Tesis por compendio / [EN] The dimensionality of the system plays a decisive role in the behavior of the electronic dynamics of interacting electrons. In particular, the quasi-2D dimensionality is responsible for the unusual behavior observed in graphene-like materials and layered van-der-Waal systems. Moreover, such effects are also observed for superconducting materials of high critical temperature, even in the normal state, due to their low-dimensionality. The experimental study of graphene triggered a growing attention to respective electronic properties, because the honeycomb lattice defines a band structure with two nodal points in the Brillouin zone which determines a relativistic Dirac-type electronic dynamics. Within a theoretical framework, many properties of single-layer graphene have been studied to allow further characterization of this material. These properties are unconventional due to the unique band structure of graphene, which is described in terms of Dirac fermions, creating links with certain theories of particle physics. In fact, several theoretical groups have employed phenomenological models inspired in quantum cromodynamics (i.e. Nambu-Jona Lassino and Gross-Neveu models) applied to the study of graphene properties. These properties are responsible for the unusual phenomena, such as the fractional Hall effect, which allows the possibility for magnetic catalysis of an excitonic gap, ferromagnetism and superconductivity. The research of high critical temperature superconductors with impurity centers is significant for understanding the underlying physics of such disordered systems. While the cuprate family present insulating properties in the pristine state, the undoped iron pnictides (i.e. LaOFeAs) show a semi-metallic behavior. Inspite these diferences, both compounds are layered structures, where the superconducting state is supported by a quasi-2D square lattice. While for iron pnictides this state is formed by the FeAs layer, the cuprate superconducting state is formed by the CuO layer. The current work focuses on the theoretical study of the structural, electronic and optical properties of graphene-type materials, such as bilayer graphene; and also of s- and d-wave superconductors, more specifically iron pnictides and cuprates, respectively. Furthermore, disordered systems will be focused upon since these (quasi-)2D systems are quite sensitive to disorder. Such properties have major importance for technological device applications, as can be observed in the increasing technological fields of high temperature superconductores and electronic devices. The type of perturbations applied to the systems of interest are chemical impurities and/or external electric bias, and these show variations of the electronic and optical properties when compared to the pristine systems. / [ES] La dimensionalidad de un sistema juega un papel fundamental en la conducta de la dinámica de los electrones que interactúan. En particular, la dimensionalidad cuasi-2D es responsable del comportamiento inusual observado en materiales de tipo grafeno y sistemas laminares basados en enlaces de tipo van der Waals. Además, estos efectos también se observan en materiales superconductores de alta temperatura crítica, incluso en el estado normal, debido a su baja dimensionalidad. El estudio experimental del grafeno provocó una atención creciente a sus propie-dades electrónicas, porque su estructura en forma de panal de abejas da lugar a una estructura de bandas con dos puntos nodales en la zona de Brillouin que determina una dinámica electrónica relativista de tipo Dirac. En el plano teórico, muchas propiedades del grafeno de una sola capa se han estudiado para permitir una mayor caracterización de este material. Estas propiedades son poco convencionales debido a la singular estructura de bandas del grafeno, que se describe en términos de fermiones de Dirac, lo que crea vínculos con ciertas teorías de la física de partículas. De hecho, varios grupos teóricos han empleado modelos fenomenológicos inspirados en la cromodinámica cuántica (es decir, los modelos Nambu-Jona Lassino y Gross-Neveu) aplicados al estudio de las propiedades del grafeno. Estas propiedades son responsables de inusuales fenómenos, como el efecto Hall fraccionario, que permite la posibilidad de catálisis magnética de un gap excitónico, ferromagnetismo y superconductividad. La investigación de