scholarly journals Second class particles and cube root asymptotics for Hammersley’s process

2006 ◽  
Vol 34 (4) ◽  
pp. 1273-1295 ◽  
Author(s):  
Eric Cator ◽  
Piet Groeneboom
Keyword(s):  
Cube Root ◽  
Second Class Particles

scholarly journals A Reliability Based Model for Wind Turbine Selection

2013 ◽  
Vol 2 (2) ◽  
pp. 69-74 ◽  
Author(s):  
A.K. Rajeevan ◽  
P.V. Shouri ◽  
Usha Nair
Keyword(s):  
Power Generation ◽  
Wind Speed ◽  
Wind Turbine ◽  
Wind Power ◽  
Point Of View ◽  
Cube Root ◽  
Mathematical Relationship ◽  
Turbine Generator ◽  
Wind Turbine Generator ◽  
A Site

A wind turbine generator output at a specific site depends on many factors, particularly cut- in, rated and cut-out wind speed parameters. Hence power output varies from turbine to turbine. The objective of this paper is to develop a mathematical relationship between reliability and wind power generation. The analytical computation of monthly wind power is obtained from weibull statistical model using cubic mean cube root of wind speed. Reliability calculation is based on failure probability analysis. There are many different types of wind turbinescommercially available in the market. From reliability point of view, to get optimum reliability in power generation, it is desirable to select a wind turbine generator which is best suited for a site. The mathematical relationship developed in this paper can be used for site-matching turbine selection in reliability point of view.

Estimating the Parameters of a Cube Root Normal Distribution from Reduced Sample Data

1985 ◽  
Vol 21 (1) ◽  
pp. 89-90
Author(s):  
C. J. Potratz ◽  
R. K. Steinhorst ◽  
C. L. Hanson
Keyword(s):  
Normal Distribution ◽  
Cube Root ◽  
Sample Data

Cage size and flight speed of the tobacco hawkmoth Manduca sexta

1995 ◽  
Vol 198 (8) ◽  
pp. 1665-1672 ◽  
Author(s):  
R Stevenson ◽  
K Corbo ◽  
L Baca ◽  
Q Le
Keyword(s):  
Manduca Sexta ◽  
Flight Speed ◽  
Flight Behavior ◽  
Cube Root ◽  
The Third ◽  
Chamber Volume ◽  
Cage Size ◽  
Allometric Analysis ◽  
Size Limits ◽  
Chamber Size

Flight speeds and behaviors of the sphinx moth Manduca sexta were recorded in chambers of four different sizes (0.57, 8.5, 44 and 447 m3). Mean horizontal speed increased linearly with the cube root of chamber volume from 0.57 m s-1 in the smallest chamber to 3.4 m s-1 in the largest. The maximum horizontal speed observed was 5.3 m s-1 in the largest chamber. Speeds decreased linearly with the logarithm of hawkmoth proximity to the wall. In a tunnel chamber (the third largest), moths often flew in a scalloped-shaped path. At the top of the scallop, they glided for 1­5 wing beats. In the largest chamber, moths could be recorded flying at angles other than horizontal (0 °). At flight angles greater or less than 0 °, mean speed decreased linearly with angle until ±40 °. At greater angles, speeds remained between 1 and 2 m s-1. Moths also flew closer to the wall at flight angles deviating from the horizontal. An allometric analysis of the flight speeds of insects and birds suggests that M. sexta may be able to fly at 7­10 m s-1. We conclude that chamber size limits the flight speed and modifies the flight behavior of the tobacco hawkmoth.

Evidence for the homothetic scaling of urban forms

2018 ◽  
Vol 47 (5) ◽  
pp. 870-888 ◽  
Author(s):  
Rémi Lemoy ◽  
Geoffrey Caruso
Keyword(s):  
Land Use ◽  
Population Density ◽  
Scaling Laws ◽  
Radial Distance ◽  
Three Dimensions ◽  
City Size ◽  
Cube Root ◽  
Radial Profiles ◽  
Population Grid ◽  
Urban Scaling

The size and form of cities influence their social and environmental impacts. Whether cities have the same form irrespective of their size is still an open question. We analyse the profile of artificial land and population density, with respect to the distance to their main centre, for the 300 largest European cities. Our analysis combines the GMES/Copernicus Urban Atlas 2006 land use database at 5 m resolution for 300 larger urban zones with more than 100,000 inhabitants and the Geostat population grid at 1 km resolution. We find a remarkable constancy of radial profiles across city sizes. Artificial land profiles scale in the two horizontal dimensions with the square root of city population, while population density profiles scale in three dimensions with its cube root. In short, cities of different size are homothetic in terms of land use and population density, which challenges the idea that larger cities are more parsimonious in the use of land per capita. While earlier literature documented the scaling of average densities (total surface and population) with city size, we document the scaling of the whole radial distance profile with city size, thus liaising intra-urban radial analysis and systems of cities. Our findings also yield homogenous spatial definitions of cities, from which we can re-question urban scaling laws and Zipf’s law for cities.

