Free-induction decay in a fluctuating two-level system

We study theoretically free-induction decay (FID) in an inhomogeneously broadened system of two-level atoms whose transition frequencies fluctuate according to the Ornstein-Uhlenbeck process. A numerical solution of the model shows that at low intensities the saturation behaviour of FID may depend strongly on the statistics of the fluctuations, but at high intensities the fluctuations play a minor role. The results mimic qualitatively the recent experimental data of DeVoe and Brewer, but a full quantitative agrrement with experiments is not reached.     

Production of fullerenes by a near infrared laser

Preparation of macroscopic amount of C₆₀ clusters (fullerenes) by the iodine laser is reported.     

A statistical study of the additivities of substituent effects in the 13C NMR chemical shifts of hydroxy- and chloro-substituted benzenes

The ¹³C NMR spectra of six hydroxybenzenes, all chlorobenzenes, all chlorophenols and eight chlorocatechols are measured and assigned. The additivity of the substituent effects and the usefulness of some corrective parameters are studied with regression analysis. The order of the chemical shifts is most efficiently predicted by the simplest substituent effect model, containing only the direct effects of the substituents, although the 95% confidence limits of the calculated shifts are as high as 5.6 ppm. If the chemical shifts need to be predicted within the measuring errors (approximately 0.05–0.10 ppm, in the present data), the number of necessary corrections is very impractical. The correction parameters are found to be independent of the solvent if no conformational effects are operative. These corrections, or the non-additivity parameters, are thus theoretically interesting. Approximate ¹J(CH) couplings are also reported and the additivity of substitution effects on these parameters are discussed.     

Detection of laser induced dielectric breakdown in water using a laser doppler vibrometer

This study is focused on exploring the feasibility of an all-optic surface scanning method in determining the size and position of a submerged, laser generated, optoacoustic (OA) source. The optoacoustic effect in this case was generated when the absorption of a short electromagnetic pulse in matter caused a dielectric breakdown, a plasma emission flash and a subsequent acoustic wave. In the experiment, a laser pulse with λ = 1064 nm and 12 ns pulse length was aimed at a volume of deionized water. When the laser beam was focused by a f = 16 mm lens, a single dielectric breakdown spot occurred. When a f = 40 mm was used several breakdowns in a row were induced. The breakdowns were photographed using a double shutter camera. The acoustic wave generated by the dielectric breakdowns were detected at a point on the water surface using a laser Doppler vibrometer (LDV). First, the LDV signal was used to calculate the speed of sound with an accuracy of 10 m/s. Secondly, the location and length of the dielectric breakdown was calculated with an accuracy of 1 mm. The calculated position matched the breakdown location recorded by a camera. The results show that it is possible to use LDV surface measurements from a single spot to determine both the position and length of the OA source as well as the speed of sound in the medium. Furthermore, the LDV measurements also show a secondary peak that originates from the OA source. To unravel the origin and properties of this interesting feature, further investigations are necessary     

Optical and X-ray emission spectroscopy of high-power laser-induced dielectric breakdown in molecular gases and their mixtures

Large-scale plasma was created in molecular gases (CO, CO2, N2, H2O) and their mixtures by high-power laser-induced dielectric breakdown (LIDB). Compositions of the mixtures used are those suggested for the early earth's atmosphere of neutral and/or mildly reducing character. Time-integrated optical spectra emitted from the laser spark have been measured and analyzed. The spectra of the plasma generated in the CO-containing mixtures are dominated by emission of both C2 and CN radicals. A vibrational temperature of approximately 10(4) K was determined according to an intensity distribution in a vibronic structure of the CN (B2Sigma(+)u-X2Sigma(+)g) violet band. For comparison, the NH3-CH4-H2-H2O mixture has been irradiated as a model of the strongly reducing version of the early earth's atmosphere. In this mixture, excited CN seems to be significantly less abundant than C2. The LIDB experiments were in the molecular gases carried out not only in the static cell but also using a large, double stream pulse jet (gas puff target) placed in the vacuum interaction chamber. The obtained soft X-ray emission spectra indicate the presence of highly charged atomic ions in the hot core of high-power laser sparks.     

A degenerate elliptic-parabolic system arising in competitive contaminant transport

The objective of this work is to study a coupled system of degenerate and nonlinear partial differential equations governing the transport of reactive solutes in groundwater. We show that this system admits a unique weak solution provided the nonlinear adsorption isotherm associated with the reaction process satisfies certain physically reasonable structural conditions, by addressing a more general problem. In addition, we conclude, that the solute concentrations stay non-negative if the source term is componentwise non-negative and investigate numerically the finite speed of propagation of compactly supported initial concentrations, in a two-component test case.     

The De Giorgi measure and an obstacle problem related to minimal surfaces in metric spaces

We study the existence of a set with minimal perimeter that separates two disjoint sets in a metric measure space equipped with a doubling measure and supporting a Poincaré inequality. A measure constructed by De Giorgi is used to state a relaxed problem, whose solution coincides with the solution to the original problem for measure theoretically thick sets. Moreover, we study properties of the De Giorgi measure on metric measure spaces and show that it is comparable to the Hausdorff measure of codimension one. We also explore the relationship between the De Giorgi measure and the variational capacity of order one. The theory of functions of bounded variation on metric spaces is used extensively in the arguments.     

The discrete maximal operator in metric spaces

We study the action of the so-called discrete maximal operator on Newtonian, Hölder and BMO spaces on metric measure spaces equipped with a doubling measure and a Poincaré inequality. The discrete maximal operator has better regularity properties than the standard Hardy-Littlewood maximal operator and hence is a more flexible tool in this context.