An Immersed Interface Method for the Incompressible Navier-Stokes Equations in Irregular Domains

We present an immersed interface method for the incompressible Navier Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the no-slip condition on the boundary is satisfied, singular forces are applied on the fluid at the immersed boundary. The forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, and are interpolated using cubic splines. The strength of singular forces is determined by solving a small system of equations at each time step. The Navier-Stokes equations are discretized on a staggered Cartesian grid by a second order accurate projection method for pressure and velocity.

Numerical comparison between Maxwell stress method and equivalent multipole approach for calculation of the dielectrophoretic force in octupolar cell traps

This work presents detailed numerical calculations of the dielectrophoretic force in octupolar traps designed for single-cell trapping. A trap with eight planar electrodes is studied for spherical and ellipsoidal particles using an indirect implementation of the boundary element method (BEM). Multipolar approximations of orders one to three are compared with the full Maxwell stress tensor (MST) calculation of the electrical force on spherical particles. Ellipsoidal particles are also studied, but in their case only the dipolar approximation is available for comparison with the MST solution. The results show that the full MST calculation is only required in the study of non-spherical particles.

Active regions for colour texture segmentation integrating region and boundary information

In this paper a colour texture segmentation method, which unifies region and boundary information, is proposed. The algorithm uses a coarse detection of the perceptual (colour and texture) edges of the image to adequately place and initialise a set of active regions. Colour texture of regions is modelled by the conjunction of non-parametric techniques of kernel density estimation (which allow to estimate the colour behaviour) and classical co-occurrence matrix based texture features. Therefore, region information is defined and accurate boundary information can be extracted to guide the segmentation process. Regions concurrently compete for the image pixels in order to segment the whole image taking both information sources into account. Furthermore, experimental results are shown which prove the performance of the proposed method

A new efficient approach to the direct restricted active space self-consistent field method

An implicitly parallel method for integral-block driven restricted active space self-consistent field (RASSCF) algorithms is presented. The approach is based on a model space representation of the RAS active orbitals with an efficient expansion of the model subspaces. The applicability of the method is demonstrated with a RASSCF investigation of the first two excited states of indole

Image segmentation integrating colour, texture and boundary information

La tesis se centra en la Visión por Computador y, más concretamente, en la segmentación de imágenes, la cual es una de las etapas básicas en el análisis de imágenes y consiste en la división de la imagen en un conjunto de regiones visualmente distintas y uniformes considerando su intensidad, color o textura. Se propone una estrategia basada en el uso complementario de la información de región y de frontera durante el proceso de segmentación, integración que permite paliar algunos de los problemas básicos de la segmentación tradicional. La información de frontera permite inicialmente identificar el número de regiones presentes en la imagen y colocar en el interior de cada una de ellas una semilla, con el objetivo de modelar estadísticamente las características de las regiones y definir de esta forma la información de región. Esta información, conjuntamente con la información de frontera, es utilizada en la definición de una función de energía que expresa las propiedades requeridas a la segmentación deseada: uniformidad en el interior de las regiones y contraste con las regiones vecinas en los límites. Un conjunto de regiones activas inician entonces su crecimiento, compitiendo por los píxeles de la imagen, con el objetivo de optimizar la función de energía o, en otras palabras, encontrar la segmentación que mejor se adecua a los requerimientos exprsados en dicha función. Finalmente, todo esta proceso ha sido considerado en una estructura piramidal, lo que nos permite refinar progresivamente el resultado de la segmentación y mejorar su coste computacional. La estrategia ha sido extendida al problema de segmentación de texturas, lo que implica algunas consideraciones básicas como el modelaje de las regiones a partir de un conjunto de características de textura y la extracción de la información de frontera cuando la textura es presente en la imagen. Finalmente, se ha llevado a cabo la extensión a la segmentación de imágenes teniendo en cuenta las propiedades de color y textura. En este sentido, el uso conjunto de técnicas no-paramétricas de estimación de la función de densidad para la descripción del color, y de características textuales basadas en la matriz de co-ocurrencia, ha sido propuesto para modelar adecuadamente y de forma completa las regiones de la imagen. La propuesta ha sido evaluada de forma objetiva y comparada con distintas técnicas de integración utilizando imágenes sintéticas. Además, se han incluido experimentos con imágenes reales con resultados muy positivos.

The counter-propagating Rossby-wave perspective on baroclinic instability. I: Mathematical basis

It is shown that Bretherton's view of baroclinic instability as the interaction of two counter-propagating Rossby waves (CRWs) can be extended to a general zonal flow and to a general dynamical system based on material conservation of potential vorticity (PV). The two CRWs have zero tilt with both altitude and latitude and are constructed from a pair of growing and decaying normal modes. One CRW has generally large amplitude in regions of positive meridional PV gradient and propagates westwards relative to the flow in such regions. Conversely, the other CRW has large amplitude in regions of negative PV gradient and propagates eastward relative to the zonal flow there. Two methods of construction are described. In the first, more heuristic, method a ‘home-base’ is chosen for each CRW and the other CRW is defined to have zero PV there. Consideration of the PV equation at the two home-bases gives ‘CRW equations’ quantifying the evolution of the amplitudes and phases of both CRWs. They involve only three coefficients describing the mutual interaction of the waves and their self-propagation speeds. These coefficients relate to PV anomalies formed by meridional fluid displacements and the wind induced by these anomalies at the home-bases. In the second method, the CRWs are defined by orthogonality constraints with respect to wave activity and energy growth, avoiding the subjective choice of home-bases. Using these constraints, the same form of CRW equations are obtained from global integrals of the PV equation, but the three coefficients are global integrals that are not so readily described by ‘PV-thinking’ arguments. Each CRW could not continue to exist alone, but together they can describe the time development of any flow whose initial conditions can be described by the pair of growing and decaying normal modes, including the possibility of a super-modal growth rate for a short period. A phase-locking configuration (and normal-mode growth) is possible only if the PV gradient takes opposite signs and the mean zonal wind and the PV gradient are positively correlated in the two distinct regions where the wave activity of each CRW is concentrated. These are easily interpreted local versions of the integral conditions for instability given by Charney and Stern and by Fjørtoft.

