A FEM-BEM coupling procedure through the Steklov-Poincarè operator

Many advantages can be got in combining finite and boundary elements.It is the case, for example, of unbounded field problems where boundary elements can provide the appropriate conditions to represent the infinite domain while finite elements are suitable for more complex properties in the near domain. However, in spite of it, other disadvantages can appear. It would be, for instance, the loss of symmetry in the finite elements stiffness matrix, when the combination is made. On the other hand, in our days, with the strong irruption of the parallel proccessing the techniques of decomposition of domains are getting the interest of numerous scientists. With their application it is possible to separate the resolution of a problem into several subproblems. That would be beneficial in the combinations BEM-FEM as the loss of symmetry would be avoided and every technique would be applicated separately. Evidently for the correct application of these techniques it is necessary to establish the suitable transmission conditions in the interface between BEM domain and FEM domain. In this paper, one parallel method is presented which is based in the interface operator of Steklov Poincarè.

Medidas experimentales de la complejidad computacional de un código autoadaptativo HP para problemas abiertos acelerado mediante ACA

The aim of the novel experimental measures presented in this paper is to show the improvement achieved in the computation time for a 2D self-adaptive hp finite element method (FEM) software accelerated through the Adaptive Cross Approximation (ACA) method. This algebraic method (ACA) was presented in an previous paper in the hp context for the analysis of open region problems, where the robust behaviour, good accuracy and high compression levels of ACA were demonstrated. The truncation of the infinite domain is settled through an iterative computation of the Integral Equation (IE) over a ficticious boundary, which, regardless its accuracy and efficiency, turns out to be the bottelneck of the code. It will be shown that in this context ACA reduces drastically the computational effort of the problem.

Transient behavior of a system composed of conductive thin wire structures excited by harmonic and lightning type signals

The transient response of a system of independent electrodes buried in a semi-infinite conducting medium is studied. Using a simple and versatile numerical scheme written by the authors and based on the Electric Field Integral Equation (EFIE), the effect caused by harmonic signals ranging on frequency from Hz to hundred of MHz, and also by lightning type driving signal striking at a remote point far from the conductors, is extensively studied. The value of the scalar potential appearing on the electrodes as a function of the frequency of the applied signal is one of the variables investigated. Other features such as the input impedance at the injection point of the signal and the Ground Potential Rise (GPR) over the electrode system are also discussed

Beam Spectral Element with FRP Debonding

The behaviour of the interface between the FRP and the concrete is the key factor controlling debonding failures in FRP-strengthened RC structures. This defect can cause reductions in static strength, structural integrity and the change in the dynamic behavior of the structure. The adverse effect on the dynamic behavior of the defects can be utilized as an effective means for identifying and assessing both the location and size of debonding at its earliest stages. The presence of debonding changes the structural dynamic characteristics and might be traced in modal parameters, dynamic strain and wave patterns etc. Detection of minor local defects, as those origin of a future debonding, requires working at high frequencies so that the wavelength of the excited is small and sensitive enough to detect local damage. The development of a spectral element method gives a large potential in high-frequency structural modeling. In contrast to the conventional finite element, since inertial properties are modeled exactly few elements are necessary to capture very accurate solutions at the highest frequencies in large regions. A wide variety of spectral elements have been developed for structural members over finite and semi-infinite regions. The objective of this paper is to develop a Spectral Finite Element Model to efficiently capture the behavior of intermediate debonding of a FRP strengthened RC beam during wave-based diagnostics.

Resonadores piezoeléctricos de cizalladura: estudio de la formación de biofilms y caracterización de fluidos magneto‐reológicos

