The infra-red spectra of crystals

1960 ◽  
Vol 258 (1294) ◽  
pp. 377-401 ◽  
Keyword(s):  
Fourth Order ◽  
Second Order ◽  
Order Moment ◽  
Order Effects ◽  
Ionic Crystals ◽  
Third Order ◽  
Main Band ◽  
The Third ◽  
Cross Terms ◽  
Infra Red

The higher-order effects in the intrinsic infra-red absorption of crystals are investigated in a systematic way. In agreement with a previous paper which dealt with the static dielectric constant, it is found that in the case of ionic crystals the third- and fourth-order potential, the second- and the third-order dipole moment, and the cross-terms between the second-order moment and the third-order potential, all contribute terms of the same order to the infra-red spectrum. In the lowest approximation, the third-order moment and the fourth-order potential only affect the absorption in the immediate neighbourhood of the maximum and hence have little effect on the shape of the spectrum. The broadening of the main band is due mainly to the third-order potential, while the side bands may be caused by the second-order moment as well as by the third-order potential and by cross-terms between the two. But due to an internal field effect, in strongly ionic crystals a large second-order moment automatically leads to a large third-order potential; thus a large second-order moment may increase the width of the main band as well as the intensity of the side bands. Although the intrinsic infra-red absorption of valency crystals, such as diamond or germaniam, is due to the second-order moment only, nevertheless, there is a strong similarity between the expressions for the infra-red absorption of valency crystals and for the side-band absorption of ionic crystals. This similarity suggests that the spectra of all ionic crystals should exhibit a number of secondary maxima. The available experimental evidence does not seem sufficient to decide whether this suggestion is correct.

Higher-order terms in the dielectric constant of ionic crystals

1959 ◽  
Vol 252 (1269) ◽  
pp. 217-235 ◽  
Keyword(s):  
Dielectric Constant ◽  
Dipole Moment ◽  
Higher Order ◽  
Second Order ◽  
Static Dielectric Constant ◽  
Order Moment ◽  
Ionic Crystals ◽  
Third Order ◽  
The Third ◽  
Infra Red

The infra-red absorption of ionic crystals differs in important details from the predictions of the theory based on first approximations. It is known that this discrepancy may be due to two effects which are neglected in such a theory, namely, to the anharmonic terms in the potential energy and to those terms in the dipole moment which are of higher order than the first in the displacement co-ordinates. These higher-order terms in the dipole moment arise from the deformation of the electron shells. The present paper develops in a systematic way the influence of these higher-order effects on the static dielectric constant. Because of the dispersion relations, the terms occurring in the static dielectric constant must also appear in the infra-red absorption spectrum . It is found that the third- and the fourth-order potential, the second- and the third-order dipole moment, and cross-terms between the second-order moment and the third-order potential, all con­tribute terms in the same order to the static dielectric constant. It is also found that the third-order potential contains important contributions from the long-range dipolar inter­action. These dipolar contributions are proportional to the product of the first- and second-order dipole moments, and it follows that in ionic crystals a large second-order moment automatically results in a large third-order potential. It is suggested that these dipolar contributions to the third-order potential may be responsible for the fact that in the infra-red spectra of different ionic crystals not only the intensity of the side band but also the width of the main band varies in the same way as the deformability of the electron shells.

scholarly journals The Light Curves of Double-Mode Cepheids: The CO Aur Case

1998 ◽  
Vol 185 ◽  
pp. 389-390
Author(s):  
E. Poretti ◽  
I. Pardo
Keyword(s):  
Frequency Analysis ◽  
Fourth Order ◽  
A Priori ◽  
Cross Coupling ◽  
Second Order ◽  
Light Curves ◽  
Third Order ◽  
The Third ◽  
Coupling Terms ◽  
Phase Differences

In two recent papers (Pardo & Poretti 1997; Poretti & Pardo 1997) we analyzed all the available photometry of galactic double-mode Cepheids (DMCs) with the aim of detecting in each case the importance of the harmonics and of the cross coupling terms. We found that no a priori fit can be reliably applied to the measurements of a DMC, but a careful frequency analysis must be done to evaluate the importance of each term. As a further application of this technique, we obtained very precise indications about the properties of the Fourier parameters. When discussing the generalized phase differences Gi,j we demonstrated that plotting them as a function of the order |i|+|j|, there are well-defined regions where they are confined: the second order terms have π < Gi,j < 3π/2; the third order terms have π/2 < Gi,j < π; the fourth order terms cluster around 2π.

