2017 
Ruscher, C., Semenov, A. N., Baschnagel, J., & Farago, J. (2017). Anomalous sound attenuation in Voronoi liquid. J. Chem. Phys., 146(14), 15 pp.
Abstract: The physics of simple fluids in the hydrodynamic limit and notably the connection between the proper microscopic scales and the macroscopic hydrodynamical description are nowadays well understood. In particular, the three peak shape of the dynamical structure factor S(k, omega) is a universal feature, as well as the kdependence of the peak position (proportional to/k) and width proportional to k(2), the latter accounting for the sound attenuation rate. In this paper, we present a theoretical model of monodisperse fluid, whose interactions are defined via the Voronoi tessellations of the configurations [called the Voronoi liquid and first studied in Ruscher et al., Europhys. Lett. 112, 66003 (2015)], which displays at low temperatures a marked violation of the universal features of S(k,omega) with a sound attenuation rate only proportional to k. This anomalous behaviour, which apparently violates the basic symmetries of the liquid state, is traced back to the existence of a time scale which is both short enough for the viscoelastic features of the liquid to impact the relaxational dynamics and however long enough for the momentum diffusion to be substantially slower than the sound propagation on that characteristic time. Published by AIP Publishing.


2015 
Frey, S., Weysser, F., Meyer, H., Farago, J., Fuchs, M., & Baschnagel, J. (2015). Simulated glassforming polymer melts: dynamic scattering functions, chain length effects, and modecoupling theory analysis. The European physical journal. E, Soft matter, 38(2), 97.
Abstract: We present moleculardynamics simulations for a fully flexible model of polymer melts with different chain length N ranging from short oligomers (N = 4) to values near the entanglement length (N = 64). For these systems we explore the structural relaxation of the supercooled melt near the critical temperature T c of modecoupling theory (MCT). Coherent and incoherent scattering functions are analyzed in terms of the idealized MCT. For temperatures T > T c we provide evidence for the spacetime factorization property of the beta relaxation and for the timetemperature superposition principle (TTSP) of the alpha relaxation, and we also discuss deviations from these predictions for T T c. For T larger than the smallest temperature where the TTSP holds we perform a quantitative analysis of the dynamics with the asymptotic MCT predictions for the late beta regime. Within MCT a key quantity, in addition to T c, is the exponent parameter lambda. For the fully flexible polymer models studied we find that lambda is independent of N and has a value (lambda = 0.735 ) typical of simple glassforming liquids. On the other hand, the critical temperature increases with chain length toward an asymptotic value T c () . This increase can be described by T c () – T c(N) 1/N and may be interpreted in terms of the N dependence of the monomer density rho, if we assume that the MCT glass transition is ruled by a softspherelike constant coupling parameter Gamma c = rho c T c (1/4), where rho c is the monomer density at T c. In addition, we also estimate T c from a HansenVerletlike criterion and MCT calculations based on structural input from the simulation. For our polymer model both the HansenVerlet criterion and the MCT calculations suggest T c to decrease with increasing chain length, in contrast to the direct analysis of the simulation data.


Hemmerle, A., Froehlicher, G., Bergeron, V., Charitat, T., & Farago, J. (2015). Wormlike instability of a vibrated sessile drop. Epl, 111(2).
Abstract: We study the effects of vertical sinusoidal vibrations on a liquid droplet with a low surface tension (ethanol) deposited on a solid substrate. In a precise range of amplitudes and frequencies, the drop exhibits a dramatic wormlike shape instability with a strong symmetry breaking, comparable to the one observed by Pucci et al. (Phys. Rev. Lett., 106 (2011) 024503) on a vibrated floating lens. However, the geometry of our system is much simpler since it does not involve the oscillation and deformation of a liquidliquidair contact line. We show that the Faraday waves appearing on the surface of the droplet control its shape and we draw a systematic phase diagram of the instability. A simple theoretical model allows us to derive a relation between the elongation of the droplet and the amplitude of the Faraday wave, in good agreement with measurements of both quantities. Copyright (C) EPLA, 2015


