of physical problems on domains covered with variable grids.

One-dimensional linear and logistic harvesting models

Some of the results in the literature on simple one-dimensional, density-dependent, discrete and continuous models—with and without harvesting—are reviewed. Both deterministic and stochastic models are included. Some comparisons of the various models are made, and the results are discussed in terms of their ramifications in population model building.

Pressure and flow pulses in viscoelastic arterial models with reflection sites

Herein we develop a linear one-dimensional model for impulse propagation in fluidfilled tubes. Area changes are related to pressure changes by means of convolution integrals of the creep or relaxation function for the tube wall material. The model is employed to study the propagation of pressure and flow pulses along initially uniform tubes and their subsequent interaction with various junctions characteristic of the arterial system.

Application of pseudo relative permeability curves to the simulation of stratified waterflooding.

This paper presents a discussion on the validity of approximating a two-dimensional cross sectional reservoir model by a one-dimensional linear model using two kinds of pseudo relative permeability curves. The study assumes the negligibility of gravity and capillary effects as compared with the viscous force effect. Also investigated are effects of (1) injection rate and (2) the size of a reservoir on the degree of the agreement among the calculated results. Producing water cut performance versus cumulative oil production, which are calculated by the one-dimensional simulation using pseudo functions, are compared with those computed by the two-dimensional simulation. Consequently, some insights are obtained as to the relation between the size of a reservoir and the degree of crossflow. The validity of approximating cross sectional reservoir simulation by one-dimensional simulation suggests possible manipulation of three-dimensional simulation by using a two-dimensional areal simulation model, which could reduce data preparation time and computation cost. Finally, the present method applied to a real reservoir demonstrates that a one-dimensional linear model using dynamic pseudo relative permeability curves can well approximate the water cut performance of the two-dimensional cross sectional simulation.

円筒状リニアインダクションモータの推力特性とその構成法

A design method of the cylindrical linear induction motor (abbr. C-LIM) is mentioned in this paper. An analysis method of electromagnetic characteristics of the C-LIM is developed by the onedimensional linear current model. In the case of 2 phase 2 coils C-LIM, it is difficult to use the railway LIM analysis method because its ratio of slot width/core width is different from the C-LIM's. And performing experiments about actual motors, frequency-force characteristics are obtained respect to some values of secondary surface resistivity. From these studies following results are obtained:(1) From the analysis model, flux distribution and sliding force expressions are derived by dividing input current distributions into 4 regions. (2) The equivalent magnetic gap for a slider-stator gap is estimated using the finite element method and equivalent electric circuit. (3) Difference between calculation values and experimental values of frequency-force characteristics is about 10%. (4) It is shown that the maximum starting force is obtained from the suitable polepitch, secondary surface resistivity, frequency, and equivalent magnetic gap, and C-LIM can be designed as a servomotor by taking those suitable motor parameters for the maximum starting force.

Oil spills in a river: a one-dimensional model / Les masses de pétrole déversées dans une rivère: modèle à une dimension

Abstract A linear one-dimensional model is proposed to describe the river pollution resulting from oil spills. Two interacting migratory forms, water surface pollution and water body pollution, are considered. In the coordinate system moving with the mean flow velocity, the equations for the pollutant distributions are reduced to the type of a heat conduction equation with distributed unsteady sources. The solutions for oil concentrations, obtained in the form of the ‘heat potential’ are considered in two particular cases: (a) an oil spill in an open channel; (b) river pollution from drifting ice due to the melting of polluted ice.

Estimability of linear parametric functions in a one-dimensional linear model with restrictions

The problem of estimability of the vector Cξ in the general linear model Ey=Xξ is discussed. It is assumed that the vector of parameters ξ is a linear manifold Ω given by Rξ=s, where the matrix R and the vector s are known. The vector Cξ is estimable if there exist matrices L and M such that ELy+Ms=Cξ for all ξ in Ω. Using the results of a paper by the authors [62046 above], necessary and sufficient conditions for estimability are presented with short and elegant proofs.

Direct Gravitational Driving and Tidal Energy Balance in Elongated Gulfs

Abstract Separation of oceanic and gravitational tidal driving in a linear one-dimensional model of an elongated gulf yields explicit expressions for the time-averaged energy equation. Tidal behavior is shown to depend on the interplay of four parameters: geometry, friction, and relative strength and phase of gravitational versus oceanic driving. In spite of its simplicity, the model accounts well for the various energy features of tides in the Adriatic Sea and the Gulf of California.