Numerical study of transition in the Rayleigh-B&#039 / enard problem of thermal convection between rigid plates heated from below under the influence of gravity with and without rotation is presented. The first numerical approach uses spectral element method with Fourier expansion for horizontal extent and Legendre polynomal for vertical extent for the purpose of generating a database for the subsequent analysis by using Karhunen-Lo&#039 / eve (KL) decomposition. KL decompositions is a statistical tool to decompose the dynamics underlying a database representing a physical phenomena to its basic components in the form of an orthogonal KL basis. The KL basis satisfies all the spatial constraints such as the boundary conditions and the solenoidal (divergence-free) character of the underlying flow field as much as carried by the flow database. The optimally representative character of the orthogonal basis is used to investigate the convective flow for different parameters, such as Rayleigh and Prandtl numbers. The second numerical approach uses divergence free basis functions that by construction satisfy the continuity equation and the boundary conditions in an expansion of the velocity flow field. The expansion bases for the thermal field are constructed to satisfy the boundary conditions. Both bases are based on the Legendre polynomials in the vertical direction in order to simplify the Galerkin projection procedure, while Fourier representation is used in the horizontal directions due to the horizontal extent of the computational domain taken as periodic. Dual bases are employed to reduce the governing Boussinesq equations to a dynamical system for the time dependent expansion coefficients. The dual bases are selected so that the pressure term is eliminated in the projection procedure. The resulting dynamical system is used to study the transitional regimes numerically. The main difference between the two approaches is the accuracy with which the solenoidal character of the flow is satisfied. The first approach needs a numerically or experimentally generated database for the generation of the divergence-free KL basis. The degree of the accuracy for the KL basis in satisfying the solenoidal character of the flow is limited to that of the database and in turn to the numerical technique used. This is a major challenge in most numerical simulation techniques for incompressible flow in literature. It is also dependent on the parameter values at which the underlying flow field is generated. However the second approach is parameter independent and it is based on analytically solenoidal basis that produces an almost exactly divergence-free flow field. This level of accuracy is especially important for the transition studies that explores the regions sensitive to parameter and flow perturbations.

High Rayleigh number(Ra) turbulent free convection has many unresolved issues related to the phenomenology behind the flux scaling, the presence of a mean wind and its effects, exponential probability distribution functions, the Prandtl number dependence and the nature of near wall structures. Few studies have been conducted in the high Prandtl number regime and the understanding of near wall coherent structures is inadequate for $Ra > 10^9$. The present thesis deals with the results of investigations conducted on high Rayleigh number turbulent free convection in the high Schmidt number(Sc) regime, focusing on the role of near wall coherent structures. We use a new method of driving the convection using concentration difference of NaCl across a horizontal membrane between two tanks to achieve high Ra utilising the low molecular diffusivity of NaCl. The near wall structures are visualised by planar laser induced fluorescence. Flux is estimated from transient measurement of concentration in the top tank by a conductivity probe. Experiments are conducted in tanks of $15\times15\times 23$cm (aspect ratio,AR = 0.65) and $10\times10\times 23$cm (AR = 0.435). Two membranes of 0.45$\mu$ and 35$\mu$ mean pore size were used. For the fine membrane (and for the coarse membrane at low driving potentials), the transport across the partition becomes diffusion dominated, while the transport above and below the partition becomes similar to unsteady non penetrative turbulent free convection above flat horizontal surfaces (Figure~\ref{fig:schem}(A)). In this type of convection, the flux scaled as $q\sim \Delta C_w ^{4/3}$,where $\Delta C_w$ is the near wall concentration difference, similar to that in Rayleigh - B\'nard convection . Hence, we are able to study turbulent free convection over horizontal surfaces in the Rayleigh Number range of $\sim 10^- 10 ^$ at Schmidt number of 602, focusing on the nature and role of near wall coherent structures. To our knowledge, this is the first study showing clear images of near wall structures in high Rayleigh Number - high Schmidt number turbulent free convection. We observe a weak flow across the membrane in the case of the coarser membrane at higher driving potentials (Figure \ref(B)). The effect of this through flow on the flux and the near wall structures is also investigated. In both the types of convection the near wall structure shows patterns formed by sheet plumes, the common properties of these patterns are also investigated. The major outcomes in the above three areas of the thesis can be summarised as follows \subsection* \label \subsubsection* \label The non-dimensional flux was similar to that reported by Goldstein\cite at Sc of 2750. Visualisations show that the near wall coherent structures are line plumes. Depending on the Rayleigh number and the Aspect ratio, different types of large scale flow cells which are driven by plume columns are observed. Multiple large scale flow cells are observed for AR = 0.65 and a single large scale flow for AR= 0.435. The large scale flow create a near wall mean shear, which is seen to vary across the cross section. The orientation of the large scale flow is seen to change at a time scale much larger than the time scale of one large scale circulation The near wall structures show interaction of the large scale flow with the line plumes. The plumes are initiated as points and then gets elongated along the mean shear direction in areas of larger mean shear. In areas of low mean shear, the plumes are initiated as points but