Scaling law of radiative opacities for ICF elements

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.

Download Full-text

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.

Download Full-text

Fracture of Soft Elastic Foam

Journal of Applied Mechanics ◽

10.1115/1.4032050 ◽

2015 ◽

Vol 83 (3) ◽

Cited By ~ 6

Author(s):

Zhuo Ma ◽

Xiangchao Feng ◽

Wei Hong

Keyword(s):

Fracture Toughness ◽

Fracture Energy ◽

Cell Walls ◽

Scaling Law ◽

Phase Field Model ◽

Base Material ◽

Network Connectivity ◽

High Fracture Toughness ◽

High Fracture ◽

Order Of Magnitude

Consisting of stretchable and flexible cell walls or ligaments, soft elastic foams exhibit extremely high fracture toughness. Using the analogy between the cellular structure and the network structure of rubbery polymers, this paper proposes a scaling law for the fracture energy of soft elastic foam. To verify the scaling law, a phase-field model for the fracture processes in soft elastic structures is developed. The numerical simulations in two-dimensional foam structures of various unit-cell geometries have all achieved good agreement with the scaling law. In addition, the dependences of the macroscopic fracture energy on geometric parameters such as the network connectivity and spatial orientation have also been revealed by the numerical results. To further enhance the fracture toughness, a type of soft foam structures with nonstraight ligaments or folded cell walls has been proposed and its performance studied numerically. Simulations have shown that an effective fracture energy one order of magnitude higher than the base material can be reached by using the soft foam structure.

Download Full-text

Scaling law for supersonic core length in circular and elliptic free jets

Physics of Fluids ◽

10.1063/5.0051872 ◽

2021 ◽

Vol 33 (5) ◽

pp. 051707

Author(s):

Arun Kumar Perumal ◽

Ethirajan Rathakrishnan

Keyword(s):

Scaling Law ◽

Free Jets ◽

Core Length ◽

Supersonic Core Length

Download Full-text

On the pinning force in high density MgB2 samples

Scientific Reports ◽

10.1038/s41598-021-85209-2 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

V. Sandu ◽

A. M. Ionescu ◽

G. Aldica ◽

M. A. Grigoroscuta ◽

M. Burdusel ◽

...

Keyword(s):

Magnetic Field ◽

Field Dependence ◽

Scaling Law ◽

Critical Force ◽

High Density ◽

Pinning Force ◽

Pinning Mechanism ◽

Grain Boundary Pinning ◽

Peaked Function ◽

Main Factor

AbstractAn analysis of the field dependence of the pinning force in different, high density sintered samples of MgB2 is presented. The samples were chosen to be representative for pure MgB2, MgB2 with additives, and partially oriented massive samples. In some cases, the curves of pinning force versus magnetic field of the selected samples present peculiar profiles and application of the typical scaling procedures fails. Based on the percolation model, we show that most features of the field dependence of the critical force that generate dissipation comply with the Dew-Hughes scaling law predictions within the grain boundary pinning mechanism if a connecting factor related to the superconducting connection of the grains is used. The field dependence of the connecting function, which is dependent on the superconducting anisotropy, is the main factor that controls the boundary between dissipative and non-dissipative current transport in high magnetic field. Experimental data indicate that the connecting function is also dependent on the particular properties (e.g., the presence of slightly non-stoichiometric phases, defects, homogeneity, and others) of each sample and it has the form of a single or double peaked function in all investigated samples.

Download Full-text