Multi-Scale Physics (2025)

The Symposium at Schloss Elmau from 6/8–6/15 was a dynamic and interactive exploration of the broad problem of multiscale physics across many different disciplines. Here we summarize some of the main themes of the talks and discussions. The participants covered a wide range of disciplines including astrophysics, climate science, ecology, exoplanets, cosmology, applied math, and classical field theory. This second instalment of the symposium series on multiscale physics focused more on the underlying fundamental physics of these systems rather than the modelling methodology, highlighting the rich conceptual core of the subject, although “method” was never far behind the “madness”, and some happy synergy was achieved.

There was a broad range of talks on atmospheric physics applied to both exoplanets, the Earth, and other solar system objects. Caroline Morley discussed the critical and uncertain physics of clouds and their role in Earth’s climate and exoplanets. Similar themes were emphasized in Emily Raucher and Yamila Miguel’s summary of what observations of exoplanets are currently possible, new results from the James Webb Space Telescope (JWST), and the key theoretical uncertainties in exoplanet atmosphere models. Nadir Jeevanjee highlighted the role of infrared absorption of light by water vapor in setting the thermal structure of the Earth’s atmosphere (in particular the temperature at the tropopause) and the need for wavelength-dependent radiation transfer to capture its effects correctly. Mike Byrne gave a nice summary of how the land temperature on Earth is determined by the neighboring water temperature and basic physical principles that are analytically tractable across a range of climate conditions. Yu Zhang showed how convective physics limits the temperature achievable in heat waves on Earth (a useful talk given the heat wave the east coast and midwest US participants faced soon after returning from the symposium). Wanying Kang extended the discussion of planetary climates to the water-ice moons of Jupiter and Saturn and showed how convection, tides, and baroclinicity regulate the thermal structure of the oceans.

François Rincon made key connections between models of climate change on Earth and its implications for ecology. He also eloquently highlighted his own intellectual journey from astrophysical fluid dynamics to ecology, and ways in which expertise gained in the former could be brought to bear on the latter. In a discussion session, Jonathan Squire and Phil Hopkins explained the nature of newly discovered instabilities of multi-fluid systems in astrophysics (particles and gas); and there was an active discussion regarding whether such instabilities could also be present in Earth’s atmosphere and/or exoplanet atmospheres. Overall, there was a particularly productive exchange of ideas and methods among the diverse climate/atmosphere scientists/fluid dynamicists at the symposium.

A second theme of the symposium was the diverse range of astrophysical systems in which multiscale and often multiphysics problems play a critical role. Greg Bryan highlighted one of the most challenging of these, which is the impact of energy produced by black hole accretion on the properties of the hot plasma in galaxies (which is the fuel for star formation and the growth of the black hole itself). A subsequent discussion session focused in part on the role of buoyant ‘thermals’ created by black hole jets in heating the surrounding plasma and the similarities/differences in the physics of astrophysical and atmospheric thermals. Daniel Lecoanet and Valentin Skoutnev stressed the importance of 3D physical processes in the structure and evolution of stars (convection, magnetism), and the need for developing approximate techniques to model such physics in 1D stellar models. Barry Ginat and Frank van den Bosch both showed how even the comparatively scale-free problem of dark matter and its nonlinear evolution on cosmological timescales required techniques similar to those used in multi-scale physics problems. Giant showed that the power spectrum of dark matter density fluctuations on nonlinear scales can be understood by importing ideas of critical balance and phase-space cascades from MHD and plasma turbulence. Van den Bosch emphasized the connections between the gravitational dynamics of the inner cores of dark matter halos and related kinetic theory problems in plasma physics. It was clear that the aficionados of 1/r potentials — gravitational and electrical — had much to learn from each other, and did.

Finally, a number of talks focused on methodologies for tackling multi-scale physics problems. There were excellent discussions at the breaks and meals of whether these methodologies could be applied to an even broader range of problems than is currently done. Grisha Falkovich showed how renormalization group techniques can be applied in theories of turbulence to connect formally the weak and strong turbulence regimes. Leanardo Senatore showed how related techniques of effective field theory can be applied to parametrize small-scale feedback on large-scale structure on mildly non-linear scales, and described why these techniques are so important for analyzing current and future cosmological data sets. Jonathan Squire used the example of the problem of the heating and acceleration of the solar wind to illustrate the importance of reduced models, in this case specific orderings applied to magnetized plasma turbulence that make the problem of turbulence and heating in the solar wind tractable (drawing on some theoretical strategies originating from fusion plasmas), and revealed a number of previously under-appreciated ways such turbulence is driven. David Hosking highlighted the importance of nonlinear instabilities in magnetized plasmas and their analogy to similar dynamics in atmospheric science. He also described how the outcome of such nonlinear instabilities can be evaluated using statistical mechanics, an approach that has not been applied in atmospheric science but that could be fruitful (and indeed started to bear fruit in his interactions with the atmospheric scientists in the room). Finally, Phil Hopkins and Steve Tobias organized a joint presentation and discussion of numerical methods for multi-scale physics problems. Hopkins highlighted the increasing diversity of “refinement” techniques in astrophysics, in which an Eulerian grid or Lagrangian cells are refined/derefined in resolution, adaptively allowing one to capture a much broader range of scales in a numerical simulation. Tobias introduced analogous methods in spectral simulations, in which Fourier space was sampled logarithmically rather than linearly. This has the advantage of allowing a much larger dynamic range but the disadvantage of only simulating a subset of the nonlinear couplings. The final discussion session focused, inter alia, on synthesizing the basic scenarios of nonlinear saturation in systems comprised of mean fields and fluctuations and the strategies for predicting the outcomes of saturation in terms of transport and quasi-stationary profiles depending which of the (two) saturation classes that were identified the system belonged to.