A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation

We present a variable time step, fully adaptive in space, hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions. The method is based on the hybrid level set/front-tracking approach proposed in [H. D. Ceniceros and A. M. Roma, J. Comput. Phys., 205, 391400, 2005]. Geometric, interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance (level set) function, which is evaluated fast and to machine precision, is used as a fluid indicator. The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in [S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, J. Comput. Phys., 203, 493-516, 2005] whose success for greatly reducing parasitic currents has been demonstrated. The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude. To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic, adaptive mesh refinements. This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step, linearly implicit time integration scheme. We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications: the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability, an example of bubble ascending dynamics, and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.

A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients

In this paper, we derive a new nonlinear two-sided space-fractional diffusion equation with variable coefficients from the fractional Fick’s law. A semi-implicit difference method (SIDM) for this equation is proposed. The stability and convergence of the SIDM are discussed. For the implementation, we develop a fast accurate iterative method for the SIDM by decomposing the dense coefficient matrix into a combination of Toeplitz-like matrices. This fast iterative method significantly reduces the storage requirement of O(n2)O(n2) and computational cost of O(n3)O(n3) down to n and O(nlogn)O(nlogn), where n is the number of grid points. The method retains the same accuracy as the underlying SIDM solved with Gaussian elimination. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

Measuring color differences in automotive samples with lightness flop: a test of the AUDI2000 color-difference formula

From a set of gonioapparent automotive samples from different manufacturers we selected 28 low-chroma color pairs with relatively small color differences predominantly in lightness. These color pairs were visually assessed with a gray scale at six different viewing angles by a panel of 10 observers. Using the Standardized Residual Sum of Squares (STRESS) index, the results of our visual experiment were tested against predictions made by 12 modern color-difference formulas. From a weighted STRESS index accounting for the uncertainty in visual assessments, the best prediction of our whole experiment was achieved using AUDI2000, CAM02-SCD, CAM02-UCS and OSA-GP-Euclidean color-difference formulas, which were no statistically significant different among them. A two-step optimization of the original AUDI2000 color-difference formula resulted in a modified AUDI2000 formula which performed both, significantly better than the original formula and below the experimental inter-observer variability. Nevertheless the proposal of a new revised AUDI2000 color-difference formula requires additional experimental data.

Simulación numérica de un problema de contaminación atmosférica

La ecuación en derivadas parciales de advección difusión con reacción química es la base de los modelos de dispersión de contaminantes en la atmósfera, y los diferentes métodos numéricos empleados para su resolución han sido objeto de amplios estudios a lo largo de su desarrollo. En esta Tesis se presenta la implementación de un nuevo método conservativo para la resolución de la parte advectiva de la ecuación en derivadas parciales que modela la dispersión de contaminantes dentro del modelo mesoescalar de transporte químico CHIMERE. Este método está basado en una técnica de volúmenes finitos junto con una interpolación racional. La ventaja de este método es la conservación exacta de la masa transportada debido al empleo de la ley de conservación de masas. Para ello emplea una formulación de flujo basado en el cálculo de la integral ponderada dentro de cada celda definida para la discretización del espacio en el método de volúmenes finitos. Los resultados numéricos obtenidos en las simulaciones realizadas (implementando el modelo conservativo para la advección en el modelo CHIMERE) se han comparado con los datos observados de concentración de contaminantes registrados en la red de estaciones de seguimiento y medición distribuidas por la Península Ibérica. Los datos estadísticos de medición del error, la media normalizada y la media absoluta normalizada del error, presentan valores que están dentro de los rangos propuestos por la EPA para considerar el modelo preciso. Además, se introduce un nuevo método para resolver la parte advectivadifusiva de la ecuación en derivadas parciales que modeliza la dispersión de contaminantes en la atmósfera. Se ha empleado un método de diferencias finitas de alto orden para resolver la parte difusiva de la ecuación de transporte de contaminantes junto con el método racional conservativo para la parte advectiva en una y dos dimensiones. Los resultados obtenidos de la aplicación del método a diferentes situaciones incluyendo casos académicos y reales han sido comparados con la solución analítica de la ecuación de advección-difusión, demostrando que el nuevo método proporciona un resultado preciso para aproximar la solución. Por último, se ha desarrollado un modelo completo que contempla los fenómenos advectivo y difusivo con reacción química, usando los métodos anteriores junto con una técnica de diferenciación regresiva (BDF2). Esta técnica consiste en un método implícito multipaso de diferenciación regresiva de segundo orden, que nos permite resolver los problemas rígidos típicos de la química atmosférica, modelizados a través de sistemas de ecuaciones diferenciales ordinarias. Este método hace uso de la técnica iterativa Gauss- Seidel para obtener la solución de la parte implícita de la fórmula BDF2. El empleo de la técnica de Gauss-Seidel en lugar de otras técnicas comúnmente empleadas, como la iteración por el método de Newton, nos proporciona rapidez de cálculo y bajo consumo de memoria, ideal para obtener modelos operativos para la resolución de la cinética química atmosférica. ABSTRACT Extensive research has been performed to solve the atmospheric chemicaladvection- diffusion equation and different numerical methods have been proposed. This Thesis presents the implementation of an exactly conservative method for the advection equation in the European scale Eulerian chemistry transport model CHIMERE based on a rational interpolation and a finite volume algorithm. The advantage of the method is that the cell-integrated average is predicted via a flux formulation, thus the mass is exactly conserved. Numerical results are compared with a set of observation registered at some monitoring sites in Spain. The mean normalized bias and the mean normalized absolute error present values that are inside the range to consider an accurate model performance. In addition, it has been introduced a new method to solve the advectiondiffusion equation. It is based on a high-order accurate finite difference method to solve de diffusion equation together with a rational interpolation and a finite volume to solve the advection equation in one dimension and two dimensions. Numerical results obtained from solving several problems include academic and real atmospheric problems have been compared with the analytical solution of the advection-diffusion equation, showing that the new method give an efficient algorithm for solving such problems. Finally, a complete model has been developed to solve the atmospheric chemical-advection-diffusion equation, adding the conservative method for the advection equation, the high-order finite difference method for the diffusion equation and a second-order backward differentiation formula (BDF2) to solve the atmospheric chemical kinetics. The BDF2 is an implicit, second order multistep backward differentiation formula used to solve the stiff systems of ordinary differential equations (ODEs) from atmospheric chemistry. The Gauss-Seidel iteration is used for approximately solving the implicitly defined BDF solution, giving a faster tool than the more commonly used iterative modified Newton technique. This method implies low start-up costs and a low memory demand due to the use of Gauss-Seidel iteration.

