Seminars this week

Abstract

In this talk, we investigate the relationship between return levels of a process and the strength of serial correlation present in the extremes of that process. Estimates of long period return levels are often used as design requirements, and peaks over thresholds (POT) analyses have, in the past, been used to obtain such estimates. However, analyses based on such declustering schemes are extremely wasteful of data, often resulting in great estimation uncertainty represented by very wide confidence intervals. Using simulated data, we show that - provided the extremal index is estimated appropriately - using all threshold excesses can give more accurate and precise estimates of return levels, allowing us to avoid altogether the sometimes arbitrary process of cluster identification. We then apply our method to two data examples concerning sea-surge and wind speed extremes.

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Abstract

We construct a triangulated category DK_(k) of K-motives in the style of Voevodsky's construction of the category DM(k). Each smooth k-variety has its K-motive M_K(X) in the category DK_(k) of K-motives and
Hom(M_K(X),M_K(pt)[n])=K_n(X)
where pt=Spec(k) and K_n(X) is Quillen's K-groups of X. The K-motive M_K(pt) of the point has a natural Grayson's "filtration". Due to Suslin's results successive cones of the "filtration" are the motivic complexes Z(n). This observation gives rise to a new construction of a spectral sequence which starts at motivic cohomology of a smooth variety X and converges to its Quillen K-groups. The results have been obtained joint with G. Garkusha.

Arrangements

The seminar is followed by Topology Tea in the common room, with tea and homemade cake.

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Abstract

Resonant absorption is a popular and viable mechanism to model the twin problems of MHD wave damping in solar coronal structures (e.g. coronal loops or prominences) and the heating of the plasma in the magnetised corona. Earlier modelling applied the concept of resonant absorption of slow and Alfven waves in stationary plasma where the background equilibrium is time-independent.

However, high-resolution observations of the current cohort of solar instruments clearly indicate that often there is a time-dependent plasma behaviour associated with loop oscillations. In this presentation we show the first steps made to address the challenges in the development of resonant MHD wave theory in a time-dependent plasma. Expressions for the decrease in wave amplitude and wave dissipation across both the Alfven and slow resonant points have been found for plasma structures within time-dependent models. This work also aims to show how the wave amplitude across the resonant point changes in time and contributes to the rapid damping of resonantly coupled driven MHD kink waves.

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Abstract

The rogue wave of the Nonlinear Schrodinger equation is one kind of hot topic in the studies of water wave, plasma, nonlinear optics and mathematical physics. One core problem is the generating mechanism of this very novel phenomenon. In this talk I shall discuss how to make different patterns (including circular, triangle and their combinations) of the higher order rogue waves of the NLS from breather solutions, which provides a new insight of the mechanism of the rogue wave. I also hope to show similar results of Hirota equation if the time is sufficient.

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