Ruscher, C., Baschnagel, J., & Farago, J. (2015). The Voronoi liquid. Epl, 112(6).
Abstract: We introduce a new theoretical model of simple fluid, whose interactions, defined in terms of the Voronoi cells of the configurations, are local and manybody. The resulting system is studied both theoretically and numerically. We show that the fluid, though sharing the global features of other models of fluids with soft interactions, has several unusual characteristics, which are investigated and discussed. Copyright (C) EPLA, 2015


2014 
Farago, J., Semenov, A., Frey, S., & Baschnagel, J. (2014). New conserved structural fields for supercooled liquids. European Physical Journal E, 37(6).
Abstract: By considering Voronoi tessellations of the configurations of a fluid, we propose two new conserved fields, which provide structural information not fully accounted for by the usual 2point density correlation functions. One of these fields is scalar and associated with the volume of the Voronoi cell, whereas the other one, termed the “geometric polarisation”, is vectorial and related to the local anisotropy of the configurations. We study the static and dynamical properties of these fields in the supercooled regime of a model glassforming liquid. We show that the geometric polarisation is statically correlated to the force field, but contrary to it develops a plateau regime when the temperature is lowered. This different relaxation is related to the cage effect in glassforming liquids, which prevents a complete relaxation of the shape of the cage around particle on intermediate time scales.


Helfferich, J., Ziebert, F., Frey, S., Meyer, H., Farago, J., Blumen, A., et al. (2014). Continuoustime randomwalk approach to supercooled liquids. I. Different definitions of particle jumps and their consequences. Physical Review E, 89(4).
Abstract: Singleparticle trajectories in supercooled liquids display long periods of localization interrupted by “fast moves.” This observation suggests a modeling by a continuoustime randomwalk (CTRW). We perform molecular dynamics simulations of equilibrated shortchain polymer melts near the critical temperature of modecoupling theory Tc and extract “moves” from the monomer trajectories. We show that not all moves comply with the conditions of a CTRW. Strong forwardbackward correlations are found in the supercooled state. A refinement procedure is suggested to exclude these moves from the analysis. We discuss the repercussions of the refinement on the jumplength and waitingtime distributions as well as on characteristic time scales, such as the average waiting time (“exchange time”) and the average time for the first move (“persistence time”). The refinement modifies the temperature (T) dependence of these time scales. For instance, the average waiting time changes from an Arrheniustype to a VogelFulchertype T dependence. We discuss this observation in the context of the bifurcation of the a process and (Johari) beta process found in many glassforming materials to occur near Tc. Our analysis lays the foundation for a study of the jumplength and waitingtime distributions, their temperature and chainlength dependencies, and the modeling of the monomer dynamics by a CTRW approach in the companion paper.


Helfferich, J., Ziebert, F., Frey, S., Meyer, H., Farago, J., Blumen, A., et al. (2014). Continuoustime randomwalk approach to supercooled liquids. II. Meansquare displacements in polymer melts. Physical Review E, 89(4).
Abstract: The continuoustime random walk (CTRW) describes the singleparticle dynamics as a series of jumps separated by random waiting times. This description is applied to analyze trajectories from molecular dynamics (MD) simulations of a supercooled polymer melt. Based on the algorithm presented by Helfferich et al. [Phys. Rev. E 89, 042603 (2014)], we detect jump events of the monomers. As a function of temperature and chain length, we examine key distributions of the CTRW: the jumplength distribution (JLD), the waitingtime distribution (WTD), and the persistencetime distribution (PTD), i.e., the distribution of waiting times for the first jump. For the equilibrium (polymer) liquid under consideration, we verify that the PTD is determined by the WTD. For the meansquare displacement (MSD) of a monomer, the results for the CTRW model are compared with the underlying MD data. The MD data exhibit two regimes of subdiffusive behavior, one for the early a process and another at later times due to chain connectivity. By contrast, the analytical solution of the CTRW yields diffusive behavior for the MSD at all times. Empirically, we can account for the effect of chain connectivity in Monte Carlo simulations of the CTRW. The results of these simulations are then in good agreement with the MD data in the connectivitydominated regime, but not in the early a regime where they systematically underestimate the MSD from the MD.


