10th Nordic Workshop on Statistical Physics: Biological, Complex and Non-Equilibrium Systems

20 Mar 2019, 09:00 → 22 Mar 2019, 18:00 Europe/Stockholm

132:028 (Nordita, Stockholm)

Alberto Imparato (Aarhus University), Ralf Eichhorn (Nordita)

Venue

Nordita, Stockholm, Sweden

Scope

This workshop series provides a “forum” where scientists in the Nordic countries working in the area of Statistical Physics can meet regularly. It has been initiated at Nordita in 2010, such that in 2019 we proudly celebrate the 10th edition in the workshop series.

The meeting brings together experts interested in the broad spectrum of timely problems in (classical) Statistical Physics, ranging from fundamental aspects in the theory of non-equilibrium processes to modern applications in biophysics. Topics covered include diffusion problems, physics of DNA and bio-molecules, population dynamics, pattern formation, non-equilibrium transport, active matter, single-molecule kinetics, dynamics and structure of networks, statistical inference, Monte-Carlo simulation techniques, self-assembly, soft condensed matter (colloids, liquid crystals etc.), work relations and fluctuation theorems, and many more.

The workshop will start on Wednesday morning at around 9.00 with registration and coffee/cake. It will end on Friday (early) afternoon. It is planned to have a conference dinner on Thursday evening.

[Timetable - available from start of the workshop]

Invited Participants

Tapio Ala-Nissilä (Aalto University) Miguel Caro (Aalto University) Marcelo Dias (Aarhus University) Hans Fogedby (Aarhus University) Simone Borlenghi Garoia (KTH) Mogens Hogh Jensen (Niels Bohr Institute) Supriya Krishnamurthy (Stockholm University) Chun-Biu Li (Stockholm University)

Soon Hoe Lim (Nordita) Heiner Linke (Lund University) Bernhard Mehlig (Gothenburg University) Namiko Mitarai (Niels Bohr Institute) Kristine Niss (Roskilde University) Sigurdur Örn Stefansson (University of Iceland) Damiano Verardo (Lund University) Giovanni Volpe (Gothenburg University) Astrid de Wijn (Norwegian University of Science and Technology)

Special Guest

Marco Pettini (Aix-Marseille University)

Registration

If you want to participate in the workshop, please fill in the registration form.

Registration deadline: 24 February, 2019

There is no registration fee.

There is a (very) limited number of travel grants available for PhD students and young Postdoc fellows from the Nordic countries. If you are interested in such a grant, please contact the organizers via email.

Sponsored by:

Wednesday, 20 March

1 Registration (Coffee & Cake)

2 Opening

Speakers: Prof. Alberto Imparato (Department of Physics and Astronomy University of Aarhus), Ralf Eichhorn (Nordita)

3 Solitons and the inverse scattering method

We review briefly some of the soliton-carrying 1D evolution equations: The Korteweg-de-Vries equation for shallow water waves, the Non Linear Schrödinger equation for self-focussing light beams, and the Sine-Gordon equation in field theory. These systems are all integrable by means of the remarkable Inverse Scattering Method. We next focus on the classical continuous 1D Heisenberg model which likewise is completely integrable. We discuss the Heisenberg soliton-spin wave spectrum and the Inverse Scattering Method applied to this model. We conclude with some general remarks (of dubious relevance).

Speaker: Hans Fogedby (Aarhus University)

4 Cyclic competition in space

Cyclic competition is an extension of Rock-Paper-Scissor game, where one kind of species dominate another in a cyclic relation. Its nontrivial behaviors have been widely studied both in well-mixed systems and spatially structured systems. We study the behavior of cyclic competition in one dimensional lattice with a finite mixing rate [1] and the system with three parallel one-dimensional lattices with finite interaction rate between lines [2], to reveal how the final outcome depends on the dimensionality. [1] Feldager, C. W., Mitarai, N., & Ohta, H. (2017). Deterministic extinction by mixing in cyclically competing species. Physical Review E, 95(3), 032318. [2] Mitarai, N., Gunnarson, I., Pedersen, B. N., Rosiek, C. A., & Sneppen, K. (2016). Three is much more than two in coarsening dynamics of cyclic competitions. Physical Review E, 93(4), 042408.

