Dynamic Coarse-Graining and Memory Effects in Soft Matter Systems

Dynamic Coarse-Graining and Memory Eﬀects in Soft Matter Systems

October 25, 2018 - October 26, 2018 Hermann-Staudinger Lecture Hall MPIP Mainz, Germany

Gerhard Jung Johannes Gutenberg University Mainz, Germany [email protected]

Dominika Leśnicki Sorbonne Université, France [email protected]

Contents

1 General Information 4

2 Workshop Description 6

3 Program 9

4 Abstracts: Talks 12

5 Abstracts: Posters 27

6 List of Participants 41

3 1 General Information Venue

Max Planck Institute for Polymer Research Room: Hermann Staudinger Lecture Hall Address: Ackermannweg 10, 55128 Mainz, Germany

To get there from Mainz train station: Tram lines number 51 and 53 (direction Lerchenberg/Hindemithstraße) Tram number 51 departs from platform A, number 53 from platform L. Get oﬀ at the stop "Hochschule Mainz". The institute can be reached after a two-minute walk across Koblenzer Straße into Ackermannweg.

4 Social Dinner

Heiliggeist Rentengasse 2 55116 Mainz

Map

5 2 Workshop Description

Whether we consider small or large molecules, nanoparticles or colloids, all objects suspended in a fluid evolve in conjunction with this fluid. In general, we are only interested in the dynamics of these molecules and not in the details of the fluid flow. Therefore, we describe the effect of the fluid only implicitly, through friction and random forces. The Brownian movement model, introduced by Einstein more than a century ago, applies well when the objects in question relax very slowly in relation to their environment. Or, in other words, if a time scale separation between the dynamics of the large molecules and the fluid can be assumed. However, in general, the effect of the fluid is not instantaneous [1,2]. The movement of the molecules in the fluid will induce a disturbance of the flow field that affects the movement of other molecules or themselves. The latter is also known as the hydrodynamic backflow effect and usually described by a frequency-dependent friction term in the equations of motion for the solute [3]. One prominent consequence of this “memory effect” is the slow (algebraic) decrease in certain properties, such as the velocity autocorrelation function [1]. This is only one of many examples in soft matter physics, where frequency- dependent phenomena and memory effects can be observed [4-7]. In the present workshop, we address the general problem of dynamic coarse-graining in situations where the separation of time scales is incomplete. This includes the general analysis of frequency-dependent phenomena in soft matter systems using experiments, theory or computer simulations [4,8,9], as well as the detailed discussion of methods that can be used for systematic dynamic coarse-graining [10-18].

6 The purpose of this workshop is to bring together scientists with very diﬀerent background that work or have worked on non-Markovian dynamics and dynamic coarse-graining. Since the community in this special area of research is still very small, we hope, that the workshop can stimulate discussions and ideas for future research topics. The need of advanced theoretical understanding and coarse-graining techniques is especially important due to the emerging ﬁelds of active particles and nonequilibrium statistical physics. The workshop takes place in Mainz, Germany, where two large condensed matter groups are located: The condensed matter research group at University of Mainz, Komet1/2, headed by Prof. Friederike Schmid and the theory group of MPIP, headed by Prof. Kurt Kremer. This event is organized in the scope of our research project SFB TRR146 (https://trr146.de) of the German Science Foundation about "Multiscale Simulation Methods for Soft Matter Systems".

References [1] B. J. Alder and T. E. Wainwright, Phys. Rev. A 1, 18 (1970). [2] J. T. Padding and A. A. Louis, Phys. Rev. E 74, 031402 (2006). [3] A. B. Basset, A Treatise on Hydrodynamics: With Numerous Examples (Deighton, Bell and Co., Cambridge, 1888). [4] T. Franosch, M. Grimm, M. Belushkin, F. M. Mor, G. Foﬃ, L. Forro, and S. Jeney, Nature 100, 85 (2011). [5] A. Carof, V. Marry, M. Salanne, J.-P. Hansen, P. Turq, and B. Rotenberg, Mol. Simul. 40, 237 (2014). [6] B. Cui, J. Yang, J. Qiao, M. Jiang, L. Dai, Y.-J. Wang, and A. Zaccone, Phys. Rev. B 96, 094203 (2017). [7] M. Schmidt, J. Chem. Phys. 148, 044502 (2018). [8] A. V. Mokshin, R. M. Yulmetyev, and P. Hänggi, Phys. Rev. Lett. 95, 200601 (2005). [9] G. Jung and F. Schmid, Phys. Fluids 29, 126101 (2017). [10] M. Ceriotti, G. Bussi, and M. Parrinello, J. Chem. Theory Comput. 6, 1170 (2010). [11] H. K. Shin, C. Kim, P. Talkner, and E. K. Lee, Chem. Phys. 375, 316 (2010).