Collagen and elastin fibers in human pulmonary alveolar walls

1988 ◽  
Vol 64 (4) ◽  
pp. 1659-1675 ◽  
Author(s):  
S. S. Sobin ◽  
Y. C. Fung ◽  
H. M. Tremer
Keyword(s):  
Transpulmonary Pressure ◽  
Collagen Fibers ◽  
Capillary Blood ◽  
Fiber Bundles ◽  
Cube Root ◽  
Inflation Pressure ◽  
Frequency Distributions ◽  
Normal Distributions ◽  
Statistical Frequency ◽  
The Mean

The morphology and morphometric data of collagen and elastin fibers in the pulmonary alveolar walls are presented. Specimens were obtained from postmortem lungs quick-frozen at specified transpulmonary pressures. Collagen was stained by silver, and elastin was stained by orcein. Photomicrographs were composed by computer. Young lungs typically show small collagen fibers that radiate from the "posts," whereas larger fiber bundles traverse the septum irrespective of capillary blood vessels. In older lungs, rings of collagen around the posts appear enlarged. Elastin bundles do not show obvious variation in pattern with age and inflation pressure. Statistical frequency distributions of the fiber width and curvature are both skewed, but the square root of the width and the cube root of the curvature have approximate normal distributions. Typically, for young lungs at transpulmonary pressure of 4 cmH2O, the mean of (width)1/2 (in micron1/2) for collagen fibers is 0.952 +/- 0.242 (SD), that of (curvature)1/3 (in micron-1/3) is 0.349 +/- 0.094. The corresponding values for elastin are 0.986 +/- 0.255 and 0.395 +/- 0.094.

Electrostatic lattice energy in ionic crystals: optimization of the convergence of Ewald series

1978 ◽  
Vol 34 (6) ◽  
pp. 974-979 ◽  
Author(s):  
M. Catti
Keyword(s):  
Lattice Energy ◽  
Rates Of Convergence ◽  
Unit Cell ◽  
Group Symmetry ◽  
Cube Root ◽  
Cell Dimensions ◽  
Madelung Energy ◽  
Direct Lattice ◽  
Unit Cell Dimensions ◽  
Theoretical Results

Ewald's method is reconsidered to express the dependence of Madelung energy on the ionic charges explicitly, also taking into account the space-group symmetry of the structure. Upper bounds for the residues of the two partial series have been calculated by integral approximation; that relative to the direct-lattice series is shown to depend on the cube root of the unit-cell volume. The optimum value of the parameter A, which equalizes the rates of convergence of the two sums and minimizes the total number of terms, has been determined numerically for a given termination error and for a range of unit-cell dimensions. Theoretical results are tested by calculations on some specific crystal structures.

Source comparisons between nuclear and chemical explosions detonated at Rainier Mesa, Nevada Test Site

1999 ◽  
Vol 89 (2) ◽  
pp. 409-422 ◽  
Author(s):  
Brian W. Stump ◽  
D. Craig Pearson ◽  
Robert E. Reinke
Keyword(s):  
Source Region ◽  
Spectral Ratio ◽  
Test Site ◽  
Source Model ◽  
Transverse Component ◽  
Propagation Path ◽  
Cube Root ◽  
Nevada Test Site ◽  
Spectral Difference ◽  
Receiver Array

Abstract A series of nuclear [MINERAL QUARRY (MQ), HUNTERS TROPHY (HT)] and chemical [NON-PROLIFERATION EXPERIMENT (NPE) and NPECAL] explosions were detonated in the same geological material at Rainier Mesa, Nevada Test Site. These sources were extensively instrumented with the same near-source, free-surface instrumentation array. The data from these explosions allow the establishment of empirical source scaling relations as well as investigation of possible chemical and nuclear source differences. Even in the near-source region at common receivers, the data display propagation path effects resulting from slight differences in source locations. These effects are effectively taken into account by smoothing the source comparisons across the different stations in the receiver array. As many as 30 individual waveforms from each source are used in this smoothing process. Comparison of HT and NPE at near-source distances indicates that within the bandwidth of the data (0.36 to 100 Hz), there is no apparent spectral difference between the nuclear and single-fired chemical source. The smoothed spectral ratio between the NPE and NPE CAL is consistent with the long-period source spectral difference (104), corner frequencies (2 to 3 Hz/NPE and 40 to 60 Hz/NPE CAL), and high-frequency decay (ƒ−2) similar to the Mueller-Murphy source model for wet tuff after modifying the cavity radius to scale as the cube root of yield. Comparison of the two nuclear sources, HT and MQ, indicates that at long periods, the HT/MQ ratio is 0.4 to 0.6 with the spectra from the two explosions merging above 5 Hz, which is consistent with the 0.3 magnitude difference observed for the two sources. In all the source comparisons, the spectral ratios of the transverse components of motion are indistinguishable from those produced by either the vertical or radial components. This fact argues that the transverse component of motion from an explosion is generated at very close-in distances, in this case on the order of 1 to 2 km. These observations are in agreement with some type of linear scattering mechanism.

Polynomial Families for Flat-Faced Underwater Bodies and Wall-Sided Ship Sections

1979 ◽  
Vol 23 (04) ◽  
pp. 297-300
Author(s):  
Paul S. Granville
Keyword(s):  
Cube Root ◽  
Infinite Slope ◽  
Zero Curvature ◽  
Inflection Points ◽  
Wide Range ◽  
Root Term

Polynomial families that contain a cube-root term are developed to satisfy requirements of infinite slope and zero curvature. Adjustable parameters are used to provide a wide range of curves without inflection points. Applications are to flat-faced underwater bodies and wall-sided ship sections.

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