Coarse-grained Dynamics Research Articles

Stochastic Mode Reduction for Particle-Based Simulation Methods for Complex Microfluid Systems

We illustrate the stochastic mode reduction procedure as formulated recently by Majda, Timofeyev, and Vanden-Eijnden [Comm. Pure Appl. Math., 54 (2001), pp. 891--974] (MTV) on the equations of motion underlying various particle-based simulation approaches (such as Stokesian dynamics and Brownian dynamics) and the conceptually distinct dissipative particle dynamics (DPD) simulation approaches for complex microfluid systems. The resulting coarse-grained dynamics are compared and contrasted with each other. We show that the stochastic mode reduction procedure provides a way to recover the Smoluchowski dynamics for a standard model of multiple interacting particles in a fluid. The DPD, however, has some subtle aspects which obstruct the application of the stochastic mode reduction procedure. We discuss the mathematical and physical properties of the DPD method that underlie thisdifficulty.

Anomalous dislocation multiplication in FCC metals.

Direct atomistic simulations of dislocation multiplication in fcc aluminum reveal an unexpected mechanism, in which a Frank-Read source emits dislocations with Burgers vectors different from that of the source itself. The mechanism is traced to a spontaneous nucleation of partial dislocation loops within the stacking fault. Understanding and a quantitative description of this unusual process are achieved through the development of a continuum model for dislocation nucleation based on the coarse-grained dislocation dynamics approach and a minimal amount of atomistic input.

Dileptons and photons from coarse-grained microscopic dynamics and hydrodynamics compared to experimental data

We compute the radiation of dileptons and photons using relativistic hydrodynamics and a coarse-grained version of the microscopic event generator UrQMD, both of which provide a good description of the hadron spectra. The currently most accurate dilepton and photon emission rates from perturbative QCD and from experimentally-based hadronic calculations are used. Comparisons are made to data on central Pb Pb and Pb Au collisions taken at the CERN SPS at a beam energy of 158 A GeV. Both hydrodynamics and UrQMD provide very good descriptions of the photon transverse momentum spectrum measured between 1 and 4 GeV, but very slightly undersestimate the low mass spectrum of e +e − pairs, even with greatly broadened ϱ and ω vector mesons.

Topological jamming and the glass transition in a frustrated system.

The relationship between extended structures, glassy dynamics and an underlying critical point is examined in the context of a lattice model of fluctuating lines. Monte Carlo simulations are used to construct an effective, coarse-grained dynamics for the "order parameter" near the critical point. Analysis of the effective dynamics reveals that the critical point is associated with diverging barriers leading to the observed Vogel-Fulcher divergence of the relaxation times. A direct connection is established between the presence of extended structures and the activated dynamics.

Escaping free-energy minima.

We introduce a powerful method for exploring the properties of the multidimensional free energy surfaces (FESs) of complex many-body systems by means of coarse-grained non-Markovian dynamics in the space defined by a few collective coordinates. A characteristic feature of these dynamics is the presence of a history-dependent potential term that, in time, fills the minima in the FES, allowing the efficient exploration and accurate determination of the FES as a function of the collective coordinates. We demonstrate the usefulness of this approach in the case of the dissociation of a NaCl molecule in water and in the study of the conformational changes of a dialanine in solution.

Dileptons and photons from coarse-grained microscopic dynamics and hydrodynamics compared to experimental data

Radiation of dileptons and photons from high-energy nuclear collisions provides information on the space-time evolution of the hot dense matter produced therein. We compute this radiation using relativistic hydrodynamics and a coarse-grained version of the microscopic event generator UrQMD, both of which provide a good description of the hadron spectra. The currently most accurate dilepton and photon emission rates from perturbative QCD and from experimentally based hadronic calculations are used. Comparisons are made to data on central Pb-Pb and Pb-Au collisions taken at the CERN SPS at a beam energy of $158A \mathrm{GeV}.$ Both hydrodynamics and UrQMD provide very good descriptions of the photon transverse momentum spectrum measured between 1 and 4 GeV, but slightly underestimate the low-mass spectrum of ${e}^{+}{e}^{\ensuremath{-}}$ pairs, even with greatly broadened \ensuremath{\rho} and \ensuremath{\omega} vector mesons. Predictions are given for the transverse momentum distribution of dileptons.

On Coarse-Graining by the Inverse Monte Carlo Method: Dissipative Particle Dynamics Simulations Made to a Precise Tool in Soft Matter Modeling

We present a promising coarse-graining strategy for linking micro- and mesoscales of soft matter systems. The approach is based on effective pairwise interaction potentials obtained from detailed atomistic molecular dynamics (MD) simulations, which are then used in coarse-grained dissipative particle dynamics (DPD) simulations. Here, the effective potentials were obtained by applying the inverse Monte Carlo method [Lyubartsev and Laaksonen, Phys. Rev. E. 52, 3730 (1995)] on a chosen subset of degrees of freedom described in terms of radial distribution functions. In our first application of the method, the effective potentials were used in DPD simulations of aqueous NaCl solutions. With the same computational effort we were able to simulate systems of one order of magnitude larger than the MD simulations. The results from the MD and DPD simulations are in excellent agreement.