La presente tesis revisa y analiza algunos aspectos fundamentales relativos al comportamiento de los sensores basados en resonadores piezoeléctricos TSM (Thickness Shear Mode), así como la aplicación de los mismos al estudio y caracterización de dos medios viscoelásticos de gran interés: los fluidos magnetoreológicos y los biofilms microbianos. El funcionamiento de estos sensores está basado en la medida de sus propiedades resonantes, las cuales varían al entrar en contacto con el material que se quiere analizar. Se ha realizado un análisis multifrecuencial, trabajando en varios modos de resonancia del transductor, en algunas aplicaciones incluso de forma simultánea (excitación pulsada). Se han revisado fenómenos como la presencia de microcontactos en la superficie del sensor y la resonancia de capas viscoelásticas de espesor finito, que pueden afectar a los sensores de cuarzo de manera contraria a lo que predice la teoría convencional (Sauerbrey y Kanazawa), pudiéndonos llevar a incrementos positivos de la frecuencia de resonancia. Además, se ha estudiado el efecto de una deposición no uniforme sobre el resonador piezoeléctrico. Para ello se han medido deposiciones de poliuretano, modelándose la respuesta del resonador con estas deposiciones mediante FEM. El modelo numérico permite estudiar el comportamiento del resonador al modificar distintas variables geométricas (espesor, superficie, no uniformidad y zona de deposición) de la capa depositada. Se ha demostrado que para espesores de entre un cuarto y media longitud de onda aproximadamente, una capa viscoelástica no uniforme sobre la superficie del sensor, amplifica el incremento positivo del desplazamiento de la frecuencia de resonancia en relación con una capa uniforme. Se ha analizado también el patrón geométrico de la sensibilidad del sensor, siendo también no uniforme sobre su superficie. Se han aplicado sensores TSM para estudiar los cambios viscoelásticos que se producen en varios fluidos magneto-reológicos (FMR) al aplicarles distintos esfuerzos de cizalla controlados por un reómetro. Se ha podido ver que existe una relación directa entre diversos parámetros reológicos obtenidos con el reómetro (fuerza normal, G’, G’’, velocidad de deformación, esfuerzo de cizalla…) y los parámetros acústicos, caracterizándose los FMR tanto en ausencia de campo magnético, como con campo magnético aplicado a distintas intensidades. Se han estudiado las ventajas que aporta esta técnica de medida sobre la técnica basada en un reómetro comercial, destacando que se consigue caracterizar con mayor detalle algunos aspectos relevantes del fluido como son la deposición de partículas (estabilidad del fluido), el proceso de ruptura de las estructuras formadas en los FMR tanto en presencia como en ausencia de campo magnético y la rigidez de los microcontactos que aparecen entre partículas y superficies. También se han utilizado sensores de cuarzo para monitorear en tiempo real la formación de biofilms de Staphylococcus epidermidis y Eschericia coli sobre los propios resonadores de cristal de cuarzo sin ningún tipo de recubrimiento, realizándose ensayos con cepas que presentan distinta capacidad de producir biofilm. Se mostró que, una vez que se ha producido una primera adhesión homogénea de las bacterias al sustrato, podemos considerar el biofilm como una capa semi-infinita, de la cual el sensor de cuarzo refleja las propiedades viscoelásticas de la región inmediatamente contigua al resonador, no siendo sensible a lo que sucede en estratos superiores del biofilm. Los experimentos han permitido caracterizar el módulo de rigidez complejo de los biofilms a varias frecuencias, mostrándose que el parámetro característico que indica la adhesión de un biofilm tanto en el caso de S. epidermidis como de E. coli, es el incremento de G’ (relacionado con la elasticidad o rigidez de la capa), el cual viene ligado a un incremento de la frecuencia de resonancia del sensor. ABSTRACT This thesis reviews and analyzes some key aspects of the behavior of sensors based on piezoelectric resonators TSM (Thickness Shear Mode) and their applications to the study and characterization in two viscoelastic media of great interest: magnetorheological fluids and microbial biofilms. The operation of these sensors is based on the analysis of their resonant properties that vary in contact with the material to be analyzed. We have made a multi-frequency analysis, working in several modes of resonance of the transducer, in some applications even simultaneously (by impulse excitation). We reviewed some phenomena as the presence of micro-contacts on the sensor surface and the resonance of viscoelastic layers of finite thickness, which can affect quartz sensors contrary to the conventional theory predictions (Sauerbrey and Kanazawa), leading to positive resonant frequency shifts. In addition, we studied the effect of non-uniform deposition on the piezoelectric resonator. Polyurethane stools have been measured, being the resonator response to these depositions modeled by FEM. The numerical model allows studying the behavior of the resonator when different geometric variables (thickness, surface non-uniformity and deposition zone) of the deposited layer are modified. It has been shown that for thicknesses between a quarter and a half of a wavelength approximately, non-uniform deposits on the sensor surface amplify the positive increase of the resonance frequency displacement compared to a uniform layer. The geometric pattern of the sensor sensitivity was also analyzed, being also non-uniform over its surface. TSM sensors have been applied to study the viscoelastic changes occurring in various magneto-rheological fluids (FMR) when subjected to different controlled shear stresses driven by a rheometer. It has been seen that there is a direct relationship between various rheological parameters obtained with the rheometer (normal force, G', G'', stress, shear rate ...) and the acoustic parameters, being the FMR characterized both in the absence of magnetic field, and when the magnetic field was applied at different intensities. We have studied the advantages of this technique over the characterization methods based on commercial rheometers, noting that TSM sensors are more sensitive to some relevant aspects of the fluid as the deposition of particles (fluid stability), the breaking process of the structures formed in the FMR both in the presence and absence of magnetic field, and the rigidity of the micro-contacts appearing between particles and surfaces. TSM sensors have also been used to monitor in real time the formation of biofilms of Staphylococcus epidermidis and Escherichia coli on the quartz crystal resonators themselves without any coating, performing tests with strains having different ability to produce biofilm. It was shown that, once a first homogeneous adhesion of bacteria was produced on the substrate, the biofilm can be considered as a semi-infinite layer and the quartz sensor reflects only the viscoelastic properties of the region immediately adjacent to the resonator, not being sensitive to what is happening in upper layers of the biofilm. The experiments allow the evaluation of the biofilm complex stiffness module at various frequencies, showing that the characteristic parameter that indicates the adhesion of a biofilm for the case of both S. epidermidis and E. coli, is an increased G' (related to the elasticity or stiffness of the layer), which is linked to an increase in the resonance frequency of the sensor.

