# <span class=strong>Reception and Poster Session</span><br/><br/><br><b>Poster submissions welcome from all participants</b><br/><br/>

Monday, November 3, 2008 - 5:00pm - 6:30pm

Lind 400

**From atomistic to mesoscale systems without fitting: A coarse grained model for polystyrene**

Dominik Fritz (Max Planck Institute for Polymer Research)

We present a coarse grained model for polystyrene, which is only based on properties of single chains and of systems consisting of two short oligomers. We do not need any fitting to atomistic melt simulations. The model keeps the information about the tacticity of the chains and reproduces the local distributions for bond length, angles and dihedral angles. Furthermore it is modeling statical properties of atomistic melts, e.g. radial distribution functions and internal distances.**Effective dynamics using conditional expectations**

Frédéric Legoll (École Nationale des Ponts-et-Chaussées)

We consider a system described by its position X_{t}, that

evolves

according to the overdamped Langevin equation. At equilibrium,

the

statistics of X are given by the Boltzmann-Gibbs measure.

Suppose that we are only interested in some given

low-dimensional function

ξ(X) of the complete variable (the so-called reaction

coordinate). The statistics of ξ are

completely determined by the free energy associated to this

reaction coordinate. In this work, we try and design an

effective dynamics on ξ, that is

a low-dimensional dynamics which is a good approximation of

ξ(X_{t}). Using conditional expectations, we build an

original

dynamics, and discuss how it is related to the free energy

itself. Using an entropy-based approach, we are also able to

derive error estimates.

Numerical simulations will illustrate the accuracy of the

proposed dynamics.

Joint work with T. Lelievre (ENPC and INRIA).**General purpose molecular dynamics on graphic processing**

units (GPUs)

Alex Travesset (Iowa State University)

Molecular Dynamics (MD) on Graphic Processing Units (GPUs) provide

spectacular advantages: an unexpensive GPU (less than 500$) provides the equivalent computer

power of a 44 core cluster. This poster will introduce HOOMD, our new General purpose MD

code, as well as describe the challenges involved in GPU programming. It will also show the very easy to use

scripting system developed directed to the end user, so that it can make full use of HOOMD without having to learn about

GPU programming. As it will become clear in the poster, HOOMD is particularly suited for coarse-grained MD.**Force matching versus structural coarse-graining**

Alexander Lukyanov (Max-Planck Institut für Polymerforschung)

Joint work with Victor Rühle and Denis Andrienko

(Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany).

We are working on a detailed comparison of two coarse-graining methods, force matching [1] and iterative inverse Boltzmann [2]. Force matching is generalized for coarse-graining of angle and dihedral potentials, in addition to standard bond stretching and non-bonded interactions. Some initial steps are made in order to develop solvent-free coarsegraining models for polymers in solutions for systems of a particular importance for organic electronics (soluble conjugated polymers).

1. S. Izvekov, G. Voth „Multiscale coarse graining of liquid-state systems“, J. Chem. Phys. 123, 134105 (2005)

2. W. Tschoep, K. Kremer, J. Batoulis, T. Buerger and O. Hahn, Acta Polym 49, 61 (1998)**Multiscale modeling of polystyrene in different environments**

Roland Faller (University of California)

Polystyrene is a very abundant and industrially important polymer. We are modeling its dynamical behavior on multiple length scales and different environments. We start with pure PS where we develop a mesoscale polystyrene model based on atomistic simulations. The non-bonded effective potential is optimized against the atomistic simulation until the radial distribution function generated from the mesoscale model is consistent with the atomistic simulation. The mesoscale model allows understanding the polymer dynamics of long chains in reasonable computer time. Both models are investigated in the melt, the blend and in confined geometries. The dynamics of polystyrene melts are investigated at various chain lengths ranging from 15 to 240 monomers and the crossover to entangled dynamics is observed. As computer simulations cannot only address average properties of the system under study but also the distribution over any observable of interest we are study mixtures of polystyrene and polyisoprene by atomistic molecular dynamics and calculate correlation times for all segments in the system. We then identify fast and slow segments and can correlate the segment speed with the local neighborhood and obtain that fast segments have a surplus of the faster component in their neighborhood and vice versa. Finally we present a coarse grained model for the blend which is capable of showing phase separation.**Multiscale modeling of structure and phase behavior in**

heterogeneous lipid bilayers

Roland Faller (University of California)

