Lorentz Center - Coherent structures in evolutionary equations from 12 Jul 2010 through 16 Jul 2010
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    Coherent structures in evolutionary equations
    from 12 Jul 2010 through 16 Jul 2010

 

 

Scientific report

 

The goal of this workshop was to bring together researchers who work in the areas of pattern formation and evolutionary PDEs. A particular goal was to facilitate communication between those working on deterministic equations with those working on stochastic ones. Many young participants, young faculty, tenure trackers, postdocs and PhD's  got to know each other, framed their field and communicated latest results.

 

With more than 40 participants the turnout was higher than expected and provided a lively atmosphere, and sufficient mass for discussions in subgroups. The program had 26 presentations, but only about 14 main talks of 45min, a number of shorter talks and two sessions for PhD students to present in 5min each. This left much time for individualand group discussions that was highly appreciated. Wednesday's social event was the boat trip - a great success in wonderful weather.

 

The topics of the presentations ranged from analytical questions of existence and uniqueness, justification of amplitude equations and reductions, to asymptotic analysis and numerical experiments. The concept of coherent spatiotemporal patterns and coherence within evolutionary equations in broader generality have been the unifying themes. It became clear how non-trivial coherence emerges at onset of instabilities in bifurcations and through strong separation of spatiotemporal scales. In a similar vein, coherent patterns such as the propagation of fronts or motion of defects can also be observed in a robust fashion on spatiotemporally random backgrounds.

 

In 'focus groups' some topics were discussed in more depth, or served as tutorial sessions for stochastic effects, in particular on scaling laws at instabilities. The effect of noise on pattern formation and on the stability of coherent structures has been discussed from a new point of view. Some of the participants used the opportunity to work on joint papers, but were open to other people wandering in and joining the discussion.

 

Yet, the interaction between noise and coherent structures and its effect on pattern forming systems is still poorly understood and many important questions remain open.

 

Greg Pavliotis and Jens Rademacher

 



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