Very intense pulse in the groundwater flow in fissurized-porous stratum

An asymptotic solution is obtained corresponding to a very intense pulse: a sudden strong increase and fast subsequent decrease of the water level at the boundary of semi-infinite fissurized-porous stratum. This flow is of practical interest: it gives a model of a groundwater flow after a high water period or after a failure of a dam around a collector of liquid waste. It is demonstrated that the fissures have a dramatic influence on the groundwater flow, increasing the penetration depth and speed of fluid penetration into the stratum. A characteristic property of the flow in fissurized-porous stratum is the rapid breakthrough of the fluid at the first stage deeply into the stratum via a system of cracks, feeding of porous blocks by the fluid in cracks, and at a later stage feeding of advancing fluid flow in fissures by the fluid, accumulated in porous blocks.

Confiabilidade aplicada ao problema de interação estaca-solo.

Este trabalho busca aplicar técnicas de confiabilidade ao problema de grupo de estacas utilizadas como fundação de estruturas correntes. Para isso, lança-se mão de um modelo tridimensional de interação estaca-solo onde estão presentes o Método dos Elementos de Contorno (MEC) e o método dos Elementos Finitos (MEF) que atuam de forma acoplada. O MEC, com as soluções fundamentais de Mindlin (meio semi-infinito, homogêneo, isotrópico e elástico-linear é utiliza), é utilizado para modelar o solo. Já o MEF é utilizado para modelar as estacas. Definido o modelo de funcionamento estrutural das estacas, parte-se para a aplicação de métodos trazidos da confiabilidade estrutural para avaliação da adequabilidade em relação aos estados limite de serviço e estados limites últimos. Os métodos de confiabilidade utilizados foram o Método de Monte Carlo, o método FOSM (First-Order Second-Moment) e o método FORM (First-Order Reliability Method).

Dyakonons in hyperbolic metamaterials

We have analyzed surface-wave propagation that takes place at the boundary between an isotropic medium and a semi-infinite metal-dielectric periodic medium cut normally to the layers. In the range of frequencies where the periodic medium shows hyperbolic space dispersion, hybridization of surface waves (dyakonons) occurs. At low to moderate frequencies, dyakonons enable tighter confinement near the interface in comparison with pure SPPs. On the other hand, a distinct regime governs dispersion of dyakonons at higher frequencies.

Engineered surface waves in hyperbolic metamaterials

We analyzed surface-wave propagation that takes place at the boundary between a semi-infinite dielectric and a multilayered metamaterial, the latter with indefinite permittivity and cut normally to the layers. Known hyperbolization of the dispersion curve is discussed within distinct spectral regimes, including the role of the surrounding material. Hybridization of surface waves enable tighter confinement near the interface in comparison with pure-TM surface-plasmon polaritons. We demonstrate that the effective-medium approach deviates severely in practical implementations. By using the finite-element method, we predict the existence of long-range oblique surface waves.

Oblique surface waves at an interface between a metal–dielectric superlattice and an isotropic dielectric

We investigate the existence and dispersion characteristics of surface waves that propagate at an interface between a metal–dielectric superlattice and an isotropic dielectric. Within the long-wavelength limit, when the effective-medium (EM) approximation is valid, the superlattice behaves like a uniaxial plasmonic crystal with the main optical axes perpendicular to the metal–dielectric interfaces. We demonstrate that if such a semi-infinite plasmonic crystal is cut normally to the layer interfaces and brought into contact with a semi-infinite dielectric, a new type of surface mode can appear. Such modes can propagate obliquely to the optical axes if favorable conditions regarding the thickness of the layers and the dielectric permittivities of the constituent materials are met. We show that losses within the metallic layers can be substantially reduced by making the layers sufficiently thin. At the same time, a dramatic enlargement of the range of angles for oblique propagation of the new surface modes is observed. This can lead, however, to field non-locality and consequently to failure of the EM approximation.

