Theoretical studies of dusty plasmas have been performed by focusing attention principally on collective phenomena and on grain motion. This thesis consists of a collection of seven published papers that explore both the collective behavior of a complex plasma system as well as the dynamics of grains in plasmas. In paper 1, a mechanism that explains the energy gain which leads to the self excited grain oscillations is theoretically formulated. The newly developed mechanism explains the observed self excited oscillations through the coupling of plasma sheath fluctuations with the electrostatic force, which holds the dust grain. In paper 2, theoretical and simulation studies have been conducted to study the vertical oscillations of dust grains that are levitated in plasma sheaths, under low pressure conditions. The oscillations were driven either by an external force or by a plasma number density modulation. The proposed model gives a full picture of the dust grains dynamics and is capable of successfully explaining the experimental observations. Paper 3 explores both theoretically and numerically the origin of the nonlinearities that lead to the observed oscillation resonances. The feature of the confining potential well which traps the grain, the influence of an electrode voltage modulation on the trapping well, and hence on the grain dynamics, and the resulting nonlinear resonances are analyzed in detail. The numerical simulations presented successfully reproduce a broad range of dynamical phenomena, including the self excited oscillations, for a range of different parameters. Paper 4 is dedicated to the analysis of the propagation of Dust Acoustic Waves (DAW) in a medium with an equilibrium dust density distribution. It has been theoretically shown that only some harmonics of the dust density distribution will influence the propagation of the DAW, thus modifying its frequency. Paper 5 presents a theoretical and numerical analysis of the excitation of higher harmonics of electrostatic dust cyclotron waves. The instability is driven by the ion and electron currents flowing along the magnetic field. The dispersion relation and the wave instability conditions have been derived, and a detailed numerical analysis has been performed. In Paper 6, we explore theoretically some cross field instabilities of low frequency, long wavelength electrostatic modes in fully and weakly ionized plasmas. It is shown that in a magnetoplasma with a transverse equilibrium dc electric field, the energy associated with the cross field motion of the plasma particles can be coupled to low frequency electrostatic waves. Paper 7 explores the properties and instabilities of low frequency electrostatic waves propagating in a current carrying magnetoplasma with equilibrium density and field aligned ion flow with a transverse gradient. The paper contains previous results as limiting cases, together with additional instabilities related to the equilibrium plasma density distribution.

Αντικείμενο της διατριβής είναι η επίλυση των προβλημάτων της σκέδασης επιπέδων ακουστικών κυμάτων χαμηλών συχνοτήτων από ένα διαπερατό σφαιρικό κέλυφος με έκκεντρο μαλακό, σκληρό ή διαπερατό πυρήνα και από μια μαλακή σφαίρα κάτω από ένα διαπερατό επίπεδο. Η λύση των προβλημάτων σκέδασης στην περιοχή χαμηλών συχνοτήτων επιδέχεται ανάπτυγμα Taylor σε δυνάμεις του κυματικού αριθμού k, όπου οι συντελεστές του αναπτύγματος (προσεγγίσεις χαμηλής συχνότητας) συνιστούν ακολουθία λύσεων στάσιμων προβλημάτων της θεωρίας δυναμικού. Ένα πρόβλημα σκέδασης μπορεί να δεχθεί προσέγγιση χαμηλών συχνοτήτων όταν το μήκος κύματος της κυματικής διαταραχής είναι πολύ μεγαλύτερο από την ακτίνα της ελάχιστης περιγεγραμμένης σφαίρας του σκεδαστή. Το δισφαιρικό σύστημα συντεταγμένων παρέχει κατάλληλο περιβάλλον για την επίλυση προβλημάτων πολλαπλής σκέδασης από δύο σφαίρες Αυτό ισχύει μόνο στη περιοχή των χαμηλών συχνοτήτων