scholarly journals Huanglongbing-induced Anatomical Changes in Citrus Fibrous Root Orders

HortScience ◽  
2018 ◽  
Vol 53 (6) ◽  
pp. 829-837 ◽  
Author(s):  
Naveen Kumar ◽  
Fnu Kiran ◽  
Ed Etxeberria
Keyword(s):  
Fourth Order ◽  
Second Order ◽  
Vascular Bundles ◽  
Root Mass ◽  
Starch Granules ◽  
Fibrous Root ◽  
Third Order ◽  
Cortical Cells ◽  
The Third ◽  
Order Root

Citrus fibrous roots are vital for absorption and transport of water, nutrients, and other endogenous plant growth regulators. Efficient functioning of these roots in Huanglongbing (HLB)-affected citrus trees is important for their survival. One-year-old ‘Valencia’ sweet orange (Citrus sinensis L. Osbeck) trees on Swingle citrumelo were budded with HLB-infected budwood to determine the HLB-induced pathological responses at the ultrastructural level of different fibrous root orders. The fibrous root mass was dissected into four root orders: fourth-order (attached to a thick rudimentary taproot), third-order (attached to the fourth-order root), and second-order roots (attached to the third-order root). We were not able to study the ultrastructure of the first-order (attached to the second-order root) roots in this study. Severe loss in fibrous root mass was observed within 1 year following HLB infection. All root orders displayed various degrees of HLB symptoms. The fourth-order roots comprised normal phloem and disintegrated phloem. Some vascular bundles had completely disintegrated phloem tissue, whereas others showed normal ultrastructure. The fourth-order roots were also deficient in starch granules compared with controls. The pattern of phloem disintegration was similar in the third- and second-order roots. A thick layer of necrotic phloem developed near cortical cells, while the rest of the phloem structure remained normal in the third- and second-order roots. Cortical cells of both third and second orders were enriched with starch granules; therefore, soluble carbohydrates are most likely not the limiting factor for root decline in these root orders. The xylem anatomy displayed heptarch to pentarch morphology in the various root orders. These observations confirmed that various root orders in the fibrous root system are distinct and exhibit varied pathological responses during HLB pathogenesis. We propose that photosynthates deprived fourth-order roots in conjunction with necrotic phloem promoted decline in all root orders and impaired the translocation process to aboveground plant parts.

Nonlocal Convective PBL Model Based on New Third- and Fourth-Order Moments

2005 ◽  
Vol 62 (7) ◽  
pp. 2189-2204 ◽  
Author(s):  
Y. Cheng ◽  
V. M. Canuto ◽  
A. M. Howard
Keyword(s):  
Fourth Order ◽  
Potential Temperature ◽  
Turbulence Models ◽  
Second Order ◽  
Order Moment ◽  
Third Order ◽  
Mean Velocity ◽  
Eddy Simulation ◽  
Analytic Expressions ◽  
Aircraft Data

Abstract The standard approach to studying the planetary boundary layer (PBL) via turbulence models begins with the first-moment equations for temperature, moisture, and mean velocity. These equations entail second-order moments that are solutions of dynamic equations, which in turn entail third-order moments, and so on. How and where to terminate (close) the moments equations has not been a generally agreed upon procedure and a variety of models differ precisely in the way they terminate the sequence. This can be viewed as a bottom-up approach. In this paper, a top-down procedure is suggested, worked out, and justified, in which a new closure model is proposed for the fourth-order moments (FOMs). The key reason for this consideration is the availability of new aircraft data that provide for the first time the z profile of several FOMs. The new FOM expressions have nonzero cumulants that the model relates to the z integrals of the third-order moments (TOMs), giving rise to a nonlocal model for the FOMs. The new FOM model is based on an analysis of the TOM equations with the aid of large-eddy simulation (LES) data, and is verified by comparison with the aircraft data. Use of the new FOMs in the equations for the TOMs yields a new TOM model, in which the TOMs are damped more realistically than in previous models. Surprisingly, the new FOMs with nonzero cumulants simplify, rather than complicate, the TOM model as compared with the quasi-normal (QN) approximation, since the resulting analytic expressions for the TOMs are considerably simpler than those of previous models and are free of algebraic singularities. The new TOMs are employed in a second-order moment (SOM) model, a numerical simulation of a convective PBL is run, and the resulting mean potential temperature T, the SOMs, and the TOMs are compared with several LES data. As a final consistency check, T, SOMs, and TOMs are substituted from the PBL run back into the FOMs, which are again compared with the aircraft data.

