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In the theory of radiative transfer, of either thermal[1] or neutron[2] radiation, a position and direction-dependent intensity function is usually sought for the description of the radiation field. The intensity field can in principle be solved from the integrodifferential radiative transfer equation (RTE), but an exact solution is usually impossible and even in the case of geometrically simple systems can contain unusual special functions such as the Chandrasekhar's H-function and Chandrasekhar's X- and Y-functions.[3] The method of discrete ordinates, or the Sn method, is one way to approximately solve the RTE by discretizing both the xyz-domain and the angular variables that specify the direction of radiation. The methods were developed by Subrahmanyan Chandrasekhar when he was working on radiative transfer.
^Michael F. Modest "Radiative Heat Transfer 3rd ed.", pp.542-543, Elsevier 2013
^Jeremy A. Roberts “Direct Solution of the Discrete Ordinates Equations.” (2010).
^Kuo-Nan Liou, "A Numerical Experiment on Chandrasekhar's Discrete-Ordinate Method for Radiative Transfer: Applications to Cloudy and Hazy Atmospheres", J. Atmos. Sci. 30, 1303-1326 (1973)
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and Y-functions. The method of discreteordinates, or the Sn method, is one way to approximately solve the RTE by discretizing both the xyz-domain and...
fractions of meV to several MeV). Modern solutions use either discreteordinates or Monte Carlo methods, or even a hybrid of both. The neutron transport equation...
that is numerically solved using a solver such as a discreteordinatemethod or a Monte Carlo method. The radiative transfer equation is a monochromatic...
DISORT (DiscreteOrdinates Radiative Transfer Program for a Multi-Layered Plane-Parallel Medium) - general and versatile plane-parallel radiative transfer...
Newton's Philosophiae Naturalis Principia Mathematica using the language and methods of ordinary calculus. The effort resulted in the book Newton's Principia...
the United States in May 1972. A fully discrete system, it eschewed matrix technologies in favor of a method similar to the encoding of stereo FM broadcasts...
descriptions of cartographic materials and spatial data. Geographical co-ordinates. ICA Commission on Map Projections. The pair had accurate absolute distances...
Data binning, also called data discrete binning or data bucketing, is a data pre-processing technique used to reduce the effects of minor observation errors...
Harmonics Method Lectures. Alma-Ata, 1975; Spherical Harmonics and DiscreteOrdinatesMethods in the Kinetic Transfer Theory. Alma-Ata, 1979; Discrete Models...
information. Using the 2° standard observer, find the chromaticity co-ordinates of the test source in the CIE 1960 color space. Determine the correlated...
of creating a mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells. Often these cells form a simplicial complex...
axis and the curve are the ordinates. He further developed relations between the abscissas and the corresponding ordinates that are equivalent to rhetorical...
[citation needed] Discrete (digital) signals can only take on or off value (1 or 0, true or false). Examples of devices providing a discrete signal include...
parameter θ {\displaystyle \theta } , is usually defined differently for discrete and continuous probability distributions (a more general definition is...
can then be given as a score t1(i) = x(i) ⋅ w(1) in the transformed co-ordinates, or as the corresponding vector in the original variables, {x(i) ⋅ w(1)}...
infrared,...). Its approach combines the ray tracing and the discreteordinatemethods. It works with natural and urban landscapes (forests with different...
Bayesian selection methods, MML doesn't care if you change from measuring length to volume or from Cartesian co-ordinates to polar co-ordinates. MML is statistically...
{\displaystyle y'={\frac {dy}{dx}}} We can approximate the differentials as discrete increases: y ′ = d y d x ≈ Δ y Δ x = y ( x + Δ x ) − y ( x ) Δ x {\displaystyle...
component of the R-tree method of spatial indexing. In many applications the bounding box is aligned with the axes of the co-ordinate system, and it is then...
have the following parameters: Each data point contains Co-ordinates (X, Y, Z co-ordinates in a local reference system) Each point has its associated...
the ratio between ordinates and abscissas. He continued this reasoning to argue that the integral was in fact the sum of the ordinates for infinitesimal...
co-efficients. Finite volume method is probably the most popular method used for numerical discretization in CFD. This method is similar in some ways to...
space) defines conjugate generalized momenta pi, which together define co-ordinates on phase space. More abstractly, in classical mechanics phase space is...
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