scholarly journals PECULIARITIES OF THE DIAMETER DISTRIBUTIONS OBTAINED AT SUBMILISECOND DURATION OF DISCHARGE PULSES SPARK-EROSIVE ALUMINUM PARTICLES AND CAVERNS ON THE SURFACE OF ITS GRANULES

2021 ◽  
Vol 2021 (1) ◽  
pp. 10-22
Author(s):  
N.A. Shidlovska ◽  
◽  
S.M. Zakharchenko ◽  
A.O. Perekos ◽  
◽  
...  
Keyword(s):  
Single Mode ◽  
Random Variable ◽  
Size Distributions ◽  
Statistical Parameters ◽  
Aluminum Particles ◽  
Mode Size ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Gauss Distribution ◽  
Diameter Distributions

The conditions and technique for obtaining single-mode size distributions of spark-erosive aluminum particles are given. The statistical parameters of the size distributions of spark-erosive aluminum particles and caverns on the surface of its granules, obtained at a submilisecond duration of discharge pulses were calculated. A comparative analysis of the volumes of metal of erosion caverns and particles is carried out. The agreement of the diameter distributions of spark-erosive particles and caverns obtained in practice with the following theoretical distributions of a continuous random variable: Gauss, Weibull, the integral of the Rosin-Rammler function, and also log-normal distribution is verified. In this case, the parameters of theoretical distributions were calculated both by the statistical parameters of the distributions obtained in practice, and by the criterion of the smallest value of the average module of the relative deviation of the theoretical and practical distributions. It has been shown that for the values of the parameters of theoretical distributions that correspond to the statistical parameters of practical distributions, the distribution of erosive particles by diameters is in the best agreement with the Gauss distribution, and the caverns – with the distribution of integral of the Rosin-Rammler function. References 27, figures 2, tables 3.

scholarly journals A statistical approach to genome size evolution: Observations and explanations

2015 ◽  
Author(s):  
Dirson Jian Li
Keyword(s):  
Genome Size ◽  
Process Model ◽  
Fundamental Problem ◽  
Size Distributions ◽  
Statistical Features ◽  
Genome Size Evolution ◽  
Size Evolution ◽  
Level I ◽  
Log Normal ◽  
Log Normal Distribution

Genome size evolution is a fundamental problem in molecular evolution. Statistical analysis of genome sizes brings new insight into the evolution of genome size. Although the variation of genome sizes is complicated, it is indicated that the genome size evolution can be explained more clearly at taxon level than at species level. I find that the genome size distribution for species in a taxon fits log-normal distribution. And I find a relationship between the phylogeny of life and the statistical features of genome size distributions among taxa. I observed different statistical features of genome size distributions between animal taxa and plant taxa. A log-normal stochastic process model is developed to simulate the genome size evolution. The simulation results on the log-normal distributions of genome sizes and their statistical features agree with the observations.

FROM LOGNORMAL DISTRIBUTION TO POWER LAW: A NEW CLASSIFICATION OF THE SIZE DISTRIBUTIONS

2006 ◽  
Vol 17 (10) ◽  
pp. 1429-1436 ◽  
Author(s):  
LUCIEN BENGUIGUI ◽  
EFRAT BLUMENFELD-LIEBERTHAL
Keyword(s):  
Normal Distribution ◽  
Power Law ◽  
Lognormal Distribution ◽  
Size Distributions ◽  
New Classification ◽  
Multiplicative Process ◽  
Random Multiplicative Process ◽  
Log Normal ◽  
Log Normal Distribution

We propose a new classification of the size distributions of entities based on an exponent α defined from the shape of the log–log Rank Size plot. From an inspection of a large number of cases in different fields, one finds three possibilities: α = 1 giving a power law, α > 1 (parabola like curve) and 0 < α < 1 (analogous to a log normal distribution). A fourth possibility that can be defined when α < 0 was never observed. We present a modified version of models based on a random multiplicative process and an introduction of new entities during the growth. We recover all three kinds of distributions and show that the type of a distribution is conditioned by the rate of the introduction of new entities.

scholarly journals Characterization of Particle Emissions from a DGEN 380 Small Turbofan Fueled with ATJ Blends

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3368
Author(s):  
Remigiusz Jasiński ◽  
Paula Kurzawska ◽  
Radosław Przysowa
Keyword(s):  
Fine Particulate Matter ◽  
Single Mode ◽  
Jet Engines ◽  
Nucleation Mode ◽  
Fuel Blends ◽  
Fuel Flow ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Bypass Ratio

The fine particulate matter (PM) emitted from jet aircraft poses a serious threat to the environment and human health which can be mitigated by using biofuels. This paper aims to quantify PM emissions from a small turbofan fueled with the alcohol to jet (ATJ) synthetic kerosene and its various blends (5%, 20%, and 30% of ATJ) with Jet A-1 fuel. Emissions from a turbofan engine (DGEN 380) with a high bypass ratio, applicable in small private jets, were studied. Among the four fuels tested, the PM-number emission index (EIN) was the lowest for the ATJ 30% blend. EIN for ATJ 30% dropped from 1.1 × 1017 to 4.7 × 1016 particles/kg of fuel. Burning alternative fuel blends reduced the particle mass emissions over the entire range of fuel flow by at least 117 mg/kg of fuel. The particles formed in the nucleation mechanism dominate PM emission, which is characteristic of jet engines. Thus, number-based particle size distributions (PSDs) exhibit a single mode log-normal distribution. The highest values of EIN were found for Jet A-1 neat compared to other fuels. The use of the ATJ additive did not cause significant changes in the size of the particles from nucleation mode. However, a magnitude reduction of nucleation mode was found with the increase in the ATJ ratio.

