A scale invariance criterion for geophysical fluids

2020 ◽  
Author(s):  
Urs Schaefer-Rolffs
Keyword(s):  
Turbulent Diffusion ◽  
Scale Invariance ◽  
Small Scale ◽  
Scale Invariant ◽  
First Case ◽  
Geophysical Fluids ◽  
Enstrophy Cascade

<p>Scale invariance of geophysical fluids is investigated in terms of a scale invariance criterion. It was developed by Schaefer-Rolffs et al. (2015) based on the implication that each scale invariant subrange shall have its own criterion. Two particular cases are considered, namely the synoptic scales with a significant Coriolis term and a case at smaller scales where the anelastic approximation is valid. The first case is characterized by a constant enstrophy cascade, while in the second case small-scale fluctuations of density, pressure, and temperature are taken into account. In both cases, the respective scale invariance criteria are applied to simple parameterizations of turbulent diffusion. It is demonstrated that only dynamic approaches are scale invariant.</p>

scholarly journals The social brain: scale-invariant layering of Erdős–Rényi networks in small-scale human societies

2016 ◽  
Vol 13 (118) ◽  
pp. 20160044 ◽  
Author(s):  
Michael S. Harré ◽  
Mikhail Prokopenko
Keyword(s):  
Social History ◽  
Resource Sharing ◽  
Scale Invariance ◽  
Social Groups ◽  
Small Scale ◽  
Social Brain ◽  
Scale Invariant ◽  
Scale Free ◽  
The Social ◽  
Average Maximum

The cognitive ability to form social links that can bind individuals together into large cooperative groups for safety and resource sharing was a key development in human evolutionary and social history. The ‘social brain hypothesis’ argues that the size of these social groups is based on a neurologically constrained capacity for maintaining long-term stable relationships. No model to date has been able to combine a specific socio-cognitive mechanism with the discrete scale invariance observed in ethnographic studies. We show that these properties result in nested layers of self-organizing Erdős–Rényi networks formed by each individual's ability to maintain only a small number of social links. Each set of links plays a specific role in the formation of different social groups. The scale invariance in our model is distinct from previous ‘scale-free networks’ studied using much larger social groups; here, the scale invariance is in the relationship between group sizes, rather than in the link degree distribution. We also compare our model with a dominance-based hierarchy and conclude that humans were probably egalitarian in hunter–gatherer-like societies, maintaining an average maximum of four or five social links connecting all members in a largest social network of around 132 people.

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.

scholarly journals Scale-invariance, dynamically induced Planck scale and inflation in the Palatini formulation

2021 ◽  
Vol 2105 (1) ◽  
pp. 012005
Author(s):  
Ioannis D. Gialamas ◽  
Alexandros Karam ◽  
Thomas D. Pappas ◽  
Antonio Racioppi ◽  
Vassilis C. Spanos
Keyword(s):  
Scale Invariance ◽  
Planck Scale ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Scalar Fields ◽  
Scale Invariant ◽  
Expectation Value ◽  
Hilbert Action

Abstract We present two scale invariant models of inflation in which the addition of quadratic in curvature terms in the usual Einstein-Hilbert action, in the context of Palatini formulation of gravity, manages to reduce the value of the tensor-to-scalar ratio. In both models the Planck scale is dynamically generated via the vacuum expectation value of the scalar fields.

scholarly journals Multifractal analysis of radar rainfall fields over the area of Rome

2005 ◽  
Vol 2 ◽  
pp. 293-299 ◽  
Author(s):  
G. Calenda ◽  
E. Gorgucci ◽  
F. Napolitano ◽  
A. Novella ◽  
E. Volpi
Keyword(s):  
Scale Invariance ◽  
Large Scale ◽  
Doppler Radar ◽  
Risk Mitigation ◽  
Small Scale ◽  
Radar Rainfall ◽  
Invariance Properties ◽  
Meteorological Radar ◽  
Using Data ◽  
Precipitation Events

Abstract. A scale-invariance analysis of space and time rainfall events monitored by meteorological radar over the area of Rome (Italy) is proposed. The study of the scale-invariance properties of intense precipitation storms, particularly important in flood forecast and risk mitigation, allows to transfer rainfall information from the large scale predictive meteorological models to the small scale hydrological rainfall-runoff models. Precipitation events are monitored using data collected by the polarimetric Doppler radar Polar 55C (ISAC-CNR), located 15 km Southeast from downtown. The meteorological radar provides the estimates of rainfall intensity over an area of about 10 000 km2 at a resolution of 2×2 km2 in space and 5 min in time. Many precipitation events have been observed from autumn 2001 up to now. A scale-invariance analysis is performed on some of these events with the aim at exploring the multifractal properties and at understanding their dependence on the meteorological large-scale conditions.

