Three-dimensional scaling of the uniform color scales of the Optical Society of America

1989 ◽  
Vol 6 (1) ◽  
pp. 128 ◽  
Author(s):  
T. M. Man ◽  
D. L. MacAdam
Keyword(s):  
Three Dimensional ◽  
Optical Society ◽  
Dimensional Scaling ◽  
Color Scales

scholarly journals Bayesian Geographical Multi-Dimensional Scaling

2019 ◽  
Vol 1 ◽  
pp. 1-2
Author(s):  
Hayato Nishi ◽  
Yasushi Asami
Keyword(s):  
Three Dimensional ◽  
Geographical Location ◽  
Point Of View ◽  
Statistical Point ◽  
Dimensional Scaling ◽  
Regional Features ◽  
Geographical Distances ◽  
Strong Relation ◽  
Geographical Locations ◽  
Multi Dimensional Scaling

<p><strong>Abstract.</strong> Multi-dimensional scaling (MDS) is a popular method of visualizing the similarity of individuals in a dataset. When dissimilarities between individuals in a dataset are measured, MDS projects these individuals into the (typically two- or three-dimensional) map. In this map, because similar individuals are projected to be close to one another, distances between individuals correspond to their dissimilarities. In other words, MDS makes a similarity map of a dataset.</p><p>Some of the dissimilarities and distances have a strong relation to the geographical location. For example, time distances are similar to geographical distances, and regional features will be similar if the regions are close together. Therefore, it will be useful to compare the MDS projection and geographical locations. However, because MDS projection is not concerned with the rotation, parallel translation, and similarity expansion, it might be difficult to compare the projection to the actual geographical locations. When geographically related similarities are visualized, projected locations should be bound to the geographical locations.</p><p>In this article, we propose Bayesian Geographical Multidimensional Scaling (BGMDS), in which geographical restrictions of projections are given from a statistical point of view. BGMDS gives not only geographically bound projections, but also incorporates the uncertainty of the projections.</p>

High Rayleigh number convection in a three-dimensional porous medium

2014 ◽  
Vol 748 ◽  
pp. 879-895 ◽  
Author(s):  
Duncan R. Hewitt ◽  
Jerome A. Neufeld ◽  
John R. Lister
Keyword(s):  
Porous Medium ◽  
Three Dimensional ◽  
Field Measurements ◽  
Two Dimensions ◽  
Dimensional Scaling ◽  
Dynamical Flow ◽  
Background Temperature ◽  
Relationship Of ◽  
Rayleigh Numbers ◽  
Steady Convection

AbstractHigh-resolution numerical simulations of statistically steady convection in a three-dimensional porous medium are presented for Rayleigh numbers $Ra \leqslant 2 \times 10^4$. Measurements of the Nusselt number $Nu$ in the range $1750 \leqslant Ra \leqslant 2 \times 10^4$ are well fitted by a relationship of the form $Nu = \alpha _3 Ra + \beta _3$, for $\alpha _3 = 9.6 \times 10^{-3}$ and $\beta _3 = 4.6$. This fit indicates that the classical linear scaling $Nu \sim Ra$ is attained, and that $Nu$ is asymptotically approximately $40\, \%$ larger than in two dimensions. The dynamical flow structure in the range $1750 \leqslant Ra \leqslant 2\times 10^4$ is analysed, and the interior of the flow is found to be increasingly well described as $Ra \to \infty $ by a heat-exchanger model, which describes steady interleaving columnar flow with horizontal wavenumber $k$ and a linear background temperature field. Measurements of the interior wavenumber are approximately fitted by $k\sim Ra^{0.52 \pm 0.05}$, which is distinguishably stronger than the two-dimensional scaling of $k\sim Ra^{0.4}$.

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