Speaker: Namiko Mitarai (NBI)

5 Fractal catastrophes

Speaker: Bernhard Mehlig (Gothenburg University)

6 Lunch

7 Modeling Propulsion and Controlled Steering of Magnetic Micro and Nanohelices

Controlled motion of micro and nanomotors in a fluid environment is a promising tool in biology and biomedicine. Fuel-free controlled propulsion and steering in aqueous solutions have been experimentally demonstrated at the microscale by taking advantage of the coupled rotational and translational motion. The challenge in the controlled propulsion and maneuverability at the nanoscale is overcoming thermal effects which can alter the direction of motion and interfere with the propulsion. The hybrid lattice-Boltzmann -- Molecular Dynamics method with full hydrodynamic interactions and thermal fluctuations [1] is used to optimize the helical shapes and to demonstrate that controlled propulsion and maneuverability is possible for helically shaped structures at a sufficiently high Peclet number, a ratio of the diffusive and propulsive timescales. The magnetic helical structure interacts with a rotating magnetic field. The interaction induces a torque that propels the helix in the fluid through the coupled rotational and translational motion. The Peclet number and the propulsive velocity are quantified at various field frequencies of the rotating magnetic field. The propulsive velocities are observed to be linear with the field frequencies up to a certain step-out frequency which depends on the helical structures' rotational viscous drag coefficient and the magnitude of the product of the magnetic field strength and the magnetization of the helix. In the presence of thermal fluctuations, we demonstrate that the direction of motion of nanohelices may be altered and that the helices can be guided to follow a pre-defined trajectory [2]. [1] S.T. Ollila, C. Denniston, M. Karttunen, and T. Ala-Nissila, J. Chem. Phys 134, 064902 (2011); Santtu T.T. Ollila, Cristopher J. Smith, Tapio Ala-Nissila, and Colin Denniston, Multiscale Modeling & Simulation 11, 213-243 (2013). [2] M.M.T. Alcanzare, V. Thakore, M. Karttunen, S.T.T. Ollila, and T. Ala-Nissila, Soft Matter 13, 2148 (2017); M.M.T. Alcanzare, M. Karttunen, and T. Ala-Nissila, to appear in Soft Matter (2019).

Speaker: Tapio Ala-Nissilä (Aalto and Loughborough University)

8 Stochastic Thermodynamics of Information Flow in Bipartite Systems

A thermodynamic framework of entropy and information transfers at the ensemble level has been recently formulated (Horowitz et al. PRX 4:031015, 2014) for bipartite Markovian systems, where the dynamical variables of the composite subsystems can change only one at a time. Motivated by the fact that bipartite Markovian systems are ubiquitous in biomolecular systems, e.g., in the chemo-mechanical coupling of motor proteins, etc., we generalize consistently the thermodynamics of information flow to the stochastic trajectory level in terms of notions of stochastic thermodynamics. This allows us to unveil details of the information processes, namely, entropy production, heat dissipation, information flow, etc., among the composite subsystems that were masked at the ensemble level. Moreover, I will re-exam the interpretation of information flow, a concept commonly used in the literature, by making an explicit comparison to the well-known concept of transfer entropy.