superconductores de alta temperatura crítica con centros de impurezas es importante para comprender la física subyacente de tales sistemas desordenados. Mientras que la familia de los cupratos presenta propiedades aislantes en estado prístino, los pnictogenuros de hierro sin dopar (es decir, LaOFeAs) muestran un comportamiento semimetálico. A pesar de estas diferencias, ambos compuestos son estructuras en capas, donde el estado superconductor está respaldado por una red cuadrada cuasi-2D. Mientras que para los pnictogenuros de hierro este estado está formado por la capa de FeAs, el estado superconductor de cuprato está formado por la capa de CuO. El presente trabajo se centra en el estudio teórico de las propiedades estructurales, electrónicas y ópticas de los materiales de tipo grafeno, como el grafeno bicapa; y también de superconductores de ondas s y d, más específicamente pnictogenuros y cupratos de hierro, respectivamente. Además, se hace hincapié en sistemas desordenados ya que estos sistemas (cuasi-)2D son bastante sensibles al desorden. Tales propiedades tienen gran importancia para aplicaciones de dispositivos tecnológicos, como se puede observar en la creciente tecnología campos de tensiotrónica y espintrónica. El tipo de perturbaciones aplicadas a los sistemas de interés son las impurezas químicas y campos eléctricos externos. Estas perturbaciones producen variaciones de las propiedades electrónicas y ópticas cuando se comparan con los sistemas prístinos. / [CAT] La dimensionalitat d'un sistema juga un paper fonamental en la conducta de la dinámica dels electrons que interactúen. En particular, la dimensionalitat cuasi-2D és responsable del comportament inusual observat a materials de tipus grafè i sistemes laminars basats en enllaços de tipus van der Waals. A més a més, aquestos efectes també s'observen a materials superconductors d'alta temperatura crítica, inclús al seu estat normal, degut a la seua baixa dimensionalitat. L'estudi experimental del grafè va produir una atenció creixent a les seues propietats electròniques, perque la seua estructura en forma de panal d'abelles dona lloc a una estructura de bandes amb dos punts nodals a la zona de Brillouin que determinen una dinámica electrónica relativista de tipus Dirac. Al planol teòric, moltes propietats del grafè d'una sola capa s'han estudiat per a permetre una major caracterizació d'aquest material. Aquestes propietat són poc convencionals degut a la singular estructura de bandes del grafè, que es descriu mitjançant fermions de Dirac. Aquestos fermions permeten establir víncles amb certes teories de la física de particles. De fet, alguns grups teòrics han empleat models fenomenològics inspirats a la cromodinàmica quàntica (es a dir, els models Nambu-Jona Lassino i Gross-Neveu) aplicats a l'estudi de les propietats del grafè. Aquestes propietats són responsables d'inusuals fenómens, com l'efecte Hall fraccionari, que permet la possibilitat de catálisi magnètica d'un gap excitònic, ferromagnetisme i superconductivitat. La investigació de superconductors d'alta temperatura crítica amb centres d'impureses és important per a comprendre la física subjacent de tals sistemes desordenats. Mentre que la família dels cuprats presenta propietats aïllants en estat pristí, els pnictogenurs de ferro sense dopar (és a dir, LaOFeAs) mostren un comportament semimetálico. Malgrat aquestes diferències, tots dos compostos són estructures en capes, on l'estat superconductor està recolzat per una xarxa quadrada quasi-2D. Mentre que per als pnictogenurs de ferro aquest estat està format per la capa de FeAs, l'estat superconductor dels cuprats està format per la capa de CuO. El present treball es centra en l'estudi teòric de les propietats estructurals, electròniques i òptiques dels materials de tipus grafè, com el grafè bicapa; i també de superconductors d'ones s i d, més específicament pnictogenurs i cuprats de ferro, respectivament. A més a més, es fa emfasi en sistemes desordenats ja que aquestos sistemes (cuasi-)2D són prou sensibles al desordre. Aquestes propietats tenen gran importància per a aplicacions de dispositius tecnològics, com es pot observar a la creixent tecnologia dels camps de la tensiotrònica i l'espintrònica. El tipus de pertorbacions aplicades als sistemes d'interés són les impureses químiques i els camps elèctrics externs. Aquestes pertorbacions produeixen variacions de les propietats electròniques i òptiques quan es comparen amb els sistemes pristins. / César Dos Santos, MJ. (2021). Effects of symmetry breaking in low dimensional materials [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/176058 / TESIS / Compendio