2012 
Farago, J., Meyer, H., Baschnagel, J., & Semenov, A. N. (2012). Hydrodynamic and viscoelastic effects in polymer diffusion. Journal Of PhysicsCondensed Matter, 24(28), 284105.
Abstract: We develop a fluctuating hydrodynamics approach to study the impact of the hydrodynamic and viscoelastic interactions on the motion of the center of mass of a polymer as well as on the relaxation of Rouse modes, either in a Theta solvent or in a melt of identical unentangled chains. We show that this method allows us to describe the effect of hydrodynamic interactions beyond the Zimm (for a single chain in a Theta solvent) or the Rouse models (for an unentangled melt). In the latter case, we recover the same important effect of the viscoelastic hydrodynamic interactions on the centerofmass diffusion, first described in Farago et al (2011 Phys. Rev. Lett. 107 178301).


Farago, J., Meyer, H., Baschnagel, J., & Semenov, A. N. (2012). Modecoupling approach to polymer diffusion in an unentangled melt. II. The effect of viscoelastic hydrodynamic interactions. Physical Review E, 85(5), 051807.
Abstract: A modecoupling theory (MCT) version (called hMCT thereafter) of a recently presented theory [Farago, Meyer, and Semenov, Phys. Rev. Lett. 107, 178301 (2011)] is developed to describe the diffusional properties of a tagged polymer in a melt. The hMCT accounts for the effect of viscoelastic hydrodynamic interactions (VHIs), that is, a physical mechanism distinct from the densitybased MCT (dMCT) described in the first paper of this series. The two versions of the MCT yield two different contributions to the asymptotic behavior of the centerofmass velocity autocorrelation function (c.m. VAF). We show that in most cases the VHI mechanism is dominant; for long chains and prediffusive times it yields a negative tail alphaN(1/2)t(3/2) for the c. m. VAF. The case of nonmomentumconserving dynamics (Langevin or Monte Carlo) is discussed as well. It generally displays a distinctive behavior with two successive relaxation stages: first N(1)t(5/4) (as in the dMCT approach), then N(1/2)t(3/2). Both the amplitude and the duration of the first t(5/4) stage crucially depend on the Langevin friction parameter gamma. All results are also relevant for the early time regime of entangled melts. These slow relaxations of the c.m. VAF, thus account for the anomalous subdiffusive regime of the c. m. mean square displacement widely observed in numerical and experimental works.


Farago, J., Semenov, A. N., Meyer, H., Wittmer, J. P., Johner, A., & Baschnagel, J. (2012). Modecoupling approach to polymer diffusion in an unentangled melt. I. The effect of density fluctuations. Physical Review E, 85(5), 051806.
Abstract: We quantitatively assess the effect of density fluctuation modes on the dynamics of a tagged polymer in an unentangled melt. To this end, we develop a densitybased modecoupling theory (dMCT) using the MoriZwanzig approach and projecting the fluctuating force onto pairdensity fluctuation modes. The effect of dynamical density fluctuations on the centerofmass (c.m.) dynamics is also analyzed based on a perturbative approach and we show that dMCT and perturbation techniques yield identical results. The c. m. velocity autocorrelation function (c. m. VAF) exhibits a slow power law relaxation in the time range between the monomer time t(1) and the Rouse relaxation time t(N). We obtain an analytical expression for the c. m. VAF in terms of molecular parameters. In particular, the c. m. VAF scales as N(1)t(5/4) (where N is the number of monomer units per chain) in the relevant time regime. The results are qualitatively accounted for by the dynamical correlation hole effect. The predicted t(5/4) dependence of the c. m. VAF is supported by data of nonmomentumconserving computer simulations. However, the comparison shows that the theory significantly underestimates the amplitude of the effect. This issue is discussed and an alternative approach is addressed in the second part of this series [Farago et al., Phys. Rev. E 85, 051807 (2012), the following paper].


