Kolmogorov equation solution: multiple scattering expansion and photon statistics evolution modeling

• Autorzy: Guirao M. , Leble S.
• Języki publikacji: EN

Abstrakty

EN

We consider a formulation of the Cauchy problem for the Kolmogorov equation which corresponds to a localized source of particles to be scattered by a medium with a given scattering amplitude density. The multiple scattering ampl itudes are introduced and the corresponding series solution of the equation is constructed. We investigate the integral representation for the first series terms, its estimations and values of the photon number of finite and point receivers. Application to the LIDAR problem and X-ray beam scattering for orthogonal and inclined to a layer is considered.

Słowa kluczowe

EN

Kolmogorov equation; Fokker-Planck equation; multiple scattering expansion; photon statistics evolution; single scattering term; X-rays in beryl

PL

równanie Kołmogorowa; równanie Fokkera-Planka; pojedynczy termin rozpraszania

• Wydawca: Politechnika Gdańska
• Czasopismo: TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
• Rocznik: 2014
• Tom: Vol. 18, No 2
• Strony: 187--203
• Opis fizyczny: Bibliogr. 22 poz., rys., wykr., tab.

Twórcy

autor

Guirao M.

• Faculty of Applied Physics and Applied Mathematics Gdansk University of Technology Narutowicza 11/12, 80-223, Gdansk, Poland

autor

Leble S.

• Faculty of Applied Physics and Applied Mathematics Gdansk University of Technology Narutowicza 11/12, 80-223, Gdansk, Poland
• Immanuele Kant Baltic Federal University Al. Nevsky 41, Kaliningrad, Russia

Bibliografia

• [1] Compton A H 1923 Phil. Mag. 45 (270) 1121
• [2] Snigirev A, Kohn V, Snigireva I and Lengeler B 1996 Nature 384 49
• [3] Buzdin A and Leble S 1978 Boltzmann equation solution to lidar problem, Thesis Conference Lidar Probing, Tomsk
• [4] Kolomogorov A 1931 The Annals of Mathematics 104 415
• [5] Fokker A D 1914 Ann. der Phys. 43 810
• [6] Chang L-D and Waxman D 1985 J. Phys. C: Solid State Phys. 18 5873
• [7] Kunkel K E and Weinman J A 1976 J. Atmos. Sci. 33 1772
• [8] Mooradian G C, Geller M, Stotts L B, Stephens D H and Krautwald R A 1979 Applied Optics 18 429
• [9] Spinhirne J D 1979 Applied Optics 21 850
• [10] Kaul B V and Samokhvalov I V 1975 Double scattering approximation of the athmospheric laser location equation taking polarization effects into acount , Izv. VUZ Physics, 159 109
• [11] Miller S D and Stephens G L 1999 J. Geophys. Res. 104 22205
• [12] Buzdin A and Leble S 1980 A solution of LIDAR problem in double scattering approximation , Russian Institute for Scientific and Technical Information (VINITI), N2536-80dep 126
• [13] Kaul B and Samokhvalov I V V 2010 Atmospheric and Oceanic Optics 23 389
• [14] Uchaikin V V 2010 Long-Range Interaction, Stochasticity and Fractional Dynamics, Springer
• [15] Risken H 1989 The Fokker-Planck Equation. Methods of solutions and applications, Springer
• [16] Kolchuzhkin A M and Uchaikin V V 1978 Introduction into the Theory of Particle Penetration through a Matter , Atomizdat (in Russian)
• [17] Peng L M 1999 Electron atomic scattering factors and scattering potentials of crystals, Micron 30 625
• [18] Williams D B and Carter C B 2009 Transmission electron microscopy. A text book for material science , Springer
• [19] Guirao M and Leble S 2014 Modeling of X-ray attenuation via photon statistics evolution, arXiv:1412.0091
• [20] Prince E (ed.) 2004 International tables for crystallography, volume C, 3th edition, Springer
• [21] Kazarnovskii M V and Pafomov V E 1978 ZhETF 74 846
• [22] Pascucci A 2005 Progress in Nonlinear Differential Equations and Their Applications, Birkhauser Verlag