gets elongated in directions decided by the flow induced by the adjacent plumes. The effect of near wall mean shear is to align the plumes and reduce their lateral movement and merging. The time scale for the merger of the near wall line plumes is an order smaller than the time scale of the one large scale circulation. With increase in Rayleigh number, plumes become more closely and regularly spaced. We propose that the near wall boundary layers in high Rayleigh number turbulent free convection are laminar natural convection boundary layers. The above proposition is verified by a near wall model, similar to the one proposed by \cite{tjfm}, based on the similarity solutions of laminar natural convection boundary layer equations as Pr$\rightarrow\infty$. The model prediction of the non dimensional mean plume spacing $Ra_\lambda^~=~\lambda /Z_w~=~91.7$ - where $Ra_\lambda$ is the Rayleigh number based on the plume spacing $\lambda$, and $Z_w$ is a near wall length scale for turbulent free convection - matches the experimental measurements. Therefore, higher driving potentials, resulting in higher flux, give rise to lower mean plume spacing so that $\lambda \Delta C_w^$ or $\lambda q^$ is a constant for a given fluid. We also show that the laminar boundary layer assumption is consistent with the flux scaling obtained from integral relations. Integral equations for the Nusselt number(Nu) from the scalar variance equations for unsteady non penetrative convection are derived. Estimating the boundary layer dissipation using laminar natural convection boundary layers and using the mean plume spacing relation, we obtain $Nu\sim Ra^$ when the boundary layer scalar dissipation is only considered. The contribution of bulk dissipation is found to be a small perturbation on the dominant 1/3 scaling, the effect of which is to reduce the effective scaling exponent. In the appendix to the thesis, continuing the above line of reasoning, we conduct an exploratory re-analysis (for $Pr\sim 1$) of the Grossman and Lohse's\cite scaling theory for turbulent Rayleigh - B\'enard convection. We replace the Blasius boundary layer assumption of the theory with a pair of externally forced laminar natural convection boundary layers per plume. Integral equations of the externally forced laminar natural convection boundary layer show that the mixed convection boundary layer thickness is decided by a $5^{th}$ order algebraic equation, which asymptotes to the laminar natural convection boundary layer for zero mean wind and to Blasius boundary layer at large mean winds. \subsubsection*{Effect of wall normal flow on flux and near wall structures} \label{sec:effect-wall-normal} For experiments with the coarser($35\mu$) membrane, we observe three regimes viz. the strong through flow regime (Figure~\ref{fig:schem}(b)), the diffusion regime (Figure \ref{fig:schem}(a)), and a transition regime between the above two regimes that we term as the weak through flow regime. At higher driving potentials, only half the area above the coarser membrane is covered by plumes, with the other half having plumes below the membrane. A wall normal through flow driven by impingement of the large scale flow is inferred to be the cause of this (Figure \ref{fig:schem}(b)). In this strong through flow regime, only a single large scale flow circulation cell oriented along the diagonal or parallel to the walls is detected. The plume structure is more dendritic than the no through flow case. The flux scales as $\Delta C_w^n$, with $7/3\leq n\leq 3$ and is about four times that observed with the fine membrane. The phenomenology of a flow across the membrane driven by the impingement of the large scale flow of strength $W_*$, the Deardorff velocity scale, explains the cubic scaling. We find the surprising result that the non-dimensional flux is smaller than that in the no through flow case for similar parameters. The mean plume spacings in the strong through flow regime are larger and show a different Rayleigh number dependence vis-a-vis the no through flow case. Using integral analysis, an expression for the boundary layer thickness is derived for high Schmidt number laminar natural convection boundary layer with a normal velocity at the wall. (Also, solutions to the integral equations are obtained for the $Sc\sim 1$ case, which are given as an Appendix.) Assuming the gravitational stability condition to hold true, we show that the plume spacing in the high Schmidt number strong through flow regime is proportional to $\sqrt{Z_w\,Z{_{v_i}}}$, where $Z{_{v_i}}$ is a length scale from the through flow velocity. This inference is fairly supported by the plume spacing measurements At lower driving potentials corresponding to the transition regime, the whole membrane surface is seen to be covered by plumes and the flux scaled as $\Delta C_w^{4/3}$. The non-dimensional flux is about the same as in turbulent free convection over flat surfaces if $\frac{1}{2}\Delta C $ is assumed to occur on one side of the membrane. This is expected to occur in the area averaged sense with different parts of the membrane having predominance of diffusion or through flow dominant transport. At very low driving potentials corresponding to the diffusion regime, the diffusion corrected non dimensional flux match the turbulent free convection values, implying a similar phenomena as in the fine membrane. \subsubsection*{Universal probability distribution of near wall structures} \label{sec:univ-prob-distr} We discover that the probability distribution function of the plume spacings show a standard log normal distribution, invariant of the presence or the absence of wall normal through flow and at all the Rayleigh numbers and aspect ratios investigated. These plume structures showed the same underlying multifractal spectrum of singularities in all these cases. As the multifractal curve indirectly represents the processes by which these structures are formed, we conclude that the plume structures are created by a common generating mechanism involving nucleation at points, growth along lines and then merging, influenced by the external mean shear. Inferring from the thermodynamic analogy of multifractal analysis, we hypothesise that the near wall plume structure in turbulent free convection might be formed so that the entropy of the structure is maximised within the given constraints.

