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Bottom-up coarse-graining of a simple graphene model: The blob picture
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10.1063/1.3554395
/content/aip/journal/jcp/134/6/10.1063/1.3554395
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/6/10.1063/1.3554395

Figures

Image of FIG. 1.
FIG. 1.

Construction of the different blobs and their arrangement in the graphene lattice. The integer numbers indicate the number of C-atoms in one blob, i.e., the coarse-graining number .

Image of FIG. 2.
FIG. 2.

Illustration of the forces and used in the graphene model.

Image of FIG. 3.
FIG. 3.

Blob force autocorrelation function .

Image of FIG. 4.
FIG. 4.

Fourier transforms and and the time smoothing function with a suitable choice of its time constant τ. (Top) , τ = 2.42t*. (Middle) , τ = 1.97t*. (Bottom) , τ = 1.98t*.

Image of FIG. 5.
FIG. 5.

Comparison of the velocity autocorrelation function (BVACF) and of the smoothed force autocorrelation function (BFACF). (Top) . (Middle) . (Bottom) .

Image of FIG. 6.
FIG. 6.

Velocity autocorrelation functions of blobs (BVACFs) for (top) and (bottom), respectively, normalized with 2k B T/M. MD-BVACF stands for the BVACF as computed from MD. DPD-BVACF is the BVACF as computed from DPD. NDPD-BVACF denotes the result obtained by removing friction and noise from DPD.

Image of FIG. 7.
FIG. 7.

Velocity cross-correlation functions of neighboring blobs (BVCCFs) for (top) and (bottom), respectively, normalized with 2k B T/M. MD–BVCCF stands for the BVCCF as computed from MD. DPD–BVCCF is the BVCCF as computed from DPD. NDPD–BVCCF denotes the result obtained by removing friction and noise from DPD.

Image of FIG. 8.
FIG. 8.

Comparison of the decay of a shear wave of wavelength equal to the size of the system as a function of time, for MD and DPD models. While the MD simulation decays on a time scale not appreciable in the plot (0.1% per oscillation), the DPD simulation displays significant dissipation.

Tables

Generic image for table
Table I.

Computed frequencies ω and sound speeds c of longitudinal (L) and transverse (T) waves for the given wavelengths λ x and λ y , respectively. The given wavelengths are equal to the dimensions of the simulation domain containing N C = 10 368 atoms (cf. Table II). The numbers in brackets denote the error of the last decimal place.

Generic image for table
Table II.

Number of resulting blobs in the two simulated graphene sheets for each .

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/content/aip/journal/jcp/134/6/10.1063/1.3554395
2011-02-09
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Bottom-up coarse-graining of a simple graphene model: The blob picture
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/6/10.1063/1.3554395
10.1063/1.3554395
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