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.

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.

Cracks of higher modes in Cosserat continua

Rotational degrees of freedom in Cosserat continua give rise to higher fracture modes. Three new fracture modes correspond to the cracks that are surfaces of discontinuities in the corresponding components of independent Cosserat rotations. We develop a generalisation of J- integral that includes these additional degrees of freedom. The obtained path-independent integrals are used to develop a criterion of crack propagation for a special type of failure in layered materials with sliding layers. This fracture propagates as a progressive bending failure of layers – a “bending crack that is, a crack that can be represented as a distribution of discontinuities in the layer bending. This situation is analysed using a 2D Cosserat continuum model. Semi-infinite bending crack normal to layering is considered. The moment stress concentrates along the line that is a continuation of the crack and has a singularity of the power − 1/4. A model of process zone is proposed for the case when the breakage of layers in the process of bending crack propagation is caused by a crack (microcrack in our description) growing across the layer adjacent to the crack tip. This growth is unstable (in the moment-controlled loading), which results in a typical descending branch of moment stress – rotation discontinuity relationship and hence in emergence of a Barenblatt-type process zone at the tip of the bending crack.

Resistance heating of steel conductors of circular cross-section

The object of this thesis is to develop a method for calculating the losses developed in steel conductors of circular cross-section and at temperatures below 100oC, by the direct passage of a sinusoidally alternating current. Three cases are considered. 1. Isolated solid or tubular conductor. 2. Concentric arrangement of tube and solid return conductor. 3. Concentric arrangement of two tubes. These cases find applications in process temperature maintenance of pipelines, resistance heating of bars and design of bus-bars. The problems associated with the non-linearity of steel are examined. Resistance heating of bars and methods of surface heating of pipelines are briefly described. Magnetic-linear solutions based on Maxwell's equations are critically examined and conditions under which various formulae apply investigated. The conditions under which a tube is electrically equivalent to a solid conductor and to a semi-infinite plate are derived. Existing solutions for the calculation of losses in isolated steel conductors of circular cross-section are reviewed, evaluated and compared. Two methods of solution are developed for the three cases considered. The first is based on the magnetic-linear solutions and offers an alternative to the available methods which are not universal. The second solution extends the existing B/H step-function approximation method to small diameter conductors and to tubes in isolation or in a concentric arrangement. A comprehensive experimental investigation is presented for cases 1 and 2 above which confirms the validity of the proposed methods of solution. These are further supported by experimental results reported in the literature. Good agreement is obtained between measured and calculated loss values for surface field strengths beyond the linear part of the d.c. magnetisation characteristic. It is also shown that there is a difference in the electrical behaviour of a small diameter conductor or thin tube under resistance or induction heating conditions.

Time scale analysis for fluidizedbedmeltgranulation III: binder solidification rate

In series I and II of this study ([Chua et al., 2010a] and [Chua et al., 2010b]), we discussed the time scale of granule–granule collision, droplet–granule collision and droplet spreading in Fluidized Bed Melt Granulation (FBMG). In this third one, we consider the rate at which binder solidifies. Simple analytical solution, based on classical formulation for conduction across a semi-infinite slab, was used to obtain a generalized equation for binder solidification time. A multi-physics simulation package (Comsol) was used to predict the binder solidification time for various operating conditions usually considered in FBMG. The simulation results were validated with experimental temperature data obtained with a high speed infrared camera during solidification of ‘macroscopic’ (mm scale) droplets. For the range of microscopic droplet size and operating conditions considered for a FBMG process, the binder solidification time was found to fall approximately between 10-3 and 10-1 s. This is the slowest compared to the other three major FBMG microscopic events discussed in this series (granule–granule collision, granule–droplet collision and droplet spreading).

Lattice Boltzmann modeling of fluid flow and solute transport in karst aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Lattice Boltzmann Modeling of Fluid Flow and Solute Transport in Karst Aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry.