Multi-Scale Physics (2023)

Date & Time

Alex Schekochihin, Oxford University
Laure Zanna, New York University
Eliot Quataert, Princeton University.

A common problem facing a wide range of disciplines in the physical sciences is that phenomena at a diverse range of length and time-scales are critical to the dynamics and time evolution of the system. For example, the densest objects in the Universe, black holes, are one of the largest sources of energy production in the formation of structure and influence the dynamics of the Universe on scales up to ~1010 times larger than the black hole itself. On the Earth, the properties of small-scale turbulence in the atmosphere and ocean are critical for the long-term evolution of the climate, and in laboratory fusion devices, small-scale turbulence regulates the temperature achievable in fusion devices, and thus the likelihood of self-sustaining fusion reactions.

The general challenge in multi-scale physics problems is that short length and time-scale phenomena impact the long length and time-scale behavior and vice-versa. The relevant physics, and indeed often even the relevant equations, needed to describe the system on these diverse scales can be quite different. This raises significant challenges both in principle (e.g., at the applied math level) and in practice (e.g., at the theoretical and computational level) regarding how to accurately model such systems. This challenge can be viewed as formulating an “effective field theory” for the system that correctly couples the dynamics across multiple length and time-scales, as has been successfully done in particle physics, condensed matter physics, and theories of large-scale structure.

The Simons Symposium on multi-scale physics brought together experts in a range of disciplines that face these challenges, including astrophysics, climate science, plasma physics, oceanography, machine learning, applied math, and theoretical physics. By discussing the challenges facing each discipline and their methods for tackling multi-scale problems, each community learned techniques from the others, thus simultaneously advancing a wide range of disciplines.

  • Meeting Reportplus--large

    The Symposium at Schloss Elmau from 8/28 to 9/1 was an extremely engaging exploration of the broad problem of multiscale physics across many different disciplines. Here we summarize some of the main contributions from the talks and discussions and highlight a few interesting directions for future research that came up at the symposium.

    The symposium began with three overview talks on some of the multi-scale physics challenges in climate science, galaxy formation and cosmology, and magnetically confined fusion. It then moved to a discussion of methods used in different disciplines to model physics across different time and length scales. The next two and a half days focused on forefront topics, while Friday afternoon concluded with two sessions synthesizing some of the cross-cutting physics and methods discussed earlier in the week.

    Overview Talks:

    Nadir Jeevanjee gave a blackboard overview of climate science with an emphasis on atmospheric science. He derived and explained Manabe’s Nobel-Prize-winning work on radiative-convective equilibrium in atmospheric science and then highlighted the importance of cloud dynamics in determining the vertical profile of greenhouse gasses and thus the temperature of the Earth. He briefly discussed unresolved processes, such as convection, in climate models and their influence on future climate change projections. He concluded with a short summary of the role of the ocean in terms of both short- and long-term thermal exchange with the atmosphere.

    Rachel Somerville summarized the range of multiscale physics important in galaxy formation and cosmology. She highlighted in particular the important role of energy injection by stellar processes and black hole accretion and their role in both shaping the population of galaxies and influencing structure on large scales where cosmological measurements need to disentangle baryonic processes from deviations from the standard cosmological model.

    Steve Cowley summarized the multiscale physics challenge of modeling magnetic confinement fusion. He focused in particular on the role of small-scale instabilities driven by temperature gradients in regulating the transport of heat in tokamaks. He showed how the fusion community combines small-scale simulations of the turbulence driven by these instabilities with system-scale modeling to understand the global evolution of tokamak equilibria and their ability to sustain fusion.

    Methods Talks:

    Matias Zaldarriaga described a class of effective field theories that can be used to model some multi-scale physics problems. He focused on the case of effective field theories of inflation and large-scale structure and showed how in the regime of large length scales the theory is sufficiently linear that the impact of the feedback processes highlighted in Somerville’s talk can be modeled. There was extensive discussion of the approximations used in these effective field theories and their possible application to other problems.

    Eve Ostriker and Tapio Schneider gave complementary perspectives on the critical need and methods for physics-based subgrid models in galaxy formation and climate science, respectively.  Ostriker showed how small-scale simulations of galaxies can be used to inform larger-scale simulations lacking the resolution to capture the key physics, and Schneider highlighted the same point using small-scale simulations of clouds and their importance in global climate models that cannot resolve cloud formation and dynamics.

    Viviana Acquaviva and Roman Grigoriev summarized the role of machine learning in tackling multiscale physics problems. Acquaviva gave an overview of several of the methods that have been most successfully employed, while Grigoriev highlighted the ability of machine learning to ‘learn’ appropriate subgrid models. The theme of correct choice of variables and of ‘memory,’ i.e., non-locality in time for subgrid models, came up in Grigoriev’s talk and was frequently returned to later in the meeting.

