Damped Oscillator Model Research Articles

Nonlinear Electro-Optical Properties of Colloidal Crystal Latex

The Bragg-reflection condition for an ordered latex is modulated by an externally applied ac electric field. Intensity changes of the Bragg-reflected visible light are measured as a function of the field strength and its frequency. As reported previously, the force constant and the damping factor of the ordered latex had been derived from the measurements, by using a linear damping harmonic oscillator model. Nonlinear effect for the modulation signal is observed when the electric field intensity is increased. The modulation signals are analyzed, this time, by using a nonlinear damping oscillator model. Frequency dependence of the critical field strength for higher mode generation is explained successfully, and it turns out that the ordered latex is a soft spring system: the sign of the nonlinear damping factor is negative.

Raman study of Fermi resonance, hydrogen bonding, and molecular reorientation in liquid ammonia

The Fermi resonance between the ν1 and 2ν4 bands in the polarized Raman spectrum of liquid ammonia was studied as a function of temperature. The resonance interaction was quantitatively analyzed at all temperatures through utilization of the coupled damped oscillator model. The results of this analysis furnish convincing evidence for reversal of the assignment of these bands from that most commonly assumed in the past. An analysis of the temperature dependence of the parameters obtained from the coupled oscillator model (linewidths, uncoupled peak frequencies, and the resonance interaction constant) showed all the results to be self-consistent and in agreement with the behavior which has been found in other strongly hydrogen-bonded systems. The polarized and depolarized linewidths of other bands in the spectrum were examined, and they, too, were found to be consistent, given the strong hydrogen bonding in liquid ammonia.

Polarizability calculations on water, hydrogen, oxygen, and carbon dioxide

Based on the semiclassical model of damped oscillators, a procedure is developed for the calculation of the dispersion of refractive index, polarizability, and dielectric permeability, which are treated as complex quantities. Using experimental values of refractive indices and employing the frequencies of strong absorption bands, a least squares fit is used to determine oscillator strengths and damping factors. The absorption coefficient and the imaginary part of the refractive index are also calculated at the corresponding wavelengths. The procedure is applied for the cases of water, hydrogen, and oxygen in both the liquid and gaseous states and for gaseous carbon dioxide, and a good agreement is obtained between calculated and observed values of refractive indices. Results are also compared with those of previous calculations. Calculated absorption coefficients agree well with experimental values in the region of absorption bands. The calculated values of oscillator strengths and damping factors are discussed. The previously determined values for the polarizability extrapolated to infinite wavelength agree with the present results for the contribution of the electronic motion to the polarizability, this contribution being about the same for both the liquid and gaseous states of hydrogen, oxygen, and water. The value obtained in the present work for the polarizability of liquid water is about 2.8-fold greater than the results of previous calculations; most of the contribution is due to atomic and molecular motions. Onsager's theory is shown to yield the experimental value of the permanent dipole of water from the dielectric constant of liquid water when our result for the polarizability of liquid water is employed.

Phonons Optiques de CaO, SrO, BaO Au Centre de la Zone de Brillouin à 300 et 17K

The dielectric constant of CaO, SrO, BaO at 17 and 300K have been determined from Infrared measurements, by means of two different methods: the first based on Kramers-Kronig relations, the other using a one or two resonance damped oscillator model. The strong anharmoniaity of these crystals has been shown, leading to deviations from the Lyddane-Sachs-Teller relation. The Szigeti effective charge is calculated in two different ways the results are compared, when possible, to previously published data.

On the Secular Pole Motion and the Chandler Wobble

Summary The Earth's pole motion is characterized by an annual term, the Chandler wobble, and a strong secular motion. The annual is nearly periodic and the Chandler wobble is nearly a damped oscillation, but data are so limited that little about the secular term can be learned by conventional statistical analysis. Instead, we have used a new technique called ' cumulative range analysis ', which is effective in studying long-run dependence. The secular motion was found to follow a nearly Gaussian two-dimensional generalization of ' I/f noise'. The process yielding this kind of noise, for which the power diverges very slowly, can be imagined lying between stationary processes, such as white noise, for which the power is constant, and expanding processes, such as Brownian motion, for which the power diverges rapidly. One can prove that, for ' I/f noises ', uncertainty is left unchanged by averaging. Thus, one should expect the scatter of time averaged pole positions to be independent of the averaging times and nearly the same as the scatter of the monthly positions. This inference was checked empirically and verified. Averaging secular positions does not increase precision. Cumulative range analysis was also applied to the Chandler peak, confirming the accepted damped oscillator model, and yielding for Q an estimate between 30 and 35.

Absolute Infrared Intensity Measurements in Thin Films. II. Solids Deposited on Halide Plates

When a thin film of an absorbing substance is deposited on a halide plate, because of various reflection effects, the absorption coefficient measured experimentally in transmission will not correspond to the true absorption coefficient. This paper examines the relationship between this apparent absorption coefficient (α′) and the true absorption coefficient (α). Starting with a rigorous expression for the observed transmission, a relationship is established between α′ and α expressed as an infinite series in powers of d/λ (film thickness divided by wavelength). The result is valid for small d/λ. In the limit as d→0, a very simple relationship connects α and α′. For finite (but not too large) d, higher-order correction terms are derived. The theory is applied to the data of Wieder and Dows on SF6(s) deposited on AgCl and to the data of Yamada and Person on CS2(s) deposited on AgCl. For comparison and to calculate the higher-order correction terms, the data are also fit and analyzed using the damped oscillator model (DOM). The DOM results agree well with the theory. A marked change in band shape due to reflection effects is predicted for the two SF6 fundamentals. Some general suggestions are made concerning experimental procedures. It seems likely that the methods developed in this work will permit reliable corrections for reflection effects in thin film absorption measurements. In the final section, a rigorous method of treating the entire problem is outlined which is applicable, in principle, in all cases. This method depends on the fact that the transmission and phase shift can be related by a Kramers—Kronig-type dispersion relation. It is thus possible, in principle, to calculate α (and the refractive index) under any circumstances without any reference to a physical model. A preliminary application of this method to the SF6 data is presented.