Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

Frank, T. D.

doi:10.1016/j.physa.2007.10.027

Cited by 8 publications

(6 citation statements)

References 42 publications

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“…The main idea is based on the distribution theory of the potential source, where the distribution of the vehicles on the high ways can be replace by a concentric source with a specific boundary conditions different ODE and PDE with a boundary condition [3]- [5], giving us the distribution of vehicles on the roads. This Green function is used as a integral kernel for solving the non-linear PDE of the LWR model [3]- [5].…”

Section: Green Function Methodsmentioning

confidence: 99%

“…This Green function is used as a integral kernel for solving the non-linear PDE of the LWR model [3]- [5]. We look for a solution of the PDE presenting our distributed parameter process for obtaining the transfer function (6-7) and to apply it in the automation system using different control strategies, which depends on the road network and the real situation on it.…”

Section: Green Function Methodsmentioning

confidence: 99%

“…, : (5) Moreover to solve the PDE by the Green function [10], [18], based on the inverse Laplace (Fourier) transform "I.L(F).T." and based on the Hadamard variation formula.…”

Section: Green Function Methodsmentioning

confidence: 99%

“…For the LWR model we have (12) [1]- [5] The Green function G, presents the inverse of the operator and the source convolution. In this way, moreover we can say that the convolution product present the Fourier transform of the function.…”

Section: Exemple Of Lwr Traffic Model Solution and Simulation Analysismentioning

confidence: 99%

“…For solving the PDE presenting the analytically the traffic flow model we use analytical method of exact solution of the PDE called Green function. This method is based on the integral kernel changing of the differentials equations in algebraic equations and translating the phenomenon of the distribution of vehicles on the high ways [4], [5], [12]. Looking from the automation point of view we can see that all the parameters in the system presenting the traffic flow transportation are variable and are related of the road length, the speed of conduction and the momentum density.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Green function analytical method of solution of transport equation

Uzunova

Jolly

Nikolov

et al. 2008

Proceedings of the 5th International Conference on Soft Computing as Transdisciplinary Science and Technology - CSTST '08

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The main aim of this paper is using the obtain transfer function of the macroscopic traffic flow model, as distributed parameter system, to simulate this model ( fig.1), then based on the obtain results characteristics to make analysis and for further works to use all this simulations for the synthesis and analysis of corresponding control algorithms depending of the needed conditions in transportation problem model. Using this exact method we obtain directly the plant transfer function for the traffic flow model viewed as a distributed parameter system. The entire physical phenomenon is presenting through the partial differential equations whose show the distribution in vehicles on the high ways. All the research is devoted on the transfer function result and his control system model. In the presenting paper we shown the verification of the analytical result of the model simulation thought the time and frequency characteristics analysis.

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Section: Green Function Methodsmentioning

confidence: 99%

Section: Green Function Methodsmentioning

confidence: 99%

“…, : (5) Moreover to solve the PDE by the Green function [10], [18], based on the inverse Laplace (Fourier) transform "I.L(F).T." and based on the Hadamard variation formula.…”

Section: Green Function Methodsmentioning

confidence: 99%

Section: Exemple Of Lwr Traffic Model Solution and Simulation Analysismentioning

confidence: 99%