Coarse-grained Scale Research Articles

Universalities of earthquake-network characteristics

The scale-free and small-world properties are studied in detail for the complex earthquake networks constructed from the seismic data sets taken from California (USA), Japan, Iran and Chile. It is found that, in all these geographical regions, both the exponent γ of the power-law connectivity distribution and the clustering coefficient C take the universal invariant values γ≈1 and C≈0.85, respectively, as the cell size, which is the scale of coarse graining needed for construction of network, becomes larger than a certain value. A possible physical interpretation is given to the emergence of such remarkable invariance.

The Impact of Grain Size on Oxidation Behavior of TP304H Austenitic Stainless Steel at High Temperature in Air

Exposed to 650°C air, TP304H stainless steel with two different grain size was oxidized at this temperature. At the meantime, comparison of their oxidation was through the oxidation kinetics curves and analysis of the morphology and composition of oxide scale which conducted by SEM and X-ray. The results showed that the oxidation rate of TP304H stainless steel was slowed down by grain refinement and oxide scale of fine-grained TP304H steel was thinner than that of coarse-grained steel. The nucleation and the growth of nuclei of coarse-grained oxide scale were more rapid. In addition, the grain refinement of austenitic stainless steel accelerated the diffusivity of Cr and made for the formation of dense and continuous oxide scale, so that the oxidation of stainless steel can be effectively inhabited.

First-principle approach to rescale the dynamics of simulated coarse-grained macromolecular liquids

We present a detailed derivation and testing of our approach to rescale the dynamics of mesoscale simulations of coarse-grained polymer melts (I. Y. Lyubimov, J. McCarty, A. Clark, and M. G. Guenza, J. Chem. Phys. 132, 224903 (2010)). Starting from the first-principle Liouville equation and applying the Mori-Zwanzig projection operator technique, we derive the generalized Langevin equations (GLEs) for the coarse-grained representations of the liquid. The chosen slow variables in the projection operators define the length scale of coarse graining. Each polymer is represented at two levels of coarse graining: monomeric as a bead-and-spring model and molecular as a soft colloid. In the long-time regime where the center-of-mass follows Brownian motion and the internal dynamics is completely relaxed, the two descriptions must be equivalent. By enforcing this formal relation we derive from the GLEs the analytical rescaling factors to be applied to dynamical data in the coarse-grained representation to recover the monomeric description. Change in entropy and change in friction are the two corrections to be accounted for to compensate the effects of coarse graining on the polymer dynamics. The solution of the memory functions in the coarse-grained representations provides the dynamical rescaling of the friction coefficient. The calculation of the internal degrees of freedom provides the correction of the change in entropy due to coarse graining. The resulting rescaling formalism is a function of the coarse-grained model and thermodynamic parameters of the system simulated. The rescaled dynamics obtained from mesoscale simulations of polyethylene, represented as soft-colloidal particles, by applying our rescaling approach shows a good agreement with data of translational diffusion measured experimentally and from simulations. The proposed method is used to predict self-diffusion coefficients of new polyethylene samples.

Coarse-grained statistics for attributing criticality to heterogeneous neural networks

Multi-scale modelling has great use in computational neuroscience [1]. This typically involves a stage of coarse graining. However, the assumptions (e.g. that the sum of ensemble activities are dominated by the mean and fluctuations are Gaussian) that underlie a coarse-grained description have yet to be qualified, especially in the biological context where intrinsic diversity can contribute to complex activity patterns [2]. Recent work has reported on the effects that intrinsic properties can have on overall network activity [3], while parametric variance is proposed to have self-regulatory and tuning effects [4,5]. Here, we report on multi-scale analysis of data from large-scale neuronal network simulations which involves a coarse-graining procedure of the observed spike patterns. At each scale of coarse-graining, observables are calculated and the scale-dependence of summary statistics is determined. We observe whether the activity forms contiguous events, also known as avalanches, and measure their size. This study differs from others in that it uses coarse graining in both time and space. Our model system contains a heterogeneous population of adaptive exponential integrate-and-fire model neurons with various heterogeneities on a spatial sheet with toroidal boundary conditions. We then examine locally averaged spike rates calculated across space and time on different scales to form a hierarchical description. We then analyse these coarse grained variables in a detrended fluctuation analysis (DFA). We find that there is an appropriate scale for intermittency in the coarse-grained observables. We characterise the properties of contiguous events in this regime and qualify the hypothesis of a critical phase transition. In a second analysis, we study spatial correlations in the coarse grained activity and their scaling properties confirming our findings using DFA. Our numerical renormalisation group analysis allows us to determine those properties which are most relevant to meso/macroscopic statistics of spiking neural networks, while at the same time providing a means to formally investigate brain criticality.