Η έννοια της ψηφιακής αναμετάδοσης έχει μελετηθεί σαν ένα ϑεωρητικό πρόβλημα από την πλευρά της ϑεωρίας της πληροφορίας στις δεκαετίες του ’70 και ’80 όπου υπολογίστηκε η χωρητικότητα συστημάτων με ένα αναμεταδότη. Το σενάριο στο οποίο η επικοινωνία δύο τερματικών σταθμών πραγματοποείται με τη ϐοήθεια ενός τρίτου το οποίο αναλαμβάνει να αναμεταδόσει την πληροφορία, υλοποιήθηκε αρχικά στους δορυφόρους με ανακλαστική επανεκπομπή. Ενδιαφέρον, σύμφωνα με όσα γνωρίζουμε, προκαλεί το γεγονός ότι δεν υπήρχε έως πολύ πρόσφατα καμία εργασία σχετική με την ϑεωρία της αναμετάδοσης - πιο πιθανή αιτία η μη ύπαρξη σχετικών εφαρμογών. Με την ωριμότητα των ψηφιακών ασύρματων επικοινωνιών και λόγω των ϱαγδαία αυξανόμενων αναγκών για επικοινωνίες υψηλής απόδοσης, ϕαίνεται ότι έφτασε η ώρα για την ανάπτυξη ‘‘έξυπνης’’ αναμετάδοσης στο άμεσο μέλλον. Η παρούσα διδακτορική διατριβή (DD) έρχεται να συμβάλλει προς την κατεύθυνση αυ- τή και να δώσει στους μελετητές των ψηφιακών επικοινωνιών νέες τεχνικές και εργαλεία αναλύοντας και μελετώντας στο ϕυσικό επίπεδο τα ασύρματα τηλεπικοινωνιακά συστήματα (ή δίκτυα) πολλαπλών αλμάτων με μη-αναγεννητικούς αναμεταδότες δηλ. συστήματα στα οποία το σήμα εκπέμπεται από τον πηγαίο κόμβο και ϕθάνει στον κόμβο προορισμού διαμέσου ενός ή περισσοτέρων αναμεταδοτών. Με την τεχνική αυτή καταπολεμούμε τους δύο ϐασικούς παράγοντες υποβάθμισης του εκπεμπόμενου σήματος που είναι η μειωμένη μέση ισχύς λήψης λόγω απόστασης ή/και εμποδίων, και οι διακυμάνσεις του σήματος στη λήψη του, εξαιτίας του ϕαινομένου των διαλείψεων. Βασικός σκοπός της DD είναι η αξιολόγηση των επιδόσεων των συστημάτων πολλαπλών αλμάτων, που λειτουργούν σε περιβάλλον διαλείψεων Rayleigh ή Nakagami-m, με δείκτες επιδόσεων όπως ο μέσος λό- γος σήματος προς ϑόρυβο (ΛΣΘ), η πιθανότητα διακοπής της επικοινωνίας (ΠDΕ) και η μέση πιθανότητα σφάλματος bit (ΜΠΣΒ). Για να επιτευχθούν τα παραπάνω στα πολυαλ- ματικά συστήματα, απαιτείται η στατιστική μελέτη του απ’ άκρο-σε-άκρο ΛΣΘ στην έξο- δο του κόμβου προορισμού για την εξαγωγή σημαντικών στατιστικών συναρτήσεων όπως της συνάρτησης πυκνότητας πιθανότητας (ΣΠΠ), της συνάρτησης αθροιστικής πιθανότητας (ΣΑΠ), της ϱοπο-γεννήτριας συνάρτησης (ΡΓΣ) και των ϱοπών. Οι δείκτες επίδοσης παρουσιάζονται είτε σε κλειστές μαθηματικές μορφές οι οποίες εξάγουν άμεσα αποτελέ- σματα, είτε σε αναλυτικές μορφές για τις οποίες η χρήση της αριθμητικής ολοκλήρωσης είναι απαραίτητη μέσω γνωστών μαθηματικών λογισμικών όπως MATHEMATICA ή MAPLE. Παράλληλα, όπου απαιτείται, παρουσιάζονται αποτελέσματα προσομοίωσης Monte Carlo για την επαλήθευση των αριθμητικών αποτελεσμάτων. Λαμβάνοντας υπόψην όλα τα παραπάνω, ερευνάται ένα σύστημα N αλμάτων σε περι- ϐάλλον διαλείψεων Nakagami-m και παράγονται τόσο σημαντικά αποτελέσματα για την επίδοσή τους όσο και ένα καινοτόμο στατιστικό ϑεώρημα για τη ΡΓΣ τυχαίων μεταβλητών Γάμμα. Η επίδοση των συστημάτων αυτών αξιολογείται για μη-αναγεννητικούς αναμε- ταδότες και συγκεκριμένα, τόσο για αναμεταδότες μεταβλητού κέρδους (ΑΜΚ) δηλ. το κέρδος τους εξαρτάται από την εκτίμηση της κατάστασης του καναλιού (ή κέρδος κανα- λιού) στην είσοδό τους, όσο και για αναμεταδότες σταθερού κέρδους (ΑΣΚ). Επίσης στη DD προτείνεται ένα νέος τύπου μη-αναγεννητικού αναμεταδότη, ο αναμεταδότης συνδυα- σμένου κέρδους (ΑΣυΚ), του οποίου η επίδοση εξετάζεται σε ένα σύστημα διπλού άλματος (δηλ. σ’ ένα σύστημα με έναν αναμεταδότη). Η επίδοσή του συγκρίνεται με αυτή του ΑΜΚ. Η επίδοση του ΑΣυΚ εμφανίζεται να είναι καλύτερη σε κάποιες περιπτώσεις απ’ αυτήν του ΑΜΚ. Ιδιαίτερη ϐαρύτητα δίνεται τέλος και στη μελέτη πολυαλματικών συστημάτων επικοινω- νίας με διαφορική συνεργασία χρηστών. Τα συστήματα αυτά διαφέρουν από τα συμβατικά πολυαλματικά διότι εκμεταλλεύονται τα πλεονεκτήματα της ‘‘εικονικής’’ διαφορικής εκ- πομπής στον πηγαίο κόμβο και τη διαφορική λήψη στον