Session K36: Coarse-graining, Advanced Sampling and Multiscale Methods in Soft Matter

Long-time atomistic simulations with the Parallel Replica Dynamics method

Molecular Dynamics (MD) --- the numerical integration of atomistic equations of motion --- is a workhorse of computational materials science. Indeed, MD can in principle be used to obtain any thermodynamic or kinetic quantity, without introducing any approximation or assumptions beyond the adequacy of the interaction potential. It is therefore an extremely powerful and flexible tool to study materials with atomistic spatio-temporal resolution. These enviable qualities however come at a steep computational price, hence limiting the system sizes and simulation times that can be achieved in practice. While the size limitation can be efficiently addressed with massively parallel implementations of MD based on spatial decomposition strategies, allowing for the simulation of trillions of atoms, the same approach usually cannot extend the timescales much beyond microseconds. In this article, we discuss an alternative parallel-in-time approach, the Parallel Replica Dynamics (ParRep) method, that aims at addressing the timescale limitation of MD for systems that evolve through rare state-to-state transitions. We review the formal underpinnings of the method and demonstrate that it can provide arbitrarily accurate results for any definition of the states. When an adequate definition of the states is available, ParRep can simulate trajectories with a parallel speedup approaching the number of replicas used. We demonstrate the usefulness of ParRep by presenting different examples of materials simulations where access to long timescales was essential to access the physical regime of interest and discuss practical considerations that must be addressed to carry out these simulations.   

Investigating the impact of representation upon coarse-grained models

The first step in building a coarse-grained (CG) model is choosing a representation or `mapping' of the original system at a reduced resolution. In practice, the mapping is often chosen on the basis of `physical intuition.' Consequently this crucial step would greatly benefit from the development of systematic and principled methodologies. Accordingly, we have studied the relationship between the mapping and the resulting CG model. As a starting point, we have analytically derived, as a function of the CG mapping, the exact many-body potential of mean force (PMF) for the simple Gaussian Network Model (GNM) of protein fluctuations. We use this as a simple model for investigating the effect of the CG mapping upon the information loss and quality of the CG model. Moreover, by considering the GNM's for different proteins, we investigate the significance of high resolution structural features for the quality of the CG model.   

Non-Markovian coarse-grained modeling of polymeric fluids based on the Mori-Zwanzig formalism

The Mori-Zwanzig formalism for coarse-graining a complex dynamical system typically introduces memory effects. The Markovian assumption of delta-correlated fluctuating forces is often employed to simplify the formulation of coarse-grained (CG) models and numerical implementations. However, when the time scales of a system are not clearly separated, the memory effects become strong and the Markovian assumption becomes inaccurate. To this end, we incorporate memory effects into CG modeling by preserving non-Markovian interactions between CG variables based on the Mori-Zwanzig formalism. For a specific example, molecular dynamics (MD) simulations of star polymer melts are performed while the corresponding CG system is defined by grouping many bonded atoms into single clusters. Then, the effective interactions between CG clusters as well as the memory kernel are obtained from the MD simulations. The constructed CG force field with a memory kernel leads to a non-Markovian dissipative particle dynamics (NM-DPD). Quantitative comparisons on both static and dynamic properties between the CG models with Markovian and non-Markovian approximations will be presented.   

\textbf{A new graph-matching-based algorithm to study dynamical processes}

We present a new algorithm to identify and quantify the degree of local order in dynamical systems. To each particle site we associate a given number of neighboring sites the positions of which define the nodes of a pattern graph. We match this graph with a graph describing the geometry of an ordered reference system. The degree of overlap is obtained by recursively maximizing a score function having a value ranging from 0 (in the case of a completely disordered system) to 1 (in the case of a perfect crystal). While typically order parameters are tailored to specific cases, our approach is general and could be applied to different areas of condensed matter physics. Here we illustrate the approach with applications to atomic and molecular fluids, namely melting of Lennard Jones particles, direct crystallization of supercooled water and melting of Yukawa crystals.   

HOMOGENOUS NUCLEATION AND CRYSTAL GROWTH IN A MODEL LIQUID FROM DIRECT ENERGY LANDSCAPE SAMPLING SIMULATION

Nucleation and crystal growth are understood to be activated processes involving the crossing of free-energy barriers. Attempts to capture the entire crystallization process over long timescales with molecular dynamic simulations have met major obstacles because of molecular dynamics' temporal constraints. Herein, we circumvent this temporal limitation by using a brutal-force, metadynamics-like, adaptive basin-climbing algorithm and directly sample the free-energy landscape of a model liquid Argon. The algorithm biases the system to evolve from an amorphous liquid like structure towards an FCC crystal through inherent structure, and then traces back the energy barriers. Consequently, the sampled timescale is macroscopically long. We observe that the formation of a crystal involves two processes, each with a unique temperature-dependent energy barrier. One barrier corresponds to the crystal nucleus formation; the other barrier corresponds to the crystal growth. We find the two processes dominate in different temperature regimes. Compared to other computation techniques, our method requires no assumptions about the shape or chemical potential of the critical crystal nucleus. The success of this method is encouraging for studying the crystallization of more complex   

Dynamical Density Functional Theory and Hydrodynamic Interactions in Confined Systems

Colloidal systems consist of nano-micrometer sized particles suspended in a bath of many more, much smaller and much lighter particles. When the colloidal particles move through the bath, e.g. when driven by external forces such as gravity, flows are induced in the bath. These flows in turn impart forces on the colloid particles. These bath-mediated forces, known as Hydrodynamic Interactions (HI) strongly influence the dynamics of the colloid particles. This is particularly true in confined systems, in which the presence of walls substantially modifies the HI compared to unbounded geometries. For many-particle systems, the number of degrees of freedom prohibit a direct solution of the underlying stochastic equations and a reduced model is necessary. We model such systems through Dynamical Density Functional Theory (DDFT), the computational complexity of which is independent of the number of particles. We include both inter-particle and particle-wall HI, demonstrating both their combined and relative effects.   

