Letter: Anomalous diffusion in random dynamical systems
Consider a chaotic dynamical system generating diffusion-like Brownian
motion. Consider a second, nonchaotic system in which all particles
localize. Let a particle experience a random combination of both
systems by sampling between them in time. What type of diffusion is
exhibited by this random dynamical system? In our letter we show that
the resulting dynamics can generate anomalous diffusion, where in
contrast to Brownian normal diffusion the mean square displacement of
an ensemble of particles increases nonlinearly in time. It is striking
that such a simple hybrid system, which is right at the interface
between deterministic and stochastic dynamics, can generate an
entirely new type of dynamics. This provides a new mechanism to
generate anomalous dynamics, and we expect it to have wide
applications in the new field of random dynamical systems.
Letter: Normal and anomalous diffusion in soft Lorentz gases
Single particles can move in very strange ways if exposed to
periodically structured environments. Think of an electron moving
in a crystal. The crystal consists of atoms situated on a periodic
lattice. Here the electron will typically perform chaotic motion,
where the path of the electron looks seemingly random and
irregular. Naively one would expect that the average distance an
electron can pass per time step increases if, say, one increases the
distance between two nearby atoms. In a recent Letter Klages et
al. have found that this is not the case. Rather, the spreading of
particles in a periodic lattice depends in a highly non-trivial way on
the variation of system parameters. This phenomenon is microscopically
explained in terms of periodic orbits: For certain parameter values
the particles find channels along the lattice in which they can wiggle
around fast in one direction while at other values these channels
disappear. This finding may have important applications to electronic
transport in graphene-like structures, a novel material that became
very popular after being valued by a Nobel prize in 2010.
As part of the Collaborative Research Center 910 I was kindly nominated for a prestigious Mercator Fellowship by the Institute of Theoretical Physics of the Technical University of Berlin. This is given to me as a visiting professorship, which enables me to collaborate with scientists within the CRC framework. I will also give a special course to PhD students. The fellowship was awarded by the DFG to me in December 2018. The duration is 8 months, the amount awarded is EUR50,000.
PNAS article: Weak Galilean invariance as a selection principle for coarse-grained diffusive models
Galileo Galilei famously stated the principle of Galilean invariance, which links the equations of motion of closed systems as viewed in distinct inertial frames translating relative to one another at a constant velocity. This principle constrains the possible form of mathematical descriptions of classical systems. However, models for many systems models are based not on microscopic equations of motion, but on effective descriptions on a mesoscopic level using random processes, such as stochastic Langevin equations or Fokker–Planck diffusion equations. Such equations capture the consequences on a coarse-grained level of microscopic interactions such as friction or noise. The principle of Galilean invariance does not apply to such systems, and so offers no help in assessing the consistency of a given stochastic model in different inertial frames.
In a new paper, however, Klages et al. explore how Galilean invariance is broken during the coarse-graining procedure of deriving stochastic equations. Their analysis leads to a different set of rules – a principle of “weak Galilean invariance – linking general stochastic models in different inertial frames. While several standard stochastic processes are invariant in these terms, this is not true for the continuous-time random walk. In the paper, the authors derive the correct invariant description for this model. The work provides a theoretical principle to select physically consistent stochastic models well before any comparison with experimental data.
Research grant: Funding awarded by the Office of Naval Research Global
In Autumn 2017 I was awarded funding by the Office of Naval Research Global to fully focus on a research project. The funding of US$117,067 covers my own salary for 20 months.
External Fellow of the London Mathematical Laboratory
Since autumn 2017 I am an External Fellow of the London Mathematical Laboratory. The fellowship award is always for one year with a potential re-appointment and includes an annual budget of £3,000 for scientific expenses.
This international workshop, for which
full funding of US$22,305 was awarded from the Office of Naval Research Global, took place in Tampere, Finland
in August 2017 for a duration of 3 days. The meeting involved 23 international participants. Together with E.Rasanen (Tampere) and R.Metzler (Potsdam) I have been organizing this event as the main organizer.
6-months Advanced Study Group plus 6-months Visiting Scientist position awarded by the Max Planck Society
In Autumn 2014 I
awarded funding for a 6-months research project on the `Statistical
Physics and Anomalous Dynamics of Foraging' at the Max Planck Institute
for the Physics of Complex Systems in Dresden, Germany. Starting from
July 2015 I will head a team of 5 scientists from Mexico, Spain, the
Ukraine and the UK to work on this
topic at MPIPKS Dresden. Our activities will be supported by a vivid
visitors programme. Subsequently I will stay at MPIPKS for another 6
months as a visiting scientist to work on a follow-up project.
