scholarly journals On the Interpretation of the Doppler Spectra of Ionospherically Propagated Ground Backscatter Echoes

1975 ◽  
Vol 28 (5) ◽  
pp. 575
Author(s):  
JA Bennett
Keyword(s):  
Simple Model ◽  
Acoustic Wave ◽  
Group Velocity ◽  
Realistic Model ◽  
Directional Antennas ◽  
Doppler Spectrum ◽  
Sea Waves ◽  
Dispersive Waves ◽  
Time Changes ◽  
The Way

The mechanism giVing rise to the backscatter Doppler spectrum is discussed by means of a simple model. Attention is focused on the effect of movement of the region contributing to the echo which arises from time changes in the group velocity within the ionosphere. It is shown that the influence of these changes on the spectrum can be separated into two parts: (1) A change in the maximum possible width of the spectrum as a result of the change of the time for which an indiVidual scatterer is contributing to the echo; this effect is independent of the scatterer distribution. (2) A possible narrowing of the spectrum as a result of the way in which the signals from individual scatterers combine; this effect depends upon scatterer distribution. Scatter from a fixed'scattering surface and from dispersive waves (e.g. sea waves) is considered. A tentative extrapolation of the results to a more realistic model suggests that neither effect is likely to be significant in practical highfrequency radio experiments (except at short ranges with highly directional antennas), although they may be significant in acoustic wave simulations of the radio case.

Weakly nonlinear dispersive waves: group velocity

1982 ◽  
Vol 27 (3) ◽  
pp. 507-514
Author(s):  
Bhimsen K. Shivamoggi
Keyword(s):  
Group Velocity ◽  
Acoustic Waves ◽  
Specific Problem ◽  
Electron Plasma ◽  
Hot Electron ◽  
Ion Acoustic Waves ◽  
Dispersive Waves ◽  
Weakly Nonlinear ◽  
Longitudinal Waves ◽  
Wave Trains

For slowly varying wave trains in a linear system, it is known that a quantity proportional to the square of the amplitude propagates with the group velocity. It is shown here, by considering a specific problem of longitudinal waves in a hot electron-plasma and using an asymptotic analysis, that this result continues to be valid even when weak nonlinearities are introduced into the system provided they produce slowly varying wave trains. The method of analysis fails, however, for weakly nonlinear ion-acoustic waves.

Control Theory, Delays and Driving an Automobile

2005 ◽  
Vol 33 (2) ◽  
pp. 93-109 ◽  
Author(s):  
Shlomo Engelberg
Keyword(s):  
Reaction Time ◽  
Simple Model ◽  
Transfer Function ◽  
Critical Parameter ◽  
Complete System ◽  
Realistic Model ◽  
Low Frequencies ◽  
Reasonable Approximation ◽  
Phase Lead ◽  
Reasonable Choice

A simple model of the driver—automobile system is developed and several reasonable candidates for the transfer function of the human ‘controller’ are studied. The model is used to examine the controller candidates. The complete system is analysed both analytically and through simulations. It is found that a delay followed by a phase-lead controller is a reasonable choice for the transfer function that the human ‘controller’ implements. The model developed is compared with a more realistic model and is seen to be a reasonable approximation of the realistic model at low frequencies. Reaction time is shown to be a critical parameter in understanding the dynamics of the driver—automobile system.

scholarly journals Response to a Steady Poleward Outflow. Part II: Oscillations and Eddies

2009 ◽  
Vol 39 (7) ◽  
pp. 1551-1573 ◽  
Author(s):  
Theodore S. Durland ◽  
Michael A. Spall ◽  
Joseph Pedlosky
Keyword(s):  
Simple Model ◽  
Prediction Model ◽  
Group Velocity ◽  
Adjustment Process ◽  
Linear Dynamics ◽  
Velocity Response ◽  
Eddy Field ◽  
Zero Group

Abstract A conceptually simple model is presented for predicting the amplitude and periodicity of eddies generated by a steady poleward outflow in a 1½-layer β-plane formulation. The prediction model is rooted in linear quasigeostrophic dynamics but is capable of predicting the amplitude of the β plume generated by outflows in the nonlinear range. Oscillations in the plume amplitude are seen to represent a near-zero group velocity response to an adjustment process that can be traced back to linear dynamics. When the plume-amplitude oscillations become large enough so that the coherent β plume is replaced by a robust eddy field, the eddy amplitude is still constrained by the plume-amplitude prediction model. The eddy periodicity remains close to that of the predictable, near-zero group-velocity linear oscillations. Striking similarities between the patterns of variability in the model and observations south of Indonesia’s Lombok Strait suggest that the processes investigated in this study may play an important role in the generation of the observed eddy field of the Indo-Australian Basin.

