scholarly journals Coarse-graining and symplectic non-squeezing

2021 ◽  
pp. 126720
Author(s):  
Nikolaos Kalogeropoulos
Keyword(s):  
Coarse Graining

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 .

scholarly journals The Systematic Bias of Entropy Calculation in the Multi-Scale Entropy Algorithm

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 659
Author(s):  
Jue Lu ◽  
Ze Wang
Keyword(s):  
Time Series ◽  
Standard Deviation ◽  
Coarse Graining ◽  
Sample Entropy ◽  
Systematic Bias ◽  
Original Time Series ◽  
Multi Scale ◽  
Calculation Results ◽  
Surrogate Measure ◽  
Original Time

Entropy indicates irregularity or randomness of a dynamic system. Over the decades, entropy calculated at different scales of the system through subsampling or coarse graining has been used as a surrogate measure of system complexity. One popular multi-scale entropy analysis is the multi-scale sample entropy (MSE), which calculates entropy through the sample entropy (SampEn) formula at each time scale. SampEn is defined by the “logarithmic likelihood” that a small section (within a window of a length m) of the data “matches” with other sections will still “match” the others if the section window length increases by one. “Match” is defined by a threshold of r times standard deviation of the entire time series. A problem of current MSE algorithm is that SampEn calculations at different scales are based on the same matching threshold defined by the original time series but data standard deviation actually changes with the subsampling scales. Using a fixed threshold will automatically introduce systematic bias to the calculation results. The purpose of this paper is to mathematically present this systematic bias and to provide methods for correcting it. Our work will help the large MSE user community avoiding introducing the bias to their multi-scale SampEn calculation results.

scholarly journals Time-Dependent Diffusion Coefficients for Chaotic Advection due to Fluctuations of Convective Rolls

Fluids ◽  
2018 ◽  
Vol 3 (4) ◽  
pp. 99 ◽  
Author(s):  
Kazuma Yamanaka ◽  
Takayuki Narumi ◽  
Megumi Hashiguchi ◽  
Hirotaka Okabe ◽  
Kazuhiro Hara ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Liquid Crystals ◽  
Diffusion Coefficients ◽  
Coarse Graining ◽  
Chaotic Advection ◽  
Time Dependent ◽  
Local Order ◽  
Weak Turbulence ◽  
Normal Diffusion ◽  
Convective Rolls

The properties of chaotic advection arising from defect turbulence, that is, weak turbulence in the electroconvection of nematic liquid crystals, were experimentally investigated. Defect turbulence is a phenomenon in which fluctuations of convective rolls arise and are globally disturbed while maintaining convective rolls locally. The time-dependent diffusion coefficient, as measured from the motion of a tagged particle driven by the turbulence, was used to clarify the dependence of the type of diffusion on coarse-graining time. The results showed that, as coarse-graining time increases, the type of diffusion changes from superdiffusion → subdiffusion → normal diffusion. The change in diffusive properties over the observed timescale reflects the coexistence of local order and global disorder in the defect turbulence.

Effective force coarse-graining

2009 ◽  
Vol 11 (12) ◽  
pp. 2002 ◽  
Author(s):  
Yanting Wang ◽  
W. G. Noid ◽  
Pu Liu ◽  
Gregory A. Voth
Keyword(s):  
Coarse Graining ◽  
Effective Force

scholarly journals Tertiary Structure Model of Wild-Type and Mutated Actin using a Novel Coarse Graining Technique to Study Aortic Aneurysms

2010 ◽  
Vol 98 (3) ◽  
pp. 154a
Author(s):  
Joel D. Marquez ◽  
Steven Kreuzer ◽  
Jun Zhou ◽  
Chia-Cheng Liu ◽  
Esfandiar A. Khatiblou ◽  
...  
Keyword(s):  
Tertiary Structure ◽  
Coarse Graining ◽  
Aortic Aneurysms ◽  
Structure Model ◽  
Wild Type

scholarly journals Compactness by Coarse-Graining in Long-Range Lattice Systems

2020 ◽  
Vol 20 (4) ◽  
pp. 783-794
Author(s):  
Andrea Braides ◽  
Margherita Solci
Keyword(s):  
Long Range ◽  
Coarse Graining ◽  
Interaction Energies ◽  
Lattice Systems ◽  
Range Interaction ◽  
Surface Energies ◽  
Continuum Analysis ◽  
Long Range Interaction ◽  
Typical Range ◽  
Limit Energy

AbstractWe consider energies on a periodic set {\mathcal{L}} of the form {\sum_{i,j\in\mathcal{L}}a^{\varepsilon}_{ij}\lvert u_{i}-u_{j}\rvert}, defined on spin functions {u_{i}\in\{0,1\}}, and we suppose that the typical range of the interactions is {R_{\varepsilon}} with {R_{\varepsilon}\to+\infty}, i.e., if {\lvert i-j\rvert\leq R_{\varepsilon}}, then {a^{\varepsilon}_{ij}\geq c>0}. In a discrete-to-continuum analysis, we prove that the overall behavior as {\varepsilon\to 0} of such functionals is that of an interfacial energy. The proof is performed using a coarse-graining procedure which associates to scaled functions defined on {\varepsilon\mathcal{L}} with equibounded energy a family of sets with equibounded perimeter. This agrees with the case of equibounded {R_{\varepsilon}} and can be seen as an extension of coerciveness result for short-range interactions, but is different from that of other long-range interaction energies, whose limit exits the class of surface energies. A computation of the limit energy is performed in the case {\mathcal{L}=\mathbb{Z}^{d}}.

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