... infinities in the frequency spectrum. We define g(ν) so that g(ν)dν is the number of normal modes of vibration with frequencies between ν and ν+dν. A closed expression involving complete elliptic integrals is obtained for g(ν) when τ=[1+(α/2γ)]−1=⅓. For general values of τ<½, g(ν) is shown to have the following properties: (a) ... atom. (b) There is an infinity in g(ν) at ν=νLτ½. (c) The second infinity is at ν=νL(1−τ)12 if τ<15, and ν=νL(1+3τ)/4τ12 if τ>15. ( ...
Tópico(s): Mechanical and Optical Resonators
1947 - American Institute of Physics | The Journal of Chemical Physics
J. Romanko, T. Feldman, H. L. Welsh,
... 1 . Analyses of the rotational structures of the ν 1 and ν 2 totally symmetric bands were carried out; only the Q branch of the ν 2 band was observed. The structures of the degenerate ν 10 and ν 11 bands were analyzed; however, no trace of ν 12 was found. The structure of the ν 10 band shows beyond doubt that the point ... of the molecule is D 3d . From the ν 11 +ν 4 infrared band, and the ν 11 Raman band, the value, 278.4 cm. − ...
Tópico(s): Atmospheric Ozone and Climate
1955 - NRC Research Press | Canadian Journal of Physics
... 3 cm −1 , and rotational analyses of the ν and ν 2 bands were carried out. The B 0 values obtained from the ν 2 and ν 3 bands are 5.240 ± 0.002 and ... 0.0011 cm −1 , respectively; the value of ν 0 determined from the latter is 1.09403 ± 0.00016 Å. The rotational levels of the ν = 1 state of ν 2 are double with B 1 values of ... 379 cm −1 . The rotational levels of the ν = 1 state of ν 2 do not follow the theoretical formulae exactly; ... 3 is 0.054. The band origins are: ν 1 = 2916.7, ν 2 = 1533.6, and ...
Tópico(s): Atmospheric Ozone and Climate
1960 - NRC Research Press | Canadian Journal of Physics
R. A. Olafson, M. A. Thomas, H. L. Welsh,
... 4 cm −1 , and rotational analyses of the ν 2 and ν 3 bands were carried out. The B 0 values obtained from the ν 2 and ν 3 bands are 2.6330 ± 0.0007 and ... 0.00029 Å. The rotational levels of the ν = 1 state of ν 2 are split with effective B 1 values ... 1 . Thirteen of the fifteen branches of the ν 3 band were observed; these also show multiple ... Structure was observed but not analyzed in the ν 1 , 2ν 4 , and ν 2 + ν 4 bands. On the basis of the Raman ...
Tópico(s): Laser-Matter Interactions and Applications
1961 - NRC Research Press | Canadian Journal of Physics
... rate of the reaction H + Cl 2 → HCl† ν + Cl proceeding to form HCl in vibrationally excited states ν = 1–6, of the ground electronic state. In ... notable for the presence of vibrators in levels ν = 7 and 8, which are respectively 4 and ... simple model yielded a collision efficiency for HCl† ν=1 + HCl† ν=6 → HCl† ν=7 + HCl† ν=0 , of Z 1,6 t = 6 × 10 ... states indicative of a fast vibrational transfer, HCl ν=0 + HCl† ν=2 → 2 HCl† ν=1 .At reduced pressure of HCl† the stationary- ...
Tópico(s): Molecular Spectroscopy and Structure
1964 - NRC Research Press | Canadian Journal of Chemistry
M. Ogawa, Yoshio Tanaka, A. S. Jursa,
... follows: [Formula: see text], 100 824 cm −1 , ν = 0; (b 1 Π u ), 101 455 cm −1 , ν = 1; (l 1 Π u ), 104 146 cm −1 , ν = 5; [Formula: see text], 104 366 cm −1 , ν = 0; (m 1 Π u ), 105 350 cm −1 , ν = 5 ~ 7; (o 1 Π u ), 105 703 cm −1 , ν = 0; [Formula: see text], 106 649 cm −1 , ν = 4; (p 1 Π u ), 108 373 cm −1 , ν = 9 ~ 10; [Formula: see text], 109 833 cm −1 , ν = 11 ~ 12; [Formula: see text] 110 944 cm −1 , ν = 10; (s ?), 116 688 cm −1 , ν > 20; ...