Ray equations in retarded Snell midpoint coordinates

Geophysics ◽  
1984 ◽  
Vol 49 (12) ◽  
pp. 2100-2108
Author(s):  
Alfonso González‐Serrano ◽  
Mathew J. Yedlin
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Group Velocity ◽  
High Frequency ◽  
Frame Of Reference ◽  
Velocity Analysis ◽  
Acoustic Wave Equation ◽  
Arbitrary Angle ◽  
Frequency Limit ◽  
Velocity Function

Group velocity (ray) equations describe the dynamic behavior of wave‐equation extrapolators in the high‐frequency limit. They are found in general from the dispersion relation of an arbitrary acoustic wave equation. Wave‐equation operators require a background extrapolation velocity. As an application of the group velocity equations, a sensitivity analysis to the background‐operator velocity illustrates the trade‐off between uncertainty in velocity and precision in imaging. Exact wave extrapolators are most useful when the exact velocity function is known. Wave‐equation imaging for velocity analysis in Snell midpoint coordinates requires velocity‐insensitive extrapolation operators. In this frame of reference, approximations of the exact acoustic wave equation are referenced to an arbitrary angle of propagation. Group velocity equations show that in Snell midpoint coordinates, using wide‐reference propagation angles, the fifteen‐degree wave equation gives satisfactory velocity‐independent images. The forty‐five degree wave equation does not appreciably improve the image.

Effects of directional antennas at the base station on the Doppler spectrum

1997 ◽  
Vol 1 (2) ◽  
pp. 40-42 ◽  
Author(s):  
P. Petrus ◽  
J.H. Reed ◽  
T.S. Rappaport
Keyword(s):  
Directional Antennas ◽  
Base Station ◽  
Doppler Spectrum

scholarly journals Slepian models for the stochastic shape of individual Lagrange sea waves

2006 ◽  
Vol 38 (02) ◽  
pp. 430-450 ◽  
Author(s):  
Georg Lindgren
Keyword(s):  
Water Waves ◽  
Gaussian Model ◽  
Wave Model ◽  
Realistic Model ◽  
Offshore Structures ◽  
Sea Waves ◽  
Vertical Movements ◽  
Stochastic Version ◽  
Physically Based ◽  
Gaussian Theory

Gaussian wave models have been successfully used since the early 1950s to describe the development of random sea waves, particularly as input to dynamic simulation of the safety of ships and offshore structures. A drawback of the Gaussian model is that it produces stochastically symmetric waves, which is an unrealistic feature and can lead to unconservative safety estimates. The Gaussian model describes the height of the sea surface at each point as a function of time and space. The Lagrange wave model describes the horizontal and vertical movements of individual water particles as functions of time and original location. This model is physically based, and a stochastic version has recently been advocated as a realistic model for asymmetric water waves. Since the stochastic Lagrange model treats both the vertical and the horizontal movements as Gaussian processes, it can be analysed using methods from the Gaussian theory. In this paper we present an analysis of the stochastic properties of the first-order stochastic Lagrange waves model, both as functions of time and as functions of space. A Slepian model for the description of the random shape of individual waves is also presented and analysed.

Growing a vocabulary

2007 ◽  
Vol 7 ◽  
pp. 49-65 ◽  
Author(s):  
Paul Meara
Keyword(s):  
Network Structure ◽  
Boolean Network ◽  
Network Models ◽  
Realistic Model ◽  
New Words ◽  
Parameter Values ◽  
The Way

This paper describes how simple Boolean Network models can be adapted to explore the way a vocabulary network might grow. The models described have two main parameters — a New Word parameter, which determines the rate at which new words are added to the lexicon, and an independent New Link parameter, which determines the rate at which links form between words. Delaying the application of the New Link parameter by a small amount allows a core of words to establish itself. With these very simple assumptions, a network structure with some of the features of real lexicons can grow itself.  The paper describes how the parameter values interact, and how the size of the initial core affects the way the lexicon grows. The paper also speculates about how a more realistic model of lexical growth might be constructed by making the basic processes in the models slightly more complex.

Operating High-Occupancy Vehicle Lanes: Issues for Consideration

2000 ◽  
Vol 1711 (1) ◽  
pp. 6-12 ◽  
Author(s):  
Jon Obenberger ◽  
Bob Rupert
Keyword(s):  
Performance Monitoring ◽  
Monitoring And Evaluation ◽  
Federal Aid ◽  
Performance Expectations ◽  
Operational Change ◽  
And Performance ◽  
Time Changes ◽  
High Occupancy Vehicle Lanes ◽  
Relevant Factors ◽  
The Way

A commitment to proactively manage, operate, and provide the necessary services for support of a high-occupancy vehicle (HOV) system is needed so that all HOV facilities can meet intended objectives and performance expectations. This operational focus should be integrated into all phases of an HOV system, from the strategic system planning through the ongoing performance monitoring and evaluation of specific facilities. The ongoing performance monitoring and evaluation of HOV facilities should be the basis for making continuous incremental changes in the way the system is managed, the way facilities are operated, and the way that support programs and services are utilized. HOV facilities are not appropriate in every location, and conditions change over time. Changes may warrant continuous adjustments or significant revisions in HOV facility operation. Before proposal of any significant changes in operation, all relevant factors, interests, alternatives, and associated impacts should be considered and analyzed in detail. These operational alternatives should include incremental revisions to improve the performance of the HOV system or specific facilities. Significant operational changes should be considered only after all possible incremental adjustments have been made to improve the performance of the existing HOV lane. In accepting federal aid, agencies have agreed to manage, operate, and maintain HOV facilities as they were originally planned, designed, constructed, and approved. Situations in which a federal review of operational changes to HOV facilities is required, the information needed to support such a review, and the existing federal requirements against which this review will be completed are identified. A review of the important issues and possible impacts resulting from any significant operational change is needed so as to determine whether federal approval is required and to assure consistency with the federal aid program provisions of 23 U.S.C. and 49 U.S.C.

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