Topic
Ordinate
About: Ordinate is a research topic. Over the lifetime, 611 publications have been published within this topic receiving 9065 citations. The topic is also known as: ordinates.
Papers published on a yearly basis
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Papers
TL;DR: In this paper, the authors take up a point inerely mentioned in 1948 that not only is the distribution lognormal, but the constants or parameters seem to be restricted in a peculiar way.
Abstract: In an earlier paper (Preston 1948) we found that, in a sufficiently large aggregation of individuals of many species, the individuals often tended to be distributed among the species according to a lognormal law. We plotted as abscissa equal increments in the logarithms of the number of individuals representing a species, and as ordinate the number of species falling into each of these increments. We found it convenient to use as such increments the "octave," that is the interval in which representation doubled, so that our abscissae became simply a scale of "octaves," but this choice of unit is arbitrary. Whatever logarithmic unit is used, the graph tended to take the form of a normal or Gaussian curve, so that the distribution was "lognormal." \Ve called this the "Species Curve." In the present paper we take up a point inerely mentioned in 1948 that not only is the distribution lognormal, but the constants or parameters seem to be restricted in a peculiar way. They are not fixed, but they are interlocked. The nature of this restriction and interlocking is the main theme of the present paper. In the earlier paper we graduated the experimental results with curves of the form
1,942 citations
TL;DR: Two least squares methods of estimating nutrient requirements from growth data were compared and consistently good fits obtained with the nonlinear models suggest that this approach may generally be more useful.
Abstract: Two least squares methods of estimating nutrient requirements from growth data were compared One method involved fitting a broken line by the method of least squares The requirement was taken as the abscissa of the breakpoint in the curve The other method involved fitting an appropriate exponential function to the growth data and estimating the requirement as the abscissa of the point on the fitted curve whose ordinate was 95% of the upper asymptote For the nine sets of data studied, the broken line provided adequate fits for only six The nonlinear models provided adequate fits for all the data studied When both the broken line and the chosen nonlinear model provided adequate fits, the estimated requirements were nearly the same However, the consistently good fits obtained with the nonlinear models suggest that this approach may generally be more useful
751 citations
TL;DR: In this article, a new algorithm for modeling radiative transfer in inhomogeneous three-dimensional media is described, which uses a spherical harmonic angular representation to reduce memory use and time computing the source function.
Abstract: A new algorithm for modeling radiative transfer in inhomogeneous three-dimensional media is described. The spherical harmonics discrete ordinate method uses a spherical harmonic angular representation to reduce memory use and time computing the source function. The radiative transfer equation is integrated along discrete ordinates through a spatial grid to model the streaming of radiation. An adaptive grid approach, which places additional points where they are most needed to improve accuracy, is implemented. The solution method is a type of successive order of scattering approach or Picard iteration. The model computes accurate radiances or fluxes in either the shortwave or longwave regions, even for highly peaked phase functions. Broadband radiative transfer is computed efficiently with a k distribution. The results of validation tests and examples illustrating the efficiency and accuracy of the algorithm are shown for simple geometries and realistic simulated clouds.
579 citations
TL;DR: In this paper, the authors focus on the discrete ordinate method as a method for analyzing radiative heat transfer in isotropically and anisotropic scattering media and demonstrate that if ordinate sets are chosen to satisfy key moments of the radiative intensity, the resulting Nth order solution with the proposed quadrature is superior to the Nth-order solution using Gauss quadratures.
Abstract: The objective of this note is to focus on the discrete ordinate method as a method for analyzing radiative heat transfer in isotropically and anisotropically scattering media. In particular, one dimension is chosen only for simplicity, since exact solutions are available for benchmarking the discrete ordinate method. One-dimensional radiative heat transfer has been analyzed in many previous investigations and has been extensively reviewed by Viskanta. The development of the discrete ordinate method has been described in detail by Chandrasekhar and Lathrop. The discrete ordinate method using Gauss quadrature has been compared with approximate solutions. In the cases previously analyzed solutions were obtained using ordinate sets that were larger than necessary. This note demonstrates that if ordinate sets are chosen to satisfy key moments of the radiative intensity, the resulting Nth order solution with the proposed quadrature is superior to the Nth order solution using Gauss quadrature.
229 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 6 |
| 2024 | 35 |
| 2023 | 27 |
| 2022 | 38 |
| 2021 | 19 |
| 2020 | 23 |