Numerical Methods lectures for MATH6111 (and MATH3018).

These are the slides used in the joint lectures for MATH3018/MATH6111. They focus on the examples that do not appear in the course notes (see related material). Each lecture comes with example Matlab files that generate the figures used in the lectures.

Numerical Methods Worksheets

These worksheets are formative assessment for the Numerical Methods modules MATH3018 and MATH6111 (some material is only covered in MATH3018). Intended to back up both the theory and the coding (in Matlab) side

The project of land restitution in Colombia: an illustration of the civilizing force of hypocrisy?

This article offers a theoretical interpretation of the dispositions on land restitution contained in the famous “Victims’ Bill”, which was debated in the Colombian Congress during the year 2008. The bill included specific mechanisms aimed at guaranteeing the restitution of land to victims of the Colombian armed conflict. At the time, the bill was endorsed by all the main political actors in the country –notably the government and the elites that support it, on the one hand, and victims’ and human rights organizations and other opposition groups, on the other–. The fact that the restitution of land to victims of the Colombian armed conflict was being considered as a serious possibility by all political actors in the country seemed to indicate the existence of a consensus among actors whose positions are ordinarily opposed, on an issue that has traditionally led to high levels of polarization. This consensus is quite puzzling, because it seems to be at odds with the interests and/or the conceptions of justice advocated by these political actors, and because the restitution of land faces enormous difficulties both from a factual and a normative point of view, which indicates that it may not necessarily be the best alternative for dealing with the issue of land distribution in Colombia. This article offers an interpretation of said consensus, arguing that it is only an apparent consensus in which the actors are actually misrepresenting their interests and conceptions of justice, while at the same time adopting divergent strategies of implementation aimed at fulfilling their true interests. Nevertheless, the article concludes that the common adherence by all actors to the principle of restorative justice might bring about its actual realization, and thus produce an outcome that, in spite (and perhaps even because) of being unintended, might substantively contribute to solving the problem of unequal land distribution in Colombia. Even though the article focuses in some detail on the specificities of the 2008 Bill, it attempts to make a general argument about the state of the discussion on how to deal with the issue of land distribution in the country. Consequently, it may still be relevant today, especially considering that a new Bill on land restitution is currently being discussed in Congress, which includes the same restitution goals as the Victims’ Bill and many of its procedural and substantive details, and which therefore seems to reflect a similar consensus to the one analyzed in the article.

IQ and aptitude tests : assess your verbal, numerical and spatial reasoning skills.

El libro presenta un conjunto de tests de aptitud (para medir el potencial de éxito de una persona) y tests de inteligencia normalizados, cada vez más utilizados en procesos de contratación, selección y evaluación de personal. Organizados en cuatro apartados, tests de aptitud verbal, espacial, numérica y tests de inteligencia, permiten trabajar distintas áreas (significado de palabras, gramática y comprensión, aptitud verbal avanzada, análisis lógico, cálculo mental, secuencias numéricas y problemas numéricos) para mejorar las habilidades verbales, numéricas y de razonamiento del lector.

Topogenèse et sécurité en escalade. Illustration d’un cas particulier

Le cas que nous exposons ici est extrait d’un travail de recherche plus vaste ayant pour objet une analyse comparative de plusieurs institutions1 où vivent et se transmettent des savoirs sécuritaires propres à l’escalade. Notre étude met en face à face des institutions clairement identifiées comme didactiques - c’est le cas de l’école au sens large de l’acception - c’est-à-dire des institutions où l’intention de transmettre y est toujours mise en avant, mais aussi d’autres institutions «à la limite» du didactique telles les organismes de loisirs sportifs, ainsi que des institutions a priori non didactiques comme une famille ou un groupe d’amis, où le mode de transmission des savoirs relève majoritairement d’un système d’apprentissage par frayage (Delbos & Jorion, 1990), (Hutchins, 1995). Le sujet est abordé sous l’angle didactique de la gestion des risques (Mangeant, 2008). La recherche repose en partie sur la théorie des situations didactiques (Brousseau, 1998) et notamment la notion de contrat entendu comme une convention implicite, mais aussi pour nous dans notre sujet, comme accord explicite sur les règles de fonctionnement. Elle s’appuie également sur le modèle de l’action enseignante et le triplet des genèses (Sensevy, Mercier & Schubauer- Leoni, 2000) et plus précisément sur le principe de l’action conjointe du professeur et des élèves (Sensevy & Mercier, 2007). Le travail s’attache à démontrer que des phénomènes de contrat, peuvent être à l’origine de failles dans la sécurité, et potentiellement pourvoyeurs de futurs accidents. Ainsi, au-delà du manque de vigilance communément invoqué, il y aurait donc des causes didactiques à l’occurrence des accidents, dont les explications sont parfois à rechercher à l’origine dans la formation des intervenants ou dans le mode de transmission des savoirs

Numerical model of solid phase transformations governed by nucleation and growth: microstructure development during isothermal crystallization

A simple numerical model which calculates the kinetics of crystallization involving randomly distributed nucleation and isotropic growth is presented. The model can be applied to different thermal histories and no restrictions are imposed on the time and the temperature dependences of the nucleation and growth rates. We also develop an algorithm which evaluates the corresponding emerging grain-size distribution. The algorithm is easy to implement and particularly flexible, making it possible to simulate several experimental conditions. Its simplicity and minimal computer requirements allow high accuracy for two- and three-dimensional growth simulations. The algorithm is applied to explore the grain morphology development during isothermal treatments for several nucleation regimes. In particular, thermal nucleation, preexisting nuclei, and the combination of both nucleation mechanisms are analyzed. For the first two cases, the universal grain-size distribution is obtained. The high accuracy of the model is stated from its comparison to analytical predictions. Finally, the validity of the Kolmogorov-Johnson-Mehl-Avrami model SSSR, is verified for all the cases studied