scholarly journals CANNY ALGORITHM, COSMIC STRINGS AND THE COSMIC MICROWAVE BACKGROUND

2010 ◽  
Vol 19 (02) ◽  
pp. 183-217 ◽  
Author(s):  
REBECCA J. DANOS ◽  
ROBERT H. BRANDENBERGER
Keyword(s):  
Cosmic Strings ◽  
Simulated Data ◽  
String Tension ◽  
Detection Algorithm ◽  
Small Scale ◽  
Scale Invariant ◽  
South Pole Telescope ◽  
Scaling Solution ◽  
Order Of Magnitude ◽  
Canny Algorithm

We describe a new code to search for signatures of cosmic strings in cosmic microwave anisotropy maps. The code implements the Canny algorithm, an edge detection algorithm designed to search for the lines of large gradients in maps. Such a gradient signature which is coherent in position-space is produced by cosmic strings via the Kaiser–Stebbins effect. We test the power of our new code to set limits on the tension of the cosmic strings by analyzing simulated data, with and without cosmic strings. We compare maps with a pure Gaussian scale-invariant power spectrum with maps which have a contribution of a distribution of cosmic strings obeying a scaling solution. The maps have angular scale and angular resolution comparable to what current and future ground-based small-scale cosmic microwave anisotropy experiments will achieve. We present tests of the codes, indicate the limits on the string tension which could be set with the current code, and describe various ways to refine the analysis. Our results indicate that when applied to the data of ongoing cosmic microwave experiments such as the South Pole Telescope project, the sensitivity of our method to the presence of cosmic strings will be more than an order of magnitude better than the limits from existing analyses.

scholarly journals Broadband Microwave Absorption by Logarithmic Spiral Metasurface

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Shubo Wang ◽  
Bo Hou ◽  
Che Ting Chan
Keyword(s):  
Electromagnetic Wave ◽  
Scale Invariance ◽  
Logarithmic Spiral ◽  
Unit Cell ◽  
Scale Invariant ◽  
Archimedean Spiral ◽  
Broadband Absorption ◽  
Fabry Perot ◽  
Classical Waves

Abstract Metamaterials have enabled the design of electromagnetic wave absorbers with unprecedented performance. Conventional metamaterial absorbers usually employ multiple structure components in one unit cell to achieve broadband absorption. Here, a simple metasurface microwave absorber is proposed that has one metal-backed logarithmic spiral resonator as the unit cell. It can absorb >95% of normally incident microwave energy within the frequency range of 6 GHz–37 GHz as a result of the scale invariant geometry and the Fabry-Perot-type resonances of the resonator. The thickness of the metasurface is 5 mm and approaches the Rozanov limit of an optimal absorber. The physics underlying the broadband absorption is discussed. A comparison with Archimedean spiral metasurface is conducted to uncover the crucial role of scale invariance. The study opens a new direction of electromagnetic wave absorption by employing the scale invariance of Maxwell equations and may also be applied to the absorption of other classical waves such as sound.

Political protest Italian-style: The blogosphere and mainstream media in the promotion and coverage of Beppe Grillo's V-day

First Monday ◽  
2009 ◽  
Author(s):  
Alberto Pepe ◽  
Corinna Di Gennaro
Keyword(s):  
Public Perception ◽  
Small Scale ◽  
Political Protest ◽  
Core Network ◽  
Italian History ◽  
Mainstream Media ◽  
News Sources ◽  
First Case ◽  
History Of ◽  
Use Of Social Media

We analyze the organization, promotion and public perception of "V-day", a political rally that took place on 8 September 2007, to protest against corruption in the Italian Parliament. Launched by blogger Beppe Grillo, and promoted via a word of mouth mobilization on the Italian blogosphere, V-day brought close to one million Italians in the streets on a single day, but was mostly ignored by mainstream media. This article is divided into two parts. In the first part, we analyze the volume and content of online articles published by both bloggers and mainstream news sources from 14 June (the day V-day was announced) until 15 September 2007 (one week after it took place). We find that the success of V-day can be attributed to the coverage of bloggers and small-scale local news outlets only, suggesting a strong grassroots component in the organization of the rally. We also find a dissonant thematic relationship between content published by blogs and mainstream media: while the majority of blogs analyzed promote V-day, major mainstream media sources critique the methods of information production and dissemination employed by Grillo. Based on this finding, in the second part of the study, we explore the role of Grillo in the organization of the rally from a network analysis perspective. We study the interlinking structure of the V-day blogosphere network, to determine its structure, its levels of heterogeneity, and resilience. Our analysis contradicts the hypothesis that Grillo served as a top-down, broadcast-like source of information. Rather, we find that information about V-day was transferred across heterogeneous nodes in a moderately robust and resilient core network of blogs. We speculate that the organization of V-day represents the very first case, in Italian history, of a political demonstration developed and promoted primarily via the use of social media on the Web.

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