The Galerkin finite element approximation of the fractional cable equation

The cable equation is one of the most fundamental equations for modeling neuronal dynamics. Cable equations with a fractional order temporal derivative have been introduced to model electrotonic properties of spiny neuronal dendrites. In this paper, the fractional cable equation involving two integro-differential operators is considered. The Galerkin finite element approximations of the fractional cable equation are proposed. The main contribution of this work is outlined as follow: • A semi-discrete finite difference approximation in time is proposed. We prove that the scheme is unconditionally stable, and the numerical solution converges to the exact solution with order O(Δt). • A semi-discrete difference scheme for improving the order of convergence for solving the fractional cable equation is proposed, and the numerical solution converges to the exact solution with order O((Δt)2). • Based on the above semi-discrete difference approximations, Galerkin finite element approximations in space for a full discretization are also investigated. • Finally, some numerical results are given to demonstrate the theoretical analysis.

A preconditioned numerical solver for stiff nonlinear reaction-diffusion equations with fractional Laplacians that avoids dense matrices

The numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators. The dense coefficient matrices that arise from spatial discretisation of these operators mean that even one-dimensional problems can be difficult to solve using standard methods on grids comprising thousands of nodes or more. In this work we address this issue of efficiency for one-dimensional, nonlinear space-fractional reaction–diffusion equations with fractional Laplacian operators. We apply variable-order, variable-stepsize backward differentiation formulas in a Jacobian-free Newton–Krylov framework to advance the solution in time. A key advantage of this approach is the elimination of any requirement to form the dense matrix representation of the fractional Laplacian operator. We show how a banded approximation to this matrix, which can be formed and factorised efficiently, can be used as part of an effective preconditioner that accelerates convergence of the Krylov subspace iterative solver. Our approach also captures the full contribution from the nonlinear reaction term in the preconditioner, which is crucial for problems that exhibit stiff reactions. Numerical examples are presented to illustrate the overall effectiveness of the solver.

用波动方程建立蠕动爬行攻泥机器人海底土力学运动模型

针对目前国内海底蠕动爬行机器人攻打千斤洞的特点 ,在对海洋沉积土的工程性质进行分析的基础上 ,利用流变力学的理论 ,提出用波动方程来建立攻泥机器人周期性冲击土壤的力学模型 ,用后向差分法解波动方程 ,得到土壤的位移和变形公式 ,确定土壤对攻泥机的阻力 .通过对模型的仿真 ,证明了用该模型计算阻力的可行性 .