Banking Union: Ireland vs. Nevada, an illustration of the importance of an integrated banking system. CEPS Commentary, 18 October 2012

Despite their surprising similarities – in size and their housing booms – Ireland and the American state of Nevada sharply parted company when it came to who bore responsibility for bailing out their failed banks when the booms turned to bust. This latest Commentary by Daniel Gros vividly illustrates the importance of that difference and thus the shock-absorbing capacity of an integrated banking system and a banking union.

Numerical Response of Breeding Birds Following Experimental Selection Harvesting in Northern Hardwood Forests

Silvicultural treatments have been shown to alter the composition of species assemblages in numerous taxa. However, the intensity and persistence of these effects have rarely been documented. We used a before-after, control-impact (BACI) paired design, i.e., five pairs of 25-ha study plots, 1-control and 1-treated plot, to quantify changes in the density of eight forest bird species in response to selection harvesting over six breeding seasons, one year pre- and five years postharvest. Focal species included mature forest associates, i.e., Northern Parula (Setophaga americana) and Black-throated Green Warbler (Setophaga virens), forest generalists, i.e., Yellow-bellied Sapsucker (Sphyrapicus varius) and Swainson’s Thrush (Catharus ustulatus), early-seral specialists, i.e., Mourning Warbler (Geothlypis philadelphia) and Chestnut-sided Warbler (Setophaga pensylvanica), species associated with shrubby forest gaps, i.e., Black-throated Blue Warbler (Setophaga caerulescens), and mid-seral species, i.e., American Redstart (Setophaga ruticilla). As predicted, we found a negative numerical response to the treatment in the Black-throated Green Warbler, no treatment effect in the Yellow-bellied Sapsucker, and a positive treatment effect in early-seral specialists. We only detected a year effect in the Northern Parula and the American Redstart. There was evidence for a positive treatment effect on the Swainson’s Thrush when the regeneration started to reach the pole stage, i.e., fifth year postharvest. These findings suggest that selection harvesting has the potential to maintain diverse avian assemblages while allowing sustainable management of timber supply, but future studies should determine whether mature-forest associates can sustain second- and third-entry selection harvest treatments.

On the impact of humidity observations in numerical weather prediction

The impact of humidity observations on forecast skill is explored by producing a series of global forecasts using initial data derived from the ERA-40 reanalyses system, in which all humidity data have been removed during the data assimilation. The new forecasts have been compared with the original ERA-40 analyses and forecasts made from them. Both sets of forecasts show virtually identical prediction skill in the extratropics and the tropics. Differences between the forecasts are small and undergo characteristic amplification rate. There are larger differences in temperature and geopotential in the tropics but the differences are small-scale and unstructured and have no noticeable effect on the skill of the wind forecasts. The results highlight the current very limited impact of the humidity observations, used to produce the initial state, on the forecasts.

Numerical simulation of baroclinic waves with a parameterized boundary layer

A dry three-dimensional baroclinic life cycle model is used to investigate the role of turbulent fluxes of heat and momentum within the boundary layer on mid-latitude cyclones. Simulations are performed of life cycles for two basic states, both with and without turbulent fluxes. The different basic states produce cyclones with contrasting frontal and mesoscale-flow structures. The analysis focuses on the generation of potential-vorticity (PV) in the boundary layer and its subsequent transport into the free troposphere. The dynamic mechanism through which friction mitigates a barotropic vortex is that of Ekman pumping. This has often been assumed to be also the dominant mechanism for baroclinic developments. The PV framework highlights an additional, baroclinic mechanism. Positive PV is generated baroclinically due to friction to the north-east of a surface low and is transported out of the boundary layer by a cyclonic conveyor belt flow. The result is an anomaly of increased static stability in the lower troposphere which restricts the growth of the baroclinic wave. The reduced coupling between lower and upper levels can be sufficient to change the character of the upper-level evolution of the mature wave. The basic features of the baroclinic damping mechanism are robust for different frontal structures, with and without turbulent heat fluxes, and for the range of surface roughness found over the oceans.

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.

Stratosphere-troposphere transport in a numerical simulation of midlatitude convection

The transport of stratospheric air deep into the troposphere via convection is investigated numerically using the UK Met Office Unified Model. A convective system that formed on 27 June 2004 near southeast England, in the vicinity an upper level potential vorticity anomaly and a lowered tropopause, provides the basis for analysis. Transport is diagnosed using a stratospheric tracer that can either be passed through or withheld from the model’s convective parameterization scheme. Three simulations are performed at increasingly finer resolutions, with horizontal grid lengths of 12, 4, and 1 km. In the 12 and 4 km simulations, tracer is transported deeply into the troposphere by the parameterized convection. In the 1 km simulation, for which the convective parameterization is disengaged, deep transport is still accomplished but with a much smaller magnitude. However, the 1 km simulation resolves stirring along the tropopause that does not exist in the coarser simulations. In all three simulations, the concentration of the deeply transported tracer is small, three orders of magnitude less than that of the shallow transport near the tropopause, most likely because of the efficient dilution of parcels in the lower troposphere.