scholarly journals Scaling laws to predict humidity-induced swelling and stiffness in hydrogels

Soft Matter ◽  
2021 ◽  
Author(s):  
Yiwei Gao ◽  
Nicholas K. K. Chai ◽  
Negin Garakani ◽  
Sujit S. Datta ◽  
H. Jeremy Cho
Keyword(s):  
Elastic Modulus ◽  
Power Law ◽  
Scaling Laws ◽  
Simple Power ◽  
Polymer Theory

We use semi-dilute polymer theory to develop a simple power-law relationship between hydrogel elastic modulus and swelling, allowing us to predict hydrogel stiffness or swelling at arbitrary relative humidities.

Scaling

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Distribution Function ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Power Law ◽  
Scaling Laws ◽  
Power Laws ◽  
Distribution Functions ◽  
Temporal Process ◽  
Approximate Power

Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.

scholarly journals X-ray Properties of 3C 111: Separation of Primary Nuclear Emission and Jet Continuum

Universe ◽  
2020 ◽  
Vol 6 (11) ◽  
pp. 219
Author(s):  
Elena Fedorova ◽  
B.I. Hnatyk ◽  
V.I. Zhdanov ◽  
A. Del Popolo
Keyword(s):  
Accretion Disk ◽  
Power Law ◽  
Line Emission ◽  
High Energy ◽  
Power Law Model ◽  
X Ray ◽  
Additional Information ◽  
Observational Dataset ◽  
Simple Power ◽  
Photon Index

3C111 is BLRG with signatures of both FSRQ and Sy1 in X-ray spectrum. The significant X-ray observational dataset was collected for it by INTEGRAL, XMM-Newton, SWIFT, Suzaku and others. The overall X-ray spectrum of 3C 111 shows signs of a peculiarity with the large value of the high-energy cut-off typical rather for RQ AGN, probably due to the jet contamination. Separating the jet counterpart in the X-ray spectrum of 3C 111 from the primary nuclear counterpart can answer the question is this nucleus truly peculiar or this is a fake “peculiarity” due to a significant jet contribution. In view of this question, our aim is to estimate separately the accretion disk/corona and non-thermal jet emission in the 3C 111 X-ray spectra within different observational periods. To separate the disk/corona and jet contributions in total continuum, we use the idea that radio and X-ray spectra of jet emission can be described by a simple power-law model with the same photon index. This additional information allows us to derive rather accurate values of these contributions. In order to test these results, we also consider relations between the nuclear continuum and the line emission.

scholarly journals HELICAL MAGNETIC FIELDS FROM INFLATION

2009 ◽  
Vol 18 (09) ◽  
pp. 1395-1411 ◽  
Author(s):  
LEONARDO CAMPANELLI
Keyword(s):  
Magnetic Fields ◽  
Power Law ◽  
Background Field ◽  
Wave Number ◽  
Conformal Time ◽  
De Sitter ◽  
Simple Power ◽  
Dimensionless Constant ◽  
Real Positive Number

We analyze the generation of seed magnetic fields during de Sitter inflation considering a noninvariant conformal term in the electromagnetic Lagrangian of the form [Formula: see text], where I(ϕ) is a pseudoscalar function of a nontrivial background field ϕ. In particular, we consider a toy model that could be realized owing to the coupling between the photon and either a (tachyonic) massive pseudoscalar field or a massless pseudoscalar field nonminimally coupled to gravity, where I follows a simple power law behavior I(k,η) = g/(-kη)β during inflation, while it is negligibly small subsequently. Here, g is a positive dimensionless constant, k the wave number, η the conformal time, and β a real positive number. We find that only when β = 1 and 0.1 ≲ g ≲ 2 can astrophysically interesting fields be produced as excitation of the vacuum, and that they are maximally helical.

