__Keywords:__numerical simulation multiple scattering method Monte Carlo chaotically placed thick and thin cylinders

S. Y. Belonogov, V. G. Gavrilenko, G. V. Jandieri, V. G. Jandieri

This paper presents a research based on the Monte-Carlo method of the numerical simulation of multiple scattering for limited height objects chaotically placed on a horizontal plane. A point noncoherent emitter radiates uniformly in the horizontal plane and in the set of angles in the vertical plane. The corpuscular model of the radiation field is used for the numerical simulation. As a method of the numerical modeling the Monte-Carlo method has been chosen. The modeling has resulted in finding out the dependence of energy density and an angular spectrum of capacity at various positions of the transmitter and at the supervision point. The scattering properties of the objects are set with unitary scatter indicatrix in the horizontal and vertical planes.
The first part of the research is devoted to the case of the vertical opaque circular cylinders whose radius considerably surpasses an extending wave length. The indicatrix in the horizontal plane according to the law of mirror reflection is proportional to sin( /2). The is an azimuthal angle of scattering counted off the distribution direction of the falling plane wave. The absorption in the Monte-Carlo method is considered by way of the introduction of the reflection coefficient from the cylinders. The given case is compared to the results received for the statistical model of city building described in works by T.A.Ponomaryova, A.N.Kulikova and E.D.Telpuhovsky. The selection of modeling parameters was carried out according to radiation distribution in typical city conditions. We investigated the pattern of radiation distribution for the source lifted over the area scatter , and also a case when the source is located in the area containing scatter at any position of the receiver.
The second part of the research deals with the case when the diameter of the vertical cylinders chaotically located on a plane is much less than the wave length. Indicatrix in the horizontal plane of dispersion is chosen to be isotropic. The reflection coefficient from the large objects acts now as the albedo of a separate scatter. The receiver and transmitter location and the modeling parameters are chosen in the same way as in the case of the dispersion on large objects. The comparison of the results received in both cases is carried out and the basic laws are received.
The present research results in the fact, that the cases of application of Monte-Carlo statistical modeling method give the possibility to successfully analyze the basic average characteristics of the waves disseminated on objects chaotically located in a plane. The model offered in the present research corresponds to the description of wave fields within the theory of radiation transfer. It is shown, that in the cases when it is possible to be limited to unitary reflected waves extending under small angles to the spreading surface, the result of the numerical calculation corresponds to the result received in the model of city building described in the article by T.A.Ponomaryova, A.N.Kulikova and E.D.Telpuhovsky using the analytical approximation method. The advantage of the offered algorithm consists in the fact that it allows to calculate the effect of the repeated dispersion and to analyze the average field characteristics depending on the source position and the supervision point within a wide range.

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