Más allá de la infraestructura: el impacto de las bibliotecas públicas en la calidad de la educación

La literatura sobre la calidad de la educación ha prestado poca atención al papel que tienen las bibliotecas públicas dentro de los determinantes del desempeño educativo. Las bibliotecas públicas son activos externos al colegio y al hogar del estudiante, pero hacen parte del entorno social que les rodea. La puesta en marcha a finales de 2001 de tres bibliotecas de gran tamaño en Bogotá, conocidas como megabibliotecas, nos permite analizar el impacto de estas iniciativas sobre la calidad de la educación en los colegios aledaños. Dicho impacto se daría a través de mecanismos adicionales a la simple reducción de costos al acceso a la información: las bibliotecas renovaron el espacio público mediante la generación de espacios agradables y amigables hacia la educación, además ofrecen regularmente actividades lúdicas dirigidas a las habitantes del sector. Aprovechando la distancia del plantel educativo a la biblioteca como una aproximación al costo de acceso a la misma, utilizando para ello Diferencia en Diferencias junto a la descomposición Blinder Oaxaca. Encontramos que las mismas parecen no tener un impacto significativo sobre el desempeño académico general en los exámenes oficiales SABER 11 durante los años posteriores a su implementación. Se recomienda analizar programas específicos que aprovechen las bibliotecas para actividades escolares y otras posibles variables de impacto como actitudes hacia el estudio y aspiraciones a la educación superior.

Numerical coupling of thermal-electric network models and energy-transport equations including optoelectronic semiconductor devices

In this work the numerical coupling of thermal and electric network models with model equations for optoelectronic semiconductor devices is presented. Modified nodal analysis (MNA) is applied to model electric networks. Thermal effects are modeled by an accompanying thermal network. Semiconductor devices are modeled by the energy-transport model, that allows for thermal effects. The energy-transport model is expandend to a model for optoelectronic semiconductor devices. The temperature of the crystal lattice of the semiconductor devices is modeled by the heat flow eqaution. The corresponding heat source term is derived under thermodynamical and phenomenological considerations of energy fluxes. The energy-transport model is coupled directly into the network equations and the heat flow equation for the lattice temperature is coupled directly into the accompanying thermal network. The coupled thermal-electric network-device model results in a system of partial differential-algebraic equations (PDAE). Numerical examples are presented for the coupling of network- and one-dimensional semiconductor equations. Hybridized mixed finite elements are applied for the space discretization of the semiconductor equations. Backward difference formluas are applied for time discretization. Thus, positivity of charge carrier densities and continuity of the current density is guaranteed even for the coupled model.

Measuring color differences in gonioapparent materials used in the automotive industry

This paper illustrates how to design a visual experiment to measure color differences in gonioapparent materials and how to assess the merits of different advanced color-difference formulas trying to predict the results of such experiment. Successful color-difference formulas are necessary for industrial quality control and artificial color-vision applications. A color- difference formula must be accurate under a wide variety of experimental conditions including the use of challenging materials like, for example, gonioapparent samples. Improving the experimental design in a previous paper [Melgosaet al., Optics Express 22, 3458-3467 (2014)], we have tested 11 advanced color-difference formulas from visual assessments performed by a panel of 11 observers with normal colorvision using a set of 56 nearly achromatic colorpairs of automotive gonioapparent samples. Best predictions of our experimental results were found for the AUDI2000 color-difference formula, followed by color-difference formulas based on the color appearance model CIECAM02. Parameters in the original weighting function for lightness in the AUDI2000 formula were optimized obtaining small improvements. However, a power function from results provided by the AUDI2000 formula considerably improved results, producing values close to the inter-observer variability in our visual experiment. Additional research is required to obtain a modified AUDI2000 color-difference formula significantly better than the current one.

Computer methods for the heat conduction equation

The merits of various numerical methods for the solution of the one and two dimensional heat conduction equation with a radiation boundary condition have been examined from a practical standpoint in order to determine accuracies and efficiencies. It is found that the use of five increments to approximate the space derivatives gives sufficiently accurate results provided the time step is not too large; further, the implicit backward difference method of Liebmann (27) is found to be the most accurate method. On this basis, a new implicit method is proposed for the solution of the three-dimensional heat conduction equation with radiation boundary conditions. The accuracies of the integral and analogue computer methods are also investigated.