<p>We write down explicit algebraic formulas for the Szeg\H{o}, Garabedian and Bergman kernels for specific two-connected planar domains. We use these results to derive integral representations for a biholomorphic invariant relating the Bergman and Szeg\H{o} kernels. We use the formulas to study the asymptotic behavior of these kernels as a family of two-connected domains approaches the unit disc. We derive an explicit formula for the Green's function for the Laplacian for special values on two-connected domains. Every two-connected domain is biholomorphic to a unique two-connected domain of the type we consider. This allows one to write down formulas for the kernel functions on a general two-connected domain.</p>

Phonon anharmonicity is critical for describing various phenomena in crystals, including lattice thermal conductivity, thermal expansion, structural phase transitions, and many others. Including anharmonicity in the calculation of condensed matter observables developed rapidly in the past decade. First-principles computation of cubic phonon interactions have been performed in many systems, and the quartic interactions have begun to receive more attention. In this study, reliable Hamiltonians are constructed purely in terms of quadratic, cubic, and quartic irreducible derivatives, which are calculated efficiently and precisely using the lone and bundled irreducible derivative approaches (LID and BID). The resulting Hamiltonians give rise to a nontrivial many-phonon problem which requires some approximation in order to compute observables. We implemented self-consistent diagrammatic approaches to evaluate the phonon self-energy, including the Hartree-Fock approximation for phonons and quasiparticle perturbation theory, where both the 4-phonon loop and the real part of the 3-phonon bubble are employed during self-consistency. Additionally, we implemented molecular dynamics in order to yield the numerically exact solution in the classical limit. The molecular dynamics solution is robust for directly comparing to experimental results at sufficiently high temperatures, and for assessing our diagrammatic approaches in the classical limit. Anharmonic vibrational Hamiltonians were constructed for CaF₂, ThO₂, and UO₂. Diagrammatic approaches were used to evaluate the phonon self-energy, yielding the phonon lineshifts and linewidths and the thermal conductivity within the relaxation time approximation. Our systematic results allowed us to resolve the paradox of why first-principles phonon linewidths strongly disagree with results extracted from inelastic neutron scattering (INS). We demonstrated that the finite region in reciprocal space required in INS data analysis, the 𝑞-voxel, must be explicitly accounted for within the calculation in order to draw a meaningful comparison. We also demonstrated that the 𝑞-voxel is important to properly compare the spectrum measured in inelastic X-ray scattering (IXS), despite the fact that the ?-voxel is much smaller. Accounting for the 𝑞-voxel, we obtained good agreement for the scattering function linewidths up to intermediate temperatures. Additionally, good agreement was obtained for the thermal conductivity. Another topic we addressed is translation symmetry breaking caused by factors such as defects, chemical disorders, and magnetic order. These phenomena will lead to shifts and a broadening of the phonon spectrum, and formally the single-particle Green’s function encodes these effects. However, it is often desirable to obtain an approximate non-interacting spectrum that contains the effective shifts of the phonon frequencies, allowing straightforward comparison with experimentally measured scattering peak locations. Such an effective phonon dispersion can be obtained using a band unfolding technique, and in this study, we formulated unfolding in the context of irreducible derivatives. We showcased the unfolding of phonons in UZr₂, where chemical disorder is present, and compared the results with experimental IXS data. Additionally, we extended the unfolding technique to anharmonic terms and demonstrated this using 3rd and 4th order terms in the antiferromagnetic phase of UO₂.

