Homogeneous Perturbations Research Articles

Instabilities in Coupled Chemical Reactions with Pressure-Dependent Rate Coefficients

Instabilities are investigated in a model system consisting of several coupled chemical reactions; one reaction step is autocatalytic, and in another partial molar volume changes and pressure dependent rate coefficients are considered. The hydrodynamic equations of motion (for density, mass velocity, and concentration of chemical species) for this system are linearized in small deviations from steady state. The behavior of the system is analyzed by means of a set of hydrodynamic mode coordinates and their corresponding eigenvalues; the system is shown to be unstable under certain conditions not only to perturbations in concentrations but also to other hydrodynamic variables. For spatially homogeneous modes (k=0) the stable, marginally stable, unstable, oscillatory, and nonoscillatory regions of the eigenvalue spectrum are calculated for several limiting cases of the various experimental parameters. The normal modes are also calculated in the same limiting cases. A phase diagram is constructed for the stability of the system to homogeneous perturbations in terms of reduced parameters. For k≠0 there appear the expected acoustic modes but their form is altered by the presence of the reactions. Some of the reaction modes at k≠0 become unstable closer to chemical equilibrium than the corresponding modes in the homogeneous case (k=0). This result holds even in the limit of no diffusion. In that limit there exists a new mechanism of symmetry breaking which establishes inhomogeneous reaction modes due to the dynamical coupling of scalar equations of reaction (with pressure-dependent rate coefficients) and the vector equation of conservation of momentum. Possible biological applications of the theory are mentioned.

Rotational Analysis of two Mutually Interacting Electronic States of 1Π Character in Th0

Two new electronic states of 1Π character have been found for the Th0 molecule. Rotational analysis shows that there are homogeneous perturbations between the two states, and these perturbations have been analysed by computer methods. Some derived molecular constants are given below. State T 0 Bec Bed ΔG 1/2 M 21 734.320.3258570.325754850.87 K 22 635.650.3186360.318642795.5

Relaxation in an amorphous solid and the isothermal recombination luminescence following photoionization

It is shown that relaxation processes in the amorphous solid intervene significantly on the recombination luminescence (ITL) by modifying the decay kinetics. A single parameter which scales both the magnitude and the time coordinate of the ITL seen in a fully relaxed solid is capable of predicting the time course of the ITL seen in a partially relaxed solid. The one-parameter scaling relationship is the same as the one previously developed for predicting ITL behavior when the solid is subjected to some homogeneous perturbation.

Rotational analysis of the red electronic emission system of titanium nitride

An electronic emission spectrum has been obtained from a carrier identified as the diatomic molecule TiN. The system, which occurs in the red, has been analyzed as 2Πr → (X)2Σ, and it appears to be the analogue of the orange–red systems of the isoelectronic molecules CaF and ScO.The lower (ground?) state has B0″ = 0.6211 cm−1 corresponding to r0″ = 1.583 Å, whereas the excited 2Πr state has B0′ = 0.6103 cm−1. The system has a well-defined homogeneous perturbation in the excited state, showing the presence of a second, unobserved, 2Π term.

The B-X system of CF

The B-X system of CF has been observed in emission under high resolution and rotational analyses have been made of four bands. It is shown that the upper state is a regular 2 Delta state with coupling conditions approximating to Hund's case b. The spectroscopic constants derived for the B2 Delta state are T0=49341.4 cm-1, Delta G12/=1153-34, Be=1.3202, alpha e=0.0228, A0=0.76 or 4.48, gamma 0=-0.003. The potential curves for the X, A and B states are discussed and it is suggested that the B state mixes with a repulsive 2 Delta state from C(3P)+F(2P). Interpretation of this homogeneous perturbation in terms of potential curves leads to the conclusion that the curve for the B state goes to the limit C(3P)+F(2P) via a potential maximum. The A2 Sigma + state is considered as a Rydberg state with the electron configuration (1 pi )4(5 sigma )2( sigma 3s). The ionization potential is estimated to be 8.91 eV. The predissociation in the A2 Sigma + state is discussed and attributed to a quartet state, probably 4 Pi , from C(3P)+F(2P).

Time Autocorrelation of Sonic Pulses Propagated in a Random Medium

Measurements were made of the random variation produced in the amplitudes of sonic pulses propagated through a water medium in which was induced a nearly homogeneous random perturbation in temperature. The measurements were carried out at frequencies of 480 kHz and 1.42 MHz for transmitter-to receiver separations ranging from 1638 to 7658 in. The amplitude variations of the received pulses were analyzed to determine their time autocorrelation and variance as functions of range, i.e., transmitter-to-receiver separation and frequency. It was found that the time autocorrelation of the sonic-pulse amplitudes was equivalent to that measured for the temperature microstructure. The variance in sonic-pulse amplitude was determined as a function of range at both operating frequencies. These findings are compared with the theoretical findings of Mintzer and Bergmann. An equivalence of the time autocorrelation of sonic-pulse amplitude and temperature microstructure predicted by theoretical considerations is indeed supported by, experimental findings; however, the observed dependence of variance on range fell between the linear dependency predicted by Mintzer and the third-power dependency predicted by Bergmann. This was expected, since the frequency distance and parameters were in between the extremes assumed in those derivations.