κόμβο προορισμού. Οι δείκτες επίδοσης εξετάζονται είτε για συστήματα διαφορικής συνεργασίας ενός χρήστη, είτε για πολλούς χρήστες με διαφορικό δέκτη συνδυασμού επιλογής ή μεγίστου λόγου στον κόμβο προορισμού, αντίστοιχα. / The concept of digital relaying has been studied as a theoretical problem from a network information theory perspective in 70’s and 80’s, and capacity regions of simple relaying channels have been evaluated. The scenario where the communication between two terminal is achieved with the help of a third terminal, was firstly implemented in bentpipe satellites. To the best of our knowledge, there has been no other analytical study on this concept until very recently due to the fact that there were no foreseeable applications at that time. With the maturity of digital wireless technologies and with the overwhelming demand for high data rate coverage, it seems that time has finally arrived for the implementation of intelligent relaying. The present PhD thesis contributes in that direction and gives to researchers of digital communications new techniques and smart tools by analyzing and studying multihop wireless communications systems in physical layer. In multihop systems, the source terminal transmits a signal which arrives to the destination terminal via a number of relays. By applying relayed transmission we mitigate two main reasons that causes Quality of Service degradation of the received signal, which are the low average receive power, induced by the presence of obstacles or by long distance, or due to the fluctuations in the received signal induced by fading effects. The main subject of this PhD is the evaluation of the performance metrics of multihop wireless communications systems, operating over Rayleigh or Nakagamim fading channels such as average signaltonoise ratio (SNR), outage probability and average biterror rate. To achieve this, the statistics of the equivalent endtoend SNR at the output of the destination terminal is required and specifically the probability density function, the cumulative distribution function, the moments and moment generating function (MGF). The performance metrics are presented either in closed forms giving direct results or in analytical ones where the results are extracted via numerical integration with the use of standard mathematical software packages such as MATHEMATICA or MAPLE. Additionally, Monte Carlo simulation results are also presented for the verification of the numerical results. Considering all the above, a multihop system with Nhops over Nakagamim environment is studied, and important performance results are derived. Also, a novel statistical result regarding the MGF of the product of rational powers of Gamma random variables is presented for the first time in the technical literature. The performance metrics of the multihop system are evaluated for nonregenerative relays and specifically, for both channel state information (CSI)based and fixed gain relays. Moreover, in this PhD thesis a new type of relay is presented, the combined gain relay (CGR), and its performance is studied in dualhop systems. The performance of the CGRs is compared to CSIbased ones whose amplification gain depends on the channel state at their input. It is interesting that CGR performs better in some situations than CSI ones. Finally, we concentrate on multihop wireless communications systems with cooperative diversity. Cooperative diversity systems differ from conventional multihop ones since exploits the benefits of virtual transmit diversity in the source terminal and diversity reception in the destination terminal. Performance analysis is conducted for cooperative diversity systems with one or more users (relays) and selection combiner or maximal ratio combiner at the destination terminal, correspondingly.

