Variational Scaling Law for Atmospheric Propagation

Abstract Heap’s Law https://dl.acm.org/citation.cfm?id=539986 Heaps, H S 1978 Information Retrieval: Computational and Theoretical Aspects (Academic Press). states that in a large enough text corpus, the number of types as a function of tokens grows as N = K{M^\beta } for some free parameters K, \beta . Much has been written http://iopscience.iop.org/article/10.1088/1367-2630/15/9/093033 Font-Clos, Francesc 2013 A scaling law beyond Zipf’s law and its relation to Heaps’ law (New Journal of Physics 15 093033)., http://iopscience.iop.org/article/10.1088/1367-2630/11/12/123015 Bernhardsson S, da Rocha L E C and Minnhagen P 2009 The meta book and size-dependent properties of written language (New Journal of Physics 11 123015)., http://iopscience.iop.org/article/10.1088/1742-5468/2011/07/P07013 Bernhardsson S, Ki Baek and Minnhagen 2011 A paradoxical property of the monkey book (Journal of Statistical Mechanics: Theory and Experiment, Volume 2011)., http://milicka.cz/kestazeni/type-token_relation.pdf Milička, Jiří 2009 Type-token & Hapax-token Relation: A Combinatorial Model (Glottotheory. International Journal of Theoretical Linguistics 2 (1), 99–110)., https://www.nature.com/articles/srep00943 Petersen, Alexander 2012 Languages cool as they expand: Allometric scaling and the decreasing need for new words (Scientific Reports volume 2, Article number: 943). about how this result and various generalizations can be derived from Zipf’s Law. http://dx.doi.org/10.1037/h0052442 Zipf, George 1949 Human behavior and the principle of least effort (Reading: Addison-Wesley). Here we derive from first principles a completely novel expression of the type-token curve and prove its superior accuracy on real text. This expression naturally generalizes to equally accurate estimates for counting hapaxes and higher n-legomena.

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Scaling law of radiative opacities for ICF elements

Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment ◽

10.1016/s0168-9002(01)00037-7 ◽

2001 ◽

Vol 464 (1-3) ◽

pp. 218-224 ◽

Cited By ~ 6

Author(s):

E Mı́nguez ◽

R Ruiz ◽

P Martel ◽

J.M Gil ◽

J.G Rubiano ◽

...

Keyword(s):

Scaling Law

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Horizontal convection in a rectangular enclosure driven by a linear temperature profile

Applied Mathematics and Mechanics ◽

10.1007/s10483-021-2754-5 ◽

2021 ◽

Author(s):

Tianyong Yang ◽

Bofu Wang ◽

Jianzhao Wu ◽

Zhiming Lu ◽

Quan Zhou

Keyword(s):

Rayleigh Number ◽

Temperature Profile ◽

Scaling Law ◽

Thermal Plume ◽

Steady Regime ◽

Linear Temperature ◽

Square Enclosure ◽

Horizontal Convection ◽

Kinetic Boundary Layer ◽

The Mean

AbstractThe horizontal convection in a square enclosure driven by a linear temperature profile along the bottom boundary is investigated numerically by using a finite difference method. The Prandtl number is fixed at 4.38, and the Rayleigh number Ra ranges from 107 to 1011. The convective flow is steady at a relatively low Rayleigh number, and no thermal plume is observed, whereas it transits to be unsteady when the Rayleigh number increases beyond the critical value. The scaling law for the Nusselt number Nu changes from Rossby’s scaling Nu ∼ Ra1/5 in a steady regime to Nu ∼ Ra1/4 in an unsteady regime, which agrees well with the theoretically predicted results. Accordingly, the Reynolds number Re scaling varies from Re ∼ Ra3/11 to Re ∼ Ra2/5. The investigation on the mean flows shows that the thermal and kinetic boundary layer thickness and the mean temperature in the bulk zone decrease with the increasing Ra. The intensity of fluctuating velocity increases with the increasing Ra.

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