scholarly journals The Distribution of Larvae of Randomly Moving Insects

1961 ◽  
Vol 14 (4) ◽  
pp. 598 ◽  
Author(s):  
EJ Williams
Keyword(s):  
Normal Distribution ◽  
Bessel Function ◽  
Theoretical Distribution ◽  
Frequency Function ◽  
Published Data ◽  
Modified Bessel Function ◽  
Theoretical Conclusion ◽  
Constant Rate ◽  
Spatially Distributed ◽  
Good Agreement

Though randomly moving insects released from a central point in a uniform environment are often found to be distributed according to a circular normal distribution, their larvae will not conform to this distribution. When such insects lay at a constant rate and are subject to constant mortality, their larvae are found to be spatially distributed according to a highly peaked frequency function, depending on the modified Bessel function of the second kind. This theoretical conclusion is in good agreement with published data. Some of the properties of the theoretical distribution are discussed.

Quantitative Measure of EM-Induced Drift in Sub-Micron Al Lines

1998 ◽  
Vol 516 ◽  
Author(s):  
C. Witt ◽  
C.A. Volkert
Keyword(s):  
Electron Microscope ◽  
Focused Ion Beam ◽  
Ion Beam ◽  
Quantitative Measure ◽  
Published Data ◽  
X Ray ◽  
A Value ◽  
Constant Rate ◽  
Scanning Electron ◽  
Good Agreement

AbstractElectromigration-induced drift in sub-micron wide Al segments has been measured using energy dispersive x-ray analysis in a scanning electron microscope. This technique, which works on both passivated and unpassivated samples, is sensitive to uniform Al displacements as small as 100 nm. The samples were 0.3 and 0.5 µm wide runners consisting of a continuous Ti/TiN line on top of which were patterned 0.4µm thick Al (0.5wt% Cu) segments of lengths varying between 5 and 100 µm. The microstructure, as determined by focused ion beam imaging, was predominantly bamboo. We have measured the Al depletion at the cathode ends of these segments after stressing for various times at 2 MA/cm2 at 200'C. For segments shorter than roughly 15 µm, no depletion occurred during the entire 100 hours of the experiment, yielding a value of the current-length threshold product of roughly 3000 A/cm, in agreement with previously published data. Longer segments (20-25 µm) depleted at a roughly constant rate for the duration of the experiment, yielding a drift velocity of around 3 nm/hr in the 0.5 µm wide lines, also in good agreement with published data for near-bamboo lines. However, the 0.3 µm wide lines drifted faster at roughly 6.5 nm/hr. The longest segments (50-100 µm), which started drifting at the same rate as the shorter segments, accelerated after 50 hours of testing to drift velocities in excess of 40 nm/hr. This may be associated with the depletion of Cu from the drifting end.

Analysis of Thermal Variation of Length and Refractive Index of Lead Fluoride to Study its Optical Properties

1989 ◽  
Vol 172 ◽  
Author(s):  
T. S. Aurora ◽  
D. O. Pederson ◽  
S. M. Day
Keyword(s):  
Refractive Index ◽  
Room Temperature ◽  
Linear Thermal Expansion ◽  
Small Variation ◽  
Published Data ◽  
Thermal Variation ◽  
Lead Fluoride ◽  
Superionic Phase Transition ◽  
Lorenz Relation ◽  
Good Agreement

AbstractLinear thermal expansion and refractive index variation have been measured in lead fluoride with a laser interferometer as a function of temperature. Data has been analyzed using the Lorentz-Lorenz relation. Molecular polarizability, band gap, variation of refractive index with density, and strain-polarizability parameter have been studied as a function of temperature. They exhibit a small variation with temperature except near the superionic phase transition where the variation appears to be more pronounced. The results are in good agreement with the published data near room temperature.

scholarly journals Bounds and algorithms for the -Bessel function of imaginary order

2013 ◽  
Vol 16 ◽  
pp. 78-108 ◽  
Author(s):  
Andrew R. Booker ◽  
Andreas Strömbergsson ◽  
Holger Then
Keyword(s):  
Bessel Function ◽  
Convergent Series ◽  
Steepest Descent ◽  
Modified Bessel Function ◽  
Software Library ◽  
Asymptotic Bounds ◽  
Mixed Derivatives ◽  
Rigorous Computation ◽  
Working Out ◽  
Precise Asymptotic

AbstractUsing the paths of steepest descent, we prove precise bounds with numerical implied constants for the modified Bessel function${K}_{ir} (x)$of imaginary order and its first two derivatives with respect to the order. We also prove precise asymptotic bounds on more general (mixed) derivatives without working out numerical implied constants. Moreover, we present an absolutely and rapidly convergent series for the computation of${K}_{ir} (x)$and its derivatives, as well as a formula based on Fourier interpolation for computing with many values of$r$. Finally, we have implemented a subset of these features in a software library for fast and rigorous computation of${K}_{ir} (x)$.

scholarly journals An Integral involving a Modified Bessel Function of the Second Kind and an E-function

1953 ◽  
Vol 1 (3) ◽  
pp. 119-120 ◽  
Author(s):  
Fouad M. Ragab
Keyword(s):  
Positive Integer ◽  
Bessel Function ◽  
Modified Bessel Function ◽  
Image Position

§ 1. Introductory. The formula to be established iswhere m is a positive integer,and the constants are such that the integral converges.

Application of WetSpa model for assessing land use impacts on floods in the Margecany–Hornad watershed, Slovakia

2006 ◽  
Vol 53 (10) ◽  
pp. 37-45 ◽  
Author(s):  
A. Bahremand ◽  
F. De Smedt ◽  
J. Corluy ◽  
Y.B. Liu ◽  
J. Poórová ◽  
...  
Keyword(s):  
Land Use ◽  
Land Use Changes ◽  
Hydrologic Model ◽  
Land Use Impacts ◽  
M Cell ◽  
Time To Peak ◽  
Wetspa Model ◽  
Spatially Distributed ◽  
The Impact ◽  
Good Agreement

The spatially distributed hydrologic model WetSpa combines elevation, soil and land use data within GIS, to predict flood hydrographs and spatial distribution of hydrologic characteristics in a watershed. The model is applied to the Margecany–Hornad river basin (1,131 km2) in Slovakia. Daily hydrometeorological data from 1991–2000, including precipitation data from nine stations, temperature data from four stations and evaporation data measured at one station are used as input to the model. Three base maps, i.e. DEM, land use and soil type are prepared in GIS form, using 100 × 100 m cell size. Results of the simulations show good agreement between calculated and measured hydrographs. The model predicts the daily/hourly hydrographs with 75–80% accuracy according to the Nash–Sutcliff criteria. For assessing the impact of land use changes on floods, the calibrated model is applied for a reforestation scenario, which considers a 50% increase of forest areas. The model results show that the reforestation scenario decreases the peak discharge by 12%. Investigation of peak discharges from the whole simulation period, shows that the scenario results are reduced by 18% on average, while for small discharges the reduction is even about 34%. The time to peak of the simulated hydrograph of the reforestation scenario is 20 hours longer than for the present land use.

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