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.

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 Impact of Pore Geometry and Water Saturation on Gas Effective Diffusion Coefficient in Soil

2018 ◽  
Vol 8 (11) ◽  
pp. 2097 ◽  
Author(s):  
Wulong Hu ◽  
Yao Jiang ◽  
Daoyi Chen ◽  
Yongshui Lin ◽  
Qiang Han ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Power Law ◽  
Diffusion Coefficients ◽  
Effective Diffusion Coefficient ◽  
Pore Diameter ◽  
Water Saturation ◽  
Knudsen Diffusion ◽  
Effective Diffusion ◽  
Pore Geometry ◽  
Effective Diffusion Coefficients

Gas flow in soil plays a crucial role in terrestrial ecosystems, and numerical simulation of their movement needs to know their effective diffusion coefficients. How pore structure influences the effective diffusion coefficient has been studied intensively for dry porous media, but much remains unknown for unsaturated soils. Here, we employed the X-ray tomography technique at the pore scale to directly obtain the soil structures, the geometry of their pores and the water distribution under different water saturation levels were calculated using a morphological model. The results show that pore structures including porosity, interface area of gas–solid–water and pore diameter are closely related to water saturation. The increase of mean pore diameter with gas saturation can be fitted into a power law. We also investigated the impact of pore geometry and water saturation on the effective diffusion coefficients, which is independent of the molecular mass of gas after normalization. As the normalized effective Knudsen diffusion coefficient increases with average pore diameter following a power law, with the scaling factor related to pore geometry and the exponent is a constant, we explained and proved that the Knudsen diffusion coefficient increases with gas saturation, also following a power law.

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.

STUDY OF POWER-LAW CORRECTIONS TO SCALING IN A RELATIVISTIC QUARK MODEL

1990 ◽  
Vol 05 (13) ◽  
pp. 2591-2604
Author(s):  
L. S. CELENZA ◽  
A. PANTZIRIS ◽  
C. M. SHAKIN ◽  
HUI-WEN WANG
Keyword(s):  
Experimental Data ◽  
Structure Function ◽  
Quark Model ◽  
Power Law ◽  
Correction Term ◽  
Analytic Form ◽  
Recent Analysis ◽  
Relativistic Quark Model ◽  
Corrections To Scaling ◽  
Correction To Scaling

We study the approach to scaling in a relativistic quark model which we have used previously to fit the experimental data for the structure function [Formula: see text] (for all x) and for [Formula: see text] (for x > 0.4). We present values for these structure functions calculated in our model and also present an analytic form which provides a good fit to the numerical results. Our model supports one form of the power-law corrections suggested in the literature. [We reproduce the sign and magnitude of the parameter which appears in a phenomenological form used in a recent analysis made by the BEBC Collaboration. Our results are also consistent with a recent BCDMS Collaboration analysis which finds no need for "higher-twist" terms for Q2 > 20 (Gev) 2.] We also discuss certain complications which may arise when one attempts to study "higher-twist" behavior at both small and large x with a single sign for the phenomenological power-law correction term. (In particular, we predict a change in sign of the power-law correction to scaling between x = 0.65 and x = 0.7.) In addition, we calculate R(x, Q2) and find a good fit to the experimental data using the same parameters which were used in our fits to [Formula: see text] and [Formula: see text].

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.

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
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