Tópico(s): Atomic and Subatomic Physics Research
1964 - NRC Research Press | Canadian Journal of Physics
... un opérateur différentiel sur R x n , P(ν,D x ), dont les coefficients sont constants par ... x, mais sont des fonctions C ∞ du point ν d’un ouvert Ω de R n . L’ ... est dit formellement hypoelliptique dans Ω si P(ν,D) est hypoelliptique pour chaque ν et si, pour deux points ν 1 ,ν 2 quelconques de Ω, P(ν 1 ,D) et P(ν 2 ,D) sont équivalents au sens d’Hörmander. ... ci-dessus, il existe une fonction C ∞ E(ν) de ν, à valeurs dans l’espace des opérateurs continus ...
Tópico(s): Diet and metabolism studies
1959 - Association of the Annals of the Fourier Institute | Annales de l’institut Fourier
... 2, where n is a positive integer, x = {(ν" - ν')/(ν" + ν')}2 and ν', ν" are the vibration frequencies in upper and lower ... vertical line]l[vertical line]+d where q = (ν'ν")½/½(ν' + ν").
Tópico(s): Advanced Chemical Physics Studies
1966 - IOP Publishing | Proceedings of the Physical Society
... conform to a flow equation of the form ν = ν∞+ν0−ν∞1+aDn where η is the viscosity at ... se conformer à l'équation de la formule ν = ν∞+ν0−ν∞1+aDnoù est la viscosité au taux de ... conformare alla equazione di flusso della forma seguente: ν = ν∞+ν0−ν∞x dove η é la viscosità con resistenza ... von nicht Newtonschen Verhalten einer Gleichung der Form ν = ν∞+ν0−ν∞1+aDn gehorchen sollten. Hierin ...
Tópico(s): Polymer crystallization and properties
1966 - Elsevier BV | European Polymer Journal
... capability. This new structure employs a unique π-ν (nearly intrinsic p- and n-type) epitaxial-layer ... expanded second-breakdown performance. An n + -p-π-ν-n + transistor structure is constructed using alternately grown π and ν, epitaxial high-resistivity layers, p-type base and ... The depletion region for the n + -p-π-ν-n + transistor is in the π base and the ν collector, and the maximum electrical field ( E_{\max} ) is at the π-ν interface. The avalanche breakdown V B of the ... concentration ( N_{A}, N_{D} ) of the π-ν layers. Limiting the thickness of the ν collector ...
Tópico(s): Advancements in Semiconductor Devices and Circuit Design
1970 - Institute of Electrical and Electronics Engineers | IEEE Transactions on Electron Devices
H. Eugene Stanley, M. Blume, Koichiro Matsuno, S. Milošević,
... the Hamiltonian Hν=− ∑ i=1N Ji,i+1Si(ν)·Si+1(ν),where the exchange constants Ji,i+1 are arbitrary numbers. We find for all spin dimensionalities ν that the two-spin correlation function may be expressed as ρN(ν) (γ) = (λ1(ν)/λ0(ν))r, where λ0(ν) and λ1(ν) are the largest and next-largest eigenvalues of ... Thus the onset of longrange order, limr→∞ρN(ν) (γ)≠0, is characterized by the degeneracy of λ0(ν) and λ1(ν). This onset of long-range ...
Tópico(s): Opinion Dynamics and Social Influence
1970 - American Institute of Physics | Journal of Applied Physics
... of the band heads can be expressed as ν= 33062.4 + 304.3 (ν′+ 1/2)– 0.71(ν′+ 1/2)2– 246.7(ν″+ 1/2)+ 0.64(ν″+ 1/2) cm–1. A similar system of ... frequencies of the band heads are given by ν= 32172.8 + 241.1(ν′+ 1/2)– 0.17(ν′+ 1/2)2– 199.0(ν″+ 1/2)+ 0.55(ν″+1/2)2 cm–1. Consideration of the ...