7 [12] C. Hijón, P. Español, E. Vanden-Eijnden, and R. Delgado-Buscalioni, Faraday Discuss. 144, 301 (2010). [13] A. Carof, R. Vuilleumier, and B. Rotenberg, J. Chem. Phys. 140, 124103 (2014). [14] D. Lesnicki, R. Vuilleumier, A. Carof, and B. Rotenberg, Phys. Rev. Lett. 116, 147804 (2016). [15] G. Deichmann, V. Marcon, and N. F. A. van der Vegt, J. Chem. Phys. 141, 224109 (2014). [16] Z. Li, H. S. Lee, E. Darve, and G. E. Karniadakis, J. Chem. Phys. 146, 014104 (2017). [17] G. Jung, M. Hanke, and F. Schmid, J. Chem. Theory Comput. 13, 2481 (2017). [18] H. Meyer, T. Voigtmann, and T. Schilling, The Journal of Chemical Physics 147, 214110 (2017).

8 3 Program - Day 1 - 09:00 - 09:50 Registration 09:50 - 10:00 Welcome

Session 1: Introduction to Mori-Zwanzig and Memory Eﬀects

10:00 - 10:55 Burkhard Dünweg Introduction to the Mori-Zwanzig formalism 11:00 - 11:40 Tanja Schilling The non-stationary Langevin equation

11:45 - 12:45 Lunch

Session 2: Memory Eﬀects in Soft Matter Sytems I

12:50 - 13:30 Pep Español Memory in hydrodynamics near walls 13:35 - 14:15 Michele Ceriotti Fine-grained control of sampling and dynamics in molecular simulations with colored noise 14:20 - 14:55 Friederike Schmid Generalized Langevin dynamics and iterative reconstruction of memory kernels

15:00 - 17:00 Poster Session & Coﬀee Break

9 Session 3: Memory Eﬀects in Soft Matter Sytems II

17:05 - 17:45 Francisco Vega Reyes Memory eﬀects in transitory states of the same size as the stationary value, detected in granular matter

Session 4: Dynamic Coarse-Graining in a More General Framework

17:50 - 18:30 Martin Oberlack Group invariant modeling - construction of coarse-grained / eﬀective models from lie symmetries

19:30 - 23:00 Social Dinner

10 - Day 2 - 09:00 - 09:25 Coﬀee

Session 5: Memory Eﬀects in Colloidal Systems and Hydrodynamics

09:30 - 10:10 Rafael Delgado-Buscalioni Memory in the collective diﬀusion of partially conﬁned systems: colloids and lipid membranes 10:15 - 10:55 Rodolphe Vuilleumier Molecular Hydrodynamics 11:00 - 11:40 Nico van der Vegt Mori-Zwanzig dissipative particle dynamics models for molecular coarse-grained mappings

11:45 - 12:55 Lunch

Session 6: Memory Eﬀects in a More General Framework

13:00 - 13:40 Alessio Zaccone Generalized Langevin Equation modelling of viscoelastic and dielectric properties of glasses 13:45 - 14:25 Matthias Schmidt Power functional theory for many-body dynamics

14:30 - 14:40 Closing Word 14:40 - 15:30 Coﬀee

11 4 Abstracts: Talks

12 Introduction to the Mori-Zwanzig formalism Burkhard Dünweg Max Planck Institute for Polymer Research, Germany

The lecture will outline the basic steps to derive the Mori Zwanzig memory equation, and illustrate its application to derive some well- known Green-Kubo relations. The formalism quite generally aims at deriving eﬀective equations of motion for slow degrees of freedom, which often involves to study the system not only on large time scales, but on large length scales as well.

Reference [1] J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids, Elsevier Science (1990)

13 The non-stationary Langevin equation Tanja Schilling Albert Ludwigs Universität, Germany

Coauthors : H. Meyer1, T. Voigtmann2 [1] Research Unit in Engineering Science, Université du Luxembourg, [2] Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany, Department of Physics

In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble (“bundle”) of trajectories. Un- der stationary conditions, the time-evolution of such averages is described by the generalized Langevin equation. By contrast, if the dynamics is not stationary, it is not a priori clear which form the equation of motion for an averaged observable has. We employ the formalism of time-dependent projection operator techniques to derive the equation of motion for a non-equilibrium trajectory-averaged observable as well as for its non-stationary auto-correlation function. The equation is similar in structure to the generalized Langevin equation but exhibits a time-dependent memory kernel as well as a fluctuating force that implicitly depends on the initial conditions of the process. We also derive a relation between this memory kernel and the autocorrelation function of the fluctuating force that has a structure similar to a fluctuation-dissipation relation. In addition, we show how the choice of the projection operator allows us to re- late the Taylor expansion of the memory kernel to data that are accessible in MD simulations and experiments, thus allowing us to construct the equation of motion. As a numerical example, the procedure is applied to Brownian motion initialized in non-equilibrium conditions and is shown to be consistent with direct measurements from simulations.