The study of lipid structure and phase behavior at the nano scale length is of importance due to implications in understanding the role of the lipids in biochemical membrane processes. We performed a variety of simulations in homogeneous and heterogeneous membrane systems to elucidate such behaviors. Our simulations demonstrate that various coarse grained simulation models can predict different aspects of lipid phase separation and describe the change of the system under the influences of hydrophilic and hydrophobic support. The simulations are performed using models at different length scales ranging from the all atom scale to a scale where lipids are modeled by only three interaction sites. We are able to follow transformations, such as lipids phase transitions. These phase transitions are determined by analyzing parameters like area per lipid head group, the deuterium order parameter and dynamic properties. Phase diagrams of mixtures are reproduced consistent with experiments. We study the influence of a support on the systems on different length scales. We discuss the changes of the system phase behavior as well as differences between the two leaflets as induced by the support.**Spatial bounds on the effective complex permittivity for time-harmonic**

waves in random media

Lyubima Simeonova (The University of Utah)

When we consider wave propagation in random media in the case when the

wave length is finite, scattering effects must be accounted for and the

effective dielectric coefficient is no longer a constant, but a spatially

dependent function. We obtain a bound on the spatial variations of the effective

permittivity that depends on the maximum volume of the inhomogeneities and the

contrast of the medium. A related optimization problem of maximizing the spatial

average of the effective dielectric coefficient with respect to the spatial

probability density function is presented. The dependence of the effective

dielectric coefficient on the contrast of the medium is also investigated and an

approximation formula is derived.**A criterion to estimate the quality of the Mapping Scheme in Coarse-graining approaches**

Luigi Delle Site (Max-Planck Institut für Polymerforschung)

We propose a method to evaluate the approximation of separation of variables (ASV) in Molecular Dynamics (MD) and related fields. It is based on a point-by-point evaluation of the difference between the true potential and the corresponding potential where the separation of variables is applied. The major advantage of such an approach is the fact that it requires only the analytical form of the potential as provided in most of the MD codes. We provide an application of this criterion for alkane (aliphatic) chain and compare the efficiency for two different Mapping Schemes (MS).**Comparative study of water: Atomistic vs. coarse-grained**

Christoph Junghans (Max-Planck Institut für Polymerforschung)

We employ the inverse Boltzmann method to coarse-grain three commonly used three site water models (TIP3P, SPC and SPC/E) where one molecule is replaced by one coarse-grained particle with two body interactions only. The shape of the coarse-grained potentials is dominated by the ratio two lengths, which can be rationalized by the geometric constraints of the water clusters. It is shown that for simple two body potentials either the radial distribution function or the geometrical packing can be optimized. In a similar way, as needed for multiscale methods, either the pressure or the compressibility can be fitted to the all atom liquid. In total, a speedup of a factor of about 50 in computation time can be reached by this coarse-gaining procedure.**Parallel multiscale simulation for crack propagation**

Olivier Coulaud (Institut National de Recherche en Informatique Automatique (INRIA))

Concurrent multiscale methods are a powerful tool to solve with a low computational cost the local phenomena that occur at a small scale (atomic for example). Such methods are commonly used to study for example crack propagation, dislocations or nanoindentations. Even for small domain sizes, like the volume of a hundred nanometer cube, 3D atomistic simulations can lead to several hundred of millions atoms, and high performance parallel computation is naturally required. These simulations couple different parallel codes such as molecular dynamic code and elasticity code. The performance of the coupled code depends on how the data are well distributed on the processors.

Here we focus on the parallel aspects of the Bridging Method introduced by T. Belytschko and Xiao [1]. This method assumes that an atomistic model and a continuum model are coupled through an overlap zone. We present our parallel multiscale environment called LibMultiscale [2], which is based on a coupling involving a legacy parallel code for molecular dynamics (Lammps) and a parallel finite element code for continuum mechanics (LibMesh). Data redistribution and atom migration issues are discussed. Moreover 2D and 3D waves propagation simulations and a 2D penny shape crack propagation simulation are shown.

References:

[1] Coupling Methods for continuum model with molecular model. T. Belytschko, S.P. Xio. International Journal for Multiscale Computational Engineering, 11 (2003).

[2] LibMultiscale: http://libmultiscale.gforge.inria.fr/**Charge transport in discotic liquid crystals: a multiscale computer simulation study**

Denis Andrienko (Max-Planck Institut für Polymerforschung)

Charge mobilities of several derivatives of discotic liquid crystals have been determined by combining three methods into one scheme: (i) quantum chemical methods for the calculation of molecular electronic structures and reorganization energies (ii) molecular dynamics for simulation of the relative positions and orientations of molecules in a columnar mesophase, and (iii) kinetic Monte Carlo simulations and Master Equation approach to simulate charge transport. We reproduce the trends and magnitudes of mobilities as measured by pulse-radiolysis time-resolved microwave conductivity (PR-TRMC) and connect mobility directly to the microscopic morphology of the columns. Our study also shows that it is possible to understand and reproduce experimental charge transport parameters, and, in some cases, accurately predict them.**Realistic multiscale modeling of spatiotemporal behavior**

in surface reactions:

Equation-free heterogeneous coupled lattice-gas (HCLG)

simulations

James Evans (Iowa State University)