δεδομένου ότι η εξίσωση Laplace επιδέχεται διαμορφωμένο χωρισμό στις δισφαιρικές συντεταγμένες, ενώ δεν συμβαίνει το ίδιο στην εξίσωση Helmholtz. Προσαρμόζοντας το δισφαιρικό σύστημα συντεταγμένων στην δεδομένη γεωμετρία του κάθε προβλήματος απλουστεύεται η περιγραφή των χώρων που ορίζονται από το έκκεντρο σφαιρικό κέλυφος και οι σφαιρικές επιφάνειες του προβλήματός μας περιγράφονται από διαφορετικές τιμές της ίδιας συντεταγμένης μεταβλητής, ενώ ο απομακρυσμένος χώρος περιγράφεται από μια γειτονιά της αρχής των συντεταγμένων στο παραμετρικό χώρο των μεταβλητών η, θ. Επιλύοντας τα αντίστοιχα προβλήματα συνοριακών συνθηκών για μηδενική και πρώτης τάξεως προσεγγίσεις, καταλήγουμε σε αντίστοιχες αναγωγικές εξισώσεις ακολουθιών των συντελεστών ή αντίστοιχα συστήματα αναγωγικών εξισώσεων. Δεδομένου ότι οι ακολουθίες των συντελεστών συγκλείνουν ταχύτατα, περιοριζόμαστε στους πρώτους όρους συντελεστών και οι αναδρομικές εξισώσεις ή τα συστήματα αναγωγικών εξισώσεων ανάγονται σε εξισώσεις πινάκων ή γραμμικά συστήματα εξισώσεων με άγνωστους πίνακες στήλες και συντελεστές των αγνώστων τριδιαγώνιοι πίνακες. Με την πρωτότυπη αυτή μέθοδο προσδιορίζονται ακριβώς οι πρώτοι όροι χαμηλών συχνοτήτων των δύο προσεγγίσεων μηδενικής και οι πρώτης τάξεως, και στη συνέχεια οι προσεγγίσεις του πλάτους σκέδασης και των ενεργειακών διατομών σκέδασης. Μειώνοντας την απόσταση d των κέντρων συμπεραίνουμε ότι το πρόβλημα της σκέδασης ομόκεντρου σφαιρικού φλοιού δεν μπορεί να θεωρηθεί ειδική περίπτωση του προαναφερθέντος προβλήματος. / A plane wave is scattered by an acoustically soft, hard or penetrable sphere, covered by a penetrable non-concentric spherical lossless shell which disturbs the propagation of the incident plane wave field. There is exactly one bispherical coordinate system that fits the given two-sphere obstacle. If the wavelength of the incident field is much larger than the radius of the exterior sphere, Low Frequency Theory reduces the scattering problem to a sequence of potential problems which can be solved iteratively Applying the corresponding boundary value problem for each case, a set of two equations results as well as a recurrence equation with three unknown sequence of coefficients for zero-th order, and the first-order approximation is obtained, by solving two sets of two equations and a recurrence equation with three unknown sequence coefficients each for the soft core or the calculation of the zero–th order coefficients of the hard or penetrable core, leads to a solution of a linear system of two equations with two unknown columns and tri-diagonal square matrices are coefficients of the unknown columns, while the first-order approximation is obtained, by solving two linear systems of two equations with four unknown columns and eight tri-diagonal matrices as coefficients of the unknown columns. Applying the cut-off method for soft, hard and penetrable sphere, the low-frequency coefficients of the zero-th and first-order for the near field as well as the first and second-order coefficients are obtained for the normalized scattering amplitude and cross section. Decreasing the distance d of the centres we conclude that the problem of scattering concentric cell cannot be considered special case of mentioned before problem. A plane wave is scattered by an acoustical soft acoustic sphere embedded into an acoustically lossless half space, which disturbs the propagation of the incident wave field. In the first step, the problem of sound diffraction by only a penetrable plane is solved, were the amplitudes of reflective and diffractive acoustical waves are calculated. In the second step the diffractive as an incident wave is scattered by the embedded acoustical soft sphere. The low frequency zero-th and first order coefficients of the near field are calculated for the soft scatterer and finally the scattering amplitude and cross-section are determined.

