Results 251 to 260 of about 3,316,591 (299)

Basic Equations for Radiative Transfer

2020
A light-ray (a bundle of photons) travels through and interacts with gaseous materials, via emission, absorption, and scattering. The intensity of a light-ray obeys a linear integro-differential equation, the so-called radiative transfer equation, which is just the Boltzmann equation for photons.
Shoji Kato, Jun Fukue
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Transfer equation in accelerated media

Physical Review D, 1986
The transfer equation for photons is obtained from the Lindquist formalism in curvilinear coordinates (no symmetry assumed), in an arbitrary frame and in any basis (natural or physical), to first order in O(v/c). Acceleration terms in the fluid are introduced via a modification of the metric tensor.
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Energy transfer for the Burgers’ equation

The Physics of Fluids, 1978
The Burgers’ equation is considered as a simple nonlinear model equation in which to investigate energy transfer in the wavenumber domain. Spatially stationary (on the real line) random solutions are considered. The first-order nonlinear term for large time relating the spectrum and bispectrum (Fourier transform of third-order moments) of the random ...
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Equations of transfer in non-local media

International Journal of Heat and Mass Transfer, 1994
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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An Equation for Transference Numbers

The Journal of Chemical Physics, 1938
The following transference number equation is proposed, 1/t=1/t0+AC12−BC.The values for the constant A are in accord with the Onsager theory for most uni-univalent electrolytes in water, but not for abnormal salts, such as silver nitrate, or for higher valence salts. However, the transference equation appears to have quite general applicability.
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Validity conditions for the radiative transfer equation

Journal of the Optical Society of America A, 2003
We compare the radiative transfer equation for media with constant refractive index with the radiative transfer equation for media with spatially varying refractive indices [J. Opt. A Pure App. Opt. 1, L1 (1999)] and obtain approximate conditions under which the former equation is accurate for modeling light propagation in scattering media with ...
Luis, Martí-López, Jorge, Bouza-Domínguez, Jeremy C, Hebden, Simon R, Arridge, René A, Martínez-Celorio   +4 more
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Fixed Poles in Transfer Function Equations

SIAM Journal on Control and Optimization, 1988
The objective of the paper is the pole structure study of solutions in a module theoretic framework, employing the notions of pole module and zero module of a linear transfer function. The paper supplies a complete description of the pole structure. The basic result in this setting is that there is an ``essential'' pole structure which appears in every
Conte, G., Perdon, A. M., Wyman, B. F.
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Heat-Transfer Equations

2009
Abstract This article is a comprehensive collection of formulas, tables, and analytical solutions, addressing hundreds of heat-transfer scenarios encountered in science and engineering. It also demonstrates how to set up and solve real-world problems, while accounting for material properties, environmental variables, boundary and state ...
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The rosseland approximation for the radiative transfer equations

Communications on Pure and Applied Mathematics, 1987
The radiative transfer system of equations for unknown functions \(u^{\epsilon}=u^{\epsilon}(x,\Omega,\nu)\), \(T^{\epsilon}=T^{\epsilon}(x)\) \((x\in X\subset R^{N+1}\), \(\Omega\) is unit direction vector, \(\nu >0)\) is considered. Results of Rosseland approximation are given and the existence of a solution of the radiative transfer system is proved.
Bardos, C., Golse, F., Perthame, B.
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The Transfer Matrix of Differential-Algebraic Equations

Siberian Mathematical Journal, 2022
This paper is devoted to the study of the transfer function of linear differential-algebraic equations. The author considers the system \[ \begin{aligned} A\frac{d}{dt} x(t) + Bx(t)+ Uu(t)=&0,\quad t\in T=[0,\infty) \\ y(t)=Cx&(t), \end{aligned}\tag{1} \] with some known real \(n \times n\) matrices \(A\) and \(B\), such that \(\mathrm{det} A = 0\), an
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