Mesoscale methods

2017 ◽  
Author(s):  
Michael P. Allen ◽  
Dominic J. Tildesley
Keyword(s):  
Large Scale ◽  
Equations Of Motion ◽  
Dissipative Particle Dynamics ◽  
Coarse Graining ◽  
Coarse Grained ◽  
Collision Dynamics ◽  
Force Matching ◽  
Multiparticle Collision Dynamics ◽  
Long Time ◽  
Boltzmann Method

Coarse-graining is an increasingly commonplace approach to study, as economically as possible, large-scale, and long-time phenomena. This chapter covers the main methods. Brownian and Langevin dynamics are introduced, with practical details of the solution of the modified equations of motion. Several techniques which aim to bridge the gap to the hydrodynamic regime are described: these include dissipative particle dynamics, multiparticle collision dynamics, and the lattice Boltzmann method. Several examples of program code are provided. In the last part of the chapter, the derivation of a coarse-grained potential from an atomistic one is considered using force-matching and structure-matching, and the limitations of these approaches are discussed.

scholarly journals Renormalization group theory of molecular dynamics

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Daiji Ichishima ◽  
Yuya Matsumura
Keyword(s):  
Molecular Dynamics ◽  
Renormalization Group ◽  
Critical Exponent ◽  
Computational Efficiency ◽  
Large Scale ◽  
Dissipative Particle Dynamics ◽  
Computational Cost ◽  
Coarse Graining ◽  
Spatial Dimension ◽  
Deborah Number

AbstractLarge scale computation by molecular dynamics (MD) method is often challenging or even impractical due to its computational cost, in spite of its wide applications in a variety of fields. Although the recent advancement in parallel computing and introduction of coarse-graining methods have enabled large scale calculations, macroscopic analyses are still not realizable. Here, we present renormalized molecular dynamics (RMD), a renormalization group of MD in thermal equilibrium derived by using the Migdal–Kadanoff approximation. The RMD method improves the computational efficiency drastically while retaining the advantage of MD. The computational efficiency is improved by a factor of $$2^{n(D+1)}$$ 2 n ( D + 1 ) over conventional MD where D is the spatial dimension and n is the number of applied renormalization transforms. We verify RMD by conducting two simulations; melting of an aluminum slab and collision of aluminum spheres. Both problems show that the expectation values of physical quantities are in good agreement after the renormalization, whereas the consumption time is reduced as expected. To observe behavior of RMD near the critical point, the critical exponent of the Lennard-Jones potential is extracted by calculating specific heat on the mesoscale. The critical exponent is obtained as $$\nu =0.63\pm 0.01$$ ν = 0.63 ± 0.01 . In addition, the renormalization group of dissipative particle dynamics (DPD) is derived. Renormalized DPD is equivalent to RMD in isothermal systems under the condition such that Deborah number $$De\ll 1$$ D e ≪ 1 .

THE SIMULATION OF POLYSTYRENE/NANOPARTICLES COMPOSITE MICROSPHERES USING DISSIPATIVE PARTICLE DYNAMICS

2013 ◽  
Vol 12 (02) ◽  
pp. 1250111 ◽  
Author(s):  
HAILONG XU ◽  
QIUYU ZHANG ◽  
HEPENG ZHANG ◽  
BAOLIANG ZHANG ◽  
CHANGJIE YIN
Keyword(s):  
Dissipative Particle Dynamics ◽  
Sodium Dodecyl ◽  
Coarse Graining ◽  
Particle Dynamics ◽  
Coarse Grained ◽  
Polystyrene Nanoparticles ◽  
Coarse Grained Model ◽  
Composite Microspheres ◽  
Polystyrene Matrix ◽  
Materials Studio