Seismic Response Analysis of a Full-Scale Base-Isolated Structure via Measurements and Modeling

The full-scale base-isolated structure studied in this dissertation is the only base-isolated building in South Island of New Zealand. It sustained hundreds of earthquake ground motions from September 2010 and well into 2012. Several large earthquake responses were recorded in December 2011 by NEES@UCLA and by GeoNet recording station nearby Christchurch Women's Hospital. The primary focus of this dissertation is to advance the state-of-the art of the methods to evaluate performance of seismic-isolated structures and the effects of soil-structure interaction by developing new data processing methodologies to overcome current limitations and by implementing advanced numerical modeling in OpenSees for direct analysis of soil-structure interaction.

This dissertation presents a novel method for recovering force-displacement relations within the isolators of building structures with unknown nonlinearities from sparse seismic-response measurements of floor accelerations. The method requires only direct matrix calculations (factorizations and multiplications); no iterative trial-and-error methods are required. The method requires a mass matrix, or at least an estimate of the floor masses. A stiffness matrix may be used, but is not necessary. Essentially, the method operates on a matrix of incomplete measurements of floor accelerations. In the special case of complete floor measurements of systems with linear dynamics, real modes, and equal floor masses, the principal components of this matrix are the modal responses. In the more general case of partial measurements and nonlinear dynamics, the method extracts a number of linearly-dependent components from Hankel matrices of measured horizontal response accelerations, assembles these components row-wise and extracts principal components from the singular value decomposition of this large matrix of linearly-dependent components. These principal components are then interpolated between floors in a way that minimizes the curvature energy of the interpolation. This interpolation step can make use of a reduced-order stiffness matrix, a backward difference matrix or a central difference matrix. The measured and interpolated floor acceleration components at all floors are then assembled and multiplied by a mass matrix. The recovered in-service force-displacement relations are then incorporated into the OpenSees soil structure interaction model.

Numerical simulations of soil-structure interaction involving non-uniform soil behavior are conducted following the development of the complete soil-structure interaction model of Christchurch Women's Hospital in OpenSees. In these 2D OpenSees models, the superstructure is modeled as two-dimensional frames in short span and long span respectively. The lead rubber bearings are modeled as elastomeric bearing (Bouc Wen) elements. The soil underlying the concrete raft foundation is modeled with linear elastic plane strain quadrilateral element. The non-uniformity of the soil profile is incorporated by extraction and interpolation of shear wave velocity profile from the Canterbury Geotechnical Database. The validity of the complete two-dimensional soil-structure interaction OpenSees model for the hospital is checked by comparing the results of peak floor responses and force-displacement relations within the isolation system achieved from OpenSees simulations to the recorded measurements. General explanations and implications, supported by displacement drifts, floor acceleration and displacement responses, force-displacement relations are described to address the effects of soil-structure interaction.

Polishing-related optical anisotropy of semi-insulating GaAs studied by reflectance difference spectroscopy

The strong in-plane optical anisotropy of (001) semi-insulating GaAs, which comes from the submicron region under the surface, has been observed by reflectance difference spectroscopy. The optical anisotropy can be explained by the anisotropic strain that is introduced by the asymmetric distribution of 60 degrees dislocations during surface polishing. The simulated spectra reproduce the line shape of the experimental ones. The simulations show that the anisotropic strain is typically about 2.3x10(-4). (C) 2000 American Institute of Physics. [S0021-8979(00)01315-3].

One small difference after another : stories of grassroots leaders

Grassroots groups – autonomous, not-for-profit groups made up of volunteers – and grassroots initiatives play an invaluable, yet often invisible, role in our communities. The informal processes and collective efforts of grassroots associations, social movements, self-help groups and local action collectives are central to civil society and community building. Grassroots leaders are critical to such initiatives, yet little is known about their influences, motivations, successes and challenges. This study aims to address this dearth in the research literature by noting the experiences of a sample of grassroots community leaders to help gain a greater knowledge about community leadership in action. In-depth semi-structured interviews were held with nine grassroots leaders from a broad cross-section of sectors of interest. The criteria for selection were that these leaders were not in a formal non-profit organisation, were not paid for their work yet were leading grassroots groups or initiatives involved in active community building, campaigning or self-help. The paper reflects on findings in regard to the formative experiences that impacted upon the community leaders’ direction in life, their beliefs and ideas about what it means to be a leader, the strategies they use to lead and challenges they continue to face, and the role of learning and support in maintaining and developing their roles. Finally, the key themes relating to grassroots leadership and how these leaders enhance their own effectiveness and resilience are explored.

Stochastic regularization method for backward Cauchy problem in Banach spaces

We consider a stochastic regularization method for solving the backward Cauchy problem in Banach spaces. An order of convergence is obtained on sourcewise representative elements.