Η εργασία αυτή ασχολείται με το πρόβλημα της εκτίμησης καναλιού σε συστήματα μετάδοσης OFDM. Το πρόβλημα αυτό συγκεντρώνει έντονο ερευνητικό ενδιαφέρον τα τελευταία χρόνια, καθώς συναντάται σε ένα ευρύ πεδίο εφαρμογών. Η άγνωστη συνάρτηση μεταφοράς του καναλιού στα ασύρματα συστήματα μετάδοσης, καθιστά απαραίτητη την εκτίμησή του πριν από οποιαδήποτε διαδικασία μετάδοσης. Στη συγκεκριμένη μεταπτυχιακή εργασία, αντικείμενο εξέτασης αποτελεί η επίδραση καναλιού με μη γραμμικά χαρακτηριστικά σε συστήματα μετάδοσης OFDM. Αρχικά, παρουσιάζεται ένας βελτιωμένος αλγόριθμος εκτίμησης καναλιού, ο οποίος βασίζεται σε ένα παραμετρικό μοντέλο. Η απόκριση συχνότητας του καναλιού εκτιμάται χρησιμοποιώντας ένα μοντέλο με L μονοπάτια. Γίνεται χρήση της μεθόδου ESPRIT για την αρχική εκτίμηση των πολυδρομικών καθυστερήσεων, ενώ η διαδικασία παρακολούθησης γίνεται με την τεχνική IPIC DLL. Με γνωστή την πληροφορία για τις πολυδρομικές καθυστερήσεις, εκτιμάται η απόκριση του καναλιού στο πεδίο της συχνότητας με τη μέθοδο του ελαχίστου μέσου τετραγωνικού σφάλματος. Ιδιαίτερης μνείας χρήζει το κριτήριο MDL (Minimum Description Length) που χρησιμοποιείται για την εύρεση των ενεργών μονοπατιών του καναλιού. Σύμφωνα με το κριτήριο, υπολογίζεται ο ιδιοχώρος, δηλαδή οι ιδιοτιμές και τα ιδιοδιανύσματα, του πίνακα αυτοσυσχέτισης του καναλιού. Ο ιδιοχώρος αυτός εμφανίζει ιδιαίτερη δομή και μπορεί να αναλυθεί σε κάθετους μεταξύ τους υποχώρους: τον υποχώρο του σήματος (signal subspace) και αυτόν του θορύβου (noise subspace). Έχει αποδειχθεί ότι η χρήση παραμετρικού μοντέλου καναλιού μπορεί να μειώσει δραστικά τις διαστάσεις του υποχώρου του σήματος και κατά συνέπεια να βελτιώσει την απόδοση της εκτίμησης του καναλιού. Στη συνέχεια εξετάζεται η δυνατότητα εφαρμογής του αλγόριθμου PAST κατά τη διαδικασία παρακολούθησης των πολυδρομικών καθυστερήσεων και η σύγκρισή του με την απόδοση του IPIC DLL. Ο αλγόριθμος PAST έχει χαμηλή υπολογιστική πολυπλοκότητα καθώς στηρίζεται σε αναδρομικές τεχνικές παρακολούθησης του ιδιοχώρου. Στα πλαίσια της μεταπτυχιακής εργασίας έγινε συγκριτική μελέτη των τεχνικών εκτίμησης καναλιού σε συστήματα μετάδοσης OFDM. Περιγράφονται τα βασικά χαρακτηριστικά των κυριότερων αλγορίθμων της βιβλιογραφίας και στη συνέχεια παρουσιάζονται τα αποτελέσματα των προσομοιώσεων σε περιβάλλον MATLAB. Με βάση τη θεωρητική μελέτη των μεθόδων εκτίμησης και τα αποτελέσματα των προσομοιώσεων, εξάγονται συμπεράσματα για τη βελτίωση της απόδοσης που παρουσιάζουν σε σχέση με τις μη παραμετρικές τεχνικές. Τέλος, υλοποιήθηκε ένας νέος αλγόριθμος για την εύρεση του υποχώρου του σήματος, ο οποίος βελτιώνει σημαντικά την απόδοση του κριτηρίου MDL. / The basic concept in this thesis is the problem of Channel Estimation in multipath fading chanels. The method we use is based on parametric channel modeling. Firstly, we use the MDL (Minimum Descreption Length) criterium in order to estimate the number of paths in the channel. Next the ESPRIT method calculates the Time Delays for every estimated path. The second part of the algorithm is used for tracking of time delays. We firstly use an IPIC DLL (InterPath Interference Cancellation Delay Locked Loop) technique and then the path gains are calculated via a MMSE estimator. There is also a study in Subspace Tracking problem. We use the PAST and PASTd algorithms to calculate the signal subspace for every OFDM symbol transmited. The two techniques we described increase the SER performance of the non parametric channel estimator by 2dB and the MSE performance by 5dB. We also describe a new algorithm which has better performance than the MDL criterium.