Propagation of Dyakonon Wave-Packets at the Boundary of Metallodielectric Lattices

We rigorously analyze the propagation of localized surface waves that takes place at the boundary between a semi-infinite layered metal-dielectric (MD) nanostructure cut normally to the layers and a isotropic medium. It is demonstrated that Dyakonov-like surface waves (also coined dyakonons) with hybrid polarization may propagate in a wide angular range. As a consequence, dyakonon-based wave-packets (DWPs) may feature sub-wavelength beamwidths. Due to the hyperbolic-dispersion regime in plasmonic crystals, supported DWPs are still in the canalization regime. The apparent quadratic beam spreading, however, is driven by dissipation effects in metal.

Calmness of the Feasible Set Mapping for Linear Inequality Systems

In this paper we deal with parameterized linear inequality systems in the n-dimensional Euclidean space, whose coefficients depend continuosly on an index ranging in a compact Hausdorff space. The paper is developed in two different parametric settings: the one of only right-hand-side perturbations of the linear system, and that in which both sides of the system can be perturbed. Appealing to the backgrounds on the calmness property, and exploiting the specifics of the current linear structure, we derive different characterizations of the calmness of the feasible set mapping, and provide an operative expresion for the calmness modulus when confined to finite systems. In the paper, the role played by the Abadie constraint qualification in relation to calmness is clarified, and illustrated by different examples. We point out that this approach has the virtue of tackling the calmness property exclusively in terms of the system’s data.

Quantum spin Hall phase in multilayer graphene

The so-called quantum spin Hall phase is a topologically nontrivial insulating phase that is predicted to appear in graphene and graphenelike systems. In this paper we address the question of whether this topological property persists in multilayered systems. We consider two situations: purely multilayer graphene and heterostructures where graphene is encapsulated by trivial insulators with a strong spin-orbit coupling. We use a four-orbital tight-binding model that includes full atomic spin-orbit coupling and we calculate the Z2 topological invariant of the bulk states as well as the edge states of semi-infinite crystals with armchair termination. For homogeneous multilayers we find that even when the spin-orbit interaction opens a gap for all possible stackings, only those with an odd number of layers host gapless edge states while those with an even number of layers are trivial insulators. For heterostructures where graphene is encapsulated by trivial insulators, it turns out that interlayer coupling is able to induce a topological gap whose size is controlled by the spin-orbit coupling of the encapsulating materials, indicating that the quantum spin Hall phase can be induced by proximity to trivial insulators.

Stability in Linear Optimization Under Perturbations of the Left-Hand Side Coefficients

This paper studies stability properties of linear optimization problems with finitely many variables and an arbitrary number of constraints, when only left hand side coefficients can be perturbed. The coefficients of the constraints are assumed to be continuous functions with respect to an index which ranges on certain compact Hausdorff topological space, and these properties are preserved by the admissible perturbations. More in detail, the paper analyzes the continuity properties of the feasible set, the optimal set and the optimal value, as well as the preservation of desirable properties (boundedness, uniqueness) of the feasible and of the optimal sets, under sufficiently small perturbations.

The displacement and strain field of three-dimensional rheologic model of earthquake preparation

Based on the three-dimensional elastic inclusion model proposed by Dobrovolskii, we developed a rheological inclusion model to study earthquake preparation processes. By using the Corresponding Principle in the theory of rheologic mechanics, we derived the analytic expressions of viscoelastic displacement U(r, t) , V(r, t) and W(r, t), normal strains epsilon(xx) (r, t), epsilon(yy) (r, t) and epsilon(zz) (r, t) and the bulk strain theta (r, t) at an arbitrary point (x, y, z) in three directions of X axis, Y axis and Z axis produced by a three-dimensional inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model. Subsequent to the spatial-temporal variation of bulk strain being computed on the ground produced by such a spherical rheologic inclusion, interesting results are obtained, suggesting that the bulk strain produced by a hard inclusion change with time according to three stages (alpha, beta, gamma) with different characteristics, similar to that of geodetic deformation observations, but different with the results of a soft inclusion. These theoretical results can be used to explain the characteristics of spatial-temporal evolution, patterns, quadrant-distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to build physical models for earthquake precursors and to predict the earthquakes.