Optimization of Coarse-Grained Interaction Potential: Inside Inherent Limitations of Coarse-Graining Methods

2011 ◽  
Vol 115 (21) ◽  
pp. 6985-6994 ◽  
Author(s):  
Piotr Kowalczyk ◽  
Piotr A. Gauden ◽  
Alina Ciach
Keyword(s):  
Interaction Potential ◽  
Coarse Graining ◽  
Coarse Grained

scholarly journals On the three-dimensional spatial correlations of curved dislocation systems

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Joseph Pierre Anderson ◽  
Anter El-Azab
Keyword(s):  
Correlation Function ◽  
Slip System ◽  
Correlation Functions ◽  
Mean Field ◽  
Coarse Graining ◽  
Dislocation Dynamics ◽  
Coarse Grained ◽  
Spatial Correlation Function ◽  
Line System ◽  
Dislocation Densities

AbstractCoarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of re-capturing these interactions by means of the dislocation-dislocation correlation functions. The framework depends on a convolution length to define slip-system-specific dislocation densities. Following a statistical definition of this coarse-graining process, we define a spatial correlation function which will allow the arrangement of the discrete line system at two points—and thus the strength of their interactions at short range—to be recaptured into a mean field description of dislocation dynamics. Through a statistical homogeneity argument, we present a method of evaluating this correlation function from discrete dislocation dynamics simulations. Finally, results of this evaluation are shown in the form of the correlation of dislocation densities on the same slip-system. These correlation functions are seen to depend weakly on plastic strain, and in turn, the dislocation density, but are seen to depend strongly on the convolution length. Implications of these correlation functions in regard to continuum dislocation dynamics as well as future directions of investigation are also discussed.

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 Trivial low energy states for commuting Hamiltonians, and the quantum PCP conjecture

2013 ◽  
Vol 13 (5&6) ◽  
pp. 393-429
Author(s):  
Matthew Hastings
Keyword(s):  
Ground State ◽  
Coding Theory ◽  
Energy State ◽  
Ground States ◽  
Coarse Graining ◽  
Quantum Circuit ◽  
Technical Condition ◽  
Two Dimensions ◽  
Low Energy ◽  
Coarse Grained

We consider the entanglement properties of ground states of Hamiltonians which are sums of commuting projectors (we call these commuting projector Hamiltonians), in particular whether or not they have ``trivial" ground states, where a state is trivial if it is constructed by a local quantum circuit of bounded depth and range acting on a product state. It is known that Hamiltonians such as the toric code only have nontrivial ground states in two dimensions. Conversely, commuting projector Hamiltonians which are sums of two-body interactions have trivial ground states\cite{bv}. Using a coarse-graining procedure, this implies that any such Hamiltonian with bounded range interactions in one dimension has a trivial ground state. In this paper, we further explore the question of which Hamiltonians have trivial ground states. We define an ``interaction complex" for a Hamiltonian, which generalizes the notion of interaction graph and we show that if the interaction complex can be continuously mapped to a $1$-complex using a map with bounded diameter of pre-images then the Hamiltonian has a trivial ground state assuming one technical condition on the Hamiltonians holds (this condition holds for all stabilizer Hamiltonians, and we additionally prove the result for all Hamiltonians under one assumption on the $1$-complex). While this includes the cases considered by Ref.~\onlinecite{bv}, we show that it also includes a larger class of Hamiltonians whose interaction complexes cannot be coarse-grained into the case of Ref.~\onlinecite{bv} but still can be mapped continuously to a $1$-complex. One motivation for this study is an approach to the quantum PCP conjecture. We note that many commonly studied interaction complexes can be mapped to a $1$-complex after removing a small fraction of sites. For commuting projector Hamiltonians on such complexes, in order to find low energy trivial states for the original Hamiltonian, it would suffice to find trivial ground states for the Hamiltonian with those sites removed. Such trivial states can act as a classical witness to the existence of a low energy state. While this result applies for commuting Hamiltonians and does not necessarily apply to other Hamiltonians, it suggests that to prove a quantum PCP conjecture for commuting Hamiltonians, it is worth investigating interaction complexes which cannot be mapped to $1$-complexes after removing a small fraction of points. We define this more precisely below; in some sense this generalizes the notion of an expander graph. Surprisingly, such complexes do exist as will be shown elsewhere\cite{fh}, and have useful properties in quantum coding theory.