    Finally, Raffaele Ferrari and Steve Tobias led a discussion of numerical methods for modeling multiscale phenomena. They discussed formal techniques such as asymptotic methods when a system has well-defined scale separation as well as numerical techniques such as statistical closures for modeling small-scale dynamics.

    Forefront Topics and Methods:

    Several talks on climate science and modeling highlighted both the role of scale interaction in the ocean and atmosphere, the limitation of climate models to resolve them and the need for a combination of methods (numerics, machine learning and physics) to accelerate progress in climate modeling — in particular the lack of scale interactions — and potentially narrow uncertainty in future projections.

    Oliver Watt-Meyer focused on techniques from machine learning to learn corrections of model trajectories, relative to observations, that can then be used as parameterizations for missing physics or inaccurate numerics.

    Pierre Gentine showed a range of hybrid methods, combining machine learning with physics-inspired methods, demonstrating improvement in multiscale interactions in the ocean, land and atmosphere for more robust simulations.

    Tapio Schneider and Raffaele Ferrari discussed a new ocean and atmospheric model component written entirely in Julia. They emphasized the need to use observations and model data to calibrate parameterizations through Kalman inversion while Ferrari further showed the power of a GPU-based code for accelerating model simulations and better capturing ocean turbulent features necessary for heat and carbon uptake.

    Annalisa Bracco demonstrated the importance of sub-mesoscales (scales 1–10 km) on the large ocean circulation in a suite of complex simulations and their impact on biogeochemical transport — highlighting the wide range of scale interactions for carbon sequestrations.

    Roman Grigoriev discussed how in a number of ways a simple inverse-cascade picture failed to describe the dynamics of 2D turbulence in which large-scale, long-lived coherent structures emerge and what that implied for subgrid modeling.

    The astrophysics talks were perhaps more focused on new physics where multiple scales interacted in interesting ways than on modeling methods: Roger Blandford offered a bird’s-eye perspective on extreme electrodynamical phenomena in astrophysical environments (compact objects in particular); Ellen Zweibel gave a master-class on kinetic and fluid treatment of the (multiscale!) problem of cosmic-ray transport in the galaxy and beyond; Irina Zhuravleva explained how X-ray astronomy (including a new satellite due for imminent launch, XRISM) is enabling direct measurement of turbulence and transport properties of intergalactic plasmas; and Eugene Churazov highlighted extraordinarily puzzling magnetized, relativistic-particle-filled, multiscale (high-aspect-ratio) structures ubiquitously observed in these plasmas by a judicious coupling of radio and X-ray information, proposing a new hypothesis as to their origin and longevity.

    Descending back to Sun and Earth, Jono Squire described the recently discovered phenomenon of helicity barriers in the solar wind, a case of small-scale physics having a direct and game-changing effect on the large-scale behavior — explaining for the first time a number of properties of solar-wind dynamics and thermodynamics (heating) that have puzzled space physicists for a long time.

    Peter Davidson outlined a scenario of geodynamo (generation and sustenance of the Earth’s magnetic field) that relied on the inertial waves to produce mean helicity separation and long-scale coherence — another multiscale problem par excellence Steve Tobias proposed a scheme for subgrid modeling based on statistical closures at small scales (a version of time-nonlocal approach of the kind Grigoriev had called for earlier) — an approach with which he had had some success capturing zonal-flow dynamics in turbulent systems. Overall, it appeared that astrophysicists had much to learn from climate physicists’ extensive experience of reliable quantitative modeling, including, recently and especially, ML techniques, while climate physicists could usefully incorporate some of the astrophysicists’ penchant for ultra-simplified, qualitative scoping out of basic physical ingredients and their coupling in multiscale systems.

    Synthesis Sessions:

    Pierre Gentine, Jono Squire and Ellen Zweibel led a discussion session focused on cross-cutting physical processes. Together with input from the rest of the group, they identified a number of important cross-cutting physics themes: (1) turbulent transport of energy, momentum and species, including transport that is both local and non-local in time and space, (2) critical balance as an organizing principle for turbulence in wave-carrying media, (3) the role of exact and approximate conservation laws in governing the dynamics of systems, (4) the key distinction between instabilities that saturate by reaching marginal stability versus those that saturate at finite amplitude with an often difficult-to-determine saturation amplitude and (5) the role of coherent structures as an organizing principle for multi-scale physics, especially in near-marginal, low-transport regimes.