14 Memory in hydrodynamics near walls Pep Español National University of Distance Education, Spain

We have derived within the Mori-Zwanzig projection operator method the hydrodynamic equations for a fluid that interacts with a solid wall. This constitutes a formulation of Dynamic Density Functional Theory for simple fluids. In order to address problems from a computational point of view, the equations are discretized in planar flow geometries by using thin slabs. The resulting discrete hydrodynamic equations contain non-local viscosity terms, as well as forces due to the solid which are confined near the walls. Quite annoyingly, the Green-Kubo expressions display a very pronounced plateau problem. We device a new Green-Kubo expression that allows to obtain the transport coefficients even when the Green-Kubo expression does not have a plateau, provided that the dynamics is truly Markovian. Quite remarkably, we observe that near the walls the dynamics is not Markovian and a local in time hydrodynamics is not applicable. Only when the bins are sufficiently large, we recover a Markovian dynamics. However, the density layering near the walls is completely blurred for these large bins. This suggests that a proper account of the dynamics of the density near the wall requires the introduction of viscoelasticity.

15 Fine-grained control of sampling and dynamics in molecular simulations with colored noise Michele Ceriotti École Polytechnique Fédérale de Lausanne, Switzerland

Molecular dynamics provides an efficient, general framework to probe the thermodynamic and dynamical properties of matter at finite temperature. The Langevin equation has been used for a long time as a device to achieve sampling that is consistent with a classical Boltzmann distribution. I will discuss how a framework based on a generalized Langevin Equations can be used to exquisitely control the sampling behavior of a molecular dynamics trajectory, so as to converge averages more efficiently, but also to include quantum mechanical fluctuation effects. Furthermore I will show that the considerable disruption to the dynamical properties that is typically introduced by Langevin dynamics can be controlled and corrected to a large extent within this framework.

16 Generalized Langevin dynamics and iterative reconstruction of memory kernels Friederike Schmid Johannes Gutenberg University, Germany

Coauthor: G. Jung1 [1] Johannes Gutenberg University, Institute of Physics, Mainz, Ger- many.

In recent years it has become increasingly popular to construct coarse-grained models with non-Markovian dynamics in order to account for an incomplete separation of time scales. One challenge for systematic coarse-graining is to extract the coarse-grained dynamical equations, namely the memory kernel, from equilibrium all- atom simulations. Another challenge is to devise an algorithm that efficiently deals with pair-memory contributions to the dynamical equations. Such pair-memory interactions may become important, e.g., in dispersions of nanocolloids when the frequency dependence of hydrodynamic interactions cannot be neglected. The talk will address these two problems. In the first part, an iterative method for the reconstruction of memory kernels from dynamic correlation functions will be presented. Compared to previ- ously proposed non-iterative techniques, it ensures by construction that the target correlation functions of the original fine-grained systems are reproduced accurately by the coarse-grained system, taking into account the time step in the coarse-grained system. In the sec- ond part, a "generalized Langevin Dynamics" model is proposed for non-Markovian particle-based models, which has the form of a generalized Langevin equation with distance-dependent two-particle contributions to the self- and pair-memory kernels. A simulation algorithm is developed for this class of non-Markovian models that scales linearly with the number of coarse-grained particles.

17 We have applied the method to a suspension of nanocolloids with frequency-dependent hydrodynamic interactions. The results from GLD simulations perfectly reproduce the dynamics of the underly- ing ﬁn ne-grained System and are faster by a factor of roughly 10.000.

References [1] G. Jung, M. Hanke, F. Schmid, Iterative reconstruction of Memory kernels, J. Chem. Theory Comput. 13, 2481 (2017). [2] G. Jung, F. Schmid, Frequency-dependent Hydrodynamic Interaction Between Two Solid Spheres, Phys. Fluids 29, 126101 (2017). [3] G. Jung, M. Hanke, F. Schmid, Generalized Langevin dynamics: Construction and numerical integration of non-Markovian particle-based models, submitted (2018).

18 Memory eﬀects in transitory states of the same size as the stationary value, detected in granular matter Francisco Vega Reyes Universidad de Extremadura, Spain

Coauthors : A. Lasanta1, A. Prados2 and A. Santos3 [1] Universidad Carlos III de Madrid, Leganés, Spain; [2] Universidad de Sevilla, Spain; [3] Universidad de Extremadura, Spain.

We study in this work a granular fluid, when subject to a steep thermal pulse and stabilized to an intermediate granular temperature after a waiting time. We show that is possible to observe temperature humps that imply a relative transitory deviation as large as 100% when compared to the eventual stationary value. We report our results via three independent methods: perturbative analytical solution of the corresponding kinetic equation, exact solution (DSMC method) of the kinetic equation and molecular dynamics simulations. These 3 methods yield the same behavior of the thermal memory effects. The perturbative analytical solution allows us to discuss on the physical origin of these giant memory effects. It also allows for identification of a route to giant memory effects in a generic physical system.

Reference [1] A. Lasanta, F. Vega Reyes, A. Prados, and A. Santos, ‘On the emergence of large and complex memory eﬀects in non-equilibrium ﬂuids’, in preparation (2018).