Avec l’avènement du laser femtoseconde il est devenu possible de mesurer comment la démagnétisation femtoseconde peut permettre de sonder l’interaction d’échange dans les métaux ferromagnétiques. La démagnétisation induite par laser d’un matériau avec un fort couplage magnéto-élastique amène à la relaxation des contraintes mécaniques, générant ainsi des ondes acoustiques longitudinales (L) et transversales (T). Dans ce travail de thèse, la génération d’impulsions acoustiques picosecondes T par le mécanisme de démagnétostriction dans des matériaux fortement magnétostrictifs est traitée analytiquement et montrée expérimentalement dans le cas d’un alliage de Terfenol. En premier lieu, nous avons développé un modèle phénoménologique de magnétostriction directe dans un film monocristallin de Terfenol. Les expériences pompe-sonde linéaire MOKE résolues en temps montrent que la relaxation transitoire des contraintes magnéto-élastiques du film amène à l’excitation d’ondes GHz acoustiques L at T. Ces résultats sont la première observation expérimentale de l’excitation d’ondes acoustiques transversales picoseconde par mécanisme de démagnétostriction induit par laser. En second lieu, nous avons analysé le processus d’interaction d’ondes acoustiques L avec l’aimantation d’un film mince de Terfenol. L’onde acoustique picoseconde produit un changement de magnétisation du film et induit la conversion de modes acoustiques. C’est une autre voie de génération d’ondes acoustiques T que nous avons mis en évidence. La gamme de fréquence des impulsions générées est liée à l’échelle de temps de démagnétisation, qui corresponds à quelques centaines de GHz - 1 THz. / With the advent of femtosecond lasers it became possible to measure how femtosecond optical demagnetization can probe the exchange interaction in ferromagnetic metals. Laser-induced demagnetization of materials with strong magneto-elastic coupling should lead to the release of its build-in strains, thus to the generation of both longitudinal (L) and shear (S) acoustic waves. In this thesis, generation of shear picosecond acoustic pulses in strongly magnetostrictive materials such as Terfenol is processed analytically and shown experimentally. In case of Terfenol with strong magneto-crystalline anisotropy, laser induced demagnetostriction is responsible for S excitation. First, the phenomenological model of direct magnetostriction in a Terfenol monocrystalline film is developed. The shear strain generation efficiency strongly depends on the orientation of the film magnetization. Time-resolved linear MOKE pump-probe experiments show that transient laser-induced release of the magnetoelastic strains lead to the excitation of GHz L and S acoustic waves. These results are the first experimental observation of picosecond shear acoustic wave excitation by laser-induced demagnetostriction mechanism. Second, the interaction of an optically generated L acoustic pulse with the magnetization of a Terfenol thin film is reported. Arrival of the picosecond strain wave alters a change of its magnetization and leads to acoustic mode conversion, which is another pathway of shear acoustic wave generation. The frequency bandwidth of the generated acoustic pulses matches the demagnetization timescale and lies in the range of several hundreds of GHz, close to 1 THz.

Cette thèse concerne l’étude de la propagation d’ondes acoustiques dans des structures hétérogènes. Le but essentiel de ces travaux est de confronter des résultats d’expériences numériques effectuées dans le domaine physique (espace, temps) à des prédictions analytiques pour la propagation des ondes de surface SH le long d’un demi-espace stratifié périodique produisant des spectres discontinus de dispersion pour les ondes, ainsi que pour la diffusion multiple dans des milieux aléatoires inclusionnaires (fissures, cavités). Le code numérique FDTD développé lors de cette étude a permis, en autres choses, de corroborer quantitativement les fenêtres spectrales théoriques d’existence des ondes de surface dans les demi-espaces périodiques,ainsi que de montrer des zones de validité fréquentielles des approches analytiques de diffusion multiple concernant les propriétés effectives de milieux aléatoires. / The study is concerned with acoustic waves in elastic media with a different nature of in homogeneity consisting in either periodically continuous or piece wise variation of material properties, or in random sets of defects embedded into a homogeneous matrix, with a given statistical distribution. The scope of problems is topical in non-destructive testing and other applications of ultrasound.Theoretical methods describing involved acoustic phenomena (complex dispersion features, coherent wave in random media, ensemble average techniques) often rely on certain a priori assumptions which render numerical verification especially important.The thesis presents results of analytical modelling of the propagation of surface acoustic waves along periodic half-space, for which the dispersion spectrum is rather complex (discontinuous spectrum of propagation for the surface waves). A 2nd order FDTD numerical code has been developed in order to perform numerical experiments in the space and time domains, and to corroborate the analytical predictions in the frequency domain. A good agreement of simulated results with analytical modelling demonstrates applicability and consistency of the numerical tool. Finally, the code has been used for extracting numerically the coherent wave regime (mean wave over ensemble averaging of the positions of scatterers) for the acoustic propagation in different types of populations of randomly distributed scatterers. The results indicate ranges of validity of some multiple scattering analytical techniques.

