The IMTECH Newslater is live.
You can find there two enlightening interviews to our colleagues T. Guillemon and V. Mañosa.
Also J. Curbelo presented a very nice outreach article about fluid Dynamics.
You can find it: https://imtech.webs.upc.edu/2025/01/01/newsletter-07-january-december-2024/
On small breather of nonlinear Klein-Gordon equations via exponentially small homoclinic splitting, now in Inventiones mathematicae from our colleagues T. M. Seara and M. Guarda and their co-workers O. M.L. Gomide and C. Zeng..
Check it out here to learn more: https://link.springer.com/article/10.1007/s00222-025-01327-y
Breathers are nontrivial time-periodic and spatially localized solutions of nonlinear dispersive partial differential equations (PDEs). Families of breathers have been found for certain integrable PDEs but are believed to be rare in non-integrable ones such as nonlinear Klein-Gordon equations. In this paper we show that small amplitude breathers of any temporal frequency do not exist for semilinear Klein-Gordon equations with generic analytic odd nonlinearities. A breather with small amplitude exists only when its temporal frequency is close to be resonant with the linear Klein-Gordon dispersion relation. Our main result is that, for such frequencies, we rigorously identify the leading order term in the exponentially small (with respect to the small amplitude) obstruction to the existence of small breathers in terms of the so-called Stokes constant, which depends on the nonlinearity analytically, but is independent of the frequency. This gives a rigorous justification of a formal asymptotic argument by Kruskal and Segur (Phys. Rev. Lett. 58(8):747, 1987) in the analysis of small breathers. We rely on the spatial dynamics approach where breathers can be seen as homoclinic orbits. The birth of such small homoclinics is analyzed via a singular perturbation setting where a Bogdanov-Takens type bifurcation is coupled to infinitely many rapidly oscillatory directions. The leading order term of the exponentially small splitting between the stable/unstable invariant manifolds is obtained through a careful analysis of the analytic continuation of their parameterizations. This requires the study of another limit equation in the complexified evolution variable, the so-called inner equation.
Are you a graduate student or postdoc who wants to add novel developmental biology and biophysics methods to your research? Then have a look at #EMBLDevBio, where you'll learn all about highly multiplexed RNA fluorescent in situ hybridisation, quantitative imaging and analysis, machine learning based image segmentation, and more 🥼👀
📥 Apply by 26 March 2025
🔗 https://s.embl.org/ptd25-01-ma
🗺️ EMBL Heidelberg
📅 2 – 9 July 2025
Our colleague Jezabel Curbelo is organizing the 4th NonLinear processes in Oceanic and Atmospheric flows at the Institut de Ciencies del Mar (Barcelona, Spain) from January 22nd to January 24th:
NLOA 2025 intends to create cross-disciplinary interaction among mathematicians, physicists, oceanographers and atmospheric scientists in a wide sense. It will focus on nonlinear dynamics of atmospheric and oceanic phenomena, and it aims to create an international forum where international researchers explore timely open problems in ocean and atmosphere sciences, and also investigate the power and impact of mathematics in these areas.
Registration Deadline till January 8th.
More info: https://www.crm.cat/4th-nonlinear-processes-in-oceanic-and-atmospheric-flows/
#appliedMath #DynamicalSystems #Interdisciplinarity #MathEverywhere
4th Nonlinear Processes in Oceanic and Atmospheric Flows Sign in Conference From January 22, 2025 to January 24, 2025 Dates: January 22-24, 2025 Location: Institut de Ciències del Mar (CSIC) Registration deadline 08 / 01 / 2025 REGISTRATION FEE 250€ Early Registration* 300€ Late Registration Students: 190€ Early Registration* 220€ Late Registration * Deadline for
From April 27th to May 2nd we will be present at #EGU25 in the session organized by Jezabel Curbelo about Lagrangian perspectives on transport and mixing in geophysical fluids:
We invite presentations on topics including – but not limited to – the following:
- Large-scale circulation studies using direct Lagrangian modeling and/or age and chemical tracers (jets, gyres, overturning circulations);
- Exchanges between reservoirs and mixing studies (e.g. transport barriers and Lagrangian Coherent Structures in the stratosphere and in the ocean, stratosphere-troposphere exchange);
- Tracking long-range anthropogenic and natural influence (e.g. effects of recent volcanic eruptions and wildfire smoke plumes on the composition, chemistry, and dynamics of the atmosphere, transport of pollutants, dusts, aerosols, plastics, and fluid parcels in general, etc);
- Inverse modeling techniques for the assessment and constraint of emission sources (e.g. backtracking, including diffusion and buoyancy);
- Model and tool development, computational advances.
Find us at https://meetingorganizer.copernicus.org/EGU25/session/52516
#dynamicalSystems #AppliedMath #mathInGeosciences #Interdisciplinary
21st School on Interactions between #DynamicalSystems and #PartialDifferentialEquations
📅 June 30 - July 04, 2025
📍Centre de Recerca Matemàtica (Barcelona)
Registration is open.
⚠️ Registration deadline is June 12, 2025.
The registration fee (200€/75€ for granted) includes coffee breaks and lunch.
⚠️ Application deadline for grants and posters is April 13th, 2025.
The School on Interactions between Dynamical Systems and Partial Differential Equations (JISD) is an annual international summer school consisting of four short courses of around five hours given by four world-leading experts.
LECTURERS
Dmitry Dolgopyat | University of Maryland
Serena Dipierro | University of Western Australia
Luciano Mari | Università di Torino
Sylvain Crovisier | Université Paris-Saclay
JISD 2025 21st School on Interactions between Dynamical Systems and Partial Differential Equations JISD 2025 Sign in Advanced course / School From June 30, 2025 to July 04, 2025 The registration fee is 200€ / 75€ for granted and includes coffee breaks and lunch. Registration deadline 12 / 06 / 2025 LECTURERS SCHEDULE POSTER SESSION
Everyone knows about synchronization in chaotic systems. But what happens when one studies the synchronizability of periodic ones? Two main things.
The first is that new classes of synchronization stability emerge that are characteristic of periodic systems and are not found in chaotic ones. The root cause of this is that the master stability function of periodic systems is 0 at the origin, in difference to what happens in chaotic systems, for which it is strictly positive.
The second thing is that we challenge the long-held belief that periodic systems synchronize in a stable way for any coupling, no matter how small. In fact, we show that many of them, for many coupling schemes, have a non-zero lower threshold for synchronization stability.
https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.043105
#physics #mathematics #networks #complexsystems #chaos #dynamicalsystems #synchronization #complexity #stability
Barcelona Dynamical Systems
Fergus Murray
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