Invitation to become co-chair / member of EPSRC prioritisation panels
I served five
times on prioritisation panel meetings of the Engineering and Physical
Sciences Research Council (EPSRC) of the UK: as a member in
June 2014 (deciding about approx. £19,000,000 grant money
applications, 12 scientists, 60 proposals), in
November 2017 (£17,000,000 grant money applications, 13
scientists, 60 proposals), in
June 2018 (£24,500,000 grant money applications, 14 scientists, 73
proposals), November 2020 (£31,000,000 grant money applications, 13
scientists, 51 proposals) and as a co-chair in
Sept. 2016 (£12,000,000 grant money applications, 15 scientists,
40 proposals). The job of the panels was to rank all proposals in
order of quality to assist EPSRC in its decision-making about
funding. In January 2017 I was explicitly recognised in a letter
and on the EPSRC webpage for my `significant contribution to EPSRC
Peer Review' by having `achieved a ranking in the top 7% of College
members for participating in peer review activities during the last
academic year (2016/17)'.
Invitation by the American Physical Society to
join the Editorial Board of Physical Review Letters, and to serve there for a 2nd term
Book: Nonequilibrium statistical physics of small systems - Fluctuation relations and beyond
This book was published as a Special Issue in the series Reviews of Nonlinear Dynamics and Complexity
upon invitation by the series editor Prof. H.-G. Schuster. It
summarizes recent developments of Small Systems Physics with a focus
on fluctuation relations, a key topic in this field over the past
10 years. The book (428
pages) got published by Wiley-VCH in February 2013. Until January 2015 more
than 200 copies were sold, and the book was cited more than 10 times
(according to Web of Science) / more than 25 times (Google Scholar). Please see the book's homepage for further details.
Director of Postgraduate Research Studies
In June 2012 I
became director of the PhD programme at the School of Mathematical
Sciences, Queen Mary University of London. I was
later on joining various management groups both at the School and at the College.
I am currently responsible for
managing our whole PhD programme with about 50 PhD students and 50 academic staff members. This
includes in particular acquiring money for PhD studentships: I was
successful with awarding 5 PhD studentships from the College in 2012, 2013 and 2014,
based on proposals that were assessed competitively (about £230k each). I
was also awarded a grant from the EPSRC for PhD studentships in 2012, 2013 and 2014,
again based on a proposal for the School (about £210k each time).
Letter: Spatiotemporal Dynamics of Bumblebees Foraging under Predation Risk
PhD student Friedrich Lenz performed a statistical analysis of flight
paths of bumblebees foraging in a laboratory experiment carried out by
Tom Ings and Lars Chittka, School of Biological and Chemical Sciences,
Queen Mary University of London. The bumblebees were searching for
nectar in a patch of artificial flowers both without predation risk and
under predation thread by artificial spiders randomly distributed on
the flowers. We found that, surprisingly, the probability distribution
of velocities did not change under predation risk. All the changes were
contained in the velocity correlation functions quantifying the
temporal changes of the velocities along trajectories. Our result has
to be seen within the context of the ongoing debate about optimal
foraging theories, where correlation functions have so far not really
Our results have been published in the international top journal Physical Review Letters, highlighted therein as an Editor's Suggestion.
They were furthermore highlighted by a synopsis in the journal Physics of the American Physical Society.
some international press coverage of this research:
A preprint of our paper was aleady highlighted and discussed in The Physics arXiv Blog (as part of the MIT Technology Review).
This international conference, for which full funding was awarded from the Max Planck
Society, took place at the MPIPKS Dresden in July/August 2011 for
a duration of 3 weeks. The aim was to particularly bring together
mathematicians and theoretical physicists working on the conference
topic. An overwhelming number of applications was received. Together with R.Zweimueller (Surrey), E.Barkai
(Bar-Ilan) and H.Kantz (Dresden) I have been organizing this event as the main organizer.
Referee awards and activities in UK, USA, Australia, Japan, Israel, Italy and Germany
Book: Anomalous transport - Foundations and
Because of the big success of an international
conference on anomalous transport, please see
below, we organizers decided to edit a multi-author reference book
on the very same topic, as an introduction to this important, very
active field of research. The book (584 pages) got published by
Wiley-VCH in July 2008. Until March 2014 more than 265 copies were
sold, and the book was cited more than 140 times (according to Web of
Science) / more than 240 times (Google Scholar). It thus quickly
developed into a standard reference for this whole field. Please see
book's homepage for further details.
