Allowance For Dispersion Research Articles

Orientation dependence of the interfacial energies of chromium and α-iron crystals at boundaries with nonpolar organic liquids

Interfacial energies of chromium and α-iron at boundaries with nonpolar organic liquids are calculated within the modified variant of the statistical electron method. Calculations are performed with allowance for dispersion, oscillatory, polarization corrections and the contribution from temperature. The dependence of the interfacial energy on the orientation of metallic crystals, and on the macroscopic dielectric permeability of the organic liquid, is established. The profiles of the potential and electron density at the boundary of the phase separation are considered.

Radiation of a charge moving in a waveguide filled with a dielectric medium possessing resonance dispersion

The radiation of a point charged particle moving along the axis of a round waveguide filled with a dielectric medium possessing resonance dispersion is theoretically studied. It is shown that the dispersion significantly influences the frequencies of excited harmonic modes and the energy of radiation. Allowance for dispersion leads to suppression of all excited harmonics to an extent increasing with the order of harmonics.

Propagation of optical pulses in periodic nonlinear fibers

We study the conditions of formation and propagation of soliton pulses in a periodic two-mode nonlinear fiber with allowance for dispersion of the fiber material and intermode dispersion of interacting modes under the condition of their phase synchronism.

Effect of dispersion on a plane ultrasonic pulse

Propagation through typical biological media involves dispersion as well as attenuation, since the attenuation coefficient varies with frequency more slowly than f2 in the ultrasonic range. Dispersion effects are explored for plane pulses in a homogeneous medium. The smoothing of an initially steplike pulse as it propagates through different attenuating media is illustrated numerically. Pulse waveforms are compared with and without allowance for dispersion, using a family of model α(f) curves. The associated dispersion in each case is obtained from the Kramers‐Kronig relations, which ensure that the propagation transfer function is causal.

Assessment of the stability of the turbidity spectrum method to the effect of the dispersion of the particulate substance and the medium

Determinations of the parameters of disperse systems (particle radius r, mass My, and number N concentrations) by the turbidity spectrum method [I] usually omit any allowance for the dispersion of the particulate substance and the medium. In many cases this assumption is quite justifiable when the turbidity spectrum is measured far from absorption bands [2,3]. llowever, no assessment has yet been made of the general effect of omitting the dependence of the refractive indices of the particles ~ and of the dispersing medium ~o on the wavelength of the light % on light scattering data inversion by the turbidity spectrum method. This is part of the general question of the stability of methods for the inversion of light-scattering data (see [4], for example) and demands special analysis, which we provide here. In the calibration dependence of the wavelength exponent n on the relative particle size a = 2~r~o/~ (~ is the vacuum wavelength) the dispersion correction is given by [2,3] n ( ~ = no (~) F, PFz, ( I ) where no(a) is the dependence of the wavelength exponent on a without allowance for dispersion [1,2]; and FI, F2, and P are the correction coefficients appropriate to the particular system. The factor Fx allows for the dispersion of the medium: F~ = 1 d l n ~ o / d t n ~ . (2) The correction for the dispersion of the particulate substance is given by the product of F z = d m / d ~ , (3) P = 2 1 ( m 1 ) 5 ( m -1), (4) where m = ~/~o is the relative refractive index of the particles. Obviously the approximation of the function n(a) by the dispersion-free calibration no(a) [the assumption that n(a) = no(a)] introduces a systematic error into the determination of r, My, and N. If n is considered fixed, for example, determined experimentally, the error in r is 6r = ~ / % 1). 100%, (5) where a is the exact value of the parameter a found from Eq. (I) and ao is the root of the equation no (So) = n. ( 6 ) The errors ~My and 8N can be expressed in terms of ~r [I]: 8M v = {(1 qO.O18r)/(1 + no.0.016r) 1}. t00, %, (7) 6N = {1~1 + 0.016r)Z.(1 + no'0.016r) 1}. 100, %. (8) We can show that ~r corresponds to the relative increase in the parameter u, determined from the dispersion-free calibration, due to the increment Ano = no(a) -n(a): An0 (FT 1 1) n + PFz/FI. (9) Thus o u r p r o b l e m i s e s s e n t i a l l y e q u i v a l e n t t o c a l c u l a t i n g t h e s y s t e m a t i c e r r o r s i n t h e d e t e r m i n a t i o n o f r , t Iy , and N f r o m t h e c a l i b r a t i o n n o ( a ) i n t h e p r e s e n c e o f t h e s y s t e m a t i c a b s o l u t e e r r o r i n n g i v e n by Eq. ( 9 ) . We c a r r i e d o u t n u m e r i c a l c a l c u l a t i o n s o f t h e e r r o r s 6 r , 6My, and ~N o v e r a w i d e r a n g e o f v a l u e s o f n and w i t h d i f f e r e n t m f o r t h e s p e c i f i c e x a m p l e o f t h e s u s p e n s i o n o f p o l y m e r Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 31, No. I, pp. 117-121, July, 1979. Original article submitted June 19, 1978.

Effects of misplaced atoms on the residualR2in space groups of higher symmetry

In space groups of symmetry higher than P1 misplacement of a single atom implies the misplacement of all those in the same Wyckoff position, and hence the effect on the residual is larger than in P1. 'Exact' values of the residual R2 are obtained, with explicit allowance for dispersion.

Recovery of Released Male Cabbage Looper Moths in Traps Equipped with Blacklight Lamps and Baited with Virgin Females123

Moths of the male cabbage looper, Trichoplusia ni (Hubner), were marked and released and then captured in traps equipped with black light lamps, unbaited or baited with virgin females, distributed over a 690-acre experimental area at Home Gardens, California. Although moths that were 3 to 4-days old when they were liberated were caught sooner than those that were 0 to 1 day old, the total catches of the 2 age groups were not significantly different. Moths were recovered as much as 10,000 feet from the release point, but the numbers of released moths captured decreased with increasing distance of the traps from the point of release. The number of days before the catch of released moths dropped to 50 and 95% of the total recovered ranged from 1.3 to 1.5 days and from 3.0 to 4.3 days, respectively. Twenty-two baited traps in the experimental area captured as high as 17% of the released male moths and baited traps were more efficient than unbaited traps. Estimates of the total male cabbage looper moth population for July, October, and November ranged from 504 to 54/acre. The data, after allowance for dispersion, indicated that more than 9070 of the estimated cabbage looper male recoveries were made within 4000 feet from the point of release.