Length, Area and Dimension: Measuring Complexity and Scaling Properties

1992 ◽  
pp. 183-228 ◽  
Author(s):  
Heinz-Otto Peitgen ◽  
Hartmut Jürgens ◽  
Dietmar Saupe
Keyword(s):  
Scaling Properties

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

scholarly journals From Center-Vortex Ensembles to the Confining Flux Tube

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 253
Author(s):  
David R. Junior ◽  
Luis E. Oxman ◽  
Gustavo M. Simões
Keyword(s):  
Degrees Of Freedom ◽  
String Tension ◽  
Effective Field ◽  
Scaling Properties ◽  
Flux Tubes ◽  
Topological Solitons ◽  
Yang Mills ◽  
Center Vortex ◽  
Asymptotic Scaling ◽  
The Continuum

In this review, we discuss the present status of the description of confining flux tubes in SU(N) pure Yang–Mills theory in terms of ensembles of percolating center vortices. This is based on three main pillars: modeling in the continuum the ensemble components detected in the lattice, the derivation of effective field representations, and contrasting the associated properties with Monte Carlo lattice results. The integration of the present knowledge about these points is essential to get closer to a unified physical picture for confinement. Here, we shall emphasize the last advances, which point to the importance of including the non-oriented center-vortex component and non-Abelian degrees of freedom when modeling the center-vortex ensemble measure. These inputs are responsible for the emergence of topological solitons and the possibility of accommodating the asymptotic scaling properties of the confining string tension.

scholarly journals Critical Dynamics of Defects and Mechanisms of Damage-Failure Transitions in Fatigue

Materials ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2554
Author(s):  
Oleg Naimark ◽  
Vladimir Oborin ◽  
Mikhail Bannikov ◽  
Dmitry Ledon
Keyword(s):  
Fatigue Damage ◽  
Kinetic Equations ◽  
Experimental Methodology ◽  
Preliminary Deformation ◽  
Scaling Properties ◽  
In Situ Data ◽  
Number Of Cycles ◽  
Fish Eye ◽  
Very High

An experimental methodology was developed for estimating a very high cycle fatigue (VHCF) life of the aluminum alloy AMG-6 subjected to preliminary deformation. The analysis of fatigue damage staging is based on the measurement of elastic modulus decrement according to “in situ” data of nonlinear dynamics of free-end specimen vibrations at the VHCF test. The correlation of fatigue damage staging and fracture surface morphology was studied to establish the scaling properties and kinetic equations for damage localization, “fish-eye” nucleation, and transition to the Paris crack kinetics. These equations, based on empirical parameters related to the structure of the material, allows us to estimate the number of cycles for the nucleation and advance of fatigue crack.

Scaling properties of induction times in heterogeneous nucleation

1991 ◽  
Vol 95 (12) ◽  
pp. 9148-9150 ◽  
Author(s):  
Vitaly A. Shneidman ◽  
Michael C. Weinberg
Keyword(s):  
Heterogeneous Nucleation ◽  
Scaling Properties ◽  
Induction Times

scholarly journals The Effect of Polytetrafluoroethylene (PTFE) Particles on Microstructural and Tribological Properties of Electroless Ni-P+PTFE Duplex Coatings Developed for Geothermal Applications

Coatings ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 670
Author(s):  
Gifty Oppong Boakye ◽  
Arna María Ormsdóttir ◽  
Baldur Geir Gunnarsson ◽  
Sandeep Irukuvarghula ◽  
Raja Khan ◽  
...  
Keyword(s):  
Wear Resistance ◽  
Tribological Properties ◽  
Complex Geometry ◽  
Corrosion And Wear ◽  
Functional Layer ◽  
Scaling Properties ◽  
Wear Rates ◽  
Mechanical And Tribological Properties ◽  
Duplex Coating ◽  
Wear Protection

The selection of electroless nickel-phosphorus plating (ENP) has been inclined towards their properties and advantages with complex geometry applications. These properties include coating uniformity, low surface roughness, low wettability, high hardness, lubricity, and corrosion- and wear-resistance. Materials used in geothermal environments are exposed to harsh conditions such as high loads, temperature, and corrosive fluids, causing corrosion, scaling, erosion and wear of components. To improve the corrosion- and wear-resistance and anti-scaling properties of materials for geothermal environment, a ENP duplex coating with PTFE nanoparticles was developed and deposited on mild steel within the H2020 EU Geo-Coat project. ENP thin adhesive layer and ENP+PTFE top functional layer form the duplex structure of the coating. The objective of this study was to test the mechanical and tribological properties of the developed ENP-PTFE coatings with varying PTFE content. The microstructural, mechanical and tribological properties of the as-deposited coating with increasing PTFE content in the top functional layer in the order: ENP1, ENP2 and ENP3 were evaluated. The results showed maximum wear protection of the substrates at the lowest load; however, increasing load and sliding cycles increased the wear rates, and 79% increased lubrication was recorded for the ENP2 duplex coating. The wear performance of ENP3 greatly improved with a wear resistance of 8.3 × 104 m/mm3 compared to 6.9 × 104 m/mm3 for ENP2 and 2.1 × 104 m/mm3 for ENP1. The results are applicable in developing low friction, hydrophobic or wear-resistive surfaces for geothermal application.

scholarly journals Recent scaling properties of Bitcoin price returns

2021 ◽  
Vol 1730 (1) ◽  
pp. 012124
Author(s):  
T Takaishi
Keyword(s):  
Scaling Properties

scholarly journals Multi-scaling properties of truncated Lévy flights

2000 ◽  
Vol 266 (4-6) ◽  
pp. 282-289 ◽  
Author(s):  
Hiroya Nakao
Keyword(s):  
Lévy Flights ◽  
Scaling Properties ◽  
Levy Flights

Scaling properties of a Si surface patterned by selective chemical etching

2004 ◽  
Vol 36 (1-3) ◽  
pp. 353-358 ◽  
Author(s):  
G. Wisz ◽  
T.Ya. Gorbach ◽  
P.S. Smertenko ◽  
A. Blahut ◽  
K. Zembrowska ◽  
...  
Keyword(s):  
Chemical Etching ◽  
Scaling Properties ◽  
Selective Chemical ◽  
Selective Chemical Etching
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