Combination of Different Nonlinear Techniques

A combination of Doppler-free two-photon spectroscopy and polarization spectroscopy was utilized by Griitzmacher et al. [277] for the measurement of the Lyman-X line profile in a hydrogen plasma at low pressure. 

A famous example of such a combination is the first precise measurement of the Lamb shift in the IS ground state of the hydrogen atom by Hansch et al. [261]. Although new and more accurate techniques have been developed by Hansch and coworkers (Sect. 9.7), the old technique is quite instructive and shall therefore be briefly discussed here. 

The experimental arrangement is shown in Fig. 2.48. The output of a tunable dye laser at X = 486 nm is frequency-doubled in a nonlinear crystal. While the fundamental wave at 486 nm is used for Doppler-free saturation spectroscopy [261] or polarization spectroscopy [278] of the Balmer transition 2Si/2- P /2 the second harmonics of the laser at X = 243 nm induce the Doppler-free two-photon transition 15 i/2 25 i/2. In the simple Bohr model [279], both transitions should be induced at the same frequency since in this model v(lS-2S) = 4v(2S-4P). The measured frequency difference Av = v(lS-2S) — 4v(2S-4P) yields the Lamb shift vlCI ) = Av — 8v] 2S) — Avfs(45 i/2 4Pi/2) 5vl(45 ). The Lamb shift (5vl(2/S) is known and Avfs(45i/2-4Pi/2) can be calculated within the Dirac theory. The frequency markers of the FPI allow the accurate determination of the hfs splitting of the 15 state and the isotope shift Avis( H- H) between the 1S-2S transitions of hydrogen and deuterium (Fig. 2.38). 

The more recent version of this precision measurement of the 1S-2S transition is shown in Fig. 2.49. The hydrogen atoms are formed in a microwave discharge and effuse through a cold nozzle into the vacuum, forming a collimated beam of color H-atoms. The laser beam is sent through the nozzle and is reflected back anticollinear to the atomic beam axis. The metastable 2S atoms fly through an electric held where the 2S state is mixed with the 2P state. The 2P atoms emit Lyman-of fluorescence, which is detected by a solar blind photomultiplier. 

If the microwave discharge is pulsed the Lyman a-radiation emitted from the excited H-atoms can be detected behind a time gate as a function of the time de- 

A famous example of such a combination is the first precise measurement of the Lamb shift in the IS ground state of the hydrogen atom by 

The experimental arrangement is shown in Fig.7.43. The output of a tunable dye laser at A = 486 nm is frequency doubled in a nonlinear crystal. While the fundamental wave at 486 nm is used for Doppler-free saturation spectroscopy [7.54] or polarization spectroscopy [7.70] of the Balmer transition 28 /2 second harmonics of the laser at A = 243 nm induces 

The few examples shown above should have illustrated that nonlinear spectroscopy represents an important branch of laser spectroscopy of atoms and molecules. Its advantages are the Doppler-free spectral resolution if narrow-band lasers are used and the possibilities to reach high-lying states by 

In combination with double-resonance techniques, nonlinear spectroscopy has contributed particularly to the assignment of complex spectra and has therefore increased our knowledge about molecular structure and dynamics considerably. This subject will be covered in Chap. 10. 

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Certainly it is possible to apply also other display methods for the visualization of such complex environmental data, as particulate emissions. TREIGER et al. [1993 1994] describe the study of different aerosol samples by nonlinear mapping of electron probe microanalysis data. Different interpretable groups of chemical elements which determine the composition of aerosol samples can be obtained. More recent work by WIENKE and HOPKE [1994] and WIENKE et al. [1994] discuss the combination of different chemometric techniques for better graphical representation of aerosol particle data. The authors use receptor modeling with a minimal spanning tree combined with a neural network. 

A great number of studies indicated that quadratic approximation methods, which are characterized by solving a sequence of quadratic subproblems recursively belong to the most efficient and reliable nonlinear programming algorithms presently available. This method combines the most efficient characteristics of different optimization techniques (see e.g, [19]). For equality constrained problems, the general nonlinear constrained optimization problem can be formulated by an... 

Motivating the research is the need for systematic, quantitative information about how different surfaces and solvents affect the structure, orientation, and reactivity of adsorbed solutes. In particular, the question of how the anisotropy imposed by surfaces alters solvent-solute interactions from their bulk solution limit will be explored. Answers to this question promise to affect our understanding of broad classes of interfacial phenomena including electron transfer, molecular recognition, and macromolecular self assembly. By combining surface sensitive, nonlinear optical techniques with methods developed for bulk solution studies, experiments will examine how the interfacial environment experienced by a solute changes as a function of solvent properties and surface composition. 

The observed transients of the crystal size distribution (CSD) of industrial crystallizers are either caused by process disturbances or by instabilities in the crystallization process itself (1 ). Due to the introduction of an on-line CSD measurement technique (2), the control of CSD s in crystallization processes comes into sight. Another requirement to reach this goal is a dynamic model for the CSD in Industrial crystallizers. The dynamic model for a continuous crystallization process consists of a nonlinear partial difference equation coupled to one or two ordinary differential equations (2..iU and is completed by a set of algebraic relations for the growth and nucleatlon kinetics. The kinetic relations are empirical and contain a number of parameters which have to be estimated from the experimental data. Simulation of the experimental data in combination with a nonlinear parameter estimation is a powerful 1 technique to determine the kinetic parameters from the experimental... 

A comparison of the benefits and drawbacks of common numerical solution techniques for complex, nonlinear partial differential equation models is given in Table II. Note that it is common and in some cases necessary to use a combination of the techniques in the different dimensions of the model. 

Recently, there has been much interest in the development and application of multidimensional coherent nonlinear femtosecond techniques for the study of electronic and vibrational dynamics of molecules [1], In such experiments more than two laser pulses have been used [2-4] and the combination of laser pulses in the sample creates a nonlinear polarization, which in turn radiates an electric field. The multiple laser pulses create wave packets of molecular states and establish a definite phase relationship (or coherence) between the different states. The laser pulses can create, manipulate and probe this coherence, which is strongly dependent on the molecular structure, coupling mechanisms and the molecular environment, making the technique a potentially powerful method for studies of large molecules. 

The zero length column (ZLC) technique has become a common tool to measure mass transfer kinetics in microporous adsorbents. The partial loading experiment is a variant of the traditional ZLC method in which the adsorbent is not allowed to reach full equilibration with the gas phase. Even though this variant of the ZLC experiment was introduced over 10 years ago, it has been applied only by few researchers. In this contribution we review the basic theory of the partial loading experiment and show that it can be used to establish the contributions of different mass transfer mechanisms. A detailed numerical model that includes the effects of nonlinearity of the isotherm and combined diffusion and surface barrier effects is presented to allow the correlation of complex sorbate-sorbent systems. 

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