Dissipative particle dynamics (DPD) was initially used to simulate the polystyrene/nanoparticle composite microspheres (PNCM) in this paper. The coarse graining model of PNCM was established. And the DPD parameterization of the model was represented in detail. The DPD repulsion parameters were calculated from the cohesive energy density which could be calculated by amorphous modules in Materials Studio. The equilibrium configuration of the simulated PNCM shows that the nanoparticles were actually "modified" with oleic acid and the modified nanoparticles were embedded in the bulk of polystyrene. As sodium dodecyl sulfate (SDS) was located in the interface between water and polystyrene, the hydrophilic head of SDS stretched into water while the hydrophobic tailed into polystyrene. All simulated phenomena were consistent with the experimental results in preparation of polystyrene/nanoparticles composite microspheres. The effect of surface modification of nanoparticles on its dispersion in polystyrene matrix was also studied by adjusting the interaction parameters between the OA and NP beads. The final results indicated that the nanoparticles removed from the core of composite microsphere to the surface with increase of a OA-NP . All the simulated results demonstrated that our coarse–grained model was reasonable.

A new spectral coarse-graining algorithm based on K-means clustering in complex networks

2019 ◽  
Vol 33 (01) ◽  
pp. 1850421 ◽  
Author(s):  
Lang Zeng ◽  
Zhen Jia ◽  
Yingying Wang
Keyword(s):  
Complex Networks ◽  
Large Scale ◽  
Dynamic Properties ◽  
Coarse Graining ◽  
Kuramoto Model ◽  
Coarse Grained ◽  
Original Network ◽  
Topological Information ◽  
Real World Applications ◽  
Large Scale Networks

Coarse-graining of complex networks is one of the important algorithms to study large-scale networks, which is committed to reducing the size of networks while preserving some topological information or dynamic properties of the original networks. Spectral coarse-graining (SCG) is one of the typical coarse-graining algorithms, which can keep the synchronization ability of the original network well. However, the calculation of SCG is large, which limits its real-world applications. And it is difficult to accurately control the scale of the coarse-grained network. In this paper, a new SCG algorithm based on K-means clustering (KCSCG) is proposed, which cannot only reduce the amount of calculation, but also accurately control the size of coarse-grained network. At the same time, KCSCG algorithm has better effect in keeping the network synchronization ability than SCG algorithm. A large number of numerical simulations and Kuramoto-model example on several typical networks verify the feasibility and effectiveness of the proposed algorithm.

scholarly journals Exploring the landscape of model representations

2020 ◽  
Vol 117 (39) ◽  
pp. 24061-24068 ◽  
Author(s):  
Thomas T. Foley ◽  
Katherine M. Kidder ◽  
M. Scott Shell ◽  
W. G. Noid
Keyword(s):  
Statistical Physics ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Coarse Graining ◽  
Order Parameters ◽  
Microscopic Model ◽  
Coarse Grained ◽  
Proper Order ◽  
Complex Phenomena ◽  
Protein Fluctuations

The success of any physical model critically depends upon adopting an appropriate representation for the phenomenon of interest. Unfortunately, it remains generally challenging to identify the essential degrees of freedom or, equivalently, the proper order parameters for describing complex phenomena. Here we develop a statistical physics framework for exploring and quantitatively characterizing the space of order parameters for representing physical systems. Specifically, we examine the space of low-resolution representations that correspond to particle-based coarse-grained (CG) models for a simple microscopic model of protein fluctuations. We employ Monte Carlo (MC) methods to sample this space and determine the density of states for CG representations as a function of their ability to preserve the configurational information, I, and large-scale fluctuations, Q, of the microscopic model. These two metrics are uncorrelated in high-resolution representations but become anticorrelated at lower resolutions. Moreover, our MC simulations suggest an emergent length scale for coarse-graining proteins, as well as a qualitative distinction between good and bad representations of proteins. Finally, we relate our work to recent approaches for clustering graphs and detecting communities in networks.

