@ IWNET, Sint-Michielsgestel

Reduction of information will be a theme of the day.

Alexander N. Gorban, Mathematical frameworks for model reduction: invariant manifolds, singular perturbations, tropical asymptotics and beyond. He describes ours as the era of complexity [or of complicatedness?] and points out we should look at the history of ideas to understand where we’re at. Points out that when using applied mathematics for modeling, the usual paradigm of old laws – new phenomenon – new laws does not work anymore, because we adapt our models, we do model engineering, to adapt to phenomena [the problem with models without theory is obvious: does the model have any universal feature? And is that universality a property of a class of models or of “reality”, for what that means?]. Comments that complexity is not in things, it is in our problems and in our approaches to them [but is any science “in” things?]. Mentions complex balance and the fact that Boltzmann had already proved a similar property. Then goes into a mix of papers, anecdotes, some specific considerations mixed with some general considerations. No mention of fluctuations to be found here (despite mention of Boltzmann and Einstein). A person from the audience points out about several missed acknowledgements in his presentation (as by his habit), of course including some of his own. This is always the case in these presentations by elderly people who approach the final years of their career re-writing the history of science in such a way that their contribution can stem out in a more prominent way (that’s usually what they mean by “history”).

M. Cates, . JR. Howse et al PRL 99 (2007), I. Buttinoni PRL 110, J. Palacci et al, Science 2013: nice experiment on Janus particles in peroxide. They go by swarms. [My question is: is the collective behavior studied?]. P. Galajda et al, J. Bacterial 189, 8704 (2997). Mentions that this creation of asymmetry would be impossible because the potential is the same on both sides [but on this I might disagree – isn’t this the usual problem with misrepresenting equilibrium with uniformity?]. More interesting is the R. di Leonardo, 2009, where now rectification is in the sense of constant rotation. So it happens that there is a motility-induced phase separation [MEC + J Tailleur PRL 2008, EPL 2013, Fily et al PRL 2012; Stenhammar PRL 2013; Theurkauff PRL 2012; Buttinoni PRL 2013; etc.]. [Question is: are stalling states interesting for active particles?]

Stochastic field theory of phase separation: He compares MODEL B for passive phase separation and coexistence with detailed balance (quartic free energy functional). They propose an ACTIVE MODEL B by changing the free energy structure. He adds a square gradient term which is not a functional derivative and of course looks similar to interface growth KPZ models [Wittokowski et al. Nature]. But still it does not predict circulation of currents nor cluster phases. So something is missing. So he has to add up yet another term [C. Nartini et al. PRX 7, 021007 (2017); E. Tjhung et al. arXiv: 1801.07687].

P. Vagner, Electrochemistry in GENERIC. Electochemical model: Nernst-Planck, Nernst-Planck-Poisson, Bikermann. Mixture theory: Bedeux, Albano, Physica A 147 (1987), Dreyer et al preprint 2018. In the ’80s Marsden and Weinstein: Electromagnetic Poisson brackets. [The Hamiltonian structure of the Maxwell-Vlasov equations].


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