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Extended Self Similarity

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lightbulbAbout this topic
Extended Self-Similarity (ESS) is a concept in fractal geometry and statistical physics that describes a property of certain complex systems where patterns repeat at different scales, exhibiting self-similarity not only in spatial dimensions but also in time or other parameters, allowing for a broader understanding of scaling behaviors in various phenomena.
lightbulbAbout this topic
Extended Self-Similarity (ESS) is a concept in fractal geometry and statistical physics that describes a property of certain complex systems where patterns repeat at different scales, exhibiting self-similarity not only in spatial dimensions but also in time or other parameters, allowing for a broader understanding of scaling behaviors in various phenomena.

Key research themes

1. How can the concept of self-similarity be rigorously defined and quantified across diverse scientific domains?

This theme explores formal definitions, mathematical models, and quantitative measures of self-similarity applicable to fields such as philosophy, biology, network theory, and acoustics. Rigorous quantification of self-similarity addresses both structural and processual aspects, enabling clearer characterization and comparison in complex systems.

Key finding: The paper critically examines Watanabe's 'theorem of the ugly duckling' and argues that degree of resemblance between particulars cannot simply be a function of the number of shared properties. The author proposes weighting... Read more
Key finding: This study formalizes self-similarity in branching plant structures by defining formal axial trees and employs tree edit distance algorithms to quantify similarity between branching components. Applying this method to real... Read more
Key finding: By systematically removing nodes based on degree, betweenness, and coreness from real networks, the study identifies that nodes with large degree and betweenness significantly affect the network's self-similarity, while... Read more
Key finding: The authors introduce transposition-invariant self-similarity matrices, which reveal repetitive musical structures even under key transpositions. By adapting chroma-based audio feature comparisons with cyclic shifts, they... Read more
Key finding: This work demonstrates that biological processes described by Avrami functions exhibit self-similarity characterized by power-law scaling with a specific Avrami exponent. It generalizes the concept of self-similarity from... Read more

2. What are the cognitive and computational frameworks for understanding similarity, and how do they address the nuances of perceptual and structural resemblance?

Research in this theme investigates psychological, computational, and mathematical models of similarity, including structural alignment, representational distortion, and similarity measures in neural systems. It examines how similarity is represented, computed, and affects cognitive processes such as categorization, and proposes frameworks to capture similarity beyond simple property matching.

Key finding: This paper contrasts two cognitive models—structural alignment (SA) and representational distortion (RD)—for psychological similarity. It shows through experimental data that RD, which measures similarity by transformation... Read more
Key finding: The study evaluates various similarity measures—Pearson correlation, Minkowski, Mahalanobis—against neural data from fMRI. Findings reveal that preferred neural similarity measures vary across tasks but are consistent across... Read more
Key finding: Empirical studies demonstrate that opposition is a perceptually distinct relation from similarity and difference, which themselves are inversely related. Using tasks involving shape pairs, the work confirms opposition as a... Read more
Key finding: Through empirical studies, the paper validates a formal model linking the strength of category-based inferences to distances in similarity spaces. The framework models similarity-based induction as probabilistic reasoning... Read more
Key finding: This work proposes an unsupervised method to estimate the parameter β in the Information Contrast Model (ICM), a generalization of Pointwise Mutual Information, and empirically validates that optimal β values fall within... Read more

3. How does self-similarity underpin system resilience, structural complexity, and dynamic processes in both natural and engineered contexts?

This theme addresses how self-similar structures and behaviors contribute to system robustness and complexity in varied domains—from software systems and networks to dynamical systems and turbulence. It encompasses studies on the operationalisation of self-similarity for resilience, fractal dynamics in nonlinear phenomena, and scaling behaviors in physical and computational systems.

Key finding: The paper formalizes behavioural self-similarity in systems using operational semantics and shows that systems exhibiting this property can be resilient to a class of adversaries. By linking self-similarity to fault tolerance... Read more
Key finding: This study distinguishes between fractal models and empirical fractal (power-law) behaviors, demonstrating that many self-similar processes manifest as power-law functions incorporating log-periodic oscillations. It develops... Read more
Key finding: Drawing on psychological and sociological literature, the paper argues that emphasizing similarity between social groups, such as LGBTQ+ and non-LGBTQ+ individuals, can enhance social support, reduce stigma, and improve... Read more
Key finding: This work proposes leveraging similarity relations and pretopological spaces for attribute reduction in information systems, enhancing data processing efficiency. By mathematically mapping information systems to... Read more
Key finding: This survey highlights the role of self-similarity and branching in algebra, particularly group theory, showing how self-similar groups acting on rooted trees serve as models for fractal-like behavior in algebraic structures.... Read more