A rich variety of spatiotemporal pattern formation and reaction front propagation has been observed

in simple reactions on metal surfaces. Modeling has typically applied mean-field reaction-diffusion

equations - ignoring the impact of reactant ordering or islanding on the reaction kinetics, and

oversimplifying the treatment of surface diffusion in mixed reactant adlayers. In 1995, we introduced

an equation-free HCLG simulation approach [Tammaro et al. J. Chem. Phys. 103 (1995) 10277]

which performs parallel KMC simulations of an atomistic lattice-gas reaction model at spatial

locations distributed across the surface, and suitably couples these to describe the effects of

macroscopic surface diffusion. Recently, we have applied this approach to realistic models for

CO-oxidation on Pd(100) and Rh(100) surfaces [Liu & Evans, Phys. Rev. B 70 (2004) 193408;

Surf. Sci. - Ertl Nobel Issue 2008]. This requires a precise treatment of the collective and tensorial

nature of the rapid diffusion of CO through a disordered environment of relatively immobile oxygen

[Liu & Evans, J. Chem. Phys. 125 (2006) 054709].**From quantum to classical molecular dynamics**

Johannes Giannoulis (Technical University of Munich )

We are interested in the rigorous justification of the passage from quantum to classical molecular dynamics in the heavy nuclei limit, i.e., when the mass ratio of elecronic to nucleonic mass tends to zero.

For positive mass ratio the (non-relativistic) quantum dynamics is described by the time-dependent linear Schroedinger equation, where the potential U is the ground state Born-Oppenheimer potential energy surface obtained by minimization over electronic states.

The classical dynamics is governed by the Liouville equation for an (appropriately defined)

time-dependent Wigner measure W, obtained as the limit (for mass ratio tending to zero)

of the Wigner functions corresponding to the wavefunctions solving the Schroedinger equation.

Since the physically correct potential U possesses Coulomb singularities due to nuclei repulsion and can have kink type singularities if eigenvalue crossings are present, its level of smoothness is far lower than that required in previous rigorous approaches and renders the justification of the Liouville equation quite difficult.

In the poster we present our results mainly concerning the case of potentials U with only Coulomb singularities and no crossings.**Quantifying chain reptation in entangled polymers by mapping**

atomistic simulation results onto the tube model

Vlasis Mavrantzas (University of Patras)

The topological state of entangled polymers has been analyzed

recently in terms of primitive paths which allowed obtaining reliable

predictions for the static (statistical) properties of the underlying

entanglement network for many polymeric systems. Through a systematic

methodology that first maps atomistic molecular dynamics trajectories onto

time trajectories of primitive paths and then documents primitive path

motion in terms of a one-dimensional curvilinear diffusion in a tube-like

region around the coarse-grained chain contour, we further extend these

static approaches by computing the most fundamental function of the

reptation theory, namely the probability that a segment s of the

primitive chain remains inside the initial tube after time t. Linear

viscoelastic properties, such as the zero shear rate viscosity and the

spectra of storage and loss moduli, obtained on the basis of the obtained

curves, for three different polymer melts (polyethylene,

cis-1,4-polybutadiene and trans-1,4-polybutadiene) agree remarkably well

with experimental rheological data. The new methodology is general and can

be routinely applied to analyze primitive path dynamics and chain

reptation in atomistic trajectories (accumulated through computer

simulations) of other model polymers or polymeric systems (e.g.,

bidisperse, branched, grafted, etc); it is thus believed to be

particularly useful in future theoretical developments of more accurate

tube theories for entangled systems.**A bloch band base level set method in the semi-classical**

limit of the Schroedinger Equation

Zhongming Wang (University of California, San Diego)

It is now known that one can use level set description to accurately capture multi-phases in computation of high frequency waves. In this paper, we develop a Bloch band based level set method for computing the semi-classical limit of Schrdinger equations in periodic media. For the underlying equation subject to a highly oscillatory initial data a hybrid of the WKB approximation and homogenization leads to the Bloch eigenvalue problem and an associated Hamilton-Jacobi system for the phase, with Hamiltonian being the Bloch eigenvalues. We evolve a level set description to capture multi-valued solutions to the band WKB system, and then evaluate total position density over a sample set of bands. A superposition of band densities is established over all bands and solution branches when away from caustic points. Numerical results with different number of bands are provided to demonstrate the good quality of the method.**Mesoscopic model for the fluctuating hydrodynamics of binary and ternary mixtures**

Erkan Tüzel (University of Minnesota, Twin Cities)

