Exam 1998b

Exam and solutions in LaTex

Exercises D pdf

Exercises and solutions in PDF

Exam 1998a

Exam and solutions in LaTex

Exercises D

Exercises and solutions in LaTex

Ordinary Differential Equations

Exercises and solutions about ordinary differential equations.

Differential Equations II

Exercises and solutions for a second year differential equations course.

Assignment on Matlab

Considers systems of linear equations, steepest ascent optimisation and Monte Carlo simulation.

Lógica en la toma de decisiones de inversión en el sector de extracción de petróleo y gas natural

Este documento se centra en la presentación de información y análisis de la misma a la hora de establecer la manera en que empresas del sector de extracción de gas natural y generación de energía a base de dicho recurso, toman decisiones en cuanto a inversión, centrándose en la lógica que usan a la hora de emprender este proceso. Esto debido a la constante necesidad de establecer procesos que permitan tomar decisiones más acertadas, incluyendo todas las herramientas posibles para tal fin. La lógica es una de estas herramientas, pues permite encadenar factores con el fin de obtener resultados positivos. Por tal razón, se hace importante conocer el uso de esta herramienta, teniendo en cuentas de qué manera y en que contextos es usada. Con el fin de tener una mayor orientación, este estudio estará centrado en un sector específico, el cual es el de la extracción de petróleo y gas natural. Lo anterior entendiendo la necesidad existente de fundamentación teórica que permita establecer de manera clara la forma apropiada de tomar decisiones en un sector tan diverso y complejo como lo es el mencionado. El contexto empresarial actual exige una visión global, no basada en la lógica lineal causal que hoy se tiene como referencia. El sector de extracción de petróleo y gas natural es un ejemplo particular en cuanto a la manera en cuanto se toman decisiones en inversión, puesto que en su mayoría son empresas de capital intensivo, las cuales mantienen un flujo elevado de recursos monetarios.

Impacto del Internet en el ingreso laboral: análisis del lugar y manejo del Internet

Este estudio analiza el efecto del uso de Internet sobre el ingreso laboral, eliminado el problema de endogeneidad que existe por motivos de selección. También se analizan los efectos seg un el lugar de acceso y las actividades realizadas en Internet. Para esto se utiliza Propensity Score Matching, tomando información para Colombia entre el año 2009 a 2011. Los resultados muestran que existe un efecto positivo, significativo y heterogéneo entre trabajadores asalariados y cuenta propia, siendo los últimos los más beneficiados. Con respecto al lugar de uso se encuentra un impacto positivo del uso del Internet en el trabajo y/o en el hogar, con una mayor magnitud en el primer sitio de acceso. Para el tema del manejo del Internet, no se encuentra efecto cuando se utiliza en actividades de entretenimiento, pero si cuando se usa en tareas educativas diariamente. Esto siguiere que usar este servicio aumenta la productividad y el capital humano, lo que se transforma en un incremento en los ingresos. Por tanto, se encuentra que el lugar de uso es una señal informativa para el mercado laboral, mientras que el impacto del manejo de esta herramienta depende de la frecuencia con que se realicen las actividades.

A cell by cell anisotropic adaptive mesh ALE scheme for the numerical solution of the Euler equations

In this paper a cell by cell anisotropic adaptive mesh technique is added to an existing staggered mesh Lagrange plus remap finite element ALE code for the solution of the Euler equations. The quadrilateral finite elements may be subdivided isotropically or anisotropically and a hierarchical data structure is employed. An efficient computational method is proposed, which only solves on the finest level of resolution that exists for each part of the domain with disjoint or hanging nodes being used at resolution transitions. The Lagrangian, equipotential mesh relaxation and advection (solution remapping) steps are generalised so that they may be applied on the dynamic mesh. It is shown that for a radial Sod problem and a two-dimensional Riemann problem the anisotropic adaptive mesh method runs over eight times faster.

A high-order arbitrarily unstructured finite-volume model of the global atmosphere: tests solving the shallow-water equations

Simulations of the global atmosphere for weather and climate forecasting require fast and accurate solutions and so operational models use high-order finite differences on regular structured grids. This precludes the use of local refinement; techniques allowing local refinement are either expensive (eg. high-order finite element techniques) or have reduced accuracy at changes in resolution (eg. unstructured finite-volume with linear differencing). We present solutions of the shallow-water equations for westerly flow over a mid-latitude mountain from a finite-volume model written using OpenFOAM. A second/third-order accurate differencing scheme is applied on arbitrarily unstructured meshes made up of various shapes and refinement patterns. The results are as accurate as equivalent resolution spectral methods. Using lower order differencing reduces accuracy at a refinement pattern which allows errors from refinement of the mountain to accumulate and reduces the global accuracy over a 15 day simulation. We have therefore introduced a scheme which fits a 2D cubic polynomial approximately on a stencil around each cell. Using this scheme means that refinement of the mountain improves the accuracy after a 15 day simulation. This is a more severe test of local mesh refinement for global simulations than has been presented but a realistic test if these techniques are to be used operationally. These efficient, high-order schemes may make it possible for local mesh refinement to be used by weather and climate forecast models.

A combined BIE-FE method for the Stokes equations

A numerical algorithm for the biharmonic equation in domains with piecewise smooth boundaries is presented. It is intended for problems describing the Stokes flow in the situations where one has corners or cusps formed by parts of the domain boundary and, due to the nature of the boundary conditions on these parts of the boundary, these regions have a global effect on the shape of the whole domain and hence have to be resolved with sufficient accuracy. The algorithm combines the boundary integral equation method for the main part of the flow domain and the finite-element method which is used to resolve the corner/cusp regions. Two parts of the solution are matched along a numerical ‘internal interface’ or, as a variant, two interfaces, and they are determined simultaneously by inverting a combined matrix in the course of iterations. The algorithm is illustrated by considering the flow configuration of ‘curtain coating’, a flow where a sheet of liquid impinges onto a moving solid substrate, which is particularly sensitive to what happens in the corner region formed, physically, by the free surface and the solid boundary. The ‘moving contact line problem’ is addressed in the framework of an earlier developed interface formation model which treats the dynamic contact angle as part of the solution, as opposed to it being a prescribed function of the contact line speed, as in the so-called ‘slip models’. Keywords: Dynamic contact angle; finite elements; free surface flows; hybrid numerical technique; Stokes equations.

A double-Gerdien instrument for simultaneous bipolar air conductivity measurements on balloon platforms

A bipolar air conductivity instrument is described for use with a standard disposable meteorological radiosonde package. It is intended to provide electrical measurements at cloud boundaries, where the ratio of the bipolar air conductivities is affected by the presence of charged particles. The sensors are two identical Gerdien-type electrodes, which, through a voltage decay method, measure positive and negative air conductivities simultaneously. Voltage decay provides a thermally stable approach and a novel low current leakage electrometer switch is described which initiates the decay sequence. The radiosonde supplies power and telemetry, as well as measuring simultaneous meteorological data. A test flight using a tethered balloon determined positive (σ+) and negative (σ−) conductivities of σ+ = 2.77±0.2 fS m−1 and σ− = 2.82±0.2 fS m−1, respectively, at 400 m aloft, with σ+/σ− = 0.98±0.04.