Modern
Mathematics
for Complex
Systems

June 29-30, 2022
De Morgan House, London

Modern Mathematics for Complex Systems

The quest for a unifying framework to describe complex systems out of equilibrium has recently produced numerous promising results. This workshop will aim to bundle some of these advances, bringing together different perspectives to trigger new ideas and equip young researchers with cutting-edge tools and knowledge.

To this end, the workshop will focus on two main themes:

  • Turbulence on day 1 

  • Dynamics and Transfer Operator Theory on day 2 .  

Topics of the conference include:

  • Out-of-equilibrium dynamics

  • Spatio-temporal chaos

  • Periodic Orbit Theory

  • Critical transitions (tipping points) in high-dimensional systems

  • Rare, extreme and persistent events and large deviations.

We are planning for this conference to be in-person in order to build back, after a two-year online hiatus, a sense of scientific community, especially for postgraduate students and early career researchers. There will also be the opportunity to register for online attendance. 

The conference will include poster sessions and social events. We particularly encourage applications from early career researchers and PhD students.

 
 

Important information

  • Dates of the conference: Wednesday June 29 - Thursday June 30, 2022

  • Venue: De Morgan House, 57-58 Russel Square, London, WC1B 4HS, UK

  • Start: 10.30 am on Wednesday. Badge pick-up and poster drop-off from 9.30 am.

  • Registration is required to attend the conference (both in-person and online). Registration is now closed.

  • Detailed information will be sent out to in-person participants by email after registration has closed. Online participants will receive a joining link by email one day before the event.

  • The fee for in-person attendance is 30£ (to be paid in the registration process; the optional conference dinner on Wednesday costs 40£). Online participation is free of charge.

  • Abstract submission for posters is now closed.

 

Programme & Speakers

mmcs_schedule_EDITED_25June.png

Note: This schedule is provisional.

Turbulence // Day 1

Universality at the onset of turbulence

Björn Hof

Institute of Science and Technology Austria

The difficulties and challenges in understanding turbulent fluid motion in shear flows (e.g. pipes and channels) already arise at the transition from laminar flow. In fact high dimensional chaotic dynamics emerge long before turbulence can be observed in practice. Moreover even simple aspects of this transition, like the definition of a critical point, turn out to be highly non-trivial. The aim of this talk is to show how the complex spatio-temporally intermittent dynamics that are characteristic for the onset of turbulence can be explained as a non equilibrium phase transition, which at least for some of these flows falls into the directed percolation universality class.

Inhomogeneity and anisotropy in planetary turbulence

Peter Read

University of Oxford

Theoretical approaches to understanding and quantifying the properties of turbulence have traditionally started with assumptions of homogeneity and isotropy of flow structure and/or forcing and dissipation. But realistic flows seldom satisfy such assumptions. In a planetary atmosphere, flows are forced primarily by buoyancy contrasts on both large and small scales, leading to both large scale overturning and localised patches of convective turbulence that are far from homogeneous. Flow structure is also strongly influenced by stratification and background rotation, leading to highly anisotropic behaviours in the form of layered structures, flows confined to horizontal interfaces or strong zonal jets. In an attempt to understand the influence of rotation on large-scale planetary turbulence, the concept of the zonostrophic regime was proposed some 15 years ago by Galperin and Sukoriansky. This concept takes direct account of the non-local upscale transfers of kinetic energy by large-scale waves, leading to a pattern of zonally symmetric jets with a characteristic universal spatial spectrum. The zonal flows coexist with a non-axisymmetric turbulent flow that participates in a more conventional Kolmogorov-Kraichnan local inverse energy cascade on scales larger than the principal forcing of barotropic modes. Observations and models of atmospheres, oceans and planetary interiors, and also some laboratory experiments, are partly consistent with the zonostrophic regime, but with some marked discrepancies. However, the zonostrophic concept only applies to the barotropic component of the flow, leaving unaddressed the role of stratification in both the forcing of large-scale turbulence and the structure and characteristics of scales smaller than the forcing scale. Observations indicate the presence of a direct energy cascade at small scales, even at scales expected to be anisotropic due to either rotation or stratification. Elucidating the nature of this transition from inverse to direct cascade at decreasing scales is one of the key challenges to our understanding of planetary turbulence in atmospheres, oceans and planetary interiors.