A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model immiscible binary mixtures. Excluded volume interactions between the two components are modeled by stochastic multiparticle collisions which depend on the local velocities and densities. Momentum and energy are conserved locally, and entropically driven phase separation occurs for high collision rates. An explicit expression for the equation of state is derived, and the concentration dependence of the bulk free energy is shown to be the same as that of the Widom-Rowlinson model. Analytic results for the phase diagram are in excellent agreement with simulation data. Results for the line tension obtained from the analysis of the capillary wave spectrum of a droplet agree with measurements based on the Laplace's equation. The dispersion relation for the capillary waves is derived and compared with the numerical measurements of the time correlations of the radial fluctuations in the damped and over-damped limits. The introduction of amphiphilic dimers makes it possible to model the phase behavior of ternary surfactant mixtures.**All-atom multiscale computational modeling of**

bionanosystem dynamics

The use of traditional techniques, such as Molecular Dynamics (MD), to model the long-time dynamics of bionanosystems (e.g., viruses, liposomes, or engineered nanocapsules for drug delivery) have proven infeasible, as the computational time required to obtain accurate results for the time scales of interest is on the order of many years. Using statistical mechanics, stochastic calculus, and techniques of multiscale analysis, we have recently designed (and are currently constructing) tools which greatly improve upon this problem by introducing and tracking slow variables that account for the large-scale behavior of the given system. The new VirusX simulator decreases computational time to the order of hours, rendering such simulations feasible for the first time. This is joint work with Peter Ortoleva and the Center for Cell and Virus Theory at Indiana University.**Ligand access/escape from protein cavities:**

A computational study of the insulin-phenol complex

Cameron Abrams (Drexel University)

We apply random acceleration molecular dynamics (RAMD) simulation to identify potential escape routes of phenol from hydrophobic cavities in the hexameric insulin-phenol complex. We find three major pathways which provide new insights into (un)binding mechanisms for phenol. We identify several residues directly participating in escape events that serve to resolve ambiguities from recent NMR experiments. Reaction coordinates (RC) for dissociation of phenol are developed based on these exit pathways. Potentials of mean force (PMFs) along the RC for each pathway are resolved using multiple independent steered molecular dynamics (SMD) simulations with second order cumulant expansion of Jarzynski's equality. Our results for ΔF agree reasonably well within the range of known experimental and previous simulation magnitudes of this quantity. Based on structural analysis and energetic barriers for each pathway, we suggest a plausible preferred mechanism of phenolic exchange that differs from previous mechanisms. Several weakly-bound metastable states are also observed for the first time in the phenol dissociation reaction.**Adaptive resolution simulation of model mixtures**

Simon Poblete (Max Planck Institute for Polymer Research)

We have systematically developed a set of coarse-grained potentials able to describe a system of spherical monomers solved in tetrahedral molecules. The potentials are able to reproduce the basic structure and thermodynamics of the original mixture over a wide range of concentrations, and have been successfully tested in the Adaptive Resolution Scheme (AdResS), showing a symmetric behavior between the explicit and coarse-grained descriptions.**A new procedure to building stabilized explicit**

Runge-Kutta methods for large systems of ODEs

Jesús Martín-Vaquero (University of Salamanca)

Joint work with B. Janssen and B. Wade.

Stabilized Runge-Kutta

methods (or Chebyshev-Runge-Kutta methods) are explicit methods with

extended stability domains, usually along the negative real axis. They are

easy to use (they do not require algebra routines) and they are especially

suited for MOL discretizations of two and three dimensional parabolic

partial differential equations. However, existing codes have some

difficulties in cases when the eigenvalues are very large. We have

developed a new procedure to build this kind of algorithm and derive

second-order methods with up to 320 stages, all with good stability

properties. These methods are efficient numerical integrators of very

large stiff ordinary differential equations. Applications to the numerical

solution of reaction-diffusion problems will be presented.**Charge transport in polypyrrole: the role of morphology**

Victor Rühle (Max Planck Institute for Polymer Research)

A combination of methods is used to study charge transport in polypyrrole melts. First, the OPLS atomistic force field is refined using first-principles calculations. Amorphous and partially ordered melts are then generated with the help of this force-field. Finally, the charge mobility is calculated within the temperature activated hopping picture for charge transport [1].

[1] J. Kirkpatrick, V. Marcon, J. Nelson, K. Kremer, D. Andrienko, Phys. Rev. Lett. 98, 227402 (2007)**Techniques for coarse-grained modeling and mechanics of**

viral capsids

William Klug (University of California, Los Angeles)

As revealed by techniques of structural biology and single-molecule experimentation, the capsids of viruses are some of nature's best examples of highly symmetric multiscale self-assembled structures with impressive mechanical properties of strength and elasticity. We present a novel method for creating three-dimensional finite element meshes of viral capsids from both atomic data from PDB files and electron density data from EM files. The meshes capture heterogeneous geometric features and are used in conjunction with three-dimensional continuum elasticity to simulate nanoindentation experiments as performed using atomic force microscopy. Meshes and nanoindentation simulations are presented for several viruses: Hepatitis B, CCMV, HK97, and Phi 29.