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Under the electric dipole approximation, second harmonic of the incident light is scattered by a collection of randomly oriented molecular dipoles in solution due to instantaneous orientational fluctuation which is directional. If two such dipoles are correlated in space through intermolecular or other interactions, the intensity of the second harmonic scattered light (SHSL) will be related to the extent of such interactions. If two dipoles are arranged in a particular geometry by design, the geometry will determine the intensity of the SHSL. If a molecule has no dipole moment, the intensity of the SHSL will be less and is only allowed by higher order electric multipoles. If two such zero-dipole molecules interact with each other and transfer some amount of electronic charge from one to the other, the induced dipole moment will give rise to an enhanced SHSL. However, along with the direction of the dipole moment from the donor to the acceptor, the actual geometry of such molecular dimer/complex should also play an important role to determine the nature of the SHSL response. If all the isotropic nonzero components of first hyperpolarizability (β) are taken into account, from the measurement of β and related quantities such as depolarization ratios, in solution it should be possible to derive information about the geometry of the dimer/complex. This is precisely the motivation behind this thesis. Chapter 1 gives a brief introduction of 1:1 charge transfer (CT) complexes between a donor and an acceptor and their importance in chemistry. It also contains an introduction to nonlinear optics, various spectroscopic techniques to characterize CT complexes, etc. The motivation of extracting the geometry of such complexes from hyper-Rayleigh scattering (HRS) measurements in solution is presented in this chapter. In Chapter 2, all the experimental details of the unpolarized and polarization resolved HRS measurements at various excitation wavelengths have been described. Generation of infrared wavelengths (1543 nm and 1907 nm) using stimulated Raman scattering in gases have also been discussed. In Chapter 3, the first hyperpolarizability (βHRS) for two series of 1:1 molecular complexes between methyl substituted benzene donors with tetrachloro-p-benzoquinone (CHL) and dicyanodichloro-p-benzoquinone (DDQ) acceptors in solution at 1543 nm have been presented. Enhancement of βHRS due to charge transfer from the donor to the acceptor molecule which was predicted theoretically has been verified. Using linearly (electric field vector along X direction) and circularly polarized incident light, respectively, two macroscopic depolarization ratios D = I2ω,X,X/I2ω,Z,X and D' = I2ω,X,C/I2ω,Z,C in the laboratory fixed XYZ frame by detecting the SHSL in a polarization resolved fashion have been measured. The experimentally obtained first hyperpolarizability (βHRS), D and D' values, are then matched with the theoretically calculated values from single and double configuration interaction calculations using the Zerner’s intermediate neglect of differential overlap and the self-consistent reaction field (ZINDO–SDCI– SCRF) approach by adjusting the geometrical parameters. It has been found that in most of the CT complexes studied here, there exists a significant twist in the equilibrium geometry at room temperature which is not a simple slipped parallel geometry as was believed. In chapter 4, the βHRS, D and D' values of 1:1 pyridine (PY)-chloranil (CHL) complex at 1064 nm have been described. Previous theoretical studies have shown that there is a tilt angle of 77.9 degree in the gas phase PY-CHL complex. In this chapter, this prediction about the geometry of 1:1 PY-CHL complex has been probed. The experimentally found βHRS, D and D' are matched well with theoretically calculated values, using ZINDO–SDCI–SCRF, for a cofacial geometry of PY-CHL complex in solution indicating that the solution geometry is different from the gas phase geometry. In Chapter 5, the βHRS, D and D' for a series of 1:1 complexes of tropyliumtetrafluoroborate and methyl-substituted benzenes in solution at 1064 nm have been reported. The measured D and D' values vary from 1.36 to 1.46 and 1.62 to 1.72, respectively and are much lower than the values expected from a typical sandwich or a T-shaped geometry. The lowering in D and D' indicates that these complexes have higher symmetry than C2v. The value of D close to 1.5 indicates there is a significant octupolar contribution in such complexes. In order to probe it further, βHRS, D and D' were computed using the ZINDO-SDCI-SCRF technique in the presence of BF4-anion. By arranging the three BF4-ions in a C3 symmetry around the complex in such a way that electrical neutrality is maintained, the computed values are brought to agreement with experiments. This unprecedented influence of the anion on the HRS, D and D' values of these complexes are discussed in this chapter. In Chapter 6, the effect of dipolar interactions, within a multichromophoric system, on the second order nonlinear optical properties have been studied. It has been found that the βHRS response of the multichromophoric system is always larger than expected for uncorrelated chromophores demonstrating that the dipole moment of individual chromophores are not merely additive within the multichromophoric system but contribute cooperatively to the SHSL signal. Also the relative orientation and nature of the chromophores and the angle of interaction between them alter the HRS values. Chapter 7 is the concluding chapter in which all the work done in the thesis has been summarized and future direction has been proposed.