The work in this thesis is basically divided into two related but separate investigations. The first part treats simple chemical reactions of adsorbate molecules on metallic surfaces, induced by means of a scanning tunneling probe (STM). The investigation serves as a parameter free extension to existing theories. The theoretical framework is based on a combination of density functional theory (DFT) and non-equilibrium Green's functions (NEGF). Tunneling electrons that pass the adsorbate molecule are assumed to heat up the molecule, and excite vibrations that directly correspond to the reaction coordinate. The theory is demonstrated for an OD molecule adsorbed on a bridge site on a Cu(110) surface, and critically compared to the corresponding experimental results. Both reaction rates and pathways are deduced, opening up the understanding of energy transfer between different configurational geometries, and suggests a deeper insight, and ultimately a higher control of the behaviour of adsorbate molecules on surfaces. The second part describes a method to calculate STM images in the low bias regime in order to overcome the limitations of localized orbital DFT in the weak coupling limit, i.e., for large vacuum gaps between a tip and the adsorbate molecule. The theory is based on Bardeen's approach to tunneling, where the orbitals computed by DFT are used together with the single-particle Green's function formalism, to accurately describe the orbitals far away from the surface/tip. In particular, the theory successfully reproduces the experimentally well-observed characteristic dip in the tunneling current for a carbon monoxide (CO) molecule adsorbed on a Cu(111) surface. Constant height/current STM images provide direct comparisons to experiments, and from the developed method further insights into elastic tunneling are gained.

No description available.

A modified source and dipole panel method to calculate the flow properties around an oscillating arbitrary body in the presence of a free surface is proposed. To demonstrate the feasibility of the method the problem of a pulsating line source submerged under a free surface is treated. The technique chosen is based on Green's identity whereby the boundary-value problem is expressed as a boundary integral equation which is solved numerically. The near field of the water surface is represented by singularity panels with constant strength. The work was motivated by the reported large computing times for existing programs using Green's functions satisfying the free surface boundary condition. The present approach uses free-space Green's function. The free surface boundary condition is applied to surface singularity panels using Green's theorem. Thus free surface effects are included in the solution while panel integrations are simplified considerably by the use of simpler Green's function. The matrix equations resulting from Green's identity were solved by using IMSL routines for Gaussian Elimination, and the behavior of the influence coefficient matrix was tested by using LINPACK routines. The depth of the submerged-source and wave number was kept constant while the length of near field and the number of panels per wavelength was varied systematically. A minimum of 10 panels per wavelength and paneled water surface length of 2 wavelengths gives good agreement with the known exact solution. Computing times were low, indicating the feasibility of the technique for application to unsteady ship problems. / Ph. D.

Cette thèse étudie l'utilisation de certains invariants asymptotiques en géométrie conforme et géométrie CR.La première partie est consacrée à la géométrie conforme. Nous calculons les premiers termes du développement asymptotique de la fonction de Green des opérateurs GJMS au voisinage de la diagonale, pour un facteur conforme normal au sens de Lee et Parker. Nous montrons que le terme constant de ce développement est covariant sous un changement de facteur conforme normal. Nous le rattachons à un invariant à l'infini de type masse ADM d'une métrique non compacte obtenue par projection stéréographique.La deuxième partie est consacrée à la géométrie CR. Nous calculons les premiers termes du développement asymptotique de la fonction de Green de l'opérateur de Yamabe CR au voisinage de sa singularité,dans le cas CR sphérique, et en dimension 3 dans une carte CR-normale au sens de Jerison et Lee, lorsque la constante de Yamabe-CR est strictement positive. Nous montrons la covariance pseudo-conforme du terme constant sous les changements de cartes respectivement CR-sphériques et CR-normales.La troisième partie donne une explication formelle à une annulation algébrique sur laquelle repose la définition de plusieurs invariants à l'infini de type masse ADM, qui n'avait pu jusqu'à présent qu'être constatée par un calcul direct. / In this thesis we study the use of some asymptotic invariants in conformal and CR geometry.The first chapter is devoted to conformal geometry. We compute an asymptotic expansion ofthe Green function of GJMS operators near the diagonal, for a normal conformal factorin the sense of Lee and Parker. We show that the constant term in this expansion is covariant through achange of normal conformal factor. We relate it to an invariant at infinity of the type of the ADM massof a non-compact metric obtained by some kind of stereographic projection.In the second chapter we study CR geometry. We compute the first terms of the asymptotic expansion of the Greenfunction of the Yamabe-CR operator near its singularity, when the Yamabe-CR constant is positive, in the CR-sphericalcase, and in dimension 3 in a CR-normal chart in the sense of Jerison and Lee.We show the pseudo-conformal covariance of the constant term in this asymptotic expansion through a change of spherical chart andof CR-normal chart respectively.In the third chapter we give a formal explanation to an algebraic cancellationon which the defintion of some invariants at infinity such as the ADM mass relies.