    Eliot Quataert, Alex Schekochihin and Laure Zanna continued the synthesis discussion by focusing on methods for tackling multiscale physics problems highlighting the similarity of different methods used across very different fields. They then proposed that it would be useful to have a model problem with a “known” solution in which different techniques for handling multi-scale processes of various complications could be explored. One proposed problem was thermal convection in stratified atmospheres with background mean flows. This is a problem in which a reference statistical solution can be obtained using high-resolution simulations. The challenge is then to reproduce the coarse-grained properties of the high-resolution simulation using low-resolution simulations with various strategies for subgrid models. That is the essence of many of the multiscale physics challenges faced by different communities. The problem can be made more challenging by including chemical/nuclear reactions, moist convection (i.e., clouds), many density scale-heights, etc. The advantage of a model problem like this is that it is a useful testing ground for subgrid models that are physics based, ML based, etc. Although attendees differed on whether they thought the problem was too easy or too hard (!), there was broad agreement that it would be interesting to explore further. Several people brought up that posing this as a challenge to the broader physics community could be valuable and stimulate additional work.

  • Agendaplus--large


    10:00 - 11:00 AMNadir Jeevanjee | An Introduction to Climate Science
    11:30 - 12:30 PMRachel Somerville | An Introduction to Astrophysics and Cosmology
    5:00 - 6:00 PMSteve Cowley | An Introduction to Plasma Physics
    6:15 - 7:15 PMEugene Churazov & Matias Zaldarriaga | Methods: Effective Field Theories


    10:00 - 11:00 AMEve Ostriker & Tapio Schneider | Methods: Microphysics-based Subgrid Models
    11:30 - 12:30 PMRoman Grigoriev & Viviana Acquaviva | Methods: Machine Learning
    5:00 - 6:00 PMRafaelle Ferrari & Steve Tobias | Methods: Numerical Modeling of Multiscale Phenomena
    6:15 - 7:15 PMRoger Blandford | FRBs, Pulsars and Spinning Black Holes - Particles or Fields?


    5:00 - 6:00 PMEllen Zweibel | Cosmic-Rays: Fluid Models of Kinetic Plasma Processes
    6:15 - 7:15 PMJono Squire | Violation of the Zeroth Law of Turbulence in Magnetized Collisionless Plasmas


    10:00 - 10:30 AMRoman Grigoriev | The Direct Cascade and Information Flow Between Scales in Quasi-2D Turbulence
    10:30 - 11:00 AMOliver Watt-Meyer | Challenges in Coupling ML-Based Sub-Grid Models to a Global Atmospheric Model
    11:30 - 12:30 PMAnnalisa Bracco | Multi-Time Scale Impacts of Ocean Mesoscale and Submesoscale Dynamics
    5:00 - 6:00 PMPierre Gentine | LEAPing Across Scales for New Generation Climate Models
    6:15 - 6:45 PMIrina Zhuravleva | LProbing Multi-Scale Physics of ICM with X-ray Observations
    6:45-7:15 PMEugene Churazov | How Well does the Synchrotron Emission Trace Intracluster Medium (ICM) Motions from Small to Large Scales


    10:00 - 11:00 AMTapio Schneider & Rafaelle Ferrari | Harnessing AI and Computing to Advance Climate Modeling and Prediction
    11:30 - 12:00 PMPeter Davidson | From Random Small-Scale Wave Motion to Coherent Planetary Dynamos
    12:00 - 12:30 PMSteve Tobias | Driving of Zonal Flows: Nonlinear Dynamics and Statistical Theories
    5:00 - 6:00 PMPierre Gentine, Jono Squire, Ellen Zweibel | Discussion of Cross-cutting Physics and Methods
    6:15 - 7:15 PMEliot Quataert, Alex Schekochihin, Laure Zanna | Discussion of Cross-cutting Physics and Methods
  • Abstracts & Slidesplus--large

    Roger Blandford
    Stanford University

    FRBs, Pulsars and Spinning Black Holes — Particles or Fields?
    View Slides (PDF)

    Most discussions of these sources of high brightness, low frequency waves have been explicitly or implicitly based on the dynamics of the constituent plasma particles. Roger Blandford will discuss an alternative, “Maxwellian” approach wherein the current is considered in the continuum fluid limit.

    Annalisa Bracco
    Georgia Institute of Technology

    Multi-Time Scale Impacts of Ocean Mesoscale and Submesoscale Dynamics
    View Slides (PDF)

    Annalisa Bracco will discuss the interplay of mesoscale and submesoscale circulations using modeling and both direct and indirect observations. The focus will be on a limited but compelling set of cases that highlights the complexity of the physical interactions and the challenges for parameterization efforts. Focal to this presentation will also be the consequences of these interactions on ocean carbon and heat storage, and on the marine ecosystem, from days to millennia.

    Eugene Churazov
    Max Planck Institute for Astrophysics

    How Well Does the Synchrotron Emission Trace Intracluster Medium (ICM) Motions from Small to Large Scales?

    Unlike the ICM, which is volume filling, the density of relativistic electrons varies by a large factor across a cluster. As a result, only a small fraction of volume shines in the radio band. This opens a possibility to probe small and large scales without complications associated with diluting the signal that we see in a projection.