19 Group invariant modeling - construction of coarse- grained / eﬀective models from Lie symmetries Martin Oberlack Technische Universität Darmstadt, Germany

Symmetries represent the central axiomatic basis in all physics, and they can be calculated from the fundamental equations. In many cases this process can be inverted, i.e. initial equations can be generated from the symmetries (invariant modelling). Since symmetries simultaneously represent central physical properties, it is obvi- ous that these properties should also be preserved in coarse-grained models. Recent work in turbulence research has shown that the process of coarse-graining preserves the classical symmetries of the original equation, but at the same time induces further symmetries into the resulting effective equation. On the one hand, it is shown that these new symmetries of the effective model have an important physical significance and can also be used to generate dimension- ally reduced effective model equations. Since both dimensions and symmetries have to be "selected", models with predefined physical properties may be generated.

20 Memory in the collective diﬀusion of partially con- ﬁned systems: colloids and lipid membranes Rafael Delgado-Buscalioni Autonomous University of Madrid , Spain

I will discuss the different regimes observed in quasi-two dimensional diffusion of particles moving in a plane which is embedded in a 3d solvent. The problem is illustrated with the case of the collective diffusion of lipid membranes. I will present results for the mutual displacement correlation between lipids to illustrate how the mobility changes over time. I will show that the Saffmann-Delbruck picture does not hold at short times (<10 ns), where the inertial and enhanced diffusion regimes are determinant, being controlled by the solvent hydrodynamics.

21 Molecular Hydrodynamics Rodolphe Vuilleumier École Normale Supérieure, France

We have derived and implemented an algorithm to extract Mori- Zwanzig (MZ) memory kernels from molecular dynamics simulations. We have then studied the Mori-Zwanzig kernel for a tagged particle in a ﬂuid. It is shown that the MZ kernel possesses a long- time tail as does the velocity autocorrelation function and show how the hydrodynamic Basset-Boussinesq force naturally emerges from it. By generalizing the concept of added mass, it is then possible to reproduce the measured MZ kernel over a large range of time-scales. We further discuss the crossover between molecular and hydrodynamic regimes by directly studying the ﬂow of particles around the tagged particle.

22 Mori-Zwanzig dissipative particle dynamics models for molecular coarse-grained mappings Nico van der Vegt Technische Universität Darmstadt, Germany

Coauthor: G. Deichmann1 [1] TU Darmstadt, Germany.

The derivation of force ﬁelds based on statistical mechanical coarse-graining methods is well established. Some of these methods naturally combine with the Mori-Zwanzig projection operator formalism, which provides a generalized Langevin equation for the time evolution of the slow degrees of freedom determined by the mapping scheme employed. We have implemented a variant of the Mori- Zwanzig dissipative particle dynamics (MZ-DPD) method, which approximates the potential of mean force with pairwise-additive con- ditional reversible work (CRW) or eﬀective force coarse graining (EFCG) interactions. I will discuss the applicability and limitations of this method to coarse-grained models that keep close link to the chemistry. The dynamics of “united-atom type” coarse-graining models is discussed in which consecutively linked beads are mapped onto small groups of atoms within a larger (macro)molecule.

23 Generalized Langevin Equation modelling of viscoelastic and dielectric properties of glasses Alessio Zaccone University of Cambridge, United Kingdom

The linear response of glasses is a topic of fundamental rele- vance in condensed matter physics, and also has plenty of applications in materials science and engineering. At present there is no theory which can describe the response of glasses well below the glass transition temperature. The validity of Mode-Coupling theory is limited to supercooled liquids above Tg, whereas other theories such as replica-based theories are valid only for large-dimensional systems. We recently developed a new approach to the linear response of glasses from first principles. Starting from a particle-bath Hamiltonian we derive a Generalized Langevin equation of motion for atomic displacements under an external field (which can be ei- ther dc or ac). This leads directly to analytical expressions for the complex moduli (for e.g. viscoelastic or dielectric response) which involve the vibrational density of states (DOS) of the glass, together with a memory kernel for the friction. While the DOS can be measured experimentally or in simulations, the memory kernel has to be gauged in a phenomenological way resorting to previous results in kinetic theory. Results of framework predictions in comparison with experimental data on different systems are shown, which are able to recover the hallmarks of glassy response, such as alpha and beta relaxation and elucidate the effect of various features in the DOS on the observed response spectra.

References [1] B Cui, J. Yang, J. Qiao, M. Jiang, L. Dai, Y.-J. Wang, A. Zaccone. Atomic theory of viscoelastic response and memory eﬀects in metallic glasses. Physical Review B 96, 094203 (2017). [2] B. Cui, J. Gebbia, J.-L. Tamarit, A. Zaccone. Disentangling alpha and beta relaxation in orientationally disordered crystals with theory and experiments. Physical

24 Review E 97, 053001 (2018). [3] B. Cui and A. Zaccone. Generalized Langevin Equation and ﬂuctuation-dissipation theorem for particle-bath systems in external oscillating ﬁelds. Physical Review E 97, 060102(R) (2018). [4] B. Cui, R. Milkus, and A. Zaccone. Direct link between boson-peak modes and dielectric alpha-relaxation in glasses. Physical Review E 95, 022603 (2017).