Estudamos o problema de valores de contorno {\'DELTA POT. 2\' u = f em \'OMEGA\', \'BETA\' u = 0 em \'PARTIAL OMEGA\', um aberto limitado \'OMEGA\' \'ESTÁ CONTIDO\' \'R POT. N\' , sob diferentes condições de contorno. As questões de existência e positividade de soluções para este problema são abordadas com condições de contorno de Dirichlet, Navier e Steklov. Deduzimos condições de contorno naturais através do estudo de um modelo para uma placa com carga estática. Estudamos ainda propriedades do primeiro autovalor de \'DELTA POT. 2\' e o problema semilinear {\'DELTA POT. 2\' u = F (u) em \'OMEGA\' u = \'PARTIAL\'u SUP . \'PARTIAL\' v = 0 em \'PARTIUAL\' \'OMEGA\', para não-linearidades do tipo F(t) = \'l t l POT. p-1\', p \' DIFERENTE\' t, p > 0. Para tal problema estudamos existência e não-existência de soluções e positividade / We study the boundary value problem {\'DELTA POT. 2\' u = f in \'OMEGA\', \'BETA\' u = 0 in \'PARTIAL OMEGA\', in a bounded open \'OMEGA\'\'THIS CONTAINED\' \'R POT. N\' , under different boundary conditions. The questions of existence and positivity of solutions for this problem are addressed with Dirichlet, Navier and Steklov boundary conditions. We deduce natural boundary conditions through the study of a model for a plate with static load. We also study properties of the first eigenvalue of \'DELTA POT. 2\' and the semi-linear problem { \'DELTA POT. 2\' e o problema semilinear {\'DELTA POT. 2\' u = F (u) in \'OMEGA\' u = \'PARTIAL\'u SUP . \'PARTIAL\' v = 0 in \'PARTIUAL\' \'OMEGA\', for non-linearities like F(t) = \'l t l POT. p-1\', p \' DIFFERENT\' t, p > 0. For such problem we study existence and non-existence of solutions and its positivity

Ces dernières décennies, l'urgence croissante de la crise énergétique et la prise de conscience qu'une grande partie de l'énergie utilisée dans le monde est dissipée sous forme de chaleur ont provoqué un engouement pour le développement de modules thermoélectriques performants. Ces dispositifs pourraient récupérer la chaleur provenant de procédés industriels ou d'autres sources, transformant un gradient de température en voltage grâce à l'effet Seebeck. Les matériaux thermoélectriques performants doivent posséder une faible conductivité thermique, une haute conductivité électrique et un grand coefficient Seebeck. L'optimisation simultanée de ces paramètres est un défi majeur pour la physique de la matière condensée et la science des matériaux. Dans l'optique d'améliorer les propriétés thermoélectriques de plusieurs matériaux prometteurs, nous explorons plusieurs stratégies dans lesquelles les défauts (substitutions atomiques, lacunes…), le désordre et le confinement dimensionnel jouent un rôle central. Nous réalisons des calculs en théorie de la fonctionnelle densité et des projections sur des orbitales de Wannier afin de construire des Hamiltoniens et des matrices dynamiques réalistes décrivant leur structure électronique et vibrationnelle dans l'espace réel. Ces paramètres sont ensuite utilisés pour calculer les propriétés de transport thermoélectrique en utilisant le formalisme de Kubo, l'équation de Boltzmann, le formalisme de Landauer et la méthode Chebyshev polynomial Green's function, qui permet un traitement exact du désordre. Nous étudions les propriétés de transport électronique et les performances thermoélectriques de deux matériaux prometteurs pour la production d'énergie à hautes températures, le titanate de strontium et l'oxyde de titane rutile. Nous obtenons un très bon accord entre nos prédictions et un grand nombre de données expérimentales. Nous montrons que l'augmentation du coefficient Seebeck observée dans les superlayers de titanate de strontium, jusque-là attribuée à des effets de confinement quantique, est en réalité très bien expliquée par l'hypothèse d'électrons délocalisés. Nous explorons les effets généraux des états résonant sur le transport électronique dans le cadre d'une étude modèle, et nous trouvons une augmentation d'un facteur six des performances thermoélectriques. Nous examinons ensuite le cas particulier du titanate de strontium, et nous montrons que les performances sont détruites par des effets de localisation si des atomes de Vanadium sont introduits comme impuretés résonantes. Nous étudions