Diffusion Wavelet Decomposition for Coarse-Graining of Polymer Chains

2015 ◽  
Vol 1753 ◽  
Author(s):  
B. Christopher Rinderspacher ◽  
Jaydeep P. Bardhan ◽  
Ahmed E. Ismail
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Coarse Graining ◽  
Polymer Chains ◽  
Coarse Grained ◽  
Small Scale ◽  
Bonding Structure ◽  
Ring Structures ◽  
Spatial Coordinates ◽  
Molecular Bonding

ABSTRACTHere we present an alternative approach to coarse graining, based on the multiresolution diffusion-wavelet approach to operator compression, which does not require explicit atomistic-to-coarse-grained mappings. Our diffusion-wavelet method takes as input the topology and sparsity of the molecular bonding structure of a system, and returns as output a hierarchical set of degrees of freedom (DoFs) of system-specific coarse-grained variables. Importantly, the hierarchical compression provides a clear framework for modeling at many model scales (levels), beyond the common two-level CG representation. Our results show that the resulting hierarchy separates localized modes, such as a single C-C vibrational mode, from larger-scale motions, e.g., long-range concerted backbone vibrational modes. Our approach correctly captures small-scale chemical features, such as cellulose ring structures, and alkane side chains or CH2 units, as well as large-scale features of the backbone. In particular, the new method’s finest-scale modes describe DoFs similar to united atom models and other chemically-defined CG models. Modes at coarser levels describe increasingly large connected portions of the target polymers. For polyethylene and polystyrene, spatial coordinates and their associated forces were compressed by up to two orders of magnitude. The compression in forces is of particular interest as this allows larger timesteps as well as reducing the number of DoFs.

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.

scholarly journals Dynamic Loads and Response of a Spar Buoy Wind Turbine with Pitch-Controlled Rotating Blades: An Experimental Study

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3598
Author(s):  
Sara Russo ◽  
Pasquale Contestabile ◽  
Andrea Bardazzi ◽  
Elisa Leone ◽  
Gregorio Iglesias ◽  
...  
Keyword(s):  
Wind Speed ◽  
Wind Turbine ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Laboratory Data ◽  
Nonlinear Behavior ◽  
Offshore Wind ◽  
Small Scale ◽  
Wave Steepness ◽  
Design Factor

New large-scale laboratory data are presented on a physical model of a spar buoy wind turbine with angular motion of control surfaces implemented (pitch control). The peculiarity of this type of rotating blade represents an essential aspect when studying floating offshore wind structures. Experiments were designed specifically to compare different operational environmental conditions in terms of wave steepness and wind speed. Results discussed here were derived from an analysis of only a part of the whole dataset. Consistent with recent small-scale experiments, data clearly show that the waves contributed to most of the model motions and mooring loads. A significant nonlinear behavior for sway, roll and yaw has been detected, whereas an increase in the wave period makes the wind speed less influential for surge, heave and pitch. In general, as the steepness increases, the oscillations decrease. However, higher wind speed does not mean greater platform motions. Data also indicate a significant role of the blade rotation in the turbine thrust, nacelle dynamic forces and power in six degrees of freedom. Certain pairs of wind speed-wave steepness are particularly unfavorable, since the first harmonic of the rotor (coupled to the first wave harmonic) causes the thrust force to be larger than that in more energetic sea states. The experiments suggest that the inclusion of pitch-controlled, variable-speed blades in physical (and numerical) tests on such types of structures is crucial, highlighting the importance of pitch motion as an important design factor.

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 Nature does not play Dice at the Planck scale

2020 ◽  
Vol 29 (14) ◽  
pp. 2043012
Author(s):  
Tejinder P. Singh
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Planck Scale ◽  
Coarse Graining ◽  
Lagrangian Dynamics ◽  
Time Intervals ◽  
Spacetime Geometry ◽  
The Status ◽  
Planck Time ◽  
Matter Fields

We start from classical general relativity coupled to matter fields. Each configuration variable and its conjugate momentum, as also spacetime points are raised to the status of matrices [equivalently operators]. These matrices obey a deterministic Lagrangian dynamics at the Planck scale. By coarse-graining this matrix dynamics over time intervals much larger than Planck time, one derives quantum theory as a low energy emergent approximation. If a sufficiently large number of degrees of freedom get entangled, spontaneous localisation takes place, leading to the emergence of classical spacetime geometry and a classical universe. In our theory, dark energy is shown to be a large-scale quantum gravitational phenomenon. Quantum indeterminism is not fundamental, but results from our not probing physics at the Planck scale.

scholarly journals The impact of inhomogeneous subgrid clumping on cosmic reionization

2019 ◽  
Vol 491 (2) ◽  
pp. 1600-1621
Author(s):  
Yi Mao ◽  
Jun Koda ◽  
Paul R Shapiro ◽  
Ilian T Iliev ◽  
Garrelt Mellema ◽  
...  
Keyword(s):  
High Resolution ◽  
Large Scale ◽  
Power Spectra ◽  
Coarse Grained ◽  
Small Scale ◽  
Sources And Sinks ◽  
Coarse Grained Simulations ◽  
Cent Error ◽  
Spatially Varying ◽  
The Impact