Tópico(s): Nonlinear Optical Materials Research
1968 - Royal Society of Chemistry | Transactions of the Faraday Society
Robert K. Thomas, H. W. Thompson,
... investigated with high resolving power. Five parallel bands (ν 1 , ν 2 , ν 5 , 2ν 9 and 2ν 8 ) have been ... rotational structure of four degenerate fundamental vibration bands ν 6 , ν 7 , ν 8 and ν 9 has been analysed. Perturbations of ν 7 by Coriolis interaction with ν 7 , and Fermi resonance with (ν 8 + ν 10 ) have been detected, and analysed ...
Tópico(s): Advanced Chemical Physics Studies
1968 - Pergamon Press | Spectrochimica Acta Part A Molecular Spectroscopy
Robert K. Thomas, H. W. Thompson,
... Structure has been resolved in five parallel bands (ν 1 , ν 2 , ν 3 , 2ν 9 and 2ν 8 ) and values ... four fundamental degenerate vibrations have been measured. For ν 6 and ν 8 the Q branches have been analysed and ... A − α B ) have been determined. The band ν 7 is perturbed by both Coriolis interaction and ... analysis has been made. The Coriolis perturbation between ν 7 and ν 4 , and Fermi resonance between ν 7 and (ν 8 + ν 10 ) have been interpreted. An unusual ...
Tópico(s): Spectroscopy and Laser Applications
1968 - Pergamon Press | Spectrochimica Acta Part A Molecular Spectroscopy
Craig B. Murchison, John Overend,
Abstract The i.r. spectra of the ν 2 , 2ν 3 , 2ν 1 ,ν 1 + 2ν 2 0 and 4 ν 2 0 bands of 35 Cl 12 C 14 N ... effects of the Fermi resonance between the states ¦ν 1 , ν 2 , l 2 , ν 3 , > and ¦ν 1 −1, ν + 2, l 2 , ν 3 >. The dependence of the matrix element of ... number J and on the vibrational quantum numbers ν 2 and ν 3 has also been determined ...
Tópico(s): Atmospheric Ozone and Climate
1971 - Pergamon Press | Spectrochimica Acta Part A Molecular Spectroscopy
... effect of the V – V couplings between mode ν 3 and modes ν 1 +ν 2 on the relaxation of mode ν 1 (ν 2 ) is not appreciable due to the small vibrational heat capacity of mode ν 3 , and the apparent relaxation rate for mode ν 1 (ν 2 ) is nearly equal to a mean rate ... K ∞ of the T – V processes of modes ν 1 and ν 2 . If the rate of the intramolecular V – ...
Tópico(s): Phase Equilibria and Thermodynamics
1971 - Physical Society of Japan | Journal of the Physical Society of Japan
George Birnbaum, W. W. Ho, A. Rosenberg,
... variation of the absorption is fitted by α(ν, ρa) = ρa2α2(ν) + ρa3α3(ν) to obtain values of α2(ν) and α3(ν). The coefficient α2(ν) and its temperature dependence is discussed in the previous paper of this series. The coefficient α3(ν) is negative in sign and has a band shape considerably sharper than that found for α2(ν). The Kramers–Kronig integral π−2∫α3(ν)ν−2dν is in reasonable agreement with the theoretical ...
Tópico(s): Phase Equilibria and Thermodynamics
1971 - American Institute of Physics | The Journal of Chemical Physics
J.L. Duncan, David Ellis, I.J. Wright,
... of the Fermi and Coriolis interacting band system ν 3, ν 6, ν 7 + ν 8 of methyl cyanide has been performed with ... the effects of both the Fermi resonance of ν 6 with ν 7 + ν 8 and the Coriolis resonance of ...
Tópico(s): Spectroscopy and Laser Applications
1971 - Taylor & Francis | Molecular Physics
... More than 150 maxima were resolved in the ν 17 band and the spectrum was analyzed with a computer program to give ν 17 = 1177.776(10) cm −1 , B 1 – ... 1). About 60 maxima were recorded in the ν 18 band; molecular constants were determined but with less precision than for ν 17 . The ν 15 band (partially overlapped by ν 1 ) and the (ν 16 , ν 2 + ν 18 ) Fermi diad showed resolved structure but no detailed analyses were possible. The ν 11 band showed no resolved structure.