l'influence des défauts dans les matériaux bidimensionnels. Contrairement aux adatomes, nous montrons que les substitutions dans les dichalcogénures de métaux de transition ont pour effet de localiser les porteurs de charge. Nous étudions l'effet des lacunes sur le transport de phonons dans le graphène, et nous déterminons les taux de diffusion phonon-lacune. Nous obtenons un très bon accord entre notre théorie et des mesures de conductivité thermique dans des échantillons de graphène irradiés et de tailles finies / Over the past decades, the increasingly pressing need for clean energy sources and the realization that a huge proportion of the world energy consumption is wasted in heat have prompted great interest in developing efficient thermoelectric generation modules. These devices could harvest waste heat from industrial processes or other sources, turning a temperature gradient into a voltage through the Seebeck effect. Efficient thermoelectric materials should exhibit a low thermal conductivity, a high electrical conductivity and a high Seebeck coefficient. Simultaneously optimizing these parameters is a great challenge of condensed matter physics and materials science. With a view to enhance the thermoelectric properties of several promising materials, we explore several strategies in which defects (atomic substitutions, vacancies…), disorder and dimensional confinement play a crucial role. We perform density functional theory calculations and projections on Wannier orbitals to construct realistic Hamiltonians and dynamical matrices describing their electronic and vibrational structure in real space. These parameters are then used to compute the thermoelectric transport properties using the Kubo formalism, the Boltzmann transport equation, the Landauer formalism, and the Chebyshev polynomial Green's function method that allows for an exact treatment of disorder. We investigate the electronic transport properties and thermoelectric performances of two promising materials for high-temperature power generation, strontium titanate and rutile titanium dioxide. Comparison of our predictions with a wealth of experimental data yields a very good agreement. We show that the increase of the Seebeck coefficient observed in strontium titanate superlayers, until now attributed to quantum confinement effects, is in fact well explained assuming delocalized electrons. The general effects of resonant states on electronic transport are explored in a model study, showing a sixfold increase of the thermoelectric performances. The particular case of strontium titanate is then examined, and localization effects are shown to destroy the performances if Vanadium atoms are introduced as resonant impurities. The influence of defects in two-dimensional materials is investigated. Contrary to adatoms, substitutions in transition metal dichalcogenides are shown to localize the charge carriers. We study the effect of vacancies on phonon transport in graphene, and determine the phonon-vacancy scattering rate. Comparison with thermal conductivity data for irradiated and finite-size graphene samples yields a very good agreement between theory and experiments

The flow-reversal elliptical cylindrical end chamber mufflers of short length are used often in the modern day automotive exhaust systems. The conventional 1-D axial plane wave theory is not able to predict their acoustical attenuation performance in view of the fact that the chamber length is not enough for the evanescent 3-D modes generated at the junctions to decay sufficiently for frequencies below the cut-off frequency. Also, due to the large area expansion ratio at the inlet, the first few higher order modes get cut on even in the low frequency regime. This necessitates a 3-D FEM or 3-D BEM analysis, which is cumbersome and time consuming. Therefore, an ingenious 1-D transverse plane wave theory is developed by considering plane wave propagation along the major-axis of the elliptical section, whereby a 2-port axially short elliptical and circular chamber muffler is characterized by means of the transfer matrix [T] or impedance matrix [Z]. Two different approaches are followed: (1) a numerical scheme such as the Matrizant approach, and (2) an analytical approach based upon