25 Power functional theory for many-body dynamics Matthias Schmidt Universität Bayreuth, Germany

I give an overview of a recent, formally exact framework for describing nonequilibrium many-body dynamics on the one-body level of correlation functions, i.e. the density proﬁle and the current distribution1−6. The theory is based on an exact extremal principle of minimization of the (unique) free power functional with respect to the current, in the case of overdamped Brownian dynamics6. In classical1 and quantum5 Hamiltonian systems, the minimization principle holds for the time derivative of the current. Density functional theory is derived as the equilibrium limit of power functional theory. Applications include the study of viscous3 and structural forces that occur in inhomogeneous shear ﬂow, where excellent agreement with Brownian Dynamics computer simulation data is obtained. I discuss in particular application to out-of-equilibrium Molecular Dynamics.

References [1] Power functional theory for Newtonian many-body dynamics, M. Schmidt, J. Chem. Phys. 148, 044502 (2018). [2] Better than counting: Density proﬁles from force sampling, D. de las Heras and M. Schmidt, Phys. Rev. Lett. 120, 218001 (2018) (Editors’ Suggestion). [3] Velocity gradient power functional for Brownian dynamics, D. de las Heras and M. Schmidt, Phys. Rev. Lett. 120, 028001 (2018). [4] Nonequilibrium phase behaviour from minimization of free power dissipation, P. Krinninger, M. Schmidt, and J. M. Brader, Phys. Rev. Lett. 117, 208003 (2016); Erratum 119, 029902 (2017). [5] Quantum power functional theory for many-body dynamics, M. Schmidt, J. Chem. Phys. 143, 174108 (2015). [6] Power functional theory for Brownian dynamics, M. Schmidt and J. M. Brader, J. Chem. Phys. 138, 214101 (2013).

26 5 Abstracts: Posters

27 Memory eﬀects in the Fermi-Pasta-Ulam Model Graziano Amati University of Freiburg, Germany

We study the intermediate scattering function of the Fermi-Pasta- Ulam Model by means of coarse-graining techniques derived via projection operator formalism as well as molecular dynamics simulations. For a strongly anharmonic interaction potential, the simulations show that the relaxation time of density correlations to their equilibrium value depends sensitively on the system’s temperature. We present a recursive method for an exact reconstruction of the time evolution of the function; its dynamics can be associated to a Generalized Langevin Equation, whose memory kernel is estimated with a cross analytical and numerical approach.

Reference [1] G. Amati, H. Meyer, T. Schilling, https://arxiv.org/pdf/1806.06210.pdf

28 Dynamic coarse-graining and memory eﬀects in soft matter systems Antoine Carof École Normale Supérieure, France

Modelling macroscopic diffusion and transport in porous materials requires a coarse-grained description. In the case of the diffusion of ions in hydrated clay particle, such coarse-grained description is generally: (i) a rigid clay framework and (ii) and a fast relaxing water. Those assumptions lead to a Markovian dynamics for the ion [1]. But the idea of a fast relaxing water originates from bulk properties, whereas the fluid dynamics can be dramatically altered in a small pore, questioning the validity of the time scale separation necessary for a Markovian modelisation. The verification of the time scale seperation is a difficult task, because only the motion of water actually coupled to the ion diffusion should be taken into account. The framework of the generalized Langevin equation and the Mori-Zwanzig projection theory provides a formally exact tool to define a so-called memory kernel, where all time scale information is encoded [2]. Extracted the memory kernel from molecular dynamics simulation proved to be a difficult task. We developed an algorithm to calculate the memory kernel from molecular dynamics simulation [3]. Our algorithm also permits the decomposition of the memory kernel in different contribution, to probe the role and the time scale of the different environments around the ion. We apply this strategy to the diffusion of cesium ion in a small porosity in clay [4]. We highlight that the water is much slower than in the bulk and forms cages that trap the cesium ion. The cesium dynamics is not Markovian but rather a site-to-site hopping.

References [1] B. Rotenberg, V. Marry, JF Dufrêche, E. Giﬀaut, P. Turq, J. Collid Interface Sci. 2007, 309 [2] R. Zwanzig, Nonequilibrium statistical mechanics, 1st ed. Oxford, Oxford Uni-

29 versity Press, 2001 [3] A. Carof, R. Vuilleumier, B. Rotenberg, J. Chem. Phys., 140, 12, 2014 [4] A. Carof, V. Marry, M. Salanne, JP Hansen, P. Turq, B. Rotenberg, Mol. Sim., 40, 1-3, 2014

30 Phase coexistence in active Brownian particles Sophie Hermann Universität Bayreuth, Germany

Coauthors: Philip Krinninger, Daniel de las Heras and Matthias Schmidt

We investigate motility-induced phase separation that occurs in active Brownian particles, modelled as repulsive spheres that are driven out of equilibrium by a swimming force of constant magnitude and freely diffusing orientation. We compare Brownian dynamics computer simulation data for the structure of the free interface between the two bulk phases against the predictions of an analytical interfacial model [1], which extends [2-6]. The physical effects that occur both at the interface and in bulk are rationalized, and results for the inhomogeneous density, current and polarization profile are presented.

