Analytical solutions of the radiative transport equation

2022 Fiscal Year Final Research Report

• Project/Area Number: 17K05572
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Hamamatsu University School of Medicine
• Principal Investigator: Machida Manabu 浜松医科大学, 光尖端医学教育研究センター, 指定講師 (40396916)
• Project Period (FY): 2017-04-01 – 2023-03-31
• Keywords: 輻射輸送方程式 / 線型ボルツマン輸送 / 光トモグラフィー

Outline of Final Research Achievements

A numerical method for the radiative transport equation using analytical solutions was proposed. In addition, a novel radiative transport equations with fractional-order time derivatives was studied. Furthermore, we revealed that the radiative transport equation is the governing equation for the transport of molecules in water which move in porous media. Related inverse problems were studied. A numerical method with random numbers was proposed for optical tomography. A numerical method was developed for measurements in the spatial frequency domain. In the former, the problem was reduced to an inverse problem for the diffusion equation by the diffusion approximation. In the latter, by using analytical solutions, we created a numerical method for the inverse problem of determining coefficients of the radiative transport equation. Parameter estimation was done using the radiative transport equation.

Free Research Field

物理応用数学

Academic Significance and Societal Importance of the Research Achievements

多孔質媒体中の分子輸送の支配方程式が輻射輸送方程式であることが明らかになったが、この研究は土壌汚染の問題などに波及効果がある。光トモグラフィーにおいて、輻射輸送方程式の利用は困難であるとされており、拡散近似によって得られる拡散方程式の逆問題として定式化される。今回、解析解を利用することにより輻射輸送方程式の高速な数値手法が確立し、それを用いた逆問題の解法の開発も行った。これにより、光トモグラフィーの分野に新たな展開が期待できる。