Theoretical study of homogeneous perturbations. II. Least-squares fitting method to obtain "deperturbed" crossing Morse curves. Application to the perturbed 1Σu+ states of N2

A method to obtain a "deperturbation" of perturbed vibrational levels is developed. The vibrational functions associated with two (or three) crossing Morse curves are used to set up an interaction matrix. The eigenvalues of this matrix are compared with the observed levels and the "deperturbed" Morse curves are obtained by a least-squares fitting. This method applied to the 1Σu+ states of N2 confirms the interpretation given by Dressler (following paper).

Ein neues c′1Πg — b1IIu-Bandensystem des C2-Moleküls

Homogeneous rotational perturbations (Δ Λ = 0) were found in the DESLANDRES-D’AZAMBUJA bands (c1Πg — b1Πu) for v′ ≧ 3. The rotational analysis showed that the c1Πg state is perturbed by an hitherto unknown c′1Πg state. Vibrational levels of the c′1Πg state were determined from ν = 0 up to ν = 5. Furthermore some additional vibrational levels of the c1Πg state could be identified up to ν = 8. The detection of the c′1Πg state explains the observed strong vibrational perturbation of the c1Πg state. The mutual position of the two 1Πg potential curves is plotted approximately.

ÉTUDE THÉORIQUE DES PERTURBATIONS HOMOGÈNES : I. APPLICATION AUX INTERACTIONS Π–Π ET Δ–Δ DE NO

A theoretical interpretation of homogeneous perturbations is proposed for the case of two electronic excited states that differ strongly in electron configuration. The interaction parameter H can be expressed in terms of the vibrational overlap integral and the electrostatic interaction between the two states. In the case of the Π–Π and Δ–Δ interactions in the spectrum of the NO molecule, a semi-empirical calculation of this parameter is made, using Morse functions for the vibrational part and the LCAO-MO SCF function for the electronic part. The comparison with the "experimental" values given by Lagerqvist and Miescher supports this interpretation.

Absorption Spectra of H2 in the Vacuum Ultraviolet Region. II. The B′—X, B″—X, D—X, and D′—X Bands

The absorption spectrum of the H2 molecule has been studied in the wavelength region 840 to 930 Å with a 6.8 m grazing incidence vacuum spectrograph in combination with the helium continuum. All the possible levels, which lie below the dissociation limit H(12Sg)+H(22Sg,22Pu), of the odd singlet states have been identified in the present investigation. There are strong heterogeneous perturbations between the B′ and the D states, weak heterogeneous perturbations between the B′ and D′ states and a medium strength homogeneous perturbation between the B′ and the B″ states. The perturbation parameters have been estimated in each case. In the present paper, the results of the rotational and vibrational analyses are given for the B′—X, B″—X, D—X, and D′—X bands. The experimental evidence found in the present study suggests that the predissociation in the levels with v≥3 of the D state is of the type b0, according to Mulliken's classification.

On the rotational constant B J of molecular energy levels

The importance of the rotational constants\(E_J = \frac{{\partial E}}{{\partial J(J + 1)}}\) is emphasised, these being quantities resulting directly from band spectra as combination differences and being more characteristic than the constants appearing in the power series expansion ofE=E(J(J+1)) atJ=0. Neglecting the coupling between rotation and electronic motionBJ can be interpreted as the quantum mechanical average value of 1/r2 in the given molecular state, this being still valid also in the case of stong homogeneous perturbations. Taking into account the coupling between rotation and electronic motion the interpretation has an approximate validity.

Molecular perturbations

The interaction between rotation and electronic motion in a diatomic molecule is investigated by giving the direct wave mechanical form of the components of angular momenta. In order to get a suitable form of the interaction a reference system connected with the nuclei and independent from the electrons is used, defined by the Eulerian angles, in which the rectangular components of both total angular momentum and electronic angular momentum can be given. The adventage of this way of description in comparison with other used reference systems is emphasised. Observed perturbations are connected with a part of the effect of rotational coupling called here accidental, while there may be a considerable coupling between rotation and electronic motion without manifesting itself in irregularities. This is still more the case with respect to the coupling between vibration and electronic motion, since the nuclear motion may affect also the electronic part of the wave function with respect to which the averaging of the interactions of the particles leads to the potential curve characterising the regular sequence of energy levels. The fact that this electronic part of the wave function cannot be identified in general with an eigenfunction of the two center problem, yields a term which can play essential role in homogeneous perturbations. The analogous and different features of homogeneous and heterogeneous perturbations are discussed.