La méthode de minimisation de l'intégrale d'action (principe variationnel) permet d’obtenir les équations de propagation des ondes. Cette méthode a été généralisée aux milieux poreux de dimensions fractales, pour étudier la propagation acoustique dans le domaine temporel, en se basant sur le modèle du fluide équivalent. L'équation obtenue réécrite dans le domaine fréquentiel représente une généralisation de l'équation d'Helmholtz. Dans le cadre du modèle d'Allard-Johnson, l'équation de propagation a été résolue de manière analytique dans le domaine temporel, dans les régimes des hautes et des basses fréquences. La résolution a été faite par la méthode de la transformée de Laplace, et a porté sur un milieu poreux semi-infini. Il a été trouvé que la vitesse de propagation dépend de la dimension fractale. Pour un matériau poreux fractal d'épaisseur finie qui reçoit une onde acoustique en incidence normale, les conditions d’Euler ont été utilisées pour déterminer les champs réfléchi et transmis. La résolution du problème direct a été faite dans le domaine temporel, par la méthode de la transformée de Laplace, et par l’usage des fonctions de Mittag-Leffler. Le problème inverse a été résolu par la méthode de minimisation aux sens des moindres carrés. Des tests ont été effectués avec succès sur des données expérimentales, en utilisant des programmes numériques développés à partir du formalisme établi dans cette thèse. La résolution du problème inverse a permis de retrouver les paramètres acoustiques de mousses poreuses, dans les régimes des hautes et des basses fréquences. / The action integral minimization method (variational principle) provides the wave propagation equations. This method has been generalized to fractal dimensional porous media to study the acoustic propagation in the time domain, based on the equivalent fluid model. The resulting equation rewritten in the frequency domain represents a generalization for the Helmholtz equation. As part of the Allard-Johnson model, the propagation equation was solved analytically in the time domain, for both high and low frequencies fields. The resolution was made by the method of the Laplace transform, and focused on a semi-infinite porous medium. It was found that the wave velocity depends on the fractal dimension.For a fractal porous material of finite thickness which receives an acoustic wave at normal incidence, the Euler conditions were used to determine the reflected and transmitted fields. The resolution of the direct problem was made in the time domain by the method of the Laplace transform, and through the use of the Mittag-Leffler functions. The inverse problem was solved by the method of minimizing the least squares sense. Tests have been performed successfully on experimental data; programs written from the formalism developed in this work have allowed finding the acoustic parameters of porous foams, in the fields of high and low frequencies.

This diploma thesis deals with creating of finite element model for the analysis of acustic waves radiation through human vocal tract and through the head surrounding space. The thesis contains a short overview of the anatomy of relevant parts and a short overview of formerly published models relevant to the topic. Then the process of creating the 3D model of human head, including the vocal tract, based on CT scans, and the mesh itself follows. This is succeeded by the computational solution taking in the acount the acoustic absorption of the vocal tract walls and radiation into the open space. The results gained are compared to relevant literature on this topic. The changes in frequency spectra in specific nodes of the mesh are reviewed and compared to relevant literature on the topic. The results could be used as basis of eventual frequention corrections of microphones used for voice diagnosis or registration in general, eg of speach or singing.

