Simple K-Energy Radiative Scaling Law for Imploding Wire Arrays And Gas Puffs.

1982 ◽  
Author(s):  
Joseph B. Workman ◽  
Clifford W. Prettie
Keyword(s):  
Scaling Law ◽  
Wire Arrays

Scaling Law of Coupling Coefficient and Coil Size in Wireless Power Transfer Design via Magnetic Coupling

2017 ◽  
Vol 137 (4) ◽  
pp. 326-333
Author(s):  
Chiaki Nagai ◽  
Kenji Inukai ◽  
Masato Kobayashi ◽  
Tatsuya Tanaka ◽  
Kensho Abumi ◽  
...  
Keyword(s):  
Coupling Coefficient ◽  
Scaling Law ◽  
Magnetic Coupling ◽  
Wireless Power Transfer ◽  
Power Transfer ◽  
Wireless Power ◽  
Coil Size

scholarly journals Types, Tokens, and Hapaxes: A New Heap’s Law

Glottotheory ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 113-129
Author(s):  
Victor Davis
Keyword(s):  
First Principles ◽  
Scaling Law ◽  
Written Language ◽  
Zipf’S Law ◽  
Academic Press ◽  
Zipf's Law ◽  
New Words ◽  
Size Dependent ◽  
Link Type ◽  
Combinatorial Model

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.

Scaling law of radiative opacities for ICF elements

2001 ◽  
Vol 464 (1-3) ◽  
pp. 218-224 ◽  
Author(s):  
E Mı́nguez ◽  
R Ruiz ◽  
P Martel ◽  
J.M Gil ◽  
J.G Rubiano ◽  
...  
Keyword(s):  
Scaling Law

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

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.

Fracture of Soft Elastic Foam

2015 ◽  
Vol 83 (3) ◽  
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.

scholarly journals Ultralong π-Conjugated Bis(terpyridine)metal Polymer Wires Covalently Bound to a Carbon Electrode: Fast Redox Conduction and Redox Diode Characteristics

Molecules ◽  
2021 ◽  
Vol 26 (14) ◽  
pp. 4267
Author(s):  
Kuo-Hui Wu ◽  
Ryota Sakamoto ◽  
Hiroaki Maeda ◽  
Eunice Jia Han Phua ◽  
Hiroshi Nishihara
Keyword(s):  
Metal Complex ◽  
Electrochemical Method ◽  
Redox Reactions ◽  
Cyclic Voltammograms ◽  
Wire Arrays ◽  
Reversible Redox ◽  
Complex Linear ◽  
Complex Polymer ◽  
Metal Polymer ◽  
Hclo4 Solution

We developed an efficient and convenient electrochemical method to synthesize π-conjugated redox metal-complex linear polymer wires composed of azobenzene-bridged bis(terpyridine)metal (2-M, M = Fe, Ru) units covalently immobilized on glassy carbon (GC). Polymerization proceeds by electrochemical oxidation of bis(4′-(4-anilino)-2,2′:6′,2″-terpyridine)metal (1-M) in a water–acetonitrile–HClO4 solution, affording ultralong wires up to 7400 mers (corresponding to ca. 15 μm). Both 2-Fe and 2-Ru undergo reversible redox reactions, and their redox behaviors indicate remarkably fast redox conduction. Anisotropic hetero-metal-complex polymer wires with Fe and Ru centers are constructed via stepwise electropolymerization. The cyclic voltammograms of two hetero-metal-complex polymer wires, GC/[2-Fe]–[2-Ru] (3) and GC/[2-Ru]–[2-Fe] (4), show irreversible redox reactions with opposite electron transfer characteristics, indicating redox diodelike behavior. In short, the present electrochemical method is useful to synthesize polymer wire arrays and to integrate functional molecules on carbon.

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

2021 ◽  
Vol 33 (5) ◽  
pp. 051707
Author(s):  
Arun Kumar Perumal ◽  
Ethirajan Rathakrishnan
Keyword(s):  
Scaling Law ◽  
Free Jets ◽  
Core Length ◽  
Supersonic Core Length
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