Wavelet Analysis in Turbulence

The objective of this thesis is to study wavelets and their role in turbulence applications. Under scrutiny in the thesis is the intermittency in turbulence models. Wavelets are used as a mathematical tool to study the intermittent activities that turbulence models produce. The first section generally introduces wavelets and wavelet transforms as a mathematical tool. Moreover, the basic properties of turbulence are discussed and classical methods for modeling turbulent flows are explained. Wavelets are implemented to model the turbulence as well as to analyze turbulent signals. The model studied here is the GOY (Gledzer 1973, Ohkitani & Yamada 1989) shell model of turbulence, which is a popular model for explaining intermittency based on the cascade of kinetic energy. The goal is to introduce better quantification method for intermittency obtained in a shell model. Wavelets are localized in both space (time) and scale, therefore, they are suitable candidates for the study of singular bursts, that interrupt the calm periods of an energy flow through various scales. The study concerns two questions, namely the frequency of the occurrence as well as the intensity of the singular bursts at various Reynolds numbers. The results gave an insight that singularities become more local as Reynolds number increases. The singularities become more local also when the shell number is increased at certain Reynolds number. The study revealed that the singular bursts are more frequent at Re ~ 107 than other cases with lower Re. The intermittency of bursts for the cases with Re ~ 106 and Re ~ 105 was similar, but for the case with Re ~ 104 bursts occured after long waiting time in a different fashion so that it could not be scaled with higher Re.

Non-Markovian Dynamics and the Quantum-To-Classical Transition for Quantum Brownian Motion

In this Thesis I discuss the dynamics of the quantum Brownian motion model in harmonic potential. This paradigmatic model has an exact solution, making it possible to consider also analytically the non-Markovian dynamics. The issues covered in this Thesis are themed around decoherence. First, I consider decoherence as the mediator of quantum-to-classical transition. I examine five different definitions for nonclassicality of quantum states, and show how each definition gives qualitatively different times for the onset of classicality. In particular I have found that all characterizations of nonclassicality, apart from one based on the interference term in the Wigner function, result in a finite, rather than asymptotic, time for the emergence of classicality. Second, I examine the diverse effects which coupling to a non-Markovian, structured reservoir, has on our system. By comparing different types of Ohmic reservoirs, I derive some general conclusions on the role of the reservoir spectrum in both the short-time and the thermalization dynamics. Finally, I apply these results to two schemes for decoherence control. Both of the methods are based on the non-Markovian properties of the dynamics.

Advanced analysis and design methods for preparative chromatographic separation processes

Preparative liquid chromatography is one of the most selective separation techniques in the fine chemical, pharmaceutical, and food industries. Several process concepts have been developed and applied for improving the performance of classical batch chromatography. The most powerful approaches include various single-column recycling schemes, counter-current and cross-current multi-column setups, and hybrid processes where chromatography is coupled with other unit operations such as crystallization, chemical reactor, and/or solvent removal unit. To fully utilize the potential of stand-alone and integrated chromatographic processes, efficient methods for selecting the best process alternative as well as optimal operating conditions are needed. In this thesis, a unified method is developed for analysis and design of the following singlecolumn fixed bed processes and corresponding cross-current schemes: (1) batch chromatography, (2) batch chromatography with an integrated solvent removal unit, (3) mixed-recycle steady state recycling chromatography (SSR), and (4) mixed-recycle steady state recycling chromatography with solvent removal from fresh feed, recycle fraction, or column feed (SSR–SR). The method is based on the equilibrium theory of chromatography with an assumption of negligible mass transfer resistance and axial dispersion. The design criteria are given in general, dimensionless form that is formally analogous to that applied widely in the so called triangle theory of counter-current multi-column chromatography. Analytical design equations are derived for binary systems that follow competitive Langmuir adsorption isotherm model. For this purpose, the existing analytic solution of the ideal model of chromatography for binary Langmuir mixtures is completed by deriving missing explicit equations for the height and location of the pure first component shock in the case of a small feed pulse. It is thus shown that the entire chromatographic cycle at the column outlet can be expressed in closed-form. The developed design method allows predicting the feasible range of operating parameters that lead to desired product purities. It can be applied for the calculation of first estimates of optimal operating conditions, the analysis of process robustness, and the early-stage evaluation of different process alternatives. The design method is utilized to analyse the possibility to enhance the performance of conventional SSR chromatography by integrating it with a solvent removal unit. It is shown that the amount of fresh feed processed during a chromatographic cycle and thus the productivity of SSR process can be improved by removing solvent. The maximum solvent removal capacity depends on the location of the solvent removal unit and the physical solvent removal constraints, such as solubility, viscosity, and/or osmotic pressure limits. Usually, the most flexible option is to remove solvent from the column feed. Applicability of the equilibrium design for real, non-ideal separation problems is evaluated by means of numerical simulations. Due to assumption of infinite column efficiency, the developed design method is most applicable for high performance systems where thermodynamic effects are predominant, while significant deviations are observed under highly non-ideal conditions. The findings based on the equilibrium theory are applied to develop a shortcut approach for the design of chromatographic separation processes under strongly non-ideal conditions with significant dispersive effects. The method is based on a simple procedure applied to a single conventional chromatogram. Applicability of the approach for the design of batch and counter-current simulated moving bed processes is evaluated with case studies. It is shown that the shortcut approach works the better the higher the column efficiency and the lower the purity constraints are.

Comparison of thinning methods in a Scots pine stand on drained peatland : a simulation study

Tiivistelmä: Harvennusmenetelmien vertailu ojitetun turvemaan männikössä. Simulointitutkimus