References [1] P. Krinninger, S. Hermann, D. de las Heras and M. Schmidt (to be published) [2] M. Schmidt and J. M. Brader, J. Chem. Phys. 138 214101 (2013) [3] P. Krinninger, M. Schmidt and J. M. Brader, Phys. Rev. Lett. 117 208003 (2016); Erratum 119 029902 (2017) [4] S. Hermann and M. Schmidt, Soft Matter 14 1614 (2018) [5] P. Krinninger and M. Schmidt (to be published) [6] D. de las Heras and M. Schmidt, Phys. Rev. Lett. 120 028001 (2018)

31 Improved dynamics in self-consistent ﬁeld molecular dynamics simulations of polymers Andreas Kalogirou Technische Universität Darmstadt, Germany

There is a long-standing research interest in multiscale simulations of polymers and nanocomposites. Furthermore there is a need for methods, which are fast and accurate at the same time. The Self Consistent Field Molecular Dynamics (hPF) method evaluates the non-bonded interactions with density ﬁelds resulting in a tunable coarse grained resolution at low computational costs. The lack of hard-core repulsions and entanglements though, leads to chain cross- ing. By combining Slip-Springs, temporary bonds between chains, with DPD we had been successful to repair the entanglement deﬁcit. Our goal is to combine hPF with Slip-Springs to a new method which restores the entanglement dynamics.

32 Non-equilibrium Generalized Langevin Equations Hugues Meyer University of Luxembourg, Luxembourg

Coauthors: Graziano Amati and Tanja Schilling Albert-Ludwigs Universität Freiburg

In statistical physics, one frequently wants to simplify the study of a process involving a large number of degrees of freedom into the description of a set of observables that capture the state of a system at a larger time and length-scale. In biology for instance, one commonly describes the evolution of the global shape of a protein without specifying the positions of all its atoms. These upscaling methods are called coarse-graining procedures and have been widely studied over many decades. In more general terms, a systematic way to derive an equation of motion for an arbitrary phase-space observable from the microscopic dynamics and known as the Mori- Zwanzig formalism exists for equilibrium processes ands leads to the Generalized Langevin Equation. We adapt here this formalism in non-equilibrium situations, namely in non-stationary processes as well as in driven systems. We show that the global structure for the equation of motion is quite robust to any kind of phenomena, although the various quantities involved in it have diﬀerent contributions. In particular we focus on the so-called memory kernel for which we sketch a simple method to estimate its timescales and allows to assess Markovian assumptions. Finally, we show concrete examples in which these concepts are implemented, namely the FPU problem and the study of nucleation and growth.

Reference [1] Meyer, H., Voigtmann, T. and Schilling, T. (2017). On the non-stationary generalized Langevin equation. The Journal of chemical physics, 147(21), 214110.

33 Phase diagram and dynamical properties of micellar solutions from DPD simulations Maria Panoukidou University of Manchester, United Kingdom

Coauthor: Carbone Paola1 [1] School of Chemical Engineering and Analytical Sciences, Univer- sity of Manchester, UK

Surfactants are used for many purposes in many commercial products since they undergo a variety of physicochemical behaviour. The addition of salt into the mixture results to surfactants self- aggregation into micelles. Different salt concentration leads to different microstructure and thus many of the systems’properties are affected among which is viscosity. In the current study the temperature specific phase diagram of a micellar solution is obtained using DPD simulations for different salt concentrations while an updated Green- Kubo relation is used for viscosity calculations.

34 Towards custom ﬂow in many-body dynamics Johannes Renner University Bayreuth, Germany

Coauthor: Daniel de las Heras and Schmidt Matthias

We present an iterative scheme for the determination of the unique external force field that yields a prescribed inhomogeneous stationary flow in an overdamped Brownian many-body system. The computer simulation method is based on the exact one-body force balance equation and allows to specifically tailor both gradient and rotational velocity contributions, as well as to freely control the one- body density distribution. Hence compressibility of the flow field can be fully adjusted. The practical convergence to a unique external force field demonstrates the existence of a functional map from both velocity and density to external force field, as predicted by the power functional variational framework. In equilibrium, the method allows to find the conservative force field that generates a prescribed target density profile, and hence implements the Mermin-Evans classical density functional map from density distribution to external potential. Using this method we analyse time-dependent situations in molecular dynamics by splitting the internal force field into equilibrium adiabatic, Brownian superadiabatic, and super-Brownian contributions.

