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This workshop focuses on the study of Multidimensional localized structures (MLS)
(often referred to as nonlinear waves, dissipative solitons or coherent structures)
which play an essential role in many branches of science and engineering
as diverse as general relativity, high-energy particle physics, fluid and solid mechanics, plasmas, nonlinear electrical circuits, Bose-Einstein condensation, nonlinear optics, random media, atmosphere and ocean dynamics, chemical reactions, and biology. The workshop is to be of a truly
interdisciplinary nature: combining state-of-the-art and leading mathematical methods,
scientific computation, and rigorous mathematical analysis with models which
are based on experimental observations of nonlinear phenomena. The aim of this program is to provide an intensive experience in the mathematical sciences which highlights some of the cutting edge methods for characterizing the dynamics, stability, and behavior of multidimensional localized structures.
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There is no registration fee, but enrollment in the workshop will be limited to approximately 100 participants. To register, please send a cover letter (electronic mail) explaining your interest in the program along with a brief (two-page) CV to the program director: Prof. J. Nathan Kutz (kutz@amath.washington.edu). The SIAG has procured limited funds from NSF to help defray the cost of flights and hotels for graduate students and postdoctoral researchers from US institutions (approximately US$400 for each person accepted for funding). Support for such attendees will be awarded based on an application stating (i) the reason for wanting to attend the workshop, and (ii) the potential impact of the workshop on the applicant's research and long-term future goals. Preference will be given to students and postdocs already committed to attending and/or presenting at the Conference for Nonlinear Waves and Coherent Structures 2008. To apply for funding, please send a cover letter (electronic mail) explaining your interest in the program along with a brief (two-page) CV to the program director: Prof. J. Nathan Kutz (kutz@amath.washington.edu). Acceptance to the workshop is on a rolling admission (first come first serve basis), so please apply early as the limited funds will be committed early. |
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| The invited workshop speakers are leaders in the field of MLSs who have a proven record of clear lecturing and excellent exposition. We have selected carefully from a large group of international experts with the aim of maximizing the learning of the graduate students and postdocs attending the workshop. The speakers also reflect a tremendous diversity in mathematical and scientific breadth and knowledge. No doubt their interactions will provide a stimulus for discussion and research insight. Each workshop speaker will give 3 hours worth of lectures. Thus over the two day period, 12 hours of lecture will be given with dedicated times for break-out and discussion sessions. The following is the list of the four speakers along with information about their areas of interest and the courses they will teach. |
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Course 1: Spatially Localized Structures in Continuum Systems Professor Edgar Knobloch, Department of Physics, University of California, Berkeley The first lecture will focus on the properties of the bistable Swift-Hohenberg equation as a canonical PDE that admits spatially localized structures, and on the origin of homoclinic snaking in this system. The second lecture will describe experimental and numerical results on granular media ("oscillons") and fluid flow ("convectons"), and attempt to interpret these results in terms of the understanding developed in earlier lectures. |
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Course 2: Localised patterns and Embedded Solitons Professor Alan Champneys, Department of Mathematics, University of Bristol The first lecture will discuss several extensions of homoclinic snaking, for instance to non-variational and non-reversible systems, to the planar Swift-Hohenberg equation, and to discrete systems such as the discrete optical parametric amplifier. The second lecture will give an introduction to embedded solitons: Topics that will be discussed are multi-pulses, semi-stability, and beyond-all-orders analyses. Also discussed will be applications to water waves with surface tension and to discrete breathers in the discrete NLS and the Ablowitz-Ladik lattice. |
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Course 3: Existence, bifurcations and stability of coherent structures Professor Arnd Scheel, Department of Mathematics, University of Minnesota Localized structures such as pulses and fronts are often analyzed using dynamical systems methods in a traveling-wave ODE, in particular homoclinic and heteroclinic bifurcation methods. I will show how such methods prove quite useful in understanding and analyzing more complicated structures, such as time-periodic pulses, wave sources, point defects, or spiral waves. The spatial dynamics view point can sometimes give unexpected insight into physical properties of these coherent structures and facilitate numerical computations. A special emphasis will be on spectral properties of the linearization at such structures, in particular continuous spectra, the Evans function, and spectra in large bounded domains. |
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Course 4: Dissipative cavity solitons Dr. Thorsten Ackemann, Department of Physics, University of Strathclyde The following topics will be covered:
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Schedule
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Friday, July 18
9:00-10:30 Knobloch I |
Saturday, July 19
9:00-10:30 Ackemann II |
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Professor Claudio Conti Department of Physics University of Roma "La Sapienza" (Local Organizer)
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Professor Edgar Knobloch Department of Physics University of California, Berkeley (Vice-Chair of SIAG)
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Professor J. Nathan Kutz Department of Applied Mathematics University of Washington ( Program Director of SIAG)
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Professor Bjorn Sandstede Department of Mathematics University of Surrey (Chair of SIAG)
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| The two-day workshop will be held at the University of Roma, ``La Sapienza". It will start on 7/18/2008 and end on 7/19/2008. The workshop is immediately preceeding the third SIAM Conference on Nonlinear Waves and Coherent Structures (NW08) which will take place July 21-24, 2008 at the University of Roma, ``La Sapienza". The physics department at the university has graciously granted access to one of their large lecture rooms in order to hold the conference. In addition to soliciting attendance from graduate students (US citizens) at US institutions, we will work to promote the workshop among European Universities. |
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