Hidden Scale Invariance in Polydisperse Mixtures of Exponential Repulsive Particles

2020 ◽  
Author(s):  
Trond S. Ingebrigtsen ◽  
Thomas B. Schrøder ◽  
Jeppe C. Dyre
Keyword(s):  
Scale Invariance

D-test: A New Test for Analyzing Scale Invariance Using Symbolic Dynamics and Symbolic Entropy

Methodology ◽  
2011 ◽  
Vol 7 (3) ◽  
pp. 88-95 ◽  
Author(s):  
Jose A. Martínez ◽  
Manuel Ruiz Marín
Keyword(s):  
Symbolic Dynamics ◽  
Scale Invariance ◽  
Rating Scales ◽  
Rating Scale ◽  
Marketing Research ◽  
Response Patterns ◽  
Measurement Scales ◽  
Improve Measurement ◽  
Entropy Measures ◽  
The Difference

The aim of this study is to improve measurement in marketing research by constructing a new, simple, nonparametric, consistent, and powerful test to study scale invariance. The test is called D-test. D-test is constructed using symbolic dynamics and symbolic entropy as a measure of the difference between the response patterns which comes from two measurement scales. We also give a standard asymptotic distribution of our statistic. Given that the test is based on entropy measures, it avoids smoothed nonparametric estimation. We applied D-test to a real marketing research to study if scale invariance holds when measuring service quality in a sports service. We considered a free-scale as a reference scale and then we compared it with three widely used rating scales: Likert-type scale from 1 to 5 and from 1 to 7, and semantic-differential scale from −3 to +3. Scale invariance holds for the two latter scales. This test overcomes the shortcomings of other procedures for analyzing scale invariance; and it provides researchers a tool to decide the appropriate rating scale to study specific marketing problems, and how the results of prior studies can be questioned.

Fluid membranes in the “semi-rigid regime”: scale invariance

1991 ◽  
Vol 1 (9) ◽  
pp. 1121-1132 ◽  
Author(s):  
M. Skouri ◽  
J. Marignan ◽  
J. Appell ◽  
G. Porte
Keyword(s):  
Scale Invariance ◽  
Fluid Membranes

Scale invariance of shallow seismicity and the prognostic signs of earthquakes

2016 ◽  
Vol 187 (05) ◽  
pp. 505-524
Author(s):  
Igor R. Stakhovsky
Keyword(s):  
Scale Invariance

scholarly journals Scale Invariance, Horizons, and Inflation

2021 ◽  
Author(s):  
Andre Maeder ◽  
Vesselin G Gueorguiev
Keyword(s):  
Scalar Field ◽  
Scale Invariance ◽  
Maxwell Equations ◽  
High Redshift ◽  
Empty Space ◽  
Causal Connection ◽  
Cosmological Constant Problem ◽  
Scale Invariant ◽  
Starting Point ◽  
Final Answer

Abstract Maxwell equations and the equations of General Relativity are scale invariant in empty space. The presence of charge or currents in electromagnetism or the presence of matter in cosmology are preventing scale invariance. The question arises on how much matter within the horizon is necessary to kill scale invariance. The scale invariant field equation, first written by Dirac in 1973 and then revisited by Canuto et al. in 1977, provides the starting point to address this question. The resulting cosmological models show that, as soon as matter is present, the effects of scale invariance rapidly decline from ϱ = 0 to ϱc, and are forbidden for densities above ϱc. The absence of scale invariance in this case is consistent with considerations about causal connection. Below ϱc, scale invariance appears as an open possibility, which also depends on the occurrence of in the scale invariant context. In the present approach, we identify the scalar field of the empty space in the Scale Invariant Vacuum (SIV) context to the scalar field ϕ in the energy density $\varrho = \frac{1}{2} \dot{\varphi }^2 + V(\varphi )$ of the vacuum at inflation. This leads to some constraints on the potential. This identification also solves the so-called “cosmological constant problem”. In the framework of scale invariance, an inflation with a large number of e-foldings is also predicted. We conclude that scale invariance for models with densities below ϱc is an open possibility; the final answer may come from high redshift observations, where differences from the ΛCDM models appear.

Sign in / Sign up

Export Citation Format

Share Document