35 Excess entropy scaling relations and the dynamics of coarse-grained polymer models Gustavo Rondina Technische Universität Darmstadt, Germany

Coarse-graining modeling is a very successful multiscale method in the field of molecular dynamics. It makes it possible to simulation system that are considerably larger in size with respect to fully atomistic systems, and for times that are impossible to reach with all-atom models. The reason for such enhancements is that degrees of freedom that are considered less important are eliminated from the model upon corase-graining, leading to a reduction of the number of interaction sites. As a consequence, molecular friction is removed from the system and the dynamics is greatly accelerated. Even though this accelerated dynamics is favorable and even desir- able in terms of enabling investigation of larger length scales and longer time scales, it affects dynamical properties that are extracted from the simulations and thus make comparison of such quantities to experimental data impossible. For example, self-diffusion coefficients of coarse-grained systems are increased by up to three orders of magnitude with respect to the corresponding atomistic system and experimental values. Other dynamical properties such as shear viscosities or bond relaxation times are also heavily influenced. The lack of accurate dynamics is not only scientifically unsatisfactory but precludes the aplication of multiscale concepts to predictive calcu- lation of technologically important dynamical and transport properties, such as rheological properties that play a key role for ex- trusion and injection molding of polymer melts. In this work the question addressed is whether the artificially accelerated dynamics of coarse-grained models can be quantified in terms of the variation of excess entropy between bead-spring polymer models at different resolutions.

36 Understanding three-body contributions to coarse- grained force ﬁelds Christoph Scherer Max Planck Institute for Polymer Research, Germany

Coauthor: Denis Andrienko

Coarse-graining (CG) is a systematic reduction of the number of degrees of freedom (DOF) used to describe a system of interest. CG can be thought of as a projection on the CG DOF and is therefore dependent on the number and type of CG basis functions. We present an extension of the two-body basis set with three-body basis functions of the Stillinger-Weber (SW) type with a flexible angular potential. The CG scheme is implemented in the VOTCA- CSG toolkit [1]. We show that those many-body extensions of the coarse-grained force field can result in substantial changes of the two-body interactions, making them much more attractive at short distances. This interplay can be alleviated by first parametrizing the two-body potential and then fitting the additional three-body contribution to the residual forces. The approach is illustrated on liquid water where three-body interactions are essential to reproduce the structural properties, and liquid methanol where two-body interactions are sufficient to reproduce the main structural features of the atomistic system. Furthermore, we demonstrate that the structural and thermodynamic accuracy of the coarse-grained models can be controlled by varying the magnitude of the three-body interactions. Our findings motivate basis set extensions which separate the many- body contributions of different order. A possible approach into this direction is the application of machine learning (ML) techniques.

Reference [1] Raehle, Junghans, Lukyanov, Kremer, Andrienko, JCTC, 5, 3211 (2009)

37 Equations of motion for generalized coarse-grained particles obtained from Mori-Zwanzig projection Mark Thachuk University of British Columbia, Canada

Coauthor: Hudson Lynn

In the present work, a generalized CG mapping procedure is presented that allows for atomistic particles to be assigned to more than a single CG particle at the same time, and allows for this mapping to change in time. Mori-Zwanzig projection operator techniques are then used to derive the equations of motion corresponding to this generalized mapping. It produces a generalized Langevin equation with the appropriate dissipative and random forces, along with a prescription for obtaining the correct CG potential. In addition to familiar terms, the generalized equation also has forces arising from the mapping itself. That is, the change of the mapping with time produces forces that in turn affect the particle motions. Examples of different applications of the generalized mapping are given. In particular, it should be very useful for describing solvents, since many independent solvent molecules can be grouped together to form larger, fluid-like CG particles, with individual molecules being allowed to flow into and out of particular CG particles as time progresses. The generalized equation forms a fundamental basis upon which a wide variety of CG mapping schemes can be systematically described, all the while producing a correct formulation for evaluating the corresponding CG potentials, and the dissipative and random forces necessary for obtaining the correct dynamical description of the CG system.

38 Nonlocal memory in power functional theory for a hard sphere liquid Lucas L. Treﬀenstädt Universität Bayreuth, Germany

Coauthors : Matthias Schmidt

We study the Brownian dynamics of a hard sphere liquid under inhomogeneous shear. Event driven Brownian dynamics simulation [1] (BD) gives us a benchmark to evaluate different models for memory effects in power functional theory [2] (PFT). We examine both the steady state under constant step shear and the dynamics after switching-off of the shearing force. We obtain good aggreement between BD and PFT with a spatially nonlocal Gaussian-Exponential memory model in steady state. We observe a surprising switching-off effect in BD which is readily reproduced and explained by the same memory model in PFT. We discuss the relationship of our findings with recent investigations of memory in systems governed by Molec- ular Dynamics [3,4].