scholarly journals A scaled MP-PIC method for bubbling fluidization

2021 ◽  
Author(s):  
Xing Zhao ◽  
Yong Jiang ◽  
Fei Li ◽  
Wei Wang
Keyword(s):  
Fluidized Beds ◽  
Volume Fraction ◽  
Phase Particle ◽  
Scaling Law ◽  
Coarse Graining ◽  
Coarse Grained ◽  
Particle In Cell ◽  
Wide Range ◽  
Pic Method ◽  
Multi Phase

Coarse-grained methods have been widely used in simulations of gas-solid fluidization. However, as a key parameter, the coarse-graining ratio, and its relevant scaling law is still far from reaching a consensus. In this work, a scaling law is developed based on a similarity analysis, and then it is used to scale the multi-phase particle-in-cell (MP-PIC) method, and validated in the simulation of two bubbling fluidized beds. The simulation result shows this scaled MP-PIC can reduce the errors of solids volume fraction and velocity distributions over a wide range of coarse-graining ratios. In future, we expect that a scaling law with consideration of the heterogeneity inside a parcel or numerical particle will further improve the performance of coarse-grained modeling in simulation of fluidized beds.

scholarly journals Coarse-graining for fast dynamics of order parameters in the phase-field model

2018 ◽  
Vol 376 (2113) ◽  
pp. 20170203 ◽  
Author(s):  
D. Jou ◽  
P. K. Galenko
Keyword(s):  
Master Equation ◽  
Thermodynamic Equilibrium ◽  
Phase Field ◽  
Order Parameter ◽  
Field Model ◽  
Local Thermodynamic Equilibrium ◽  
Phase Field Model ◽  
Coarse Graining ◽  
Order Parameters ◽  
Coarse Grained

In standard descriptions, the master equation can be obtained by coarse-graining with the application of the hypothesis of full local thermalization that is equivalent to the local thermodynamic equilibrium. By contrast, fast transformations proceed in the absence of local equilibrium and the master equation must be obtained with the absence of thermalization. In the present work, a non-Markovian master equation leading, in specific cases of relaxation to local thermodynamic equilibrium, to hyperbolic evolution equations for a binary alloy, is derived for a system with two order parameters. One of them is a conserved order parameter related to the atomistic composition, and the other one is a non-conserved order parameter, which is related to phase field. A microscopic basis for phenomenological phase-field models of fast phase transitions, when the transition is so fast that there is not sufficient time to achieve local thermalization between two successive elementary processes in the system, is provided. In a particular case, when the relaxation to local thermalization proceeds by the exponential law, the obtained coarse-grained equations are related to the hyperbolic phase-field model. The solution of the model equations is obtained to demonstrate non-equilibrium phenomenon of solute trapping which appears in rapid growth of dendritic crystals. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.

scholarly journals Coarse Graining, Nonmaximal Entropy, and Power Laws

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 737
Author(s):  
Fernando Pérez-Cárdenas ◽  
Lorenzo Resca ◽  
Ian Pegg
Keyword(s):  
Maximum Entropy ◽  
Power Law ◽  
Lattice Gas ◽  
Maximum Entropy Principle ◽  
Coarse Graining ◽  
Power Laws ◽  
Density Fluctuations ◽  
Coarse Grained ◽  
Dimensional Lattice ◽  
Entropy Principle

We show that coarse graining produces significant and predictable effects on the entropy of states of equilibrium when the scale of coarse graining becomes comparable to that of density fluctuations. We demonstrate that a coarse-grained entropy typically evolves toward a state of effective equilibrium with a lower value than that of the state of maximum entropy theoretically possible. The finer the coarse graining, the greater the drop in effective entropy, and the more relevant the fluctuations around that. Fundamental considerations allow us to derive a remarkable power law that relates coarse graining to the effective entropy gap. Another power law is found that precisely relates the noise range of effective entropy fluctuations to coarse graining. We test both power laws with numerical simulations based on a well-studied two-dimensional lattice gas model. As expected, the effects of these power laws diminish as our description approaches a macroscopic level, eventually disappearing in the thermodynamic limit, where the maximum entropy principle is reasserted.

scholarly journals Coarse-graining via EDP-convergence for linear fast-slow reaction systems