All papers in Extended Self Similarity

The solar wind is a highly turbulent and intermittent medium at frequencies between 10 -4 and 10 -1 Hz. Power spectra are used to look at fluctuations in the components of the magnetic field at high frequencies over a wide range of... more
We propose a novel method for analysing back-ground seismic noise data before an earthquake by using Markov Time Scale algorithm to predict large earthquakes.Alert time obtained based on the data from broad-band stations by analyzing 200... more
We propose a novel method for analysing back-ground seismic noise data before an earthquake by using Markov Time Scale algorithm to predict large earthquakes.Alert time obtained based on the data from broad-band stations by analyzing 200... more
The high-order statistics of fluctuations in velocity gradients in the crossover range from the inertial to the Kolmogorov and sub-Kolmogorov scales are studied by direct numerical simulations (DNS) of homogeneous isotropic turbulence... more
Using data of a direct numerical simulation (DNS) of 3D turbulence it is shown that the moments of order between 1 and 6 of both longitudinal and transverse components of velocity increment for forced as well as decay turbulence can be... more
In this paper we report numerical and experimental results on the scaling properties of the velocity turbulent fields in several flows. The limits of a new form of scaling, named Extended Self Similarity(ESS), are discussed. We show that,... more
Measurements have been made using Laser Doppler Anemometry (LDA) in a fully developed turbulent channel flow with the aim of determining second-order and third-order temporal and spatial structure functions of the longitudinal velocity... more
Using a generalization of extended self-similarity we have studied local scaling properties of incompressible homogeneous isotropic 3D turbulence in a direct numerical simulation. We have found that these properties are consistent with... more
The scaling properties of the temperature structure functions are experimentally investigated in turbulent Rayleigh-BBnard convection at low Prandtl number. It is found that the temperature has the same scaling exponents of a passive... more
The scaling properties of the temperature structure functions are experimentally investigated in turbulent Rayleigh-BBnard convection at low Prandtl number. It is found that the temperature has the same scaling exponents of a passive... more
We measure temperature fluctuations in the Rayleigh-Bénard apparatus, which is a closed cylindrical container with the bottom wall heated and the top wall cooled. The aspect ratio, which is the diameter-to-height ratio of the apparatus,... more
In this work we studied the effect of grain size on retention and transport of deuterium in tungsten. Tungsten consists of grains with distinct crystal structure that are separated by grain boundaries. These grain boundaries can act as... more
The ceramic material Li 2 ZrO 3 has superior thermo-physical and thermo-chemical properties and is highly compatible with other blanket materials used in nuclear reactors. Like LiAlO 2 , it could be used in the form of an annular pellet... more
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
In a solid tritium breeding blanket, Li 4 SiO 4 is in contact with reduced activation ferritic/martensitic (RAFM) steel at high temperatures for years and forms a corrosion layer. The effects of the corrosion layer on the hydrogen isotope... more
We present a pseudospectral study of the randomly forced Navier-Stokes equation (RFNSE) stirred by a stochastic force with zero mean and a variance ϳk 42d2y , with k the wave vector and the dimension d 3. We provide the first evidence for... more
We present a study of the multiscaling of time-dependent velocity and magnetic-field structure functions in homogeneous, isotropic magnetohydrodynamic (MHD) turbulence in three dimensions. We generalize the formalism that has been... more
Recently, Tritium Plasma Experiment (TPE), a unique high-flux linear plasma device that can handle beryllium, tritium and neutron-irradiated plasma facing materials, has undergone major upgrades in its electrical and control systems. The... more
The SORGENTINA-RF project aims to develop a 14 MeV fusion neutron source to produce medical radioisotopes with special focus on $$^{99}$$ 99 Mo. The facility is based on a positive ion source with an acceleration stage to produce a... more
In this work the relation between integral scale and fractal dimension and the type of stratification in fully developed turbulence is analyzed. The integral scale corresponds to that in which energy from larger scales is incoming into a... more
We present an introductory overview of several challenging problems in the statistical characterisation of turbulence. We provide examples from fluid turbulence in three and two dimensions, from the turbulent advection of passive scalars,... more
The Kolmogorov relation for the third order structure function is used to derive the energy spectrum in the far dissipation range (k~oo). With no unspecified constants and methods from matched asymptotic expansions, a uniformly valid form... more
The existence of the "21" spectral law in wall turbulence is explained by the effect of superposition of Kolmogorov's eddy cascades generated at all possible distances from the wall, within an equilibrium layer. This concept is justified... more