A collocation method for high frequency scattering by convex polygons

We consider the problem of scattering of a time-harmonic acoustic incident plane wave by a sound soft convex polygon. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the computational cost required to achieve a prescribed level of accuracy grows linearly with respect to the frequency of the incident wave. Recently Chandler–Wilde and Langdon proposed a novel Galerkin boundary element method for this problem for which, by incorporating the products of plane wave basis functions with piecewise polynomials supported on a graded mesh into the approximation space, they were able to demonstrate that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency. Here we propose a related collocation method, using the same approximation space, for which we demonstrate via numerical experiments a convergence rate identical to that achieved with the Galerkin scheme, but with a substantially reduced computational cost.

Small- and waiting-time behaviour of the thin-film-equation

We consider the small-time behavior of interfaces of zero contact angle solutions to the thin-film equation. For a certain class of initial data, through asymptotic analyses, we deduce a wide variety of behavior for the free boundary point. These are supported by extensive numerical simulations. © 2007 Society for Industrial and Applied Mathematics

Boundary value problems for third-order linear PDEs in time-dependent domains

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.

Assessment of the effect of time and temperature on the availability of residual phosphate in a glasshouse study of four soils using the Olsen method

The Olsen method is an indicator of plant-available phosphorus (P). The effect of time and temperature on residual phosphate in soils was measured using the Olsen method in a pot experiment. Four soils were investigated: two from Pakistan and one each from England (calcareous) and Colombia (acidic). Two levels of residual phosphate were developed in each soil after addition of phosphate by incubation at either 10degreesC or 45degreesC. The amount of phosphate added was based on the P maximum of each soil, calculated using the Langmuir equation. Rvegrass was used as the test crop. The pooled data for the four soils incubated at 10degreesC showed good correlation between Olsen P and dry matter yield or P uptake (r(2) = 0.85 and 0.77, respectively), whereas at 45 degreesC, each soil had its own relationship and pooled data did not show correlation of Olsen P with dry matter yield or P uptake. When the data at both temperatures were pooled, Olsen P was a good indicator of yield and uptake for the English soil. For the Pakistani soils, Olsen P after 45 degreesC treatment was an underestimate relative to the 10 degreesC data and for the Colombian soil it was an overestimate. The reasons for these differences need to be explored further before high temperature incubation can be used to simulate long-term changes in the field.

A numerical study of the probe method

The goal of this work is the numerical realization of the probe method suggested by Ikehata for the detection of an obstacle D in inverse scattering. The main idea of the method is to use probes in the form of point source (., z) with source point z to define an indicator function (I) over cap (z) which can be reconstructed from Cauchy data or far. eld data. The indicator function boolean AND (I) over cap (z) can be shown to blow off when the source point z tends to the boundary aD, and this behavior can be used to find D. To study the feasibility of the probe method we will use two equivalent formulations of the indicator function. We will carry out the numerical realization of the functional and show reconstructions of a sound-soft obstacle.

Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

The method of least squares used to invert an orbit problem

Six parameters uniquely describe the orbit of a body about the Sun. Given these parameters, it is possible to make predictions of the body's position by solving its equation of motion. The parameters cannot be directly measured, so they must be inferred indirectly by an inversion method which uses measurements of other quantities in combination with the equation of motion. Inverse techniques are valuable tools in many applications where only noisy, incomplete, and indirect observations are available for estimating parameter values. The methodology of the approach is introduced and the Kepler problem is used as a real-world example. (C) 2003 American Association of Physics Teachers.

The Klein-Gordon equation on the half line: a Riemann-Hilbert approach

We solve an initial-boundary problem for the Klein-Gordon equation on the half line using the Riemann-Hilbert approach to solving linear boundary value problems advocated by Fokas. The approach we present can be also used to solve more complicated boundary value problems for this equation, such as problems posed on time-dependent domains. Furthermore, it can be extended to treat integrable nonlinearisations of the Klein-Gordon equation. In this respect, we briefly discuss how our results could motivate a novel treatment of the sine-Gordon equation.

Spectral analysis of the elliptic sine-Gordon equation in the quarter plane

We study the elliptic sine-Gordon equation in the quarter plane using a spectral transform approach. We determine the Riemann-Hilbert problem associated with well-posed boundary value problems in this domain and use it to derive a formal representation of the solution. Our analysis is based on a generalization of the usual inverse scattering transform recently introduced by Fokas for studying linear elliptic problems.