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  • 1
    Electronic Resource
    Electronic Resource
    A novel nonlinear car-following model (1998)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 8 (1998), S. 791-799 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The mathematical models used to describe the dynamical behavior of a group of road vehicles traveling in a single lane without overtaking are known as car-following models. These models are widely used in many commercially available microscopic traffic simulation software packages. They attempt to mimic the interactions between individual vehicles that are traveling sufficiently close together for the behavior of each vehicle to be dependent upon the motion of the vehicle immediately in front. In this paper we modify the traditional car-following model by adding a new nonlinear term to take account of the driver attempting to achieve a certain desired intervehicle separation distance as well as the traditional aim of matching the velocity of the vehicle ahead. Numerical solution of the resulting coupled system of nonlinear differential equations is used to analyze the stability of the equilibrium solution to a periodic perturbation. For certain parameter values chaotic oscillations are generated, consisting of a broad spectrum of frequency components. Such chaotic motion produces extremely complicated dynamical behavior that has an inherent lack of predictability associated with it. The results of simulating over a range of parameter values are presented and, where it is present, the degree of chaos is estimated. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166364
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  • 2
    Electronic Resource
    Electronic Resource
    A Particle Tracking Model for Non-Fickian Subsurface Diffusion (1998)
    Springer
    Mathematical geology 30 (1998), S. 695-716 
    Details
    ISSN: 1573-8868
    Keywords: non-Fickian diffusion ; numerical modeling ; particle tracking ; fractal geometry ; contamination
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract In this paper, a new particle tracking technique is described which can simulate non-Fickian diffusion within porous media. The technique employs fractional Brownian motions (fBms), a generalization of regular Brownian motion. These random fractal functions allow both super- and subdiffusive particle paths to be produced and hence non-Fickian diffusion of the resulting panicle clouds can be modeled. In recent years, fBm trace functions have been used by many authors to reproduce self-affine random fields to simulate various porous media properties. In contrast, a method is detailed herein which uses self-similar spatial fBm trajectories to simulate directly non-Fickian behavior of the particle clouds. Although fractal trajectories have been previously suggested as the basis for possible methods of modeling non-Fickian diffusion, the authors believe that this paper contains the first algorithm to be presented which does not require an a priori knowledge of the end condition of the random walk and, more importantly, allows both a definable scaling exponent and (fractal) diffusion coefficient to be specified. The resulting non-Fickian diffusion using the new algorithm is illustrated and some applications are discussed. The purpose of this paper is to bring the potential usefulness of fBm trajectories in simulating non-Fickian processes within homogeneous media to the attention of numerical modelers active in the simulation of subsurface diffusive processes. The method has a particular environmental application in the simulation of the non-Fickian dispersion of groundwater contaminants through porous media.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022395319141
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  • 3
    Electronic Resource
    Electronic Resource
    An Integrated Approach to Street Canyon Pollution Modelling (2000)
    Springer
    Environmental monitoring and assessment 65 (2000), S. 333-342 
    Details
    ISSN: 1573-2959
    Keywords: street canyon ; dispersion ; pollution concentration ; traffic microsimulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract An integrated method for the prediction of the spatial pollution distribution within a street canyon directly from a microscopic traffic simulation model is outlined. The traffic simulation package Paramics is used to model the flow of vehicles in realistic traffic conditions on a real road network. This produces details of the amount of pollutant produced by each vehicle at any given time. The authors calculate the dispersion of the pollutant using a particle tracking diffusion method which is superimposed on a known velocity and turbulence field. This paper shows how these individual components may be integrated to provide a practical street canyon pollution model. The resulting street canyon pollution model provides isoconcentrations of pollutant within the road topography.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006400406047
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  • 4
    Electronic Resource
    Electronic Resource
    A Nonlinear Temporal Headway Model of Traffic Dynamics (1998)
    Springer
    Nonlinear dynamics 16 (1998), S. 127-151 
    Details
    ISSN: 1573-269X
    Keywords: Car-following models ; nonlinear systems ; delay-differential equations ; chaos