the Frobenius series solution of the Webster’s equation governing the transverse plane wave propagation. The convective effects of mean flow are neglected; however the dissipative effects at the ports are taken into account. The TL predicted by this 1-D transverse plane wave analysis is compared with that obtained by means of the 3-D analytical approach and numerical (FEM/BEM) methods. An excellent agreement is observed between this simplified 1-D approach and the 3-D approaches at least up to the cut-on frequency of the (1, 1) even mode in the case of elliptical cylindrical chambers, or the (1, 0) mode in the case of circular cylindrical chambers, thereby validating this 1-D transverse plane wave theory. The acoustical attenuation characteristics of such short chamber mufflers for various configurations are discussed, qualitatively as well as quantitatively. Moreover, the Frobenius series solution enables one to obtain non-dimensional frequencies for determining the resonance peak and trough in the TL graph. The use of this theory is, however, limited to configurations in which both the ports are located along the major axis in the case of elliptical chambers and along the same diameter for circular chambers. The method of cascading the [T] matrices of the 2-port elements cannot be used to analyze a network arrangement of 2-port elements owing to the non-unique direction of wave propagation in such a network of acoustic elements. Although, a few papers are found in the literature reporting the analysis of a network of 2-port acoustic elements, no work is seen on the analysis of a network of multi-port elements having more than two external ports. Therefore, a generalized algorithm is proposed for analyzing a general network arrangement of linear multi-port acoustic elements having N inlet ports and M outlet ports. Each of these multi-port elements constituting the network may be interconnected to each other in an arbitrary manner. By appropriate book-keeping of the equations obtained by the [Z] matrix characterizing each of the multi-port and 2-port elements along with the junction laws (which imply the equality of acoustic pressure and conservativeness of mass velocity at a multi-port junction), an overall connectivity matrix is obtained, whereupon a global [Z] matrix is obtained which characterizes the entire network. Generalized expressions are derived for the evaluation of acoustic performance evaluation parameters such as transmission loss (TL) and insertion loss (IL) for a multiple inlet and multiple outlet (MIMO) system. Some of the characteristic properties of a general multi-port element are also studied in this chapter. The 1-D axial and transverse plane wave analysis is used to characterize axially long and short chambers, respectively, in terms of the [Z] matrix. Different network arrangements of multi-port elements are constructed, wherein the TL performance of such MIMO networks obtained on the basis of either the 1-D axial or 1-D transverse plane wave theory are compared with 3-D FEA carried on a commercial software. The versatility of this algorithm is that it can deal with more than two external or terminal ports, i.e., one can have multiple inlets and outlets in a complicated acoustic network. A generalized approach/algorithm is presented to characterize rigid wall reactive multi-port chamber mufflers of different geometries by means of a 3-D analytical formulation based upon the modal expansion and the uniform piston-driven model. The geometries analyzed here are rectangular plenum chambers, circular cylindrical chamber mufflers with and without a pass tube, elliptical cylindrical chamber mufflers, spherical and hemispherical chambers, conical chamber mufflers with and without a co-axial pass tube and sectoral cylindrical chamber mufflers of circular and elliptical cross-section as well as sectoral conical chamber mufflers. Computer codes or subroutines have been developed wherein by choosing appropriate mode functions in the generalized pressure response function, one can characterize a multi-port chamber muffler of any of the aforementioned separable geometrical shapes in terms of the [Z] matrix, subsequent to which the TL performance of these chambers is evaluated in terms of the