Analysis of Multiple Folding Routes of Proteins by a Coarse-Grained Dynamics Model

Langevin dynamics of a protein molecule with Go-type potentials is developed and used to analyze long time-scale events in the folding of cytochrome c. Several trajectories are generated, starting from random coil configurations and going to the native state, that are a few angstroms root mean square deviation (RMSD) from the native structure. The dynamics is controlled, to a large scale, by the two terminal helices that are in contact in the native state. These two helices form very early during folding, and depending on the trajectory, they either stabilize rapidly or break and re-form in going over steric barriers. The extended initial chain exhibits a rapid folding transition into a relatively compact shape, after which the helices are reorganized in a highly correlated manner. The time of formation of residue pair contacts strongly points to the hierarchical nature of folding; i.e., secondary structure forms first, followed by rearrangements of larger length scales at longer times. The kinetics of formation of native contacts is also analyzed, and the onset of a stable globular configuration, referred to as the molten globule in the literature, is identified. Predictions of the model are compared with extensive experimental data on cytochrome c.

Coarse-grained dynamics of one chain in a polymer melt

In this study we present the coarse-graining of one polymer chain in a melt to a single dimer. By using the projector operator formalism we derive the equation of motions for the dimer. The different forces that occur in this equation of motion are calculated from molecular dynamics simulations of the microscopic model, using constraint forces to fix the dimer configuration. The mean constraint force serves as the conserved part of the interaction, whereas the time correlation of the constraint force fluctuation leads to the nonconserved interactions: the dissipative and fluctuating forces. Using the configurational dependent coarse-grained interactions we have performed stochastic dynamics simulations of the dimer. Dimer properties of the microscopic and the coarse-grained model are shown to be in reasonable agreement. We also discuss the application of the framework to coarse-graining polymer melts into more detail, i.e., beyond the dimer.

From Molecular Dynamics to Dissipative Particle Dynamics

A procedure is introduced for deriving a coarse-grained dissipative particle dynamics from molecular dynamics. The rules of the dissipative particle dynamics are derived from the underlying molecular interactions, and a Langevin equation is obtained that describes the forces experienced by the dissipative particles and specifies the associated canonical Gibbs distribution for the system.

Review of the fourth Johns Hopkins Protein Folding Meeting

Review of the fourth Johns Hopkins Protein Folding Meeting

Coarse graining of a spin-glass state space

The complex structure of a spin-glass state space can be simplified by a coarse-graining procedure, i.e. microscopic states being assembled into larger clusters. An algorithm for the coarse graining of the state space of a short-range Ising spin glass is provided, which is the basis of a coarse-grained dynamics. Different ways for modelling the transition rates in the coarse-grained state space are discussed. A comparison with the dynamics of the microscopic system shows that the dynamics in the coarse-grained state space gives an appropriate approximation.

Combined influence of random and regular external fields on long-range electron transfer

The dissipative dynamics of a two-level system (TLS) is studied for the case of the simultaneous modulation of the energy bias by a regular external field and by nonequilibrium dichotomic fluctuations. To describe the noise-averaged dynamics driven by the external periodic field, a set of coupled generalized master equations is derived. Quantum fluctuations of the thermal bath are taken into account within the noninteracting blip approximation, whereas the dichotomic fluctuations and the external field are treated in an exact manner. The case of nonadiabatic continuous-wave (cw) driving is considered in detail for an asymmetric TLS strongly coupled to the thermal bath. The general approach is applied to long-range electron transfer in proteins. According to the presence of dynamic disorder, the coarse-grained electron transfer dynamics becomes nonexponential. The gated regime and the inversion effect of the transfer in the strongly biased TLS with a dichotomic fluctuating energy bias are demonstrated. Additionally, it is shown that a strong cw field can switch the electron transfer dynamics between the gated (nonexponential) regime and the nonadiabatic (single-exponential) regime.

Prediction using unsupervised learning

The manner and efficiency with which neural networks use competitive learning to discover long-term regularities in the dynamics of nonlinear dissipative systems is analysed. The network creates a coarse-grained dynamics which depends both on the connectivity of the network and the intrinsic properties of the time series. The learning process is analysed using a master equation approach, and the scaling behaviour of the information entropy; while the prediction error after learning is examined as a function of network size, and the nature of dynamical clustering in phase space. Scaling arguments are deduced and compared with simulations of discrete mapping.

Coarse-grained dynamics for proton exchange in RNA

We focus on a coarse-grained description of the coupling between ribose pucker discommensuration and base swinging in a standard A-RNA helix. We view this coupling as an actual entrainment where the sugar conformation is regarded as the enslaving variable in the dynamics. Thus, we provide a semiempirical model for the relatively slow dynamics of helix opening reflecting the intermittent exposure of titratable groups to the solvent and consistent with proton exchange kinetics. Our description of bubble formation in the helix is built upon a Φ 4-type model

Derivation of an Evolution Equation for Takahashi's Coarse-Grained Dynamics

Derivation of an Evolution Equation for Takahashi's Coarse-Grained Dynamics

Resonance model for chaos near period three

A detailed study of the complex dynamics generated by a quadratic one-dimensional map near period three is presented. A resonance model for the tangent bifurcation process is constructed, which leads to an expression for the probability density as a sum of three Lorentzian contributions whose widths are expressed in terms of the fixed points of the third iterates of the map in the complex plane. It is also shown that the coarse-grained dynamics near period three can be analyzed in terms of an intermittency picture where deterministic motion, localized at the density maxima, is interspersed with chaotic bursts. An analysis of this motion explains the square-root dependence of the computed Liapunov number on the deviation of the map parameter from its bifurcation value. The origin of the fine structure, which decorates the spikes in the probability density, is described. The applicability of this model to the chaotic flows of ordinary differential equations is also discussed with respect to the dynamics on the R\ossler strange attractor.