Turbulent flows as complex systems

Nazmi Burak Budanur

Max Planck Institute for the Physics of Complex Systems

A defining property of a complex system is emergent order that is not obvious from the laws that govern the dynamics of individual constituents. Some examples are crystal structure of solids and financial markets of societies, which are only observed when a sufficiently large number of members, atoms in a material and humans in a community, are at present. Incorporation of such large-scale phenomena into the theoretical description of a complex system is crucial since doing so offers a pathway to understanding in terms of variables that are substantially fewer than the number of interacting parts. In this talk, I will argue that turbulent flows which exhibit coherent motions at long distances can be viewed from this perspective and present computational tools to put this view into practice. Specifically, I will show results from our recent work where we combine direct numerical simulations with modern data analysis methods to build reduced-order models with several orders of magnitude lower degrees of freedom than that needed for simulations.

Turbulence in spacetime

Predrag Cvitanovic

Georgia Institute of Technology

We have equations that describe motions of fluids, but we cannot solve them where we need them: for long times, on large spatial domains, turbulent instabilities preclude any accurate numerical time integration even for the simplest of flows: pipe, channel and plane shear flows. Recent progress in describing turbulence data in terms of `exact coherent structures' suggests a radically different approach. The way we perceive turbulence -the mere fact one can identify a cloud in a snapshot- suggests that turbulence be described to a given precision by a finite repertoire of patterns explored by turbulence, and graphs of transitions among them. This pattern recognition problem is exceptionally constrained by the exact differential equations that the data must respect. As in this approach the Navier-Stokes equations are recast as a spacetime theory, with both space and time taken to infinity, the traditional Direct Numerical Simulation codes have to be abandoned. Radically different kinds of codes are required, with space and time treated on equal footing. What emerges is a spacetime which is very much like a big spring mattress that obeys the familiar continuum versions of a harmonic oscillator, the Helmholtz and Poisson equations, but instead of being "springy", this metamaterial has an unstable rotor at every lattice site, that gives, rather than pushes back. In the spatiotemporal formulation of turbulence there is no evolution in time, there are only repertoires of admissible spatiotemporal patterns, or `periodic orbits', very much as the partition function of the Ising model is a weighted sum formed by enumerating its lattice states. In other words: throw away your integrators, and look for guidance in clouds' repeating patterns.

Dynamics & Transfer Operators // Day 2

Numerical methods to study shock- and rate-induced tipping phenomena

Ulrike Feudel

Carl von Ossietzky Universität Oldenburg

Critical transitions or tipping phenomena are related to sudden changes in the behavior of a dynamical system. This could be either transitions between different coexisting stable states in a multistable system or large deviations from the usual dynamics. Examples for such behavior can be found in different fields of science ranging from mechanical or chemical systems to ecosystem and climate dynamics. Such critical transitions are called tipping phenomena in climate science, regime shifts in ecology or phase transitions in physics. They can happen in various ways: (1) due to bifurcations, i.e. changes in the dynamics when external forcing or parameters are varied extremely slow (2) due to fluctuations which are always inevitable in natural systems, (3) due to rate-induced transitions, i.e. when external forcing changes on characteristic time scale comparable to the time scale of the considered dynamical system and (4) due to shocks or extreme events. We discuss in more detail two numerical approaches to study shock tipping and rate-induced tipping. Firstly, we demonstrate an algorithm how to compute the minimal fatal shock that measures the closest distance between a stable steady state and its basin boundary in high-dimensional systems like complex networks. This method does not only provide the magnitude of the fatal shock but also its direction. We show how this method can be employed to discover the most vulnerable parts of a plant pollinator network. Secondly, we analyze the collapse of a predator-prey system due to rate-induced tipping when the environmental conditions are varied with a certain rate. We illustrate how one can find the boundary between initial conditions which track a moving equilibrium and the ones which tip.