Speaker: Chun-Biu Li (SU)

9 Coffee break

10 A quantum-dot heat engine operating close to the thermodynamic efficiency limits

It has been known for some time that a perfect (delta-function) energy filter allows, in principle, thermal-to-electric energy conversion near ideal (Carnot) efficiency. [1,2] I will give an introduction to this concept and to thermoelectrics in general, focusing on reversible heat engines. Then I will focus on a recent experiment where we realized a near-ideal quantum-dot heat engine in devices based on single nanowires, realizing power production at maximum power with Curzon-Ahlborn efficiency, and reaching more than 70% of Carnot efficiency at maximum efficiency settings [3]. I will also discuss possible applications of this concept to hot-carrier solar cells. [1] Mahan, G. D., & Sofo, J. O. (1996). The best thermoelectric. Proceedings of the National Academy of Sciences of the United States of America, 93(15), 7436–7439. [2] Humphrey, T. E., Newbury, R., Taylor, R. P., & Linke, H. (2002). Reversible Quantum Brownian Heat Engines for Electrons. Physical Review Letters, 89(11), 116801. http://doi.org/10.1103/PhysRevLett.89.116801 [3] Martin Josefsson, Artis Svilans, Adam M. Burke, Eric A. Hoffmann, Sofia Fahlvik, Claes Thelander, Martin Leijnse, Heiner Linke: A quantum-dot heat engine operated close to thermodynamic efficiency limits. Nature Nanotechnology 13, 920-924 (2018)

Speaker: Heiner Linke (Lund University)

11 Efficiency fluctuations in microscopic machines

Nanoscale machines are strongly influenced by thermal fluctuations, contrary to their macroscopic counterparts. As a consequence, we need to talk about efficiency distributions and not just an average efficiency. Can such a distribution have any universal properties? In earlier work, it was shown, for a particular class of non-equilibrium systems, that, in the large time limit, this distribution always has a "universal" shape. In recent work, we have shown that if we extend this class of systems, the efficiency distribution can be one of several types. We are able to classify when and how these different types occur as well as the exact form of the efficiency distribution in each case. Joint work with Sreekanth K Manikandan, Lennart Dabelow and Ralf Eichhorn

Speaker: Supriya Krishnamurthy (SU)

Thursday, 21 March

12 Experimental support of the isomorph theory – and beyond

It is an old and open question what governs the dynamics of liquids. Particularly understanding the super-cooled liquids as they approach the glass transition and the characteristic time scales exceed experimentally accessible time scales is a challenge. The isomorph theory is an approximative theory, which has been shown to predict the dynamics of simple computer simulated liquids (e.g. LJ-systems) with surprisingly high precision, while it does not hold for complex systems with directional bonds or competing interactions [1]. In order to test the isomorph theory experimentally we have focused on van der Waals bonded glass-forming liquids. We have experimentally verified several predictions of the isomorph theory; the density scaling exponent can be found from single state-point thermo-mechanical measurements [2], the dielectric amplitude under pressure follows the isomorph prediction [3], isochronal lines in the P-T phase diagram are the same for different response functions [4], and the picosecond dynamics is invariant along alpha relaxation isochrones close to Tg [5]. Moreover, we have found that the dynamics of van der Waals bonded liquids with no visible beta relaxation is even simpler than what can be predicted from isomorph theory [4,6]: 1) the spectral shape of the alpha relaxation is independent of both temperature and pressure in a dynamical range of at least 10 decades, and 2) the alpha-relaxation time of different response functions, which probe different dynamical properties all follow the same temperature and pressure dependence. Based on this we propose that a basic (ideal-gas type) model of the dynamics of glass-forming liquids should encompass this simplicity in a natural way, while still exhibiting the dynamical hall-mark features; non-exponential spectral shape and non-Arrhenius temperature dependence of the alpha-relaxation time. REFERENCES [1] Dyre, J.C., Hidden Scale Invariance in Condensed Matter, J. Phys. Chem. B 118, 10007 (2014) [2] Gundermann, D. et al. Predicting the density scaling exponent from Prigogine-Defay ratio measurements, Nature Physics 7, 816 (2011) [3] Wence, X. et al .Isomorph theory prediction for the dielectric loss variation along an isochrone, J. Non Chryst Solid 407, 190 (2015) [4] Roed, L, Niss, K., Jacobsen, B. Communication: High pressure specific heat spectroscopy reveals simple relaxation behavior glass forming molecular liquid, J. Chem. Phys. 143, 221101 (2015). [5] Hansen, H, et al. Evidence of a one-dimensional thermodynamic phase diagram for simple glass-formers, Nature Communications 9, 518 (2018) [6] Niss, K. and Hecksher, T. Perspective: Searching for simplicity rather than universality in glass-forming liquids, J. Chem. Phys. 149, 230901 (2018).