The following master thesis deals with creating a computational model for acoustic wave distribution by the human vocal tract and then the space around a human head. Detailed mapping of the sound field around the human head is important for more accurate measurement of the human voice. Part of this work is the creation of three-dimensional finite element model of the human head and the vocal tract during phonation of the vowel /:a/ based on the data from the computational tomography. Further the literature search of the function of the vocal tract, biomechanics of the making of the human voice, an overview of the computational models so far published in the literature and in literature reported measurements of the distribution of the human voice by the vocal tract and then in the space around the head . The following is the actual numerical solution of the acoustic waves distribution from the vocal cords through the vocal tract and then the space around the human head when thinking of acoustic absorption on the walls of the vocal tract and on the skin of the head for different types of waking of the model. The results are compared with previously published measurements of the distribution of the human voice and mainly the distortion of the frequency spectra at each specific node in the space around the head and in its vicinity of where the sensor microphones are typically placed are analyzed. Results of the computational modeling will eventually be used for frequency correction for various positions of the microphones scanning the voice distribution in its diagnosis, speech or singing.

Die Ergänzung der konventionellen Elektronik durch die quantenmechanischen Spin Eigenschaften der Elektronen ermöglicht die Entwicklung von schnellen und effizienten Rechnersystemen. Ein bekannter Baustein für solch ein System ist der Datta-Das Spin-Transistor. In dieser Arbeit wird ein akustisch angetriebener Spin-Transistor untersucht, basiert auf Quantendrähten definiert mittels Molekularstrahlepitaxie. Diese Quantendrähte (QWRs: quantum wires) bilden sich während des epitaktischen Überwachsens an den Flanken von Barrenstrukturen auf GaAs (001) Substraten. Elektronen (Löcher), die optisch in den QWR injiziert werden, sind lateral durch eine Potenzialbarriere von 25.4 meV (4.8 meV) zum umgebenden Qauntum Well eingesperrt. Die Verwendung einer akustischen Oberflächenwelle (AOW) ermöglicht den Transport von Elektronen und Löchern über große Entfernungen von bis zu 90 micron. Die akustische Transportdauer der QWR Ladungsträger entspricht der Dauer, die man aufgrund der akustischen Geschwindigkeit erwartet, d.h. dass die Ladungsträger sehr effizient transportiert werden. Im Fall von niedrigen akustischen Leistungen führen unbeabsichtigte Einfangzentren zu zusätzlichen Hotspots der Ladungsträgerrekombination auf dem Transportweg. Die intrinsischen Spinlebenszeiten der QWR Ladungsträger betragen ungefähr 2 ns bis 3 ns. Akustischer Spintransport im QWR wird über Entfernungen von mindestens 15 micron beobachtet. Es wird gezeigt, dass für Ladungsträger im QWR das Spin-Bahn Feld, um welches die Spins während des Transportes rotieren, stark von der akustischen Leistung abhängt. Daher stellen Flanken-QWRs auf GaAs (001) Substraten ein vielversprechendes Konzept für die Verwendung in einem akustisch betriebenen Spin-Transistor dar. / Fast and efficient computation devices can be developed by complementing conventional electronics with quantum mechanical spin. A common example for such a building block is the Datta-Das spin transistor. In this thesis, an acoustically driven spin transistor based on acoustic spin transport in quantum wires is investigated. These quantum wires (QWRs) are defined by molecular-beam epitaxy growth. They form on the sidewalls of ridges on GaAs (001) substrates. The edges of the ridges contain deviations from a straight line, originating from the photolithography process. Optically injected electrons and holes in the QWR are laterally confined by a potential barrier between the QWR and the surrounding QW of 25.4 meV and 4.8 meV, respectively. The application of a surface acoustic wave (SAW) enables the transport of electrons and holes over long distances along the QWR. For high acoustic powers, the charge carriers are transported by the strong SAW potential over distances up to 90 micron. The acoustic transport time of QWR corresponds to the one expected from the acoustic velocity, indicating a high transport efficiency. For lower acoustic powers, unintentional trapping centers lead to hotspots of carrier recombination along the transport path. The intrinsic spin lifetimes of the QWR carriers are approximately 2 ns to 3 ns. Acoustic spin transport in the QWR is observed over distances of at least 15 micron. It is shown that the spin-orbit field, around which the spins rotate during transport, strongly depends on the acoustic power for the QWR carriers. For high acoustic powers, the QWR spin precession frequency is enhanced by 3.5 times with respect to the intrinsic one. The results presented in this thesis demonstrate that the strain field of a SAW acts as a strain gate for QWR spins which are transported over a fixed distance. Therefore, the sidewall quantum wire on GaAs (001) substrates is a promising concept to be used in an acoustically driven spin transistor.