The SORGENTINA-RF project aims to develop a 14 MeV fusion neutron source to produce medical radioisotopes with special focus on $$^{99}$$ 99 Mo. The facility is based on a positive ion source with an acceleration stage to produce a... more
A description of the work performed to set up an apparatus to measure permeation rates of hydrogen and tritium in 304L stainless steel is presented. This is in preparation for future work to find and qualify candidate materials resistant... more
The Laser Inertial Fusion Energy (LIFE) power plant is being designed to deliver a transformative source of safe, secure, sustainable electricity, in a time scale that is consistent with the global energy market needs. The LIFE market... more
Unique design of the cryogenic target with a gold conical guide and a fuel feeding capillary has been developed for the Fast Ignition Realization Experiment (FIREX) project at the Institute of Laser Engineering (ILE), Osaka University. In... more
An assumption common to many approaches to understanding and modeling turbulent mixing is that the statistics of a passive scalar at small length scales will approach the analogous statistics of the velocity field as the scale separation... more
wake behind a sphere, rotating about an axis aligned with the streamwise direction, has been experimentally investigated in a water tunnel using LIF visualizations and PIV measurements. The measurements focused on the evolution of the... more
Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Nuclear Science and Engineering, 2013.
Data from SABLES98 experimental campaign have been used in order to study the influence of stability (from weak to strong stratification) on the flux-profile relationships for momentum and heat: φ m and φ h. Standard instrumentatio n, 14... more
The High Temperature Isotopic Exchange (HITEX) process has been proposed as a simple and reliable option for detritiating impurities in the ITER plasma exhaust. 1 The process relies on the well known principle of catalytic equilibration,... more
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of... more
Alumina coating, with a thickness of 1 m, has been manufactured by Pulsed Laser Deposition on EURO-FER. A whole characterization of the interface, bare and coated, with stagnant Pb-17Li eutectic for 1000 h at 550 • C was performed using... more
Tritium management is one of the main challenges that future nuclear fusion energy has to achieve. Accurate tritium monitoring is a basic task in order to have relying fusion reactors. High temperature sensors have to be developed to make... more
The rice grain detachment strength under a straight pull is much greater than the detachment strength due to a perpendicular pull1). The field loss during rice harvesting could be minimized by avoiding the impact on the rice grain,... more
The rice grain detachment strength under a straight pull is much greater than the detachment strength due to a perpendicular pull1). The field loss during rice harvesting could be minimized by avoiding the impact on the rice grain,... more
Submitted for the DFD16 Meeting of The American Physical Society A Numerical Simulation of the Density Oscilator 1 SERGIO HER-NANDEZ ZAPATA, ERICK JAVIER LOPEZ SANCHEZ, GERARDO RUIZ CHAVARRIA, Facultad de Ciencias, UNAM-In this work we... more
h i g h l i g h t s • Radiation enhanced deuterium absorption occurs for RB-SiC. • This type of radiation enhanced absorption is related to Si rather than to C. • Most of the radiation induced absorbed deuterium is released at about the... more
Conditioning of plasma facing components (PFCs) using lithium (Li) evaporation has shown to improve plasma performance in fusion devices by imposing low recycling boundary conditions. It is important to understand the retention and... more
Over the last 7-8 years, two quantitative analyzing methods-accelerator mass spectrometry (AMS) and full combustion (FC) followed by scintillation detection have been applied for determining the tritium activity concentrations in JET... more
The Fusion reactors will use deuterium and tritium as fuel since this reaction takes place at relative ly low temperature. Tritium is not available in nature, it must be produced in the fusion reactor blanket whi ch surrounds the plasma... more
A self-developing gas chromatography (SDGC) process using a column packed with Pd-4 at.% Pt alloy powder was studied for hydrogen isotope separation at room temperature. Separation experiments of a deuterium-tritium (50% D 2-50% T 2)... more
A b s t r a c t :The state of the Earth's fluid core is usually investigated on the basis of the observed features of geomagnetic variations at t he Earth's s urface. This task also involves difficulties associated with shorter... more
Data from SABLES98 experimental campaign have been used in order to study the influence of stability (from weak to strong stratification) on the flux-profile relationships for momentum and heat: φ m and φ h. Standard instrumentatio n, 14... more
Controlled fusion based on the magnetic confinement of the plasma is one of the main aims of the Euro-fusion programme. In the fusion device, the hydrogen isotopes, in nuclear reactions, will produce helium nuclei. The products, as the... more
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