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In order to describe the dynamics of a group of road vehicles travelling in a single lane, car-following models attempt to mimic the interactions between individual vehicles where the behaviour of each vehicle is dependent upon the motion of the vehicle immediately ahead. In this paper we investigate a modified car-following model which features a new nonlinear term which attempts to adjust the inter-vehicle spacing to a certain desired value. In contrast to our earlier work, a desired time separation between vehicles is used rather than simply being a constant desired distance. In addition, we extend our previous work to include a non-zero driver vehicle reaction time, thus producing a more realistic mathematical model of congested road traffic. Numerical solution of the resulting coupled system of nonlinear delay differential equations is used to analyse the stability of the equilibrium solution to a periodic perturbation. For certain parameter values the post-transient response is a chaotic (non-periodic) oscillations consisting of a broad spectrum of frequency components. Such chaotic motion leads to highly complex dynamical behaviour which is inherently unpredictable. The model is analysed over a range of parameter values and, in each case, the nature of the response is indicated. In the case of a chaotic solution, the degree of chaos is estimated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008279031113
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  • 5
    Electronic Resource
    Electronic Resource
    A non-Fickian, particle-tracking diffusion model based on fractional Brownian motion (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 1373-1384 
    Details
    ISSN: 0271-2091
    Keywords: particle tracking ; non-Fickian distribution ; fractional Brownian motion ; fractal ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The work is motivated by the recent discovery that ocean surface drifter trajectories contain fractal properties. This suggests that the dispersion of pollutants in coastal waters may also be described using fractal statistics. The paper describes the development of a fractional Brownian motion model for simulating pollutant dispersion using particle tracking. Numerical test cases are used to compare this new model with the results obtained from a traditional Gaussian particle-tracking model. The results seems to be significantly different, which may have implications for pollution modelling in the coastal zone. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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  • 6
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    Wavelet transforms and the ECG: a review (2005)
    Institute of Physics
    Details
    Publication Date: 2005-08-08
    Print ISSN: 0967-3334
    Electronic ISSN: 1361-6579
    Topics: Medicine , Physics
    Published by Institute of Physics
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  • 7
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    A novel nonlinear car-following model (1998)
    American Institute of Physics
    Details
    Publication Date: 1998-12-01
    Print ISSN: 1054-1500
    Electronic ISSN: 1089-7682
    Topics: Physics
    Published by American Institute of Physics
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  • 8
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    A novel time–frequency-based 3D Lissajous figure method and its application to the determination of oxygen saturation from the photoplethysmogram (2004)
    Institute of Physics
    Details
    Publication Date: 2004-10-09
    Print ISSN: 0957-0233
    Electronic ISSN: 1361-6501
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Published by Institute of Physics
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  • 9
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    Introduction to redundancy rules: the continuous wavelet transform comes of age (2018)
    The Royal Society
    Details
    Publication Date: 2018-07-09
    Description: Redundancy: it is a word heavy with connotations of lacking usefulness. I often hear that the rationale for not using the continuous wavelet transform (CWT)—even when it appears most appropriate for the problem at hand—is that it is ‘redundant’. Sometimes the conversation ends there, as if self-explanatory. However, in the context of the CWT, ‘redundant’ is not a pejorative term, it simply refers to a less compact form used to represent the information within the signal. The benefit of this new form—the CWT—is that it allows for intricate structural characteristics of the signal information to be made manifest within the transform space, where it can be more amenable to study: resolution over redundancy. Once the signal information is in CWT form, a range of powerful analysis methods can then be employed for its extraction, interpretation and/or manipulation. This theme issue is intended to provide the reader with an overview of the current state of the art of CWT analysis methods from across a wide range of numerate disciplines, including fluid dynamics, structural mechanics, geophysics, medicine, astronomy and finance. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.
    Print ISSN: 1364-503X
    Electronic ISSN: 1471-2962
    Topics: Mathematics , Physics , Technology
    Published by The Royal Society
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  • 10
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    Scale-Dependent Subsurface Dispersion: A Fractal-Based Stochastic Model (2001)
    American Society of Civil Engineers
    Details
    Publication Date: 2001-01-01
    Print ISSN: 1084-0699
    Electronic ISSN: 1943-5584
    Topics: Architecture, Civil Engineering, Surveying , Geography
    Published by American Society of Civil Engineers
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