We study the expansion velocity and ion temperature evolution of ultracold neutral plasmas (UNPs) of calcium atoms under the influence of a uniform magnetic field that ranges up to 200 G. In the experiments, we use a magneto-optical trap (MOT) to capture the neutral atoms and laser-induced fluorescence (LIF) to take images of the plasma. We vary the magnetic field strengths and the initial electron temperatures and observe the plasma evolution in time. We compare the ion temperature evolution to the theory introduced in the paper by Pohl et. al. [Phys. Rev. A 70, 033416 (2004)]. The evolution of the gradient of expansion velocity suggests the presence of ion acoustic waves (IAWs). We speculate that our measurements showing that the ion temperature remains relatively high throughout the evolution is a biproduct of the IAW.

Dans le cadre de cette thèse, nous nous sommes intéressés d'abord au mécanisme de résonance locale en développant différents modèles théoriques pour l'étude de nouveaux cristaux phononiques à résonance locale (CPRL) en plaque dont l'élément principal et l'élastomère (silicone rubber). Le mode opératoire de ce mécanisme a été étudié et les ouvertures des bandes interdites ont été interprétées théoriquement ainsi que les phénomènes physiques mis en jeu. La mise en évidence expérimentale de la bande interdite a été réalisée par la fabrication et la caractérisation de structures CPRL et une parfaite concordance a été constatée entre les résultats théoriques et expérimentaux. Une étude des phénomènes de guidage a permis par ailleurs de montrer la possibilité du confinement et de la transmission d'un seul mode élastique au niveau d'un CPRL. Dans un second temps, nous avons montré que les propriétés d'un CPRL peuvent être reproduites dans le régime hypersonique. En effet, par le biais de la mise en place d'un nouveau modèle théorique et en proposant un nouveau CPRL à ondes de surface à base de films de diamant, nous avons pu montrer que ce type de cristal peut faire l'objet d'applications potentielles à des fins de guidage et de démultiplexage et ainsi initier la conception de nouveaux dispositifs miniaturisés à ondes de surface destinés aux systèmes de télécommunications (>GHz). / In this PhD work, we focused our interest on the theoretical and experimental study of locally resonant phononic crystals (LRPC) operating in sonic and hypersonic regimes. We first developed numerical models to understand the dispersion behaviour of elastic waves in those plate-type LRPC in which the silicone rubber plays a key role. We showed that with such structure, we can understand clearly how the local resonance (LR) mechanism operates to give rise to opening of low frequency BG two orders of magnitude that the one allowed by Bragg diffusion. The physics behind such structures was also figured out by means of theoretical models. An experimental study was then undertaken by manufacturing a new LRPC plate which has been characterized in terms of elastic behaviour and BG investigation. A perfect concordance was demonstrated between the theoretical an experimental results by evidencing a 2kHz BG opening using a 6mm diameter rubber stub and 1cm periodicity. In addition, waveguiding phenomena was investigated in those structures and showed the possibility of guiding of only one defect mode unlike conventional PCs in which many defects modes are generated. A second part of this study was dealt with LR mechanism in hypersonic regime. Using a new numerical and theoretical approach, we were able to show the BG opening and waveguiding for surface acoustic waves (SAW) in a LRPC composed of metallic stubs arranged on a diamond semi-infinite substrate. The added value of LR in such frequency regime remains in its ability to select only one guided mode due to the longer involved wavelengths. Such structures can then be suitable for filtering and demultiplexing applications.