Speaker: Kristine Niss (Roskilde University)

13 Asymptotic derivation of a higher-order beam model for tape springs

In this talk we shall discuss the localization of folds in a curved tape spring. This phenomena reveals a generalized mathematical structure with strong links to that of phase transitions, as seen in a van der Waals’ fluid, for which a fixed volume contains a mixture of liquid and vapor phases. This framework also captures phase transformations as material instabilities, whereby material non-linearities showcase non-convex energy functionals. To exemplify this idea, in the context of elasticity, we shall review a simple one-dimensional for instabilities in elastic bars, namely the Ericksen bar model. Then, we will construct a dimensionally reduced shell model in order to approach the problem of a curved tape spring. An asymptotic derivation of this model will be explained and demonstrated to be a possible tool to analyze the localization of folds.

Speaker: Marcelo Dias (Aarhus University)

14 Coffee break

15 Coupled Oscillators and Chaos in Gene Regulation

Oscillating patterns with periods of 2-5 hours have been observed for transcription factors in single cells. The oscillations appear as a response to DNA damage and other induced stresses. We have identified the central feed-back loops leading to oscillations and formulated genetic networks in terms of mathematical equations. By applying an external periodic protein signal, it is possible to lock the internal oscillation of a transcription factor to the external signal [1]. We have observed that the two signals lock when the ration between the two frequencies is close to basic rational numbers forming Arnold tongues[1]. When the tongues start to overlap we may observe mode hopping and chaotic dynamics in the concentration of proteins [1,2]. We investigate how this influences gene productions through stochastic simulations. In the chaotic regime, genes with high affinity decreases their production with increased external amplitude, while genes with low affinity increases their production [2]. [1] M.L. Heltberg, R. Kellogg, S. Krishna, S. Tay and M.H. Jensen, "Noise-induced NF-kB Mode Hopping Enables Temporal Gene Multiplexing", Cell Systems 3, p. 532–539 (2017). [2] M.L. Heltberg, S. Krishna and M.H. Jensen, "On chaotic dynamics in transcription factors and the associated effects in differential gene regulation", Nature Communication, DOI 10.1038/s41467-018-07932-1 (2019).

Speaker: Mogens Hogh Jensen (Niels Bohr Institute)

16 Neuromorphic computing with off-equilibrium oscillator networks

Oscillator networks are ubiquitous in Physics.Very different systems, From Bose-Einstein condensates to mechanical oscillators, spin systems and electrical power grids, can be described using the language of the discrete Nonlinear Schrödinger equation (DNLS). In this talk, I will show how the DNLS can be used to model a neural network for pattern recognition. An input is passed through the network, that reaches a off-equilibrium steady state and produces an output in the form of energy currents that flow between the oscillators. Different inputs are used to encode simple images (typically black and white digits), and the output is trained using standard machine learning techniques in order to discriminate between the various digits, with a recognition rate of more than 90%. This computational paradigm is called reservoir computing, where the term "reservoir" indicates any complex system able to perform information processing. The advantage of reservoir computing is that one can chose as network any nonlinear complex system, and the training is performed only at the output level, without modifying the network. This has huge advantages in terms of computational cost, so that a simple recognition problem can be performed on a laptop. The generality of the DNLS model suggests that a large class of microscopic and macroscopic systems can be used for this purpose, and the techinque employed is somewhat universal. References: Simone Borlenghi, Magnus Boman and Anna Delin, "Modelling reservoir computing with the discrete nonlinear Schrödinger equation", Phys. Rev. E 98, 052101 (2018) Stefano Iubini, Stefano Lepri and Antonio Politi, "Nonequilibrium discrete Nonlinear Schrödinger Equation", Phys. Rev. E, 86, 011108 (2012) ​Stefano Iubini, Stefano Lepri, Roberto Livi and Antonio Politi, "Off equilibrium Langevin dynamics of the discrete nonlinear Schrödinger chain", J. Stat. Mech, 2013 (2013) Mantas Lukosevicius and Herbert Jaeger, "Reservoir computing approaches to recurrent neural network training", Computer science reviews 3, 127 (2009)