2011 
Farago, J., Meyer, H., & Semenov, A. N. (2011). Anomalous Diffusion of a Polymer Chain in an Unentangled Melt. Physical Review Letters, 107(17).
Abstract: Contrary to common belief, hydrodynamic interactions in polymer melts are not screened beyond the monomer length and are important in transient regimes. We show that viscoelastic hydrodynamic interactions (VHIs) lead to anomalous dynamics of a tagged chain in an unentangled melt at t


Lee, N. K., Farago, J., Meyer, H., Wittmer, J. P., Baschnagel, J., Obukhov, S. P., et al. (2011). Nonideality of polymer melts confined to nanotubes. Epl, 93(4).
Abstract: Corrections to chain ideality have been demonstrated recently for polymer melts in the bulk and in ultrathin films. It has been shown that the effect of incomplete screening is stronger in the latter. We show here that the deviation from ideality is even stronger in thin capillaries. Describing the crossover from the free bulk to the confined regime as the radius of the capillary decreases below the typical coil radius we make connection to the so far disconnected work by Brochard and de Gennes (J. Phys. ( Paris), Lett., 40 ( 1979) 399) predicting chain segregation in very thin capillaries. Due to the generalized Porod scattering of the segregated chains, the Kratky representation of the intrachain structure factor reveals a plateau for all regimes although the chains become swollen with increasing confinement. Copyright (C) EPLA, 2011


Wittmer, J. P., Cavallo, A., Xu, H., Zabel, J. E., Polinska, P., Schulmann, N., et al. (2011). ScaleFree Static and Dynamical Correlations in Melts of Monodisperse and FloryDistributed Homopolymers A Review of Recent BondFluctuation Model Studies. Journal of Statistical Physics, 145(4), 1017–1126.
Abstract: It has been assumed until very recently that all longrange correlations are screened in threedimensional melts of linear homopolymers on distances beyond the correlation length xi characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bondfluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances ra parts per thousand


Wittmer, J. P., Polinska, P., Meyer, H., Farago, J., Johner, A., Baschnagel, J., et al. (2011). Scalefree centerofmass displacement correlations in polymer melts without topological constraints and momentum conservation: A bondfluctuation model study. Journal of Chemical Physics, 134(23).
Abstract: By Monte Carlo simulations of a variant of the bondfluctuation model without topological constraints, we examine the centerofmass (COM) dynamics of polymer melts in d = 3 dimensions. Our analysis focuses on the COM displacement correlation function CN(t) approximate to partial derivative(2)(t)h(N)(t)/2, measuring the curvature of the COM meansquare displacement h(N)(t). We demonstrate that CN(t) approximate to (RN/TN)(2)(rho*/rho) f(x = t/TN) with N being the chain length (16


2008 
Farago, J. (2008). The notion of persistence applied to breathers in thermal equilibrium. Physica DNonlinear Phenomena, 237(8), 1013–1020.
Abstract: We study the thermal equilibrium of nonlinear KleinGordon chains at the limit of small coupling (anticontinuum limit). We show that the persistence distribution associated to the local energy density is a useful tool to study the statistical distribution of the socalled thermal breathers, mainly when the equilibrium is characterized by longlived pinned excitations; in that case, the distribution of persistence intervals turns Out to be a power law. We demonstrate also that this generic behaviour has a counterpart in the power spectra, where the highfrequencies domains nicely collapse if properly rescaled. These results are also compared to nonlinear KleinGordon chains with a soft nonlinearity, for which the thermal breathers are rather mobile entities. Finally, we discuss the possibility of a breatherinduced anomalous diffusion law, and show that despite a strong slowing down of the energy diffusion, there are numerical evidences for a normal asymptotic diffusion mechanism, but with exceptionally small diffusion coefficients. (C) 2008 Elsevier B.V. All rights reserved.