Tópico(s): Spectroscopy and Laser Applications
1978 - NRC Research Press | Canadian Journal of Physics
Barry M. McCoy, Craig A. Tracy, Tai Tsun Wu,
... the one-parameter family of solutions, η (ϑ;ν,λ), that remain bounded as ϑ→∞ along the ... w4−1, where, as ϑ→∞, η ∼ 1−λΓ (ν+1/2)2−2νϑ−ν−1/2e−2ϑ. We further construct a representation for ψ (t;ν,λ) =−ln[η (t/2;ν,λ)], where ψ (t;ν,λ) satisfies the differential equation ψ′′+t−1ψ′= ( ... ψ). The small-ϑ behavior of η (ϑ;ν,λ) is described for ‖λ‖<π−1 by η (ϑ;ν,λ) ∼ 2σBϑσ. The parameters σ and B are given as explicit functions of λ and ν. Finally an identity involving the Painlevé transcendent η (ϑ;ν,λ) is proved. These results for the special ...
Tópico(s): Molecular spectroscopy and chirality
1977 - American Institute of Physics | Journal of Mathematical Physics
Steven C. Leasure, Joel M. Bowman,
... integral cross sections for 4 He + H 2 (ν = 0, j = 0) → 4 He + H 2 (ν′ = 1, j ′ = 0, 2) have been calculated in ... sets in the close coupling calculations, i.e., ν = 0,1, ν = 0,1, 2, ν = 0, 1, 2, 3 and ν = 0, 1, 2, 3, 4. Between 4.2 ... calculations were done with three vibration basis sets; ν = 0.–4, ν = 0–5, and ν = 0–6. It is ...
Tópico(s): Molecular Spectroscopy and Structure
1977 - Elsevier BV | Chemical Physics Letters
John E. Spencer, Harumi Endo, G. Glass,
Reactions of OH(ν=0, 1 and 2) with several species that play an important role in hydrocarbon combustion have been studied, at ... two sources: (1) the reaction O+HBr→OH(ν=1)+Br, which produces OH(ν=1) in 97% yield, and (2) the reaction H+NO2→OH(ν)+NO, which produces large amounts of OH in ν=2, 1 and 0. Rate constants for physical deactivation of OH(ν=1) by O, CO, H2 and CH4 were ... 1 sec−1 respectively. For the reactions, OH(ν=1)+O→H+O2 (5) OH(ν=1)+CO→H+CO2 (19) OH(ν=1)+H2→H2O+H (21) OH(ν=1)+CH4arH2O+CH3, (22) the following rate constants ...
Tópico(s): Spectroscopy and Laser Applications
1977 - Elsevier BV | Symposium (International) on Combustion
J.P. Hawranek, Richard N. Jones,
... investigated include (a) the iteration algorithm to obtaink(ν) andn(ν) fromka(ν); (b) truncation errors in the computation of then(ν) from thek(ν) spectrum by both the conventional (KK) and the ... the effect of truncating the wings of thek(ν) curve; (d) the influence of neighboring bands outside ... range of measurement on the calculation of then(ν) spectrum by both Kramers—Kronig methods; (e) interactive effect of errors in then(ν) spectrum on the computation ofk(ν), and of errors in theka(ν) spectrum on the computation ofn(ν), andk(ν).
Tópico(s): Spectroscopy and Chemometric Analyses
1976 - Pergamon Press | Spectrochimica Acta Part A Molecular Spectroscopy
Abstract The ν 1 + ν 3 band of ozone (O 3 ) near 2110 cm −1 has been measured and analyzed using a Watson-type Hamiltonian ... perturbations have been found between K = n of ν 1 + ν 3 and K = n + 3 of 2 ν 3 . Those perturbations locate the band center for 2 ν 3 at about 2058 cm −1 . Aside from those perturbations the interactions of ν 1 + ν 3 with 2 ν 1 and 2 ν 3 have not been taken into account in ...