Speaker: Simone Borlenghi Garoia (KTH)

17 Lunch

18 Long-distance electrodynamic interactions among biomolecules

In the first part of this talk I will report about the theoretical and experimental findings about the activation of out-of-equilibrium collective oscillations of a macromolecule as a classical phonon condensation phenomenon [Phys. Rev. X 8, 031061 (2018)]. If a macromolecule is modeled as an open system—that is, it is subjected to an external energy supply and is in contact with a thermal bath to dissipate the excess energy— the internal nonlinear couplings among the normal modes make the system undergo a nonequilibrium phase transition when the energy input rate exceeds a threshold value. This transition takes place between a state where the energy is incoherently distributed among the normal modes and a state where the input energy is channeled into the lowest-frequency mode entailing a coherent oscillation of the entire molecule. The experimental outcomes (obtained with two independent setups and performed on a model protein) are in very good qualitative agreement with the theory and provide a proof of concept of which the most significant implication is that, in compliance with another theoretical prediction [Phys. Rev. E 91, 052710 (2015)], a crucial prerequisite is fulfilled to excite intermolecular long-range electrodynamic interactions. In turn, these interactions could affect the biomolecular dynamics by contributing to drive the high efficiency and rapidity of mutual encounters of the partners of biochemical reactions in living matter. In the second part of the talk I will report on the outcomes of two other recent and independent experiments clearly showing the activation of long-range/long-distance electrodynamic interactions among biomolecules (proteins) as a consequence of the activation of out-of-equilibrium collective molecular oscillations. It has been found that the model proteins used can mutually attract at a distance as large as 1000 Angstroms, which is by far larger than all the other intermolecular interactions usually considered in action in living matter.

Speaker: Marco Pettini (Aix-Marseille University)

19 Coffee break

20 Soft Matter Meets Deep Learning

I will present an overview of recent project where we have proposed new approaches to the experimental study of active matter. In particular I will present a new algorithm for the measurement of microscopic force fields and a deep-learning approach to the tracking of microscopic particles.

Speaker: Giovanni Volpe (Gothenburg University)

21 Enhancing Fluorescence Detection with Lightguiding Nanowires

Semiconductor nanowires can act as nanoscaled optical fibers, enabling them to guide and concentrate light emitted by surface-bound fluorophores. Fluorescent emission can couple into the nanowire core due to near-field interactions and, in a free-standing nanowire, it can be guided to its tip regardless of the emitter position along the nanowire length. Harnessing this effect would potentially allow nanowires to be used as signal integrators for the fluorescence generated close to their surface, increasing the signal-to-noise ratio. Detecting the presence of fluorescently labelled molecules on free standing nanowires can be used to characterize the diffusion of molecules in a supported lipid bilayer. The simultaneous observation of hundreds of nanowires with epifluorescence microscopy allows for the determination of both concentration and diffusivity with short measurement times, as this parallel approach can be corrected for bleaching.

Speaker: Damiano Verardo (Lund University)

22 Dinner

Friday, 22 March

23 Scaling limits of random outerplanar maps

An outerplanar map is a drawing of a planar graph in the sphere which has the property that there is a face in the map such that all the vertices lie on the boundary of that face. We study the phase diagram of random outerplanar maps sampled according to non-negative weights that are assigned to each face of a map. We prove that for certain choices of weights the map looks like a rescaled version of its boundary when its number of vertices tends to infinity. The properly rescaled outerplanar maps are then shown to converge (in a precise sense) to the so-called α-stable looptree introduced by Curien and Kortchemski (2014), with the parameter α depending on the specific weight-sequence.