Magnetic circular dichroism and moments for A2 → E transition in C3ν defect centers

1970 ◽  
Vol 48 (22) ◽  
pp. 2769-2779 ◽  
Author(s):  
R. Sati ◽  
M. Inoue ◽  
S. Wang
Keyword(s):  
Circular Dichroism ◽  
Line Shape ◽  
Magnetic Circular Dichroism ◽  
Second Order ◽  
Order Moment ◽  
Third Order ◽  
Closed Expression ◽  
The Third ◽  
Jahn Teller ◽  
Circular Dichroïsm

The spectral line shape of the magnetic circular dichroism (MCD) for the A2 → E transition is investigated. The dynamic Jahn–Teller effect is taken into account by two different methods, i.e. (i) in Franck–Condon and adiabatic approximation and (ii) method of moments. The line-shape function for the magnetic circular dichroism is calculated without using the rigid shift approximation. A comparison of this line shape with the one obtained in the rigid shift shows the two line shapes to be different. General closed expression for the nth order moment is obtained, in the absence and the presence of an externally applied magnetic field, by making use of (i). Zeroth-, first-, and second-order and the change in the third-order moments have been obtained using (ii). The moments up to the second order and the change in the third-order moment have the same expressions as obtained by (i) and (ii). The MCD line shape and the different order moments have also been obtained for the 3A2 → 3E electronic transition in the R′ center.

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

scholarly journals B-splines Algorithms for Solving Fredholm Linear Integro-Differential Equations

2004 ◽  
Vol 1 (2) ◽  
pp. 340-346
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Spline Function ◽  
Cubic Spline ◽  
Second Order ◽  
Third Order ◽  
B Spline ◽  
Numerical Examples ◽  
B Splines ◽  
The Third ◽  
New Procedures

Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

A Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion

1988 ◽  
Vol 32 (02) ◽  
pp. 83-91
Author(s):  
X. M. Wang ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Model ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Potential Flow Model ◽  
Good Agreement

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.

Attenuated microvascular alterations in coarctation hypertension

1989 ◽  
Vol 256 (1) ◽  
pp. H213-H221 ◽  
Author(s):  
D. L. Stacy ◽  
R. L. Prewitt
Keyword(s):  
Fourth Order ◽  
Vascular Tone ◽  
Structural Parameters ◽  
Renal Hypertension ◽  
Second Order ◽  
Hypertensive Rats ◽  
Third Order ◽  
Flow Dependence ◽  
Vascular Beds ◽  
Microvascular Alterations

Arteriolar vasoconstriction, structural reductions in dilated diameter, and rarefaction have been observed in vascular beds with chronic renal hypertension. To determine their pressure or flow dependence, these functional and structural parameters were studied in the developing and chronic stages of coarctation hypertension in the cremaster muscle, a normotensive skeletal muscle bed that is protected from the effects of elevated microvascular pressures. Hypertension was produced in rats by placing a silver clip around the abdominal aorta above the branches of the renal arteries. In hypertensive rats, resting diameters were reduced in second-order arterioles after 4 and 8 wk, in third-order arterioles after 2, 4, and 8 wk, and in fourth-order arterioles after 4 and 8 wk, vs. controls. Vascular tone was elevated in second-order arterioles after 2, 4, and 8 wk and in third- and fourth-order arterioles after 8 wk in hypertensive rats. No increases in medial-intimal area were found at any stage of hypertension in any arteriolar order. The density of small arterioles (3rd-5th orders) was reduced by 20% in hypertensive rats at 8 wk but was unchanged at the other time periods. These arteriolar alterations, especially the absence of structural reductions in diameter, are attenuated compared with those observed in one-kidney, one-clip hypertension and suggest that most of the arteriolar alterations that occur in renal hypertension are pressure or flow dependent.

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