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Evidence for post-early Eocene tectonic activity in southeastern Ireland
Item type: Journal Article
Cunningham, M.J.M.; Densmore, A.L.; Allen, P.A.; et al. (2003)
The role played by Cenozoic deformation in denudation and landscape development in Ireland has historically been difficult to assess because of the lack of widespread pre-glacial Cenozoic deposits onshore. Here we combine analysis of apatite fission-track data and geomorphic observations to place constraints on the timing, kinematics and magnitude of onshore deformation in southeastern Ireland. Relationships between apatite fission-track central age and elevation for samples from the Wicklow and Blackstairs Mountains and Tullow Lowland suggest that these rocks record an exhumed apatite partial annealing zone, which after cooling was dismembered by differential vertical displacements of up to several hundred metres. We use inverted models of sample thermal history to show that samples across the region experienced very similar thermal histories up to and including a cooling event in late Paleocene or early Eocene time. This effectively rules out strongly spatially heterogeneous denudation, and implies that differential rock uplift occurred in post-early Eocene time. The central age–elevation relationships define at least three spatial domains with internally consistent apatite fission-track data, separated by known faults or topographic escarpments. Geomorphic analysis of these structures shows that patterns of catchment incision and sinuosity, as well as the presence of antecedent drainage, are best explained by differential vertical displacements at or near the domain boundaries. The kinematics and magnitudes of these displacements are consistent with those implied by the apatite fission-track results, and are compatible with other examples of known Cenozoic deformation from Ireland and the adjacent continental margin.
Computational analysis of the two-dimensional-three-dimensional transition in forward-facing step flow
Item type: Journal Article
Wilhelm, Dirk; Härtel, Carlos; Kleiser, Leonhard (2003)
Results are presented from a computational study of the flow over a forward-facing step in a plane channel. The aim of the study is to gain better insight into the three-dimensionality that is typically observed in the separation region of flows over steps and ribs, and in similar configurations. We consider laminar flow at a Reynolds number of 330, based on step height and bulk velocity of the oncoming flow, and the step is assumed to be infinitely extended in the spanwise direction. High-resolution simulations are undertaken using a mixed spectral/spectral-element code. Moreover, a linear stability study of the flow at the step is performed. The results show that, in the case considered, the three-dimensionality is not related to some absolute instability of the separation bubble in front of the step; rather, it is a sensitive reaction of the flow to three-dimensional perturbations present in the oncoming stream. It is demonstrated that disturbance amplitudes of less than 1% of the mean flow (at, say, 10 step heights ahead of the step) already suffice to produce a visibly three-dimensional structure of the separation zone. If the disturbance level is systematically decreased, the three-dimensional state evolves to an almost two-dimensional recirculation. Here, the key finding is that the intensity of the flow response is proportionate to the amplitude of the inflow disturbance, meaning that the breakup of the flow in the step region is a linear (i.e. small) perturbation of the two-dimensional base flow. A comparison of the present simulation results with experimental data shows close agreement concerning, for example, the flow topology in the step region, and the spanwise spacing of the characteristic streaks that form further downstream.
The game of JumbleG
Item type: Journal Article
Frieze, Alan; Krivelevich, Michael; Pikhurko, Oleg; et al. (2005)
JumbleG is a Maker–Breaker game. Maker and Breaker take turns in choosing edges from the complete graph $K_n$. Maker's aim is to choose what we call an $\epsilon$-regular graph (that is, the minimum degree is at least $(\frac12-\epsilon) n$ and, for every pair of disjoint subsets $S,T\subset V$ of cardinalities at least $\epsilon n$, the number of edges $e(S,T)$ between $S$ and $T$ satisfies $\bigl|\frac{e(S,T)}{|S|\,|T|}-\frac12\bigr|\leq \epsilon$.) In this paper we show that Maker can create an $\epsilon$-regular graph, for $\epsilon\geq 2(\log n/n)^{1/3}$. We also consider a similar game, JumbleG2, where Maker's aim is to create a graph with minimum degree at least $\bigl(\frac12-\epsilon\bigr)n$ and maximum co-degree at most $\bigl(\frac14+\epsilon\bigr)n$, and show that Maker has a winning strategy for $\epsilon> 3 (\log n/n)^{1/2}$. Thus, in both games Maker can create a pseudo-random graph of density $\frac12$. This guarantees Maker's win in several other positional games, also discussed here.
Density-driven instabilities of miscible fluids in a Hele-Shaw cell: linear stability analysis of the three-dimensional Stokes equations
Item type: Journal Article
Graf, F.; Meiburg, E.; Härtel, Carlos (2002)
We consider the situation of a heavier fluid placed above a lighter one in a vertically arranged Hele-Shaw cell. The two fluids are miscible in all proportions. For this configuration, experiments and nonlinear simulations recently reported by Fernandez et al. (2002) indicate the existence of a low-Rayleigh-number (Ra) ‘Hele-Shaw’ instability mode, along with a high-Ra ‘gap’ mode whose dominant wavelength is on the order of five times the gap width. These findings are in disagreement with linear stability results based on the gap-averaged Hele-Shaw approach, which predict much smaller wavelengths. Similar observations have been made for immiscible flows as well (Maxworthy 1989).In order to resolve the above discrepancy, we perform a linear stability analysis based on the full three-dimensional Stokes equations. A generalized eigenvalue problem
is formulated, whose numerical solution yields both the growth rate and the two-dimensional eigenfunctions in the cross-gap plane as functions of the spanwise wavenumber, an ‘interface’ thickness parameter, and Ra. For large Ra, the dispersion relations confirm that the optimally amplified wavelength is about five times the gap width, with the exact value depending on the interface thickness. The corresponding growth rate is in very good agreement with the experimental data as well. The eigenfunctions indicate that the predominant fluid motion occurs within the plane of the Hele-Shaw cell. However, for large Ra purely two-dimensional modes are also amplified, for which there is no motion in the spanwise direction. Scaling laws are provided for the dependence of the maximum growth rate, the corresponding wavenumber, and the cutoff wavenumber on Ra and the interface thickness. Furthermore, the present results are compared both with experimental data, as well as with linear stability results obtained from the Hele-Shaw equations and a modified Brinkman equation.
Strategic calculation and international socialization
Item type: Journal Article
Schimmelfennig, Frank (2005)
This article uses a rationalist approach to explain the international socialization of Central and Eastern Europe to liberal human rights and democracy norms. According to this approach, socialization consists in a process of reinforcement, and its effectiveness depends on the balance between the international and domestic costs and benefits of compliance over an extended period of time. EU and NATO accession conditionality has been a necessary condition of sustained compliance in those countries of Central and Eastern Europe that violated liberal norms initially. The pathways and long-term outcomes of international socialization, however, have varied with the constellations of major parties in the target states. Whereas conditionality has been effective with liberal and mixed party constellations, it has failed to produce compliance in antiliberal regimes. In the empirical part of the article, these propositions are substantiated with data on the development of liberal democracy in Central and Eastern Europe and case studies on Slovakia and Latvia. © 2005 by The IO Foundation.