Prediction of Bubbles, Crashes, and Antibubbles

2017 ◽  
Author(s):  
Didier Sornette
Keyword(s):  
Stock Market ◽  
Case Studies ◽  
Power Law ◽  
Statistical Tests ◽  
Statistical Significance ◽  
Large Market ◽  
Simple Power ◽  
Market Crashes ◽  
Successes And Failures

This chapter examines how to predict stock market crashes and other large market events as well as the limitations of forecasting, in particular in terms of the horizon of visibility and expected precision. Several case studies are presented in detail, with a careful count of successes and failures. After providing an overview of the nature of predictions, the chapter explains how to develop and interpret statistical tests of log-periodicity. It then considers the concept of an “antibubble,” using as an example the Japanese collapse from the beginning of 1990 to the present. It also describes the first guidelines for prediction, a hierarchy of prediction schemes that includes the simple power law, and the statistical significance of the forward predictions.

Scaling of Transport Properties of Reservoir Material at Low Saturations of a Wetting Phase

1994 ◽  
Vol 367 ◽  
Author(s):  
Y. Carolina Araujo ◽  
Pedro G. Toledo ◽  
Hada Y. Gonzalez
Keyword(s):  
Electrical Conductivity ◽  
Porous Media ◽  
Transport Properties ◽  
Capillary Pressure ◽  
Power Law ◽  
Scaling Laws ◽  
Pore Space ◽  
Conductivity Data ◽  
Phase Saturation ◽  
Electrical Conductivity Data

AbstractTransport properties of natural porous media have been observed to obey scaling laws in the wetting phase saturation. Previous work relates power-law behavior at low wetting phase saturations, i.e., at high capillary pressures, to the thin-film physics of the wetting phase and the fractal character of the pore space of porous media. Here, we present recent combined porousplate capillary pressure and electrical conductivity data of Berea sandstone at low saturations that lend support to the scaling laws. Power law is interpreted in terms of the exponent m in the relation of surface forces and film thickness and the fractal dimension D of the interface between pore space and solid matrix. Simple determination of D from capillary pressure and m from electrical conductivity data can be used to rapidly determine wetting phase relative permeability and capillary dispersion coefficient at low wetting phase saturations.

scholarly journals THE NETWORK OF INTER-REGIONAL DIRECT INVESTMENT STOCKS ACROSS EUROPE

2007 ◽  
Vol 10 (01) ◽  
pp. 29-51 ◽  
Author(s):  
STEFANO BATTISTON ◽  
JOAO F. RODRIGUES ◽  
HAMZA ZEYTINOGLU
Keyword(s):  
Power Law ◽  
Direct Investment ◽  
Policy Making ◽  
Scaling Laws ◽  
Statistical Distributions ◽  
Regional Investment ◽  
Log Normal ◽  
Geographical Space ◽  
Log Normal Distribution ◽  
Different Levels

We present an analysis of inter-regional investment stocks within Europe from a complex networks perspective. We consider two different levels: first, we compute the inward–outward investment stocks at the level of firms, based on ownership shares and number of employees; then we estimate the inward–outward investment stock at the level of regions in Europe, by aggregating the ownership network of firms, based on their headquarter location. To our knowledge, there is no similar approach in the literature so far, and we believe that it may lead to important applications for policy making. In the present paper, we focus on the statistical distributions and the scaling laws, while in further studies we will analyze the structure of the network and its relation to geographical space. We find that while outward investment and activity of firms are power law distributed with a similar exponent, for regions these quantities are better described by a log-normal distribution. At both levels we also find scaling laws relating investment to activity and connectivity. In particular, we find that investment stock scales as a power law of the connectivity, as previously found for stock market data.

scholarly journals Angular power spectra of Galactic HI

2006 ◽  
Vol 2 (S237) ◽  
pp. 413-413
Author(s):  
D. A. Green
Keyword(s):  
Power Law ◽  
Galactic Plane ◽  
Power Spectra ◽  
Simple Power ◽  
Angular Scale

AbstractAs an alternative to identifying and then studying particular features seen in Galactic HI 21-cm images, studies of the angular power spectra of the emission provide a concise, statistical description of HI emission. The angular power spectra of several fields near l = 140°, from the Canadian Galactic Plane Survey, as observed with the DRAO Synthesis Telescope, have been analysed in this way. The derived power spectra, which typically cover angular scales from about 0 · 15 to 0 · 9 degree, are generally well-fitted by a simple power-law dependence on angular scale.

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