Tópico(s): Atmospheric chemistry and aerosols
1975 - Elsevier BV | Journal of Molecular Spectroscopy
David C. Clary, J. N. L. Connor,
... out for the reaction O(3 P) + H2(ν ⩽ 2, j, mj ) →OH (ν′ ⩽ 2, j′, mj′ ) + H. A LEPS potential energy ... energy dependences of these quantities. Reactions for which ν →ν′ = ν are favoured over reactions for which ν →ν′ ≠ ν, in agreement with quasiclassical results. Initial vibrational excitation ...
Tópico(s): Spectroscopy and Laser Applications
1980 - Taylor & Francis | Molecular Physics
A. J. Bracken, Howard I. Leemon,
... be written in the form h/ω(2ν°ν+λ°⋅λ+3/2), where ν° and ν are raising and lowering (boson) operators for ν°ν, which has nonnegative integer eigenvalues k; and λ° ... only by working in the coordinating the operators ν° and λ° to a ’’vacuum’’ vector on which ν and λ vanish. The Lie algebra so(2, ... oscillator, as the eigenvectors of the lowering operators ν and λ. A brief discussion is given of the classical counterparts of ν,ν°, λ, and λ°, in order to clarify their ...
Tópico(s): Advanced Physical and Chemical Molecular Interactions
1980 - American Institute of Physics | Journal of Mathematical Physics
Mohammad Shafi, Charles L. Beckel,
... 3d σg)2Σg+ state of H2+ up to ν = 58. Dunham power series expansions are used to ... curves have positive curvatures at low and high ν and negative curvatures at intermediate ν; points of inflection for both curves are at very nearly the same values of ν. The Dν curve is qualitatively similar to those for 1s σg and 2p πu up to ν = 25; above ν = 30 the 3d σg Dν's reach a maximum and then apparently tend to zero as ν → ∞. As ν approaches 25, Hν values appear to be heading negative; with further increase in ν the Hν's rise sharply and then appear ...
Tópico(s): Atmospheric Ozone and Climate
1973 - American Institute of Physics | The Journal of Chemical Physics
... constants are calculated for the vibrational relaxation HF(ν) and DF(ν) molecules by F atoms with ν = 1, 2, 3, and 6. Three-dimensional classical ... predicted for the reactant HF molecule in the ν = 2, J = 8 state that 13.3% of ... if the reactant molecule HF is in the ν = 6, J = 8 state, it is found that ... are used to calculate the rate constants kν→ν−1 for the de-excitation of vibrationally excited ...
Tópico(s): Atmospheric Ozone and Climate
1973 - American Institute of Physics | The Journal of Chemical Physics
Jacek Z. Brzeziński, ZOFIA CZLONKOWSKA-KOHUTNICKA, Beata Czarnecka, Aleksandra Kornas-Calka,
... in the range of 3000–300,000; the [ν]-M̄ relationship for toluene, 25°, was found to ... No upward curvature of the linear relation, log [ν] = ƒ(M), at lower molecular weights was observed. Over the whole range of molecular weights, the [ν]-values in toluene were higher than [ν]θ-values in bromocyclohexane at 28°. On a ... 300.000; on a trouvé que la relation [ν]-M̄ dans le toluène à 25° est: [ɳ]= ... vers le haut de la relation linéaire log [ν] = ƒ (M) pour les bas poids moléculaires. Pour tous les poids moléculaires considérés, les valeurs de (ν)θ dans le toluène étaient plus élevées que ...
Tópico(s): Thermodynamic properties of mixtures
1973 - Elsevier BV | European Polymer Journal
Osvald Knop, Ian A. Oxton, Michael Falk,
The ν 1 and ν 4bc infrared absorptions of the NH 3 D + probe ion dispersed at low concentration in polycrystalline ammonium halides were used ... the ammonium ion. It is found that the ν 1 and ν 4bc frequencies are affected by the acceptor strength ... crystal, the volume effect. These two factors affect ν 4bc in the same direction but ν 1 in opposite directions. As a consequence, in a ν 4bc vs. ν 1 plot the halides are separated according to ... strength of hydrogen bonding.The E a vs ν 1 plot contains two branches. The low-frequency ...
Tópico(s): Crystallization and Solubility Studies
1979 - NRC Research Press | Canadian Journal of Chemistry