scholarly journals Catalyst Sintering Kinetics Data: Is There a Minimal Chemical Mechanism Underlying Kinetics Previously Fit by Empirical Power-Law Expressions—and if So, What Are Its Implications?

2017 ◽  
Vol 56 (37) ◽  
pp. 10271-10286 ◽  
Author(s):  
Eric E. Finney ◽  
Richard G. Finke
Keyword(s):  
Power Law ◽  
Chemical Mechanism ◽  
Empirical Power ◽  
Sintering Kinetics

scholarly journals Power Laws in Economics: An Introduction

2016 ◽  
Vol 30 (1) ◽  
pp. 185-206 ◽  
Author(s):  
Xavier Gabaix
Keyword(s):  
Stock Market ◽  
Power Law ◽  
Power Laws ◽  
Economic Fluctuations ◽  
Formal Definition ◽  
Empirical Power

Many of the insights of economics seem to be qualitative, with many fewer reliable quantitative laws. However a series of power laws in economics do count as true and nontrivial quantitative laws—and they are not only established empirically, but also understood theoretically. I will start by providing several illustrations of empirical power laws having to do with patterns involving cities, firms, and the stock market. I summarize some of the theoretical explanations that have been proposed. I suggest that power laws help us explain many economic phenomena, including aggregate economic fluctuations. I hope to clarify why power laws are so special, and to demonstrate their utility. In conclusion, I list some power-law-related economic enigmas that demand further exploration. A formal definition may be useful.

scholarly journals Theoretical bounds for the exponent in the empirical power-law advance-time curve for surface flow

2018 ◽  
Vol 210 ◽  
pp. 208-216 ◽  
Author(s):  
Behzad Ghanbarian ◽  
Hamed Ebrahimian ◽  
Allen G. Hunt ◽  
M. Th. van Genuchten
Keyword(s):  
Power Law ◽  
Surface Flow ◽  
Empirical Power ◽  
Time Curve ◽  
Advance Time

scholarly journals Density of Glacier Ice

1960 ◽  
Vol 3 (27) ◽  
pp. 568-573 ◽  
Author(s):  
P. A. Shumskiy
Keyword(s):  
Hydrostatic Pressure ◽  
Power Law ◽  
Air Pressure ◽  
Densification Process ◽  
Empirical Power ◽  
Density Profiles ◽  
Air Content ◽  
Glacier Ice ◽  
Viscous Behaviour

AbstractThe density of glacier ice containing a given amount of air can be computed if it is assumed that both ice and air are subjected to a pressure due to the weight of overlying material. In this way it is possible to deduce the form that a curve of density versus depth should have for ice of a constant air content. Reasons for the divergence of observed depth-density profiles from those predicted by this theory are discussed, in particular the effect of the plastic-viscous behaviour of ice, which results in an air pressure differing from the hydrostatic pressure of the ice above. The empirical power-law relation between depth and density is discussed in the light of this theory, and is also used to derive relations for useful parameters characterizing the densification process such as rate of subsidence and rate of densification in terms of the depth, accumulation, and the constants entering the power law.

Time Dependent Viscoelastic Behaviour of EPS Geofoam

2013 ◽  
Vol 330 ◽  
pp. 1095-1099 ◽  
Author(s):  
Yong Zou ◽  
Chin Jian Leo ◽  
Henry Wong
Keyword(s):  
Power Law ◽  
Elevated Temperatures ◽  
Creep Behaviour ◽  
Element Model ◽  
Time Dependent ◽  
Base Case ◽  
Power Law Model ◽  
Empirical Power ◽  
Eps Geofoam ◽  
Viscoelastic Models

A series of laboratory tests was carried out to assess the time-dependent creep behaviour of EPS geofoam at room temperature (23°C) and at 40°C. The experimental data were then used to calibrate and to validate mechanical viscoelastic models along with an empirical Power Law model, at these two temperatures. The viscoelastic models examined were the 3-element (Maxwell-Kelvin), the 4-element (Burgers) and the Modified 4-element models. The modified 4-element model and the base case, the empirical power law model, were found to give the best predictions. As anticipated, the experimental results show that creep rate is higher at elevated temperatures. The results, at 23°C and 40°C, offer a means to assess and model creep behavior in geotechnical applications at normal, and at a practical elevated, temperature where use of EPS geofoam in warmer climate may be a concern.