In this thesis, we consider two models from physics, which are characterized by the interplay of thermodynamical and fluid mechanical phenomena: demixing (spinodal decomposition) and Rayleigh--Bénard convection. In both models, we investigate the dependencies of certain intrinsic quantities on the system parameters. The first model describes a thermodynamically driven demixing process of a binary viscous fluid. During the evolution, the two components of the mixture separate into two domains of the different equilibrium volume fractions. One observes a clear tendency: Larger domains grow at the expense of smaller ones, and thus, the average domain sizes increases --- a phenomenon called coarsening. It turns out that two mechanisms are relevant for the coarsening process. At an early stage of the evolution, material transport is essentially mediated by diffusion; at a later stage, when the typical domain size exceeds a certain value, due to the viscosity of the mixture, a fluid flow sets in and becomes the relevant transport mechanism. In both regimes, the growth rates of the typical domain size obey certain power laws. In this thesis, we rigorously establish one-sided bounds on these growth rates via a priori estimates. The second model, Rayleigh--Bénard convection, describes the behavior of a fluid between two rigid horizontal plates that is heated from below and cooled from above. There are two competing heat transfer mechanisms in the system: On the one hand, thermodynamics favors a state in which temperature variations are locally minimized. Thus, in our model, the thermodynamical equilibrium state is realized by a temperature with a linearly decreasing profile, corresponding to pure conduction. On the other hand, due to differences in the densities of hot and cold fluid parcels, buoyancy forces act on the fluid. This results in an upward motion of hot parcels and a downward motion of cold parcels. We study the dependence of the average upward heat flux, measured in the so-called Nusselt number, on the temperature forcing encoded by the container height. It turns out that the efficiency of the heat transport is independent of the height of the container, and thus, the Nusselt number is a constant function of height. Using a priori estimates, we prove an upper bound on the Nusselt number that displays this dependency --- up to logarithmic errors. Further investigations on the flow pattern in Rayleigh--Bénard convection show a clear separation of length scales: Along the horizontal top and bottom plates one observes thin boundary layers in which heat is essentially conducted, whereas the large bulk is characterized by a convective heat flow. We give first rigorous results in favor of linear temperature profiles in the boundary layers, which indicate that heat is indeed essentially conducted close to the boundaries.

As many of the world’s nuclear power plants are near the end of their supposed life span a need arise to assess the components crucial to the safety of these plants. One of these crucial components is the concrete reactor confinement; to assess its condition, non-destructive testing (NDT) is an attractive method. Traditional testing of concrete structures has comprised of drilling out a sample and performing stress tests on it, but because of the radioactive environment inside the containment this method is far from ideal. NDT is of course possible to use at any structure but at reactor containments the benefits from not creating holes in the structure are prominent; NDT is also an attractive option from an esthetical point of view because it leaves the structure intact. The NDT method pertaining to this study is the impact echo method which comprise of applying a force on the structure, usually a hammer blow, and measuring the response with a receiver. The impact will excite waves propagating in the structure which gives rise to Lamb modes. Lamb modes are structural oscillations of the wall and it is the frequency of these modes that are used to determine the thickness of the wall. The elastic properties of the structure can in turn be obtained by measuring the velocities of the waves propagation. It is also possible to use the impact echo method to detect irregularities in the structure such as cracks or delamination. To simulate the dynamics of a system using NDT numerical methods such as finite element modeling (FEM) is often used. The purpose of this study is to assess the possibility to utilize absorbing layers using increasing damping (ALID) in models to reduce the computational time of FEM analyses. ALIDs are used at the edges to simulate an infinite system and are thus supposed to cancel out incoming waves to prevent unwanted reflection from the edges. The models in this study have all pertained to two dimensional plates utilizing infinitesimal strain theory; the decrease in computational time is significant when using ALIDs and for three dimensional models it would be even more so. The ALIDs are specified by length and maximum mass proportional Rayleigh damping (CMmax), in this study three different lengths are tested, 0.5, 1.5 and 4.5 m for CMmax ranging from 103 to 2*105 Ns/m. The damping is increased with increasing distance into the ALID with specified maximum value at the back edge. However, it should be noted that the increase in damping causes difference in impedance between elements and if this difference is too large it will cause reflections of waves at the boundary between the elements. The ALID must thus be defined so that it sufficiently cancels out the wave without causing unwanted reflections due to impedance differences. The conclusion is that the 0.5 m long ALID does not provide good results for any choice of maximum mass proportional Rayleigh damping. Both the 1.5 and 4.5 m long ALIDs are, however, concluded to be applicable; the 1.5 m ALID having 2*104 < CMmax <5*104 Ns/m and the 4.5 m ALID having 5*103 < CMmax < 104 Ns/m are choices that have shown promise in the performed simulations. The hope is