    Peter Davidson
    Cambridge University

    From Random Small-Scale Wave Motion to Coherent Planetary Dynamos
    View Slides (PDF)

    Rafaelle Ferrari & Steve Tobias

    Methods: Numerical Modeling of Multiscale Phenomena
    View Slides (PDF)

    Pierre Gentine
    Columbia University

    Leaping Across Scales for New Generation Climate Models
    View Slides (PDF)

    Recent advances in computational modeling tools are allowing us to simulate key climate processes at unprecedented resolution, yet only over short periods of time. Machine learning can be used to learn from those high-fidelity simulations, to better represent those physical processes and develop new generation climate models. Finally, observations such as from satellites, should be used to tune those improved simulations to better replicate past climate, yet require new types of algorithms merging data assimilation and machine learning.

    Roman Grigoriev
    Georgia Institute of Technology

    The Direct Cascade and Information Flow Between Scales in Quasi-2D Turbulence
    View Slides (PDF)
    View Slides (PDF)

    Fluid turbulence is a paradigm example of a multiscale problem, and, in two dimensions, it is sufficiently tractable to understand the information flow between scales and its relation to certain types of solutions of the governing equations describing large, intermediate and small scales. In particular, the analysis of the direct cascade shows that the information flow from small to large scales or “backscatter” can be extremely important and has to be properly accounted for in any subgrid-scale model.

    Eve Ostriker & Tapio Schneider

    Methods: Microphysics-based Subgrid Models
    View Slides (PDF)

    Tapio Schneider
    California Institute of Technology

    Harnessing AI and Computing to Advance Climate Modeling and Prediction
    View Slides (PDF)

    There are contrasting views on how to produce the accurate predictions that are needed to guide climate change responses. Here, Tapio Schneider argues that they are best achieved by harnessing AI in hybrid approaches that build on domain-specific knowledge and generating ensembles of moderately high-resolution (10–50 km) climate simulations that exploit distributed computing capabilities.

    Tapio Schneider & Rafaelle Ferrari

    Harnessing AI and Computing to Advance Climate Modeling and Prediction
    View Slides (PDF)

    Rachel Somerville
    Flatiron Institute

    An Introduction to Astrophysics and Cosmology
    View Slides (PDF)

    Jonathan Squire
    University of Otago

    Violation of the Zeroth Law of Turbulence in Magnetized Collisionless Plasmas
    View Slides (PDF)

    A common assumption in turbulence is that an energy flux stirred up at large scales can reach the small scales where it can be thermalized. Jonathan Squire will discuss how this assumption can fail in collisionless magnetized plasmas due to the “helicity barrier” effect, in which the simultaneous conservation of energy and helicity halts the turbulent energy flux as it reaches plasma microscales, restricting the heating of electrons. The effect shows that great care is needed when applying fluid models to large-scale collisionless plasma dynamics, with interesting implications for the physics of the solar corona and other astrophysical plasmas.

    Steve Tobias
    University of Leeds

    Driving of Zonal Flows: Nonlinear Dynamics and Statistical Theories
    View Slides (PDF)

    Steve Tobias will talk about the interactions that lead to the driving of zonal flows (and perhaps large-scale magnetic fields) in astrophysics and plasmas. Tobias will describe approximations that can lead to an increased understanding of this mechanism and discuss the direct statistical simulation of such phenomena.

    Oliver Watt-Meyer
    Allen Institute for Artificial Intelligence

    Challenges in Coupling ML-Based Sub-Grid Models to a Global Atmospheric Model
    View Slides (PDF)

    Oliver Watt-Meyer will present a concrete example of using machine learning to represent sub-grid processes within a conventional physics-based global atmospheric model. In particular, Watt-Meyer will show the challenges arising from feedbacks between the machine-learning and physics-based models when in a coupled setting.

    Matias Zaldarriaga
    Institute for Advanced Study

    The Effective Field Theory of Large-Scale Structure
    View Slides (PDF)

    An overview of the effective field theory of large-scale structure.

    Irina Zhuravleva
    University of Chicago

    Probing Multi-Scale Physics of ICM with X-Ray Observations
    View Slides (PDF)

    Microphysics of hot intracluster gas and its impact on astrophysical scales remains largely unexplored. Irina Zhuravleva will present ways of probing turbulent cascade, effective viscosity and parallel conduction through the observations of density and temperature variations. The challenges and future perspectives will be discussed.

    Ellen Zweibel
    University of Wisconsin-Madison

    Cosmic Rays: Fluid Models of Kinetic Plasma Processes
    View Slides (PDF)

    A background presentation on the multi-scale interaction between fluid plasma and collisionless cosmic rays (relativistic particles).

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