Speaker: Sigurdur Örn Stefansson (University of Iceland)

24 Effective Drifts in Generalized Langevin Systems

Generalized Langevin equations (GLEs) are stochastic integro-differential equations commonly used as models in non-equilibrium statistical mechanics to describe the dynamics of a particle coupled to a heat bath. From modeling point of view, it is often desirable to derive effective mathematical models, in the form of stochastic differential equations (SDEs), to capture the essential dynamics of the systems. In this talk, we consider effective SDEs describing behavior of a large class of generalized Langevin systems in the limits when natural time scales become very small. It turns out that additional drift terms, called noise-induced drifts, appear in the effective SDEs. We discuss recent progress on the phenomena of noise-induced drift in a class of systems diffusing anomalously. This is joint work with Jan Wehr and Maciej Lewenstein.

Speaker: Soon Hoe Lim (Nordita)

25 Coffee break

26 Atomic-scale sliding friction on a contaminated surface

Friction between solid surfaces is an important phenomenon in everyday life. A large portion of the total energy production in industrialised countries is lost through friction and wear. Friction is a very complex phenomenon with dynamics happening on many length and time scales. At the most basic level, however, is the dissipation at the nano-scale level. At this level, real sliding interfaces can still be fairly complex. Often, there are molecules adsorbed on the surfaces, originating from the atmosphere or additives that have been put in a lubricant to protect the surface from wear, corrosion, etc. I will discuss theoretical approaches to studying how adsorbed molecules affect the friction at the nano scale, using simple models and molecular-dynamics simulations.

Speaker: Astrid de Wijn (Norwegian University of Science and Technology)

27 Computational experiments with machine learning-based interatomic potentials: explaining the growth mechanism in amorphous carbon

Molecular dynamics (MD) simulations are a useful tool to understand the interactions between atoms and to get insight into the processes that take place at the nanoscale and give rise to the observed properties of materials. "Classical" interatomic potentials, based on i) harmonic description of bonds, ii) partial electrostatic charges and iii) Lennard-Jones approximations for dispersion interactions, are computationally efficient but do not grant accurate representation of the real underlying physics/chemistry. They tend to fail at flexibly describing molecules in changing environments, especially when there is bond rearrangement, i.e., when chemical reactions take place. Density functional theory (DFT), on the other hand, offers a satisfactory description of interatomic interactions and can be used to characterize bond formation and annihilation. Unfortunately, DFT becomes prohibitively expensive when running MD of systems beyond a few hundreds of atoms or for time scales longer than a nanosecond. To bridge this gap between computational efficiency and accuracy, algorithmic developments that make use of machine learning techniques are being adopted by the community. In this seminar, I will briefly introduce one of such approaches, the Gaussian approximation potential (GAP) framework [1]. Then I will go on to discuss two applications of this approach. In the first part of the seminar, I will present GAP simulations of amorphous carbon depositions which allowed us to explain, for the first time, how the "diamond-like" properties of dense amorphous carbon arise [2]. In the second part, I will introduce a new method that we have developed to predict adsorption energies, with application to amorphous carbon surfaces [3]. I will also present a new type of atomic descriptor which allows us to improve the predictive ability of GAP models and therefore bring them closer to full DFT accuracy [3]. [1] A.P. Bartók, M.C. Payne, R. Kondor, G. Csányi. Phys. Rev. Lett. 104, 136403 (2010). [2] M.A. Caro, V.L. Deringer, J. Koskinen, T. Laurila, and G. Csányi. Phys. Rev. Let. 120, 166101 (2018). [3] M.A. Caro, A. Aarva, V.L. Deringer, G. Csányi, and T. Laurila. Chem. Mater. 30, 7446 (2018).

Speaker: Miguel A Caro (Aalto)

28 Lunch

29 Free discussion