ABSTRACT Cosmic reionization was driven by the imbalance between early sources and sinks of ionizing radiation, both of which were dominated by small-scale structure and are thus usually treated in cosmological reionization simulations by subgrid modelling. The recombination rate of intergalactic hydrogen is customarily boosted by a subgrid clumping factor, 〈n2〉/〈n〉2, which corrects for unresolved fluctuations in gas density n on scales below the grid-spacing of coarse-grained simulations. We investigate in detail the impact of this inhomogeneous subgrid clumping on reionization and its observables, as follows: (1) Previous attempts generally underestimated the clumping factor because of insufficient mass resolution. We perform a high-resolution N-body simulation that resolves haloes down to the pre-reionization Jeans mass to derive the time-dependent, spatially varying local clumping factor and a fitting formula for its correlation with local overdensity. (2) We then perform a large-scale N-body and radiative transfer simulation that accounts for this inhomogeneous subgrid clumping by applying this clumping factor-overdensity correlation. Boosting recombination significantly slows the expansion of ionized regions, which delays completion of reionization and suppresses 21 cm power spectra on large scales in the later stages of reionization. (3) We also consider a simplified prescription in which the globally averaged, time-evolving clumping factor from the same high-resolution N-body simulation is applied uniformly to all cells in the reionization simulation, instead. Observables computed with this model agree fairly well with those from the inhomogeneous clumping model, e.g. predicting 21 cm power spectra to within 20 per cent error, suggesting it may be a useful approximation.

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.

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.

NON-SPHERICAL VOIDS: THE BEST ALTERNATIVE TO DARK ENERGY?

2011 ◽  
Vol 20 (supp01) ◽  
pp. 94-101
Author(s):  
ROBERTO A SUSSMAN
Keyword(s):  
Dark Energy ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Observation Point ◽  
Coarse Grained ◽  
Spherical Void ◽  
Cosmological Observations ◽  
Definition Of ◽  
Almost All ◽  
Spherical Voids

If our cosmic location lies within a large-scale under–dense region or "void", then current cosmological observations can be explained without resorting to a cosmological constant or to an exotic and elusive source like "dark energy". If we further assume this void region to be spherical (as almost all current void models do), then fitting observational data severely constrains our position to be very near the void center, which is a very special and unlikely observation point. We argue in this article that existing spherical void models must be regarded as gross approximations that arise by smoothing out more realistic non–spherical configurations that may fit observations without the limitations imposed by spherical symmetry. In particular, the class of quasi–spherical Szekeres models provides sufficient degrees of freedom to describe the evolution of non–spherical inhomogeneities, including a configuration consisting of several elongated supercluster–like overdense filaments with large underdense regions between them. We summarize a recently published example of such configuration, showing that it yields a reasonable coarse-grained description of realistic observed structures. While the density distribution is not spherically symmetric, its proper volume average yields a spherical density void profile of 250 Mpc that roughly agrees with observations. Also, once we consider our location to lie within a non-spherical void, the definition of a "center" location becomes more nuanced, and thus the constraints placed by the fitting of observations on our position with respect to this location become less restrictive.

scholarly journals Stochastic modeling of the oceanic mesoscale eddies

2021 ◽  
Author(s):  
Long Li ◽  
Bruno Deremble ◽  
Noé Lahaye ◽  
Etienne Mémin
Keyword(s):  
Large Scale ◽  
Mesoscale Eddy ◽  
Low Frequency ◽  
Stochastic Approach ◽  
Coarse Grained ◽  
Small Scale ◽  
Oceanic Circulation ◽  
Stochastic Representation ◽  
Stochastic Framework ◽  
Gyre Circulation

<p>In this work, a stochastic representation [Bauer2020a, Bauer2020b] based on a physical transport principle is proposed to account for mesoscale eddy effects on the the large-scale oceanic circulation. This stochastic framework [Mémin2014] arises from a decomposition of the Lagrangian velocity into a time-smooth component and a highly oscillating noise term. One important characteristic of this random model is that it conserves the energy of any transported tracer. Such an energy-preserving representation has been successfully implemented in a well established multi-layered quasi-geostrophic dynamical core (http://www.q-gcm.org). The empirical spatial correlation of the small-scale noise is estimated from the eddy-resolving simulation data. In particular, a sub-grid correction drift has been introduced in the noise due to the bias ensuing from the coarse-grained procedure. This non intuitive term seems quite important in reproducing on a coarse mesh the meandering jet of the wind-driven double-gyre circulation. In addition, a new projection method has been proposed to constrain the noise living along the iso-surfaces of the vertical stratification. The resulting noise enables us to improve the intrinsic low-frequency variability of the large-scale current. From some statistical studies and energy transfers analysis, this improvement is well demonstrated.</p><ul><li><span>[</span>Bauer2020a] W. Bauer, P. Chandramouli, B. Chapron, L. Li, and E. Mémin. Deciphering the role of small-scale inhomogeneity on geophysical flow structuration: a stochastic approach. Journal of Physical Oceanography, 50(4):983-1003, 2020a.<span>       </span></li> <li><span>[</span>Bauer2020b] W. Bauer, P. Chandramouli, L. Li, and E. Mémin. Stochastic representation of mesoscale eddy effects in coarse-resolution barotropic models. Ocean Modelling, 151:101646 (2020b). <span>   </span></li> <li>[Mémin2014] E. Mémin. Fluid flow dynamics under location uncertainty. Geophysical & Astrophysical Fluid Dynamics, 108(2):119-146, 2014.<span>     </span></li> </ul>

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.

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