Nondecaying hydrodynamic interactions along narrow channels

Particle-particle interactions are of paramount importance in every multi-body system as they determine the collective behaviour and coupling strength. Many well-known interactions like electro-static, van der Waals or screened Coulomb, decay exponentially or with negative powers of the particle spacing $r$. Similarly, hydrodynamic interactions between particles undergoing Brownian motion decay as $1/r$ in bulk, and are assumed to decay in small channels. Such interactions are ubiquitous in biological and technological systems. Here we confine two particles undergoing Brownian motion in narrow, microfluidic channels and study their coupling through hydrodynamic interactions. Our experiments show that the hydrodynamic particle-particle interactions are distance-independent in these channels. This finding is of fundamental importance for the interpretation of experiments where dense mixtures of particles or molecules diffuse through finite length, water-filled channels or pore networks.   

Topological properties and edge mode effects in classical thermal transport

Classical harmonic chains, with suitable parametrizations, can resemble quantum systems exhibiting interesting topological phases. By analytically solving the equations of motion of harmonic chains with alternating masses and coupling constants, the energy bands bear striking resemblance to topological electronic bands of the Su-Schrieffer-Heeger model. As a consequence, localized topological edge modes associated with topological invariants of the system arise in classical harmonic chains. Effects from topological properties on thermal transport through patterned harmonic chains are analyzed and the results are supported by molecular-dynamics simulations. We also found edge modes as a hindrance to achieving the maximal intrinsic thermal conductance. Possible applications in polymers will be discussed.   

Durability of Long Equipartition Times In Anharmonic Oscillator Chains

Vibrational modes, completely decoupled in the case of a purely harmonic chain do not interact, thereby preventing an even spread of energy over both low and high frequency states. The distribution of energy beyond a small set of initially excited modes, known as equipartition, proceeds over finite time scales with the admixture of an anharmonic term. However, in many cases $(e.g\ V(x) = \alpha x^{2} + \beta x^{4})$, the transfer of energy from low to high frequency modes is hampered for an isolated chain, with equipartition times diverging with increasing system size. Using Molecular Dynamics simulations we relax the isolation condition, gradually coupling the ends of the chain to a thermal bath. Calculating equipartition times for various coupling strengths, we seek to determine if: (\romannumeral 1)\ The bulk limit divergence persists for any coupling strength, (\romannumeral 2)\ Bulk equipartition times are finite beyond a coupling threshold, or (\romannumeral 3)\ Coupling to a thermal bath has a singular effect and yields finite equipartition times for any nonzero coupling strength.   

Langevin Equation for DNA Dynamics

Under physiological conditions, DNA oligomers can contain well-ordered helical regions and also flexible single-stranded regions. We describe the site-specific motion of DNA with a modified Rouse-Zimm Langevin equation formalism that describes DNA as a coarse-grained polymeric chain with global structure and local flexibility. The approach has successfully described the protein dynamics in solution and has been extended to nucleic acids. Our approach provides diffusive mode analytical solutions for the dynamics of global rotational diffusion and internal motion. The internal DNA dynamics present a rich energy landscape that accounts for an interior where hydrogen bonds and base-stacking determine structure and experience limited solvent exposure. We have implemented several models incorporating different coarse-grained sites with anisotropic rotation, energy barrier crossing, and local friction coefficients that include a unique internal viscosity and our models reproduce dynamics predicted by atomistic simulations. The models reproduce bond autocorrelation along the sequence as compared to that directly calculated from atomistic molecular dynamics simulations. The Langevin equation approach captures the essence of DNA dynamics without a cumbersome atomistic representation.   

Improving the kinetics from molecular simulations using biased Markov state models

Molecular simulations can provide microscopic insight into the physical and chemical driving forces of complex molecular processes. Despite continued advancement of simulation methodology, model errors may lead to inconsistencies between simulated and experimentally-measured observables. This work presents a robust and systematic framework for reweighting the ensemble of dynamical paths sampled in a molecular simulation in order to ensure consistency with a set of given kinetic observables. The method employs the well-developed Markov state modeling framework in order to efficiently treat simulated dynamical paths. We demonstrate that, for two distinct coarse-grained peptide models, biasing the Markov state model to reproduce a small number of reference kinetic constraints significantly improves the dynamical properties of the model, while simultaneously refining the static equilibrium properties.   

Multiscale Modeling of the Electrocaloric Effect in PVDF-based Polymers

We apply multi-scale modeling to explore the electrocaloric (EC) effect in PVDF-related ferroelectric polymers, which have application in active cooling of microsystems. The EC effect is the temperature rise and drop in some ferroelectric materials due to changes in the configurational entropy when an external electric field is applied and removed. The polymer is modeled as a series of bi-directional permanent dipoles and induced point dipoles distributed on its monomer sites. The flipping of these dipoles due to an applied electric field is leads to polarization changes. Flipping the dipole moment of the polymer chain requires rotation of the individual monomers, each of which has its own energy barrier. This energy pathway is predicted from atomic-level nudged elastic band method calculations for a variety of chain environments. We then use first-passage time analysis to convert each energy pathway into an average transition rate for a full polymer chain rotation. The transition rates for all chains are integrated into a kinetic Monte Carlo algorithm in which the polarization change due to the application of an electric field is determined.