A stochastic model of the evolution derived from elastic velocity process with mixed diffusion-jump characteristics

被引：6

作者：

Papiez, L

Tulovsky, V

机构：

[1] Indiana Univ, Med Ctr, Dept Radiat Oncol, Indianapolis, IN 46202 USA

[2] St Johns Univ, Div Math Comp & Nat Sci, Staten Isl, NY 10306 USA

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2002年 / 12卷 / 07期

关键词：

multiple scattering; phase space evolution; Boltzmann equation; small angle approximation;

D O I：

10.1142/S0218202502001969

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The phenomenon of phase spare evolution is modeled by the diffusional change in particles directions that is interrupted by independent collisions. Transition densities of stochastic process defined by this dynamical evolution are equivalent to solutions of a particular Boltzmann integro-differential equation. The general construction of solutions of this equation is developed. Specific methods of calculations of transition densities are detailed for the small angle approximation of the Boltzmann equation.

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收藏

页码：921 / 941

页数：21

相关论文

共 17 条

[1] SIMPLIFIED MONTE-CARLO SIMULATION OF ELASTIC ELECTRON-SCATTERING IN LIMITED MEDIA [J].

BARO, J ;

SEMPAU, J ;

FERNANDEZVAREA, JM ;

SALVAT, F .

NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION B-BEAM INTERACTIONS WITH MATERIALS AND ATOMS, 1994, 84 (04) :465-483

[2] A mathematical model for gamma ray transport in the cardiac region [J].

Belleni-Morante, A ;

Roach, GF .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 244 (02) :498-514

[3] Strategies of applied mathematics towards an immuno-mathematical theory on tumors and immune system interactions [J].

Bellomo, N ;

De Angelis, E .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 1998, 8 (08) :1403-1429

[4] Eternal solutions for a model of the Boltzmann equation [J].

Cabannes, H .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 1999, 9 (01) :127-137

[5] Modelling of the immune response: Conceptual frameworks and applications [J].

De Angelis, E ;

Mesin, L .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2001, 11 (09) :1609-1630

[6] MULTIPLE SCATTERING WITH ENERGY LOSS [J].

EYGES, L .

PHYSICAL REVIEW, 1948, 74 (10) :1534-1535

[7] The diffusion limit of transport equations derived from velocity-jump processes [J].

Hillen, T ;

Othmer, HG .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2000, 61 (03) :751-775

[8]

Karlin S., 1981, 2 COURSE STOCHASTIC

[9] MULTIPLE SCATTERING IN AN INFINITE MEDIUM [J].

LEWIS, HW .

PHYSICAL REVIEW, 1950, 78 (05) :526-529

[10] THE SEMICONTINUOUS BOLTZMANN-EQUATION - TOWARDS A MODEL FOR FLUID DYNAMIC APPLICATIONS [J].

LONGO, E ;

PREZIOSI, L ;

BELLOMO, N .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 1993, 3 (01) :65-93