scholarly journals A Numerical Investigation of the Effects of Fuel Composition on the Minimum Ignition Energy for Homogeneous Biogas-Air Mixtures

2020 ◽  
Author(s):  
Vassilios Papapostolou ◽  
Charles Turquand d’Auzay ◽  
Nilanjan Chakraborty
Keyword(s):  
Flame Propagation ◽  
Power Law ◽  
Turbulence Intensity ◽  
Thermal Runaway ◽  
Turbulent Velocity ◽  
Chemical Mechanism ◽  
Scaling Analysis ◽  
Ignition Energy ◽  
Minimum Ignition Energy ◽  
Wide Range

AbstractThe minimum ignition energy (MIE) requirements for ensuring successful thermal runaway and self-sustained flame propagation have been analysed for forced ignition of homogeneous stoichiometric biogas-air mixtures for a wide range of initial turbulence intensities and CO2 dilutions using three-dimensional Direct Numerical Simulations under decaying turbulence. The biogas is represented by a CH4 + CO2 mixture and a two-step chemical mechanism involving incomplete oxidation of CH4 to CO and H2O and an equilibrium between the CO oxidation and the CO2 dissociation has been used for simulating biogas-air combustion. It has been found that the MIE increases with increasing CO2 content in the biogas due to the detrimental effect of the CO2 dilution on the burning and heat release rates. The MIE for ensuring self-sustained flame propagation has been found to be greater than the MIE for ensuring only thermal runaway irrespective of its outcome for large root-mean-square (rms) values of turbulent velocity fluctuation, and the MIE values increase with increasing rms turbulent velocity for both cases. It has been found that the MIE values increase more steeply with increasing rms turbulent velocity beyond a critical turbulence intensity than in the case of smaller turbulence intensities. The variations of the normalised MIE (MIE normalised by the value for the quiescent laminar condition) with normalised turbulence intensity for biogas-air mixtures are found to be qualitatively similar to those obtained for the undiluted mixture. However, the critical turbulence intensity has been found to decrease with increasing CO2 dilution. It has been found that the normalised MIE for self-sustained flame propagation increases with increasing rms turbulent velocity following a power-law and the power-law exponent has been found not to vary much with the level of CO2 dilution. This behaviour has been explained using a scaling analysis and flame wrinkling statistics. The stochasticity of the ignition event has been analysed by using different realisations of statistically similar turbulent flow fields for the energy inputs corresponding to the MIE and it has been demonstrated that successful outcomes are obtained in most of the instances, justifying the accuracy of the MIE values identified by this analysis.

Empirical power law for magnetic turbulence spectra of an anisotropic plasma

JETP Letters ◽  
2013 ◽  
Vol 96 (10) ◽  
pp. 636-641 ◽  
Author(s):  
S. A. Romanov ◽  
S. I. Klimov ◽  
S. P. Savin
Keyword(s):  
Power Law ◽  
Anisotropic Plasma ◽  
Empirical Power ◽  
Turbulence Spectra ◽  
Magnetic Turbulence

Evaluation of the Porosity of a Coke Particle According to Its Combustion Data

2020 ◽  
Vol 65 (9) ◽  
pp. 823
Author(s):  
O. S. Chernenko ◽  
V. V. Kalinchak ◽  
A. P. Baturina
Keyword(s):  
Specific Surface ◽  
Power Law ◽  
Knudsen Diffusion ◽  
Analytic Form ◽  
Diffusion Mode ◽  
Empirical Power ◽  
Coke Particle ◽  
Diffusion Kinetic ◽  
Particle Combustion ◽  
Graphical Comparison

The dependence of the density of a porous coke particle on its diameter at the particle combustion in the external diffusion mode is analyzed. It is shown that, for the large values of the internal diffusion-kinetic ratio, Sev > 5, the required dependence can be obtained in the analytic form. The analytic formulas are found to be different for the bulk and Knudsen diffusion modes inside the pores. A graphical comparison of the obtained dependences with the empirical power-law dependence is carried out to evaluate the power exponents in the analytic dependences. The corresponding results make it possible to evaluate the effective specific surface area of the pores.

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