Mesoscale Simulation of the Structure of Star Acrylated Poly(ethylene glycol-co-lactide) Hydrogels

2012 ◽  
Vol 1418 ◽  
Author(s):  
Seyed Sina Moeinzadeh ◽  
Esmaiel Jabbari
Keyword(s):  
Ethylene Glycol ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Dissipative Particle Dynamics ◽  
Random Force ◽  
Dynamics Simulation ◽  
Coarse Grained ◽  
Poly Ethylene Glycol ◽  
The Core ◽  
Poly Ethylene

ABSTRACTIn this work the microstructures of star acrylated poly(ethylene glycol-co-lactide) (SPELA) with different LA:EG ratios in the aqueous solution have been simulated via Dissipative Particle Dynamics (DPD) approach at the mesoscale. The system components were coarse-grained into different beads (set of atoms) which moved according to the Newton’s equations of motion integrated via a modified Velocity-Verlet algorithm. The force acting on each bead, in a specific cutoff distance (rc), was divided into a conservative force (FC), random force (FR), dissipative force (FD), bond force (FS) and bond angle force (FE). The repulsion parameters of the conservative force (αij) were calculated from the solubility parameter of the beads, each of which were extracted from an atomistic molecular dynamics simulation (MD). Simulations showed the formation of micelles with lactide and acrylate beads occupied the core and hydrophilic ethylene oxide segments extending through the water to form the corona. The micelles showed an increasing trend in size and decreasing trend in number density with increase in LA:EG ratio. Results showed that the acrylate density decreased from the center of the micelles to the core surface although the overall amount of acrylates increased due to the increase in volume. Furthermore, the running integration number of acrylate-water beads showed decreasing accessibility of acrylates to water with increasing PLA volume fraction.

Numerical simulation of turbulent thermal convection based on LBM

2020 ◽  
pp. 2150070
Author(s):  
Yuxian Xia ◽  
Yuan Fu ◽  
Jiahua Li ◽  
Xiang Qiu ◽  
Yuehong Qian ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Thermal Convection ◽  
Large Scale ◽  
Coarse Grained ◽  
Field Energy ◽  
Small Scale ◽  
Temperature Spectrum ◽  
Full Field ◽  
Scale Range ◽  
Boltzmann Method

The two-dimensional (2D) turbulent thermal convection is numerically investigated by using Lattice Boltzmann Method. The 2D turbulence is considered as 2D channel flow where the flow is forced by the arrays of adiabatic cylinders placed in the inlet and wall boundary of 2D channel, which is heated uniformly from the inlet as to inspire the paradigmatic motion of thermal convection. It is found that the spacing vortex number density distribution in the large-scale range [Formula: see text], based on the Liutex vortex definition criterion, which is in fair agreement with the Benzi prediction. The energy spectrum of the Liutex field [Formula: see text]. The scaling behavior of full-field energy spectrum in the large scale is [Formula: see text]. The temperature spectrum in the large-scale range is found to be approximate to [Formula: see text], which is according with the Bolgiano theory of 2D buoyancy driven turbulence. The energy flux cascades to the large scale, the enstrophy cascades to small scale. The moments of the energy dissipation field [Formula: see text] coarse grained at the scale [Formula: see text] have the power-law behaviors with the scale [Formula: see text]. The velocity intermittency measured by PDF exists in large-scale range of 2D turbulent thermal convection. The measured scaling exponents [Formula: see text] are determined by a lognormal formula. The measured intermittency parameter is [Formula: see text], which denotes the strong intermittency in the large-scale range of 2D turbulent thermal convection.

scholarly journals Dissipative particle dynamics model of homogalacturonan based on molecular dynamics simulations

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
P. M. Pieczywek ◽  
W. Płaziński ◽  
A. Zdunek
Keyword(s):  
Molecular Dynamics ◽  
Force Field ◽  
Large Scale ◽  
Dissipative Particle Dynamics ◽  
Three Dimensional ◽  
Structural Features ◽  
Particle Dynamics ◽  
Distribution Functions ◽  
Coarse Grained ◽  
Dynamics Model