2020 ◽  
Vol 30 (09) ◽  
pp. 1765-1807 ◽  
Author(s):  
Alexander Mielke ◽  
Artur Stephan
Keyword(s):  
Detailed Balance ◽  
Reaction System ◽  
Gradient Flow ◽  
Coarse Graining ◽  
Reaction Rates ◽  
Coarse Grained ◽  
Gradient Structure ◽  
Reaction Systems ◽  
Fast Reactions ◽  
Finite State

We consider linear reaction systems with slow and fast reactions, which can be interpreted as master equations or Kolmogorov forward equations for Markov processes on a finite state space. We investigate their limit behavior if the fast reaction rates tend to infinity, which leads to a coarse-grained model where the fast reactions create microscopically equilibrated clusters, while the exchange mass between the clusters occurs on the slow time scale. Assuming detailed balance the reaction system can be written as a gradient flow with respect to the relative entropy. Focusing on the physically relevant cosh-type gradient structure we show how an effective limit gradient structure can be rigorously derived and that the coarse-grained equation again has a cosh-type gradient structure. We obtain the strongest version of convergence in the sense of the Energy-Dissipation Principle (EDP), namely EDP-convergence with tilting.

scholarly journals Coarse-Grained Models Reveal Functional Dynamics - I. Elastic Network Models – Theories, Comparisons and Perspectives

2008 ◽  
Vol 2 ◽  
pp. BBI.S460 ◽  
Author(s):  
Lee-Wei Yang ◽  
Choon-Peng Chng
Keyword(s):  
Conformational Changes ◽  
Conformational Dynamics ◽  
Computational Cost ◽  
Network Models ◽  
Coarse Graining ◽  
Coarse Grained ◽  
Elastic Network ◽  
Elastic Network Models ◽  
Time Space ◽  
Functional Dynamics

In this review, we summarize the progress on coarse-grained elastic network models (CG-ENMs) in the past decade. Theories were formulated to allow study of conformational dynamics in time/space frames of biological interest. Several highlighted models and their underlined hypotheses are introduced in physical depth. Important ENM offshoots, motivated to reproduce experimental data as well as to address the slow-mode-encoded configurational transitions, are also introduced. With the theoretical developments, computational cost is significantly reduced due to simplified potentials and coarse-grained schemes. Accumulating wealth of data suggest that ENMs agree equally well with experiment in describing equilibrium dynamics despite their distinct potentials and levels of coarse-graining. They however do differ in the slowest motional components that are essential to address large conformational changes of functional significance. The difference stems from the dissimilar curvatures of the harmonic energy wells described for each model. We also provide our views on the predictability of ‘open to close’ (open→close) transitions of biomolecules on the basis of conformational selection theory. Lastly, we address the limitations of the ENM formalism which are partially alleviated by the complementary CG-MD approach, to be introduced in the second paper of this two-part series.

scholarly journals Energy renormalization for coarse-graining polymers having different segmental structures

2019 ◽  
Vol 5 (4) ◽  
pp. eaav4683 ◽  
Author(s):  
Wenjie Xia ◽  
Nitin K. Hansoge ◽  
Wen-Sheng Xu ◽  
Frederick R. Phelan ◽  
Sinan Keten ◽  
...  
Keyword(s):  
Dynamic Properties ◽  
Interaction Strength ◽  
Configurational Entropy ◽  
Coarse Graining ◽  
Soft Materials ◽  
Polymer Materials ◽  
Coarse Grained ◽  
Art Form ◽  
Polymer Models ◽  
Energy Renormalization

Multiscale coarse-grained (CG) modeling of soft materials, such as polymers, is currently an art form because CG models normally have significantly altered dynamics and thermodynamic properties compared to their atomistic counterparts. We address this problem by exploiting concepts derived from the generalized entropy theory (GET), emphasizing the central role of configurational entropy sc in the dynamics of complex fluids. Our energy renormalization (ER) method involves varying the cohesive interaction strength in the CG models in such a way that dynamic properties related to sc are preserved. We test this ER method by applying it to coarse-graining polymer melts (i.e., polybutadiene, polystyrene, and polycarbonate), representing polymer materials having a relatively low, intermediate, and high degree of glass “fragility”. We find that the ER method allows the dynamics of the atomistic polymer models to be faithfully described to a good approximation by CG models over a wide temperature range.

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