Study of the Effect of Pinning Particles on Grain Size Distributions

2013 ◽  
Vol 753 ◽  
pp. 361-366 ◽  
Author(s):  
Han Li ◽  
Suk Bin Lee ◽  
Anthony D. Rollett
Keyword(s):  
Grain Size ◽  
Normal Distribution ◽  
Grain Growth ◽  
Volume Fraction ◽  
Medium Size ◽  
Second Phase ◽  
Size Distributions ◽  
Grain Size Distributions ◽  
Log Normal ◽  
Log Normal Distribution

The present paper studies grain growth in the presence of inert particles by performing large-scale simulations using a parallel Monte Carlo Potts model. The effect of the second phase particles on the grain size distribution (GSD) is analyzed. The GSDs diverge markedly from log-normal distribution for normal grain growth case. For the cases with low volume fraction of particles, we find that the grain size distributions approach log-normal as stagnation takes hold. For the cases with a high volume fraction of particles, however, medium-size grains reach the log-normal distribution but both lower and upper tails diverge noticeably from the log-normal distribution over time.

scholarly journals Probability Assessment of the Mechanical and Low-Cycle Properties of Structural Steels and Aluminium

Metals ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 918
Author(s):  
Žilvinas Bazaras ◽  
Vaidas Lukoševičius ◽  
Andrius Vilkauskas ◽  
Ramūnas Česnavičius
Keyword(s):  
Mechanical Properties ◽  
Normal Distribution ◽  
Low Cycle Fatigue ◽  
Relative Yield ◽  
Proportional Limit ◽  
Statistical Parameters ◽  
Area Reduction ◽  
Log Normal ◽  
Percent Area ◽  
Log Normal Distribution

Key mechanical properties used in low-cycle strength and durability calculations are the strength (proportional limit stress, σpr; relative yield strength, σ0.2; and ultimate tensile stress, σu) and strain properties (proportional limit strain, epr; percent area reduction, ψ; and percent area reduction at failure, ψu). When selecting the key mechanical properties provided in the specifications, an error may be made due to the failure to account for a series of random factors that determine the distribution of properties. The majority of research papers dealing with statistical descriptions of the low-cycle strain properties do not look deeper into the distribution of mechanical properties and the diagram parameters of strain characteristics. This paper provides a description of the distribution patterns of mechanical properties, statistical parameters, and low-cycle fatigue curves. Log-normal distribution generated the lowest values for the coefficient of variation of one of the key statistical indicators, suggesting that log-normal distribution is superior to normal or Weibull distribution in this respect. The distribution of low-cycle strain parameters exceeded the distribution of mechanical properties considerably. Minimum coefficients of variation of the parameters were generated at normal distribution. The statistical analysis showed the lower distribution of the durability parameters compared to the distribution of parameters of the strain diagrams. The findings of the paper enable a revision of the durability and life of the structural elements of in-service facilities subject to elastoplastic loading by assessing the distribution of mechanical characteristics and low-cycle strain parameters as well as the permissible distribution limits.

scholarly journals A Universal Model for the Log-Normal Distribution of Elasticity in Polymeric Gels and Its Relevance to Mechanical Signature of Biological Tissues

Biology ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 64
Author(s):  
Arnaud Millet
Keyword(s):  
Elastic Modulus ◽  
Normal Distribution ◽  
Biological Tissues ◽  
Force Microscopy ◽  
Polymeric Gels ◽  
Atomic Force ◽  
Clear Explanation ◽  
Log Normal ◽  
Log Normal Distribution

The mechanosensitivity of cells has recently been identified as a process that could greatly influence a cell’s fate. To understand the interaction between cells and their surrounding extracellular matrix, the characterization of the mechanical properties of natural polymeric gels is needed. Atomic force microscopy (AFM) is one of the leading tools used to characterize mechanically biological tissues. It appears that the elasticity (elastic modulus) values obtained by AFM presents a log-normal distribution. Despite its ubiquity, the log-normal distribution concerning the elastic modulus of biological tissues does not have a clear explanation. In this paper, we propose a physical mechanism based on the weak universality of critical exponents in the percolation process leading to gelation. Following this, we discuss the relevance of this model for mechanical signatures of biological tissues.

scholarly journals Extreme geomagnetic activities: a statistical study

2020 ◽  
Vol 72 (1) ◽  
Author(s):  
Ryuho Kataoka
Keyword(s):  
Magnetic Storms ◽  
Magnetic Observatory ◽  
Statistical Distributions ◽  
Limited Data ◽  
Data Set ◽  
Sudden Commencements ◽  
The One ◽  
Log Normal ◽  
Geomagnetic Activities ◽  
Log Normal Distribution

Abstract Statistical distributions are investigated for magnetic storms, sudden commencements (SCs), and substorms to identify the possible amplitude of the one in 100-year and 1000-year events from a limited data set of less than 100 years. The lists of magnetic storms and SCs are provided from Kakioka Magnetic Observatory, while the lists of substorms are obtained from SuperMAG. It is found that majorities of events essentially follow the log-normal distribution, as expected from the random output from a complex system. However, it is uncertain that large-amplitude events follow the same log-normal distributions, and rather follow the power-law distributions. Based on the statistical distributions, the probable amplitudes of the 100-year (1000-year) events can be estimated for magnetic storms, SCs, and substorms as approximately 750 nT (1100 nT), 230 nT (450 nT), and 5000 nT (6200 nT), respectively. The possible origin to cause the statistical distributions is also discussed, consulting the other space weather phenomena such as solar flares, coronal mass ejections, and solar energetic particles.

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