Abstract In this study we present an alternative dissipative particle dynamics (DPD) parametrization strategy based on data extracted from the united-atom molecular simulations. The model of the homogalacturonan was designed to test the ability of the formation of large-scale structures via hydrogen bonding in water. The extraction of coarse-grained parameters from atomistic molecular dynamics was achieved by means of the proposed molecule aggregation algorithm based on an iterative nearest neighbour search. A novel approach to a time-scale calibration scheme based on matching the average velocities of coarse-grained particles enabled the DPD forcefield to reproduce essential structural features of homogalacturonan molecular chains. The successful application of the proposed parametrization method allowed for the reproduction of the shapes of radial distribution functions, particle velocities and diffusivity of the atomistic molecular dynamics model using DPD force field. The structure of polygalacturonic acid molecules was mapped into the DPD force field by means of the distance and angular bond characteristics, which closely matched the MD results. The resulting DPD trajectories showed that randomly dispersed homogalacturonan chains had a tendency to aggregate into highly organized 3D structures. The final structure resembled a three-dimensional network created by tightly associated homogalacturonan chains organized into thick fibres.

Multipolar Expansion Methods for Coarse Grained Force Fields [PowerPoint Submission]

2006 ◽  
Vol 978 ◽  
Author(s):  
Sheng D. Chao
Keyword(s):  
Molecular Dynamics ◽  
Quantum Chemistry ◽  
Large Scale ◽  
Force Fields ◽  
Coarse Graining ◽  
Expansion Method ◽  
Distribution Functions ◽  
Coarse Grained ◽  
Quantum Chemistry Calculations ◽  
Multipolar Expansion

AbstractCurrent large scale atomistic simulations remain too computationally demanding to be generally applicable to industrial and bioengineering materials. It is desirable to develop multiscale modeling algorithms to perform efficient and informative mesoscopic simulations. Here we present a multipolar expansion method to construct coarse grained force fields (CGFF) for polymer nanostructures and nanocomposites. This model can effectively capture the stereochemical response to anisotropic long-range interactions and can be systematically improved upon adding higher order terms. The coarse-graining procedure forms the basis to perform a hierarchy of multiscale simulations starting with the quantum chemistry calculations to coarse grained molecular dynamics, hopefully toward continuum modeling. We have applied this procedure to molecular clusters such as alkane, benzene, and fullerene. For liquid alkane, molecular dynamics simulations using the CGFF can reproduce the pair distribution functions using atomistic force fields. Molecular mechanics simulations using the CGFF can well reproduce the energetics of benzene clusters from quantum chemistry electronic structure calculations. Subtle anisotropy in the interaction potentials of the fullerene dimer using the Brenner force field can also be well represented by the model. It is promising this procedure can be standardized and further extended.

scholarly journals Weak Galilean invariance as a selection principle for coarse-grained diffusive models

2018 ◽  
Vol 115 (22) ◽  
pp. 5714-5719 ◽  
Author(s):  
Andrea Cairoli ◽  
Rainer Klages ◽  
Adrian Baule
Keyword(s):  
Stochastic Models ◽  
Reference Frames ◽  
Equations Of Motion ◽  
A Priori ◽  
Coarse Graining ◽  
Coarse Grained ◽  
Theoretical Principle ◽  
Galilean Invariance ◽  
Inertial Frames ◽  
Closed Systems

How does the mathematical description of a system change in different reference frames? Galilei first addressed this fundamental question by formulating the famous principle of Galilean invariance. It prescribes that the equations of motion of closed systems remain the same in different inertial frames related by Galilean transformations, thus imposing strong constraints on the dynamical rules. However, real world systems are often described by coarse-grained models integrating complex internal and external interactions indistinguishably as friction and stochastic forces. Since Galilean invariance is then violated, there is seemingly no alternative principle to assess a priori the physical consistency of a given stochastic model in different inertial frames. Here, starting from the Kac–Zwanzig Hamiltonian model generating Brownian motion, we show how Galilean invariance is broken during the coarse-graining procedure when deriving stochastic equations. Our analysis leads to a set of rules characterizing systems in different inertial frames that have to be satisfied by general stochastic models, which we call “weak Galilean invariance.” Several well-known stochastic processes are invariant in these terms, except the continuous-time random walk for which we derive the correct invariant description. Our results are particularly relevant for the modeling of biological systems, as they provide a theoretical principle to select physically consistent stochastic models before a validation against experimental data.

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