Numerical Methods for the Unsteady Compressible Navier-Stokes Equations

We consider numerical methods for the compressible time dependent Navier-Stokes equations, discussing the spatial discretization by Finite Volume and Discontinuous Galerkin methods, the time integration by time adaptive implicit Runge-Kutta and Rosenbrock methods and the solution of the appearing nonlinear and linear equations systems by preconditioned Jacobian-Free Newton-Krylov, as well as Multigrid methods. As applications, thermal Fluid structure interaction and other unsteady flow problems are considered. The text is aimed at both mathematicians and engineers.

Exam 1997

Exam and solutions in LaTex

MA167exam00

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files

Exam 1999 pdf

Exam and solutions in PDF

Exam 1998b pdf

Exam and solutions in PDF

Exam 1997 pdf

Exam and solutions in PDF

Exam 1998a pdf

Exam and solutions in PDF

Exam 1999

Exam and solutions in LaTex

Exam 1998b

Exam and solutions in LaTex

Exam 1998a

Exam and solutions in LaTex

Taxonomical vs. functional responses of bee communities to fire in two contrasting climatic regions

Valuable insights into mechanisms of community responses to environmental change can be gained by analysing in tandem the variation in functional and taxonomic composition along environmental gradients. We assess the changes in species and functional trait composition (i.e. dominant traits and functional diversity) of diverse bee communities in contrasting fire-driven systems in two climatic regions: Mediterranean (scrub habitats in Israel) and temperate (chestnut forests in southern Switzerland). In both climatic regions, there were shifts in species diversity and composition related to post-fire age. In the temperate region, functional composition responded markedly to fire; however, in the Mediterranean, the taxonomic response to fire was not matched by functional replacement. These results suggest that greater functional stability to fire in the Mediterranean is achieved by replacement of functionally similar species (i.e. functional redundancy) which dominate under different environmental conditions in the heterogeneous landscapes of the region. In contrast, the greater functional response in the temperate region was attributed to a more rapid post-fire vegetation recovery and shorter time-window when favourable habitat was available relative to the Mediterranean. Bee traits can be used to predict the functional responses of bee communities to environmental changes in habitats of conservation importance in different regions with distinct disturbance regimes. However, predictions cannot be generalized from one climatic region to another where distinct habitat configurations occur.

Single tap identification for fast BCI control

One of the major aims of BCI research is devoted to achieving faster and more efficient control of external devices. The identification of individual tap events in a motor imagery BCI is therefore a desirable goal. EEG is recorded from subjects performing and imagining finger taps with their left and right hands. A Differential Evolution based feature selection wrapper is used in order to identify optimal features in the spatial and frequency domains for tap identification. Channel-frequency band combinations are found which allow differentiation of tap vs. no-tap control conditions for executed and imagined taps. Left vs. right hand taps may also be differentiated with features found in this manner. A sliding time window is then used to accurately identify individual taps in the executed tap and imagined tap conditions. Highly statistically significant classification accuracies are achieved with time windows of 0.5 s and more allowing taps to be identified on a single trial basis.

Genetic least squares for system identification

The recursive least-squares algorithm with a forgetting factor has been extensively applied and studied for the on-line parameter estimation of linear dynamic systems. This paper explores the use of genetic algorithms to improve the performance of the recursive least-squares algorithm in the parameter estimation of time-varying systems. Simulation results show that the hybrid recursive algorithm (GARLS), combining recursive least-squares with genetic algorithms, can achieve better results than the standard recursive least-squares algorithm using only a forgetting factor.

Linear-wavelet networks

This paper proposes a nonlinear regression structure comprising a wavelet network and a linear term. The introduction of the linear term is aimed at providing a more parsimonious interpolation in high-dimensional spaces when the modelling samples are sparse. A constructive procedure for building such structures, termed linear-wavelet networks, is described. For illustration, the proposed procedure is employed in the framework of dynamic system identification. In an example involving a simulated fermentation process, it is shown that a linear-wavelet network yields a smaller approximation error when compared with a wavelet network with the same number of regressors. The proposed technique is also applied to the identification of a pressure plant from experimental data. In this case, the results show that the introduction of wavelets considerably improves the prediction ability of a linear model. Standard errors on the estimated model coefficients are also calculated to assess the numerical conditioning of the identification process.

Still feeling it: the time course of emotional recovery from an attentional perspective

Emotional reactivity and the time taken to recover, particularly from negative, stressful, events, are inextricably linked, and both are crucial for maintaining well-being. It is unclear, however, to what extent emotional reactivity during stimulus onset predicts the time course of recovery after stimulus offset. To address this question, 25 participants viewed arousing (negative and positive) and neutral pictures from the International Affective Picture System (IAPS) followed by task-relevant face targets, which were to be gender categorized. Faces were presented early (400–1500 ms) or late (2400–3500 ms) after picture offset to capture the time course of recovery from emotional stimuli. Measures of reaction time (RT), as well as face-locked N170 and P3 components were taken as indicators of the impact of lingering emotion on attentional facilitation or interference. Electrophysiological effects revealed negative and positive images to facilitate face-target processing on the P3 component, regardless of temporal interval. At the individual level, increased reactivity to: (1) negative pictures, quantified as the IAPS picture-locked Late Positive Potential (LPP), predicted larger attentional interference on the face-locked P3 component to faces presented in the late time window after picture offset. (2) Positive pictures, denoted by the LPP, predicted larger facilitation on the face-locked P3 component to faces presented in the earlier time window after picture offset. These results suggest that subsequent processing is still impacted up to 3500 ms after the offset of negative pictures and 1500 ms after the offset of positive pictures for individuals reacting more strongly to these pictures, respectively. Such findings emphasize the importance of individual differences in reactivity when predicting the temporality of emotional recovery. The current experimental model provides a novel basis for future research aiming to identify profiles of adaptive and maladaptive recovery.