Farago, J., & Pitard, E. (2008). Injected power fluctuations in onedimensional dissipative systems: Role of ballistic transport. Phys. Rev. E, 78(5), 51114.
Abstract: This paper is a generalization of the models considered in J. Stat. Phys. 128, 1365 (2007). Using an analogy with free fermions, we compute exactly the large deviation function (LDF) of the energy injected up to time t in a onedimensional dissipative system of classical spins, where a drift is allowed. The dynamics are T=0 asymmetric Glauber dynamics driven out of rest by an injection mechanism, namely, a Poissonian flipping of one spin. The drift induces anisotropy in the system, making the model more comparable to experimental systems with dissipative structures. We discuss the physical content of the results, specifically the influence of the rate of the Poisson injection process and the magnitude of the drift on the properties of the LDF. We also compare the results of this spin model to simple phenomenological models of energy injection (Poisson or Bernoulli processes of domain wall injection). We show that many qualitative results of the spin model can be understood within this simplified framework.


Meyer, H., Wittmer, J. P., Kreer, T., Beckrich, P., Johner, A., Farago, J., et al. (2008). Static Rouse modes and related quantities: Corrections to chain ideality in polymer melts. European Physical Journal E, 26(12), 25–33.
Abstract: Following the Flory ideality hypothesis intrachain and interchain excludedvolume interactions are supposed to compensate each other in dense polymer systems. Multichain effects should thus be neglected and polymer conformations may be understood from simple phantom chain models. Here we provide evidence against this phantom chain, meanfield picture. We analyze numerically and theoretically the static correlation function of the Rouse modes. Our numerical results are obtained from computer simulations of two coarsegrained polymer models for which the strength of the monomer repulsion can be varied, from full excluded volume (“hard monomers”) to no excluded volume (“phantom chains”). For nonvanishing excluded volume we find the simulated correlation function of the Rouse modes to deviate markedly from the predictions of phantom chain models. This demonstrates that there are nonnegligible correlations along the chains in a melt. These correlations can be taken into account by perturbation theory. Our simulation results are in good agreement with these new theoretical predictions.


2007 
Farago, J., & Pitard, E. (2007). Injected power fluctuations in 1D dissipative systems. Journal Of Statistical Physics, 128(6), 1365–1382.
Abstract: Using fermionic techniques, we compute exactly the large deviation function (ldf) of the timeintegrated injected power in several onedimensional dissipative systems of classical spins. The dynamics are T=0 Glauber dynamics supplemented by an injection mechanism, which is taken as a poissonian flipping of one particular spin. We discuss the physical content of the results, specifically the influence of the rate of the Poisson process on the properties of the ldf.


Thalmann, F., & Farago, J. (2007). Trotter derivation of algorithms for Brownian and dissipative particle dynamics. Journal of Chemical Physics, 127(12), 124109.
Abstract: This paper focuses on the temporal discretization of the Langevin dynamics, and on different resulting numerical integration schemes. Using a method based on the exponentiation of time dependent operators, we carefully derive a numerical scheme for the Langevin dynamics, which we found equivalent to the proposal of Ermak and Buckholtz [J. Comput. Phys. 35, 169 (1980)] and not simply to the stochastic version of the velocityVerlet algorithm. However, we checked on numerical simulations that both algorithms give similar results, and share the same “weak order two” accuracy. We then apply the same strategy to derive and test two numerical schemes for the dissipative particle dynamics. The first one of them was found to compare well, in terms of speed and accuracy, with the best currently available algorithms.