PNAS article: Anomalous dynamics of cell migration
interdisciplinary collaboration with Peter
Dieterich, TU Dresden, A.
Schwab, University of Muenster, and R.
Preuss, MPI for Plasma Physics, Garching, we showed that
biological cells can exhibit a very interesting dynamical behavior:
Isolated single cells were put on substrates on which they crawl (with
a remote similarly to `caterpillars'). Recording their trajectories
with a video camera, the experimental data matches nicely to
statistical predictions of a specific theoretical model (a so-called
fractional Klein-Kramers equation), which describes a transition from
sub- to superdiffusive behavior as time increases. That is, the
cell's dynamics is very different from ordinary Brownian motion.
These results have been
published as an article in the international top journal Proceedings of the National Academy of
Sciences in January 2008; see PNAS 105,
459--463 (2008). This article was already cited more than 100
times (Web of Science) / 130 times (Google Scholar) since then.
Monograph: Microscopic chaos, fractals and transport in nonequilibrium statistical mechanics
In 2003 I completed a
summary of my research performed over the previous years. This work
got accepted as my Habilitation
Thesis at the TU
An updated and considerably amended 460 page version got published in
June 2007 as a book in the
Advanced Series in Nonlinear Dynamics, World Scientific, Vol.24. Until
December 2015 more than 400 copies were sold, and the book was cited about
50 times (Web of Science) / more than 80 times (Google Scholar). Please
book's homepage for further details.
Research grant: Anomalous deterministic transport and fluctuation relations
In September 2006 I
grant from the British
EPSRC council. With this grant (£250,000) I partially funded my own post for two years, I
received travel money, money for computers and money for inviting
collaborators. The grant included a 2-year postdoc position.
This very interdisciplinary international conference,
for which full funding was awarded from
the Heraeus Foundation, took place at the Physikzentrum Bad Honnef in
July 2006 for a duration of 4 days. The meeting involved about 70
international participants from 17 different countries. Together with G.Radons (Chemnitz) and I.M.Sokolov
(Berlin) I have been organizing this event as the main organizer. See also the multi-author
reference book related to this conference.
This international conference, for which full funding
was awarded from the Max Planck Society, took place at the MPIPKS
Dresden in August 2002 for a duration of 3 weeks. It involved about
90 participants from 22 different countries. Together with P.Gaspard (Brussels), H.van Beijeren (Utrecht)
and J.R.Dorfman (College Park) I have been organizing
this event as the main organizer. All of us were serving as guest editors
at the International scientific journal
Physica D for the accompanying
400-page Special Issue.
During my Ph.D. thesis
the phenomenon that diffusion coefficients can be fractal functions of
control parameters. At first view this finding appears
to be counter-intuitive, since usually one expects physical quantities
smoothly under parameter variation as, for example, in Ohm's
Subsequently it was shown by colleagues, coworkers and myself that this
quite typical not
only for diffusion but also for other types of transport coefficients
(e.g., electrical conductivities, chemical reaction rates)
characterizing transport in low-dimensional
deterministic dynamical systems exhibiting spatial
periodicities. This class of systems thus exhibits
that are at the borderline of traditional statistical physics revealing
fingerprints of an underlying microscopic deterministic dynamics.
Physical systems of this class being accessible in experiments are,
for example, semiconductor devices like antidots and Josephson
junctions, certain types of ratchets,
and corrugated vibratory conveyors, the latter frequently being used in
industrial applications for transporting granular entities. For all
these systems there are theoretical predictions of fractal, or at least
dependencies of physical transport properties. Although hints
on experimental observations of such irregularities already exist in
literature, it still remains to clearly match theory with experiments
at this point.
some accounts of this finding in textbooks:
R.Artuso and P.Cvitanovic, Deterministic
Chapter 20 in:
P. Cvitanović, R. Artuso, R. Mainieri, G. Tanner and G. Vattay, Chaos:
Classical and Quantum. (Niels Bohr Institute,
J.R. Dorfman, An
introduction to chaos in nonequilibrium statistical mechanics.
(Cambridge University Press, Cambridge, 1999)
P. Gaspard, Chaos,
Scattering, and Statistical Mechanics.
(Cambridge University Press, Cambridge, 1998)
see picture in H.G.Schuster, Deterministic
Chaos. 4th edition (VCH Weinheim, 2005)