that the results obtained in this study will aid in the development of numerical analysis techniques for NDT methods that can be used in the construction of new reactor confinements and/or maintenance of existing reactor confinements and other thick concrete structures. / Många av världens kärnkraftverk närmar sig slutet på sin beräknade livslängd och ett behov uppstår då att kunna utvärdera de komponenter som är väsentliga för säkerheten på dessa verk. Reaktoromslutningen i betong är en av dessa komponenter och oförstörande provning (NDT) är en attraktiv metod för att bedöma dess tillstånd. Traditionellt har utvärdering av betongkonstruktioner bestått av stresstester på borrprover men p.g.a. den radioaktiva miljön på insidan av omslutningen är denna metod ej att föredra. NDT är självklart möjligt att använda på allsköns betongkonstruktioner då det ger både konstruktionsmässiga och estetiska fördelar. NDT metoden som rör denna studie kallas impact echo och går ut på att man med en hammare slår till en punkt på väggen och mäter responsen en bit därifrån. Lasten ger upphov till vågor i form av deformation som propagerar i väggen och dessa ger i sin tur upphov till Lamb moder. Lamb moderna är strukturella oscillationer av väggen och genom att studera dess frekvenser kan väggens tjocklek bestämmas. Elastiska egenskaper i väggen erhålls utifrån de olika vågornas propageringshastigheter. Impact echo metoden kan även användas för att finna strukturella oegentligheter inuti väggen så som sprickor och delaminering. För att utföra numeriska simuleringar av dynamiska system med NDT-metoder är finita elementmetoden (FEM) användbar. Syftet med denna studie är att bedöma vilka möjligheter som finns för att implementera absorberande ränder med ökande dämpning (ALID) i datamodeller för att minska beräkningstiden av FEM-analyser. ALID används vid kanterna för att simulera ett oändligt system, dess uppgift är att dämpa bort inkommande vågor så att dessa ej reflekteras tillbaka och stör mätningarna. Samtliga modeller i denna studie är två-dimensionella med antagen oändligt liten spänning i normalriktningen. Vinsten i beräkningstid av att använda ALID är stor och ökar ytterligare om modellen utökas till tre dimensioner. Ett ALID definieras genom dess längd och maximala massproportionerlig Rayleigh-dämpning (CMmax). I denna rapport har längderna 0.5, 1.5 and 4.5 m använts med CMmax i intervallet från 103 till 2*105 Ns/m. Dämpningen ökar med ökat avstånd in i ALID med det specificerade maxvärdet vid den bakre kanten. Det bör noteras att skillnad i dämpning mellan element leder till skillnad i impedans; reflektioner av vågorna uppstår vid övergång från ett element med lägre impedans till ett med högre impedans. Ett ALID måste således vara definierat så att det dämpar bort tillräckligt av de inkommande vågorna utan att oönskade reflektioner i ALID uppstår. Studien pekar på att ett 0.5 m långt ALID inte åstadkommer önskvärda resultat för något av valen för CMmax som använts i denna rapport. Både det 1.5 och 4.5 m långa ALID har däremot get bra resultat; ett 1.5 m långt ALID bör ha 2*104 < CMmax <5*104 Ns/m och ett 4.5 m långt ALID 5*103 < CMmax < 104 Ns/m. Förhoppningen med studien är att resultaten skall underlätta utvecklingen av NDT-metoder som kan användas vid konstruktion och underhåll av reaktoromslutningar och andra tjocka betongkonstruktioner.

Dans cette thèse, les travaux présentés s’appuient sur une démarche expérimentale utilisant, outre les mesures destructives habituellement mises en œuvre pour la caractérisation des matériaux cimentaires, les techniques non destructives exploitant la propagation des ondes ultrasonores à des fréquences comprises entre 50 kHz et 600 kHz. L’objectif est d’étudier les corrélations entre les propriétés hydrauliques et mécaniques de la pâte de ciment et les paramètres linéaires des ondes ultrasonores (vitesse et atténuation). L’étude concerne plus particulièrement les relations entre la porosité et la vitesse ultrasonore des différents types d’onde (ondes de volume et onde de Rayleigh). Les matériaux étudiés sont des pâtes de ciment à porosité variable, confectionnées avec différents rapports E/C et avec différents dosages en entraineur d’air. Afin de prendre en compte l’effet de la teneur en eau, les mesures sont effectuées à différents états de saturation : état saturée, 70% de saturation, 30% de saturation et l’état sec. Les données recueillies permettent la constitution d’une base des données expérimentale regroupant les caractéristiques physiques, mécaniques et ultrasonores de la pâte de ciment. Dans la dernière partie de cette thèse, les relations entre les vitesses ultrasonores et la porosité basées sur deux approches macroscopique et microscopique sont présentées et confrontées aux mesures / In this thesis, we present an experimental study including, besides the destructive measurements usually implemented for the characterization of cementitious materials, non-destructive techniques using ultrasonic wave propagation in a frequency range from 50kHz to 600kHz. The objective is to study the correlations between hydraulic, mechanical properties and linear ultrasonic parameters (velocity and attenuation) of cement paste. This study specifically addresses the relationship between porosity and ultrasonic velocity of the different types of waves (body waves and Rayleigh wave). The studied materials are cement pastes with variable porosity, made up with different water / cement ratios and with different concentrations of air entrainer. To take into account the effect of water content, measurements are made at different states of saturation: saturated state, 70% saturation, 30% saturation and dry state. The data collected allows the creation of a database of experimental data involving physical, mechanical and ultrasonic parameters of cement paste. In the final part of this thesis, relationships between ultrasonic velocity and porosity based on macroscopic and microscopic approaches are presented and compared with measurements