Fluctuations in an equilibrium hard-disk fluid: Explicit size effects

Román, F. L.; White, J. A.; Velasco, S.

doi:10.1063/1.474824

Cited by 46 publications

(49 citation statements)

References 11 publications

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“…Salacuse et al [12] identify two types of such effects (see also Refs. [26,27]). First, fixing the total number of particles in the simulation box leads to so-called explicit (or ensemble) size effects.…”

Section: B Review Of Existing Methodsmentioning

confidence: 99%

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Small-angle scattering of dense, polydisperse granular porous media: Computation free of size effects

Brisard

Levitz

2013

Phys. Rev. E

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Small-angle x-ray and neutrons scattering is a widespread experimental tool for the investigation of the microstructure of random heterogeneous materials. Validation of (computer-generated) model microstructures often requires the numerical computation of the scattering intensity, which must be carried out with great care due to finite size effects. In this paper, a new method for this computation is presented. It is superior to previously existing methods for three reasons: First, it applies to any type of microstructure (not necessarily granular). Second, closed-form expressions of the size effects inherent to the proposed method can be rigorously derived and removed (in this sense, our method is free of size effects). Third, the complexity of the new algorithm is linear and the computation can easily be updated to account for local changes of the microstructure, while most existing algorithms are quadratic and any change of the microstructure requires a full recomputation. The present paper provides full derivation and validation of this method. Application to the computation of the scattering intensity of dense, polydisperse assemblies of spheres is then presented. A new, simple algorithm for the generation of these dense configurations is introduced. Finally, the results are critically reviewed in the perspective of hardened cement pastes.

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Section: B Review Of Existing Methodsmentioning

confidence: 99%

“…In other words, Eqs. (23) and (25)- (27) remain valid if J is substituted to J w , and the whole deconvolution procedure can be summarized as follows:…”

Section: E Deconvolution Of Blurred Spectrummentioning

confidence: 99%

Small-angle scattering of dense, polydisperse granular porous media: Computation free of size effects

Brisard

Levitz

2013

Phys. Rev. E

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“…72 In the present case, we have constructed the effective interactions to reproduce the RDFs, i.e., the structure. We have then used the model to study other structural properties, and the method used for the calculation of area compressibilities is based on the RDFs, 65,66 so major problems are not expected. However, if we would like to calculate other quantities, these issues would have to be considered.…”

Section: Discussionmentioning

confidence: 99%

“…The basic idea is the following: we first select a value for ␥ and use the IMC to obtain the interactions. We then perform a simulation for a larger system and use a block analysis method 65,66 to extrapolate the area compressibility to an infinite system. We then adjust the value of ␥ and continue until the area compressibility is of the right order of magnitude.…”

Section: Effective Potentialsmentioning

confidence: 99%

Coarse-grained model for phospholipid/cholesterol bilayer employing inverse Monte Carlo with thermodynamic constraints

Murtola¹,

Falck²,

Karttunen³

et al. 2007

The Journal of Chemical Physics

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The authors introduce a coarse-grained (CG) model for a lipid membrane comprised of phospholipids and cholesterol at different molar concentrations, which allows them to study systems that are approximately 100nm in linear size. The systems are studied in the fluid phase above the main transition temperature. The effective interactions for the CG model are extracted from atomic-scale molecular dynamics simulations using the inverse Monte Carlo (IMC) technique, an approach similar to the one the authors used earlier to construct another CG bilayer model [T. Murtola et al., J. Chem. Phys. 121, 9156 (2004)]. Here, the authors improve their original CG model by employing a more accurate description of the molecular structure for the phospholipid molecules. Further, they include a thermodynamic constraint in the IMC procedure to yield area compressibilities in line with experimental data. The more realistic description of the molecular structure of phospholipids and a more accurate representation of the interaction between cholesterols and phospholipid tails are shown to improve the behavior of the model significantly. In particular, the new model predicts the formation of denser transient regions in a pure phospholipid system, a finding that the authors have verified through large scale atomistic simulations. They also find that the model predicts the formation of cholesterol-rich and cholesterol-poor domains at intermediate cholesterol concentrations, in agreement with the original model and the experimental phase diagram. However, the domains observed here are much more distinct compared to the previous model. Finally, the authors also explore the limitations of the model, discussing its advantages and disadvantages.

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“…of ensemble and the choice of boundary conditions influences the results. These are so called explicit and implicit finite-size effects [23]. In addition this analysis visualizes the effects of the embedding medium on the compliances S ii .…”

Section: Analysis Of a Statistical Sum Rulementioning

confidence: 99%

Coarse-graining microscopic strains in a harmonic, two-dimensional solid: Elasticity, nonlocal susceptibilities, and nonaffine noise

Franzrahe

Nielaba

Sengupta³

2010

Phys. Rev. E

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In soft matter systems the local displacement field can be accessed directly by video microscopy enabling one to compute local strain fields and hence the elastic moduli in these systems using a coarse-graining procedure. Here, we study this process in detail for a simple triangular lattice of particles connected by harmonic springs in two-dimensions. Coarse-graining local strains obtained from particle configurations in a Monte Carlo simulation generates non-trivial, non-local strain correlations (susceptibilities), which may be understood within a generalized, Landau type elastic Hamiltonian containing up to quartic terms in strain gradients (K. Franzrahe et. al., Phys. Rev. E 78, 026106 (2008)). In order to demonstrate the versatility of the analysis of these correlations and to make our calculations directly relevant for experiments on colloidal solids, we systematically study in detail various parameters such as the choice of statistical ensemble, presence of external pressure and boundary conditions. Crucially, we show that special care needs to be taken for an accurate application of our results to actual experiments, where the analyzed area is embedded within a larger system, to which it is mechanically coupled. Apart from the smooth, affine strain fields, the coarse-graining procedure also gives rise to a noise field (χ) made up of non-affine displacements. Several properties of χ may be rationalized for the harmonic solid using a simple "cell model" calculation. Furthermore the scaling behavior of the probability distribution of the noise field (χ) is studied. We find that for any inverse temperature β, spring constant f , density ρ and coarsegraining length Λ the probability distribution can be obtained from a master curve of the scaling variable X = χβf /ρΛ 2 .

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Fluctuations in an equilibrium hard-disk fluid: Explicit size effects

Cited by 46 publications

References 11 publications

Small-angle scattering of dense, polydisperse granular porous media: Computation free of size effects

Small-angle scattering of dense, polydisperse granular porous media: Computation free of size effects

Coarse-grained model for phospholipid/cholesterol bilayer employing inverse Monte Carlo with thermodynamic constraints

Coarse-graining microscopic strains in a harmonic, two-dimensional solid: Elasticity, nonlocal susceptibilities, and nonaffine noise

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