scattering matrix [S] parameters by making use of the relations between [Z] and [S] matrices derived earlier. Interestingly, the [Z] matrix approach combined with the uniform piston-driven model is indeed ideally suited for the 3-D analytical formulation inasmuch as regardless of the number of ports, one deals with only one area discontinuity at a time, thereby making the analysis convenient for a multi-port muffler configuration with arbitrary location of ports. The TL characteristics of SISO chambers corresponding to each of the aforementioned geometries (especially the elliptical cylindrical chamber) are analyzed in detail with respect to the effect of chamber dimensions (chamber length and transverse dimensions), and relative angular and axial location of ports. Furthermore, the analysis of SIDO (i.e., single inlet and double outlet) chamber mufflers is given special consideration. In particular, we examine (1) the effect of additional outlet port (second outlet port), (2) variation in the relative angular or axial location of the additional or second outlet port (keeping the location of the inlet port and the outlet ports of the original SISO chamber to be constant) and (3) the effect of interchanging the location of the inlet and outlet ports on the TL performance of these mufflers. Thus, design guidelines are developed for the optimal location of the inlet and outlet ports keeping in mind the broadband attenuation characteristics for a single inlet and multiple outlet (SIMO) system. The non-dimensional limits up to which a flow-reversal elliptical (or circular) cylindrical end chamber having an end-inlet and end-outlet configuration is acoustically short (so that the 1-D transverse plane wave theory is applicable) and the limits beyond which it is acoustically long (so that the 1-D axial plane wave theory is applicable) is determined in terms of the ratio or equivalently, in terms of the ratio. Towards this end, two different configurations of the elliptical cylindrical chamber are considered, namely, (1) End-Offset Inlet (located along the major-axis of the ellipse) and End-Centered Outlet (2) End-Offset Inlet and End-Offset Outlet (both the ports located on the major-axis of the ellipse and at equal offset distance from the center). The former configuration is analyzed using 3-D FEA simulations (on SYSNOISE) while the 3-D analytical uniform piston-driven model is used to analyze the latter configuration. The existence of the higher order evanescent modes in the axially long reversal chamber at low frequency (before the cut-on frequency of the (1, 1) even mode or (1, 0) mode) causes a shift in the resonance peak predicted by the 1-D axial plane wave theory and 3-D analytical approach. Thus, the 1-D axial plane wave analysis is corrected by introducing appropriate end correction due to the modified or effective length of the elliptical cylindrical chamber. An empirical formulae has been developed to obtain the average non-dimensional end correction for the aforementioned configurations as functions of the expansion ratio, (i.e., ), minor-axis to major-axis ratio, (i.e., ) and the center-offset distance ratio, (i.e., ). The intermediate limits between which the chamber is neither short nor long (acoustically) has also been obtained. Furthermore, an ingenious method (Quasi 1-D approach) of combining the 1-D transverse plane wave model with the 1-D axial plane wave model using the [Z] matrix is also proposed for the end-offset inlet and end-centered outlet configuration. A 3-D analytical procedure has also been developed which also enables one to determine the end-correction in axially long 2-port flow-reversal end chamber mufflers for different geometries such as rectangular, circular and elliptical cylindrical as well as conical chambers, a priori to the computation of TL. Using this novel analytical technique, we determine the end correction for arbitrary locations on the two end ports on the end face of an axially long flow-reversal end chamber. The applicability of this method is also demonstrated for determination of the end corrections for the 2-port circular cylindrical chamber configuration without and with a pass tube, elliptical cylindrical chambers as well as rectangular and conical chambers.