References [1] A. Scala, T. Voigtmann, and C. De Michele, J. Chem. Phys 126.13 134109 (2007) [2] M. Schmidt, and J. M. Brader, J. Chem. Phys. 138.21 214101 (2013) [3] G. Jung, M. Hanke, and F. Schmid, J. Chem. Theory Comput. 13.6 2481-2488 (2017) [4] D. Lesnicki, R. Vuilleumier, A. Carof and B. Rotenberg, PRL 116 147804 (2016)

39 Generalized Langevin Dynamics: construction and integration of non-Markovian models Gerhard Jung Johannes Gutenberg-Universität Mainz, Germany

Coauthors : Martin Hanke and Friederike Schmid

We have recently developed a tool kit called "Generalized Langevin Dynamics" that enables the reconstruction and integration of non- Markovian particle-based models. The former is achieved using the "Iterative Memory Reconstruction", an iterative algorithm that ensures by construction that the target dynamic correlation functions of a ﬁne-grained system are accurately reproduced in the coarse- grained model [1]. The integration algorithm is based on the generalized Langevin equation, including non-Markovian dissipative interactions via memory kernels and cross-correlated, coloured noise [2]. This poster is strongly related to the invited talk "Generalized Langevin Dynamics and Iterative Reconstruction of Memory Ker- nels" given by Friederike Schmid. With the poster we want to highlight the important properties and limitations of the developed al- gorithms and clarify any open questions.

References [1] G. Jung, M. Hanke, F. Schmid, Iterative reconstruction of Memory kernels, J. Chem. Theory Comput. 13, 2481 (2017). [2] G. Jung, M. Hanke, F. Schmid, Generalized Langevin dynamics: Construction and numerical integration of non-Markovian particle-based models, submitted (2018).

40 Superadiabatic forces in overdamped Brownian Dy- namics Daniel de las Heras University of Bayreuth, Germany

Coauthors : Philip Krinninger, Thomas Geigenfeind, Lucas Tref- fenstädt, Johannes Renner, Sophie Hermann, Tobias Eckert, Nico Stuhlmüller, and Matthias Schmidt

Power functional theory [1] (PFT) is an exact generalization of equilibrium density functional theory to nonequilibrium overdamped Brownian dynamics. In PFT the exact dynamics is described by a unique time-dependent power functional of both the one-body density distribution and the one-body current. We present approxi- mated power functionals that accurately reproduce several dynamical processes in colloidal systems.

References [1] M. Schmidt and J. M. Brader, J. Chem. Phys. 138, 214101 (2013).

41 6 List of Participants

Amati, Graziano University of Freiburg, Germany [email protected] Carof, Antoine École Normale Supérieure, France [email protected] Ceriotti, Michele École Polytechnique Fédérale de Lausanne, Switzerland michele.ceriotti@epﬂ.ch de las Heras, Daniel Universität Bayreuth, Germany [email protected] Delgado-Buscalioni, Rafael Autonomous University of Madrid, Spain [email protected] Deußen, Benjamin Technische Universität Darmstadt, Germany [email protected] Dünweg, Burkhard Max Planck Institute for Polymer Research, Germany [email protected] Español, Pep National University of Distance Education, Spain pep@ﬁsfun.uned.es Hermann, Sophie Universität Bayreuth, Germany [email protected] Jabbari-Farouji, Sara Johannes Gutenberg-Universität Mainz, Germany [email protected] Jung, Maike Johannes Gutenberg-Universität Mainz, Germany [email protected] Kalogirou, Andreas Technische Universität Darmstadt, Germany [email protected] Klippenstein, Viktor Technische Universität Darmstadt, Germany [email protected] Lukacova, Maria Johannes Gutenberg University, Germany [email protected] Mebwe Pachong, Stanard Max Planck Institute for Polymer Sciences, Germany [email protected] Meyer, Hugues University of Luxembourg, Luxembourg [email protected] Morozova, Tatiana Johannes Gutenberg-Universität Mainz, Germany [email protected] Oberlack, Martin Technische Universität Darmstadt, Germany [email protected] Panoukidou, Maria University of Manchester, UK [email protected] Pelagejcev, Philipp Albert-Ludwigs-Universität Freiburg, Germany [email protected]

42 Renner, Johannes Universität Bayreuth, Germany [email protected] Rondina, Gustavo Technische Universität Darmstadt, Germany [email protected] Rosenberger, David Technische Universität Darmstadt, Germany [email protected] Scherer, Christoph Max Planck Institute for Polymer Research, Germany [email protected] Schilling, Tanja Albert-Ludwigs-Universität Freiburg, Germany [email protected] Schmid, Friederike Johannes Gutenberg-Universität Mainz, Germany [email protected] Schmidt, Matthias Universität Bayreuth, Germany [email protected] Settanni, Giovanni Johannes Gutenberg-Universität Mainz, Germany [email protected] Sulpizi, Marialore Johannes Gutenberg-Universität Mainz, Germany [email protected] Thachuk, Mark University of British Columbia, Canada [email protected] Treﬀenstädt, Lucas L. Universität Bayreuth, Germany lucas.treﬀ[email protected] van der Vegt, Nico Technische Universität Darmstadt, Germany [email protected] Vargas Guzman, Horacio Max Planck Institute for Polymer Research, Germany [email protected] Vega Reyes, Francisco Universidad de Extremadura, Spain [email protected] Vuilleumier, Rodolphe École Normale Supérieure, France [email protected] Wettermann, Sarah Johannes Gutenberg-Universität Mainz, Germany [email protected] Zaccone, Alessio University of Cambridge, UK [email protected]