Prediction from perfect partial observations and linear response

Caroline Wormell

Sorbonne Université

This talk will discuss two basic questions concerning the long-term predictability of chaotic systems: first, to what extent partial observations can give meaningful long-term information about the system, and second, what causes larger systems to have a differentiable (and thus efficiently approximable) response to time-independent dynamical perturbations. We will show that there is a common mechanism underlying these two phenomena, and give some mathematical results in this direction.

Ruelle-Pollicott Resonances of Stochastic Systems:
Challenges and Deep Perspectives

Mickaël D. Chekroun

Weizmann Institute of Science

Ruelle-Pollicott (RP) resonances are known to completely characterise the time-variability of dynamical systems, either stochastic or deterministic. In this talk, I will discuss a flexible machine-learning framework for solving spectral problems of Kolmogorov operators enabling in turn for getting access to RP resonances. The approach is data-free and improves on existing neural networks eigensolvers by demonstrating its ability to compute beyond dimension three (i) eigensolutions for non-self adjoint operators with small diffusion, (ii) eigenpairs located deep within the spectrum (iii), and to compute several eigenmodes at once. This is a joint work with Eric Simonnet (CNRS, France).

On typical properties of persistent atmospheric extreme events from a large deviation perspective

Vera Melinda Galfi

Uppsala University

In order to prepare for climate change, the challenge is to understand how global warming will affect extreme events. We frequently experience cases when not mainly the intensity but rather the duration of the event is the key factor in terms of impact. We call these long-lasting extreme events persistent extremes. Whereas a single hot summer day might be enjoyable, several days or weeks of too warm temperatures increase mortality, damage the infrastructure and crops, lead to wild fires, etc. Extreme events however do not have to be surprising or unpredictable. From a large deviation perspective, the stronger and the longer the event is, the more energy is needed to generate and maintain it, and the less possibilities the climate system has to realise it. This means that persistent extremes occur usually in a specific way. I will discuss the theoretical basis for the typicality of persistent extremes based on large deviation theory. I will show what aspects of typicality we observe in case of persistent extremes, such as heatwaves, cold spells and persistent anomalies of the North Atlantic jet stream.

Extreme event quantification for fluids and waves

Tobias Grafke

University of Warwick

Rare and extreme events are notoriously hard to handle in any complex stochastic system: They are at the same time too strong to be ignored, as they have measurable impact on statistics, but nevertheless too rare to be easily observable in experiments or numerical simulation. This is a particular complication in fluid turbulence, with its large number of strongly coupled degrees of freedom. In this talk, I discuss rare events algorithms based on instanton calculus and large deviation theory in order to compute sharp limits for rare event probabilities, as well as their most likely pathway of occurence. The efficiency of these methods is demonstrated by applying them to large spatially extended fluid and wave systems, such as oceanic Rogue Waves, transitional turbulence in pipe flows, or the 3D Navier-Stokes equation.

 

Registration

Attend in-person

Attend online

Registration deadline: June 22

Live talks, poster sessions, discussions
Lunch, tea & coffee
Conference dinner (optional)

Registration fee: 30 £
Dinner: 40 £ (sold out)

Registration deadline: June 27

Follow the talks online
Ask questions to the speakers


Registration free of charge
 

Poster submission closed on June 1.

 

Sponsors

 

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Organising Committee

Reyk Börner, University of Reading
Melanie Kobras, University of Reading
Chiara Cecilia Maiocchi, University of Reading and Imperial College London
Niccolò Zagli, Imperial College London and University of Reading


 

The background animation shows moisture contours from an idealized large-eddy simulation of the tropical atmosphere, illustrating the emergence of miniature cyclones under an amplified coriolis effect.

 

Simulation done by Romain Fiévet, Niels Bohr Insitute, University of Copenhagen, Painting by Vincent Van Gogh.

Edit by Reyk Börner