Complexity and characteristic frequency studies in ECG signals of mice based on multiple scale factors

Existing methods of physiological signal analysis based on nonlinear dynamic theories only examine the complexity difference of the signals under a single sampling frequency. We developed a technique to measure the multifractal characteristic parameter intimately associated with physiological activities through a frequency scale factor. This parameter is highly sensitive to physiological and pathological status. Mice received various drugs to imitate different physiological and pathological conditions, and the distributions of mass exponent spectrum curvature with scale factors from the electrocardiogram (ECG) signals of healthy and drug injected mice were determined. Next, we determined the characteristic frequency scope in which the signal was of the highest complexity and most sensitive to impaired cardiac function, and examined the relationships between heart rate, heartbeat dynamic complexity, and sensitive frequency scope of the ECG signal. We found that all animals exhibited a scale factor range in which the absolute magnitudes of ECG mass exponent spectrum curvature achieve the maximum, and this range (or frequency scope) is not changed with calculated data points or maximal coarse-grained scale factor. Further, the heart rate of mice was not necessarily associated with the nonlinear complexity of cardiac dynamics, but closely related to the most sensitive ECG frequency scope determined by characterization of this complex dynamic features for certain heartbeat conditions. Finally, we found that the health status of the hearts of mice was directly related to the heartbeat dynamic complexity, both of which were positively correlated within the scale factor around the extremum region of the multifractal parameter. With increasing heart rate, the sensitive frequency scope increased to a relatively high location. In conclusion, these data provide important theoretical and practical data for the early diagnosis of cardiac disorders.

Finite data-size scaling of clustering in earthquake networks

An earthquake network is known to be of the small-world type. The values of the network’s characteristics, however, depend not only on the cell size (i.e., the scale of coarse graining needed for constructing the network) but also on the size of a seismic data set. Here, discovery of a scaling law for the clustering coefficient in terms of the data size, which is referred to here as finite data-size scaling, is reported. Its universality is shown to be supported by the detailed analysis of the data taken from California, Japan and Iran. Effects of setting a threshold of magnitude are also discussed.

Statistical properties of the coarse-grained velocity gradient tensor in turbulence: Monte-Carlo simulations of the tetrad model

A proper description of the velocity gradient tensor is crucial for understanding the dynamics of turbulent flows, in particular the energy transfer from large to small scales. Insight into the statistical properties of the velocity gradient tensor and into its coarse-grained generalization can be obtained with the help of a stochastic ‘tetrad model’ that describes the coarse-grained velocity gradient tensor based on the evolution of four points. Although the solution of the stochastic model can be formally expressed in terms of path integrals, its numerical determination in terms of the Monte-Carlo method is very challenging, as very few configurations contribute effectively to the statistical weight. Here, we discuss a strategy that allows us to solve the tetrad model numerically. The algorithm is based on the importance sampling method, which consists here of identifying and sampling preferentially the configurations that are likely to correspond to a large statistical weight, and selectively rejecting configurations with a small statistical weight. The algorithm leads to an efficient numerical determination of the solutions of the model and allows us to determine their qualitative behavior as a function of scale. We find that the moments of order n⩽4 of the solutions of the model scale with the coarse-graining scale and that the scaling exponents are very close to the predictions of the Kolmogorov theory. The model qualitatively reproduces quite well the statistics concerning the local structure of the flow. However, we find that the model generally tends to predict an excess of strain compared to vorticity. Thus, our results show that while some physical aspects are not fully captured by the model, our approach leads to a very good description of several important qualitative properties of real turbulent flows.

Bimetric renormalization group flows in quantum Einstein gravity

The formulation of an exact functional renormalization group equation for quantum Einstein gravity necessitates that the underlying effective average action depends on two metrics, a dynamical metric giving the vacuum expectation value of the quantum field, and a background metric supplying the coarse graining scale. The central requirement of “background independence” is met by leaving the background metric completely arbitrary. This bimetric structure entails that the effective average action may contain three classes of interactions: those built from the dynamical metric only, terms which are purely background, and those involving a mixture of both metrics. This work initiates the first study of the full-fledged gravitational RG flow, which explicitly accounts for this bimetric structure, by considering an ansatz for the effective average action which includes all three classes of interactions. It is shown that the non-trivial gravitational RG fixed point central to the asymptotic safety program persists upon disentangling the dynamical and background terms. Moreover, upon including the mixed terms, a second non-trivial fixed point emerges, which may control the theory’s IR behavior.

Multiscale entropy of laser Doppler flowmetry signals in healthy human subjects

The cardiovascular system (CVS) regulation can be studied from a central viewpoint, through heart rate variability (HRV) data, and from a peripheral viewpoint, through laser Doppler flowmetry (LDF) signals. Both the central and peripheral CVSs are regulated by several interacting mechanisms, each having its own temporal scale. The central CVS has been the subject of many multiscale studies. By contrast, these studies at the level of the peripheral CVS are very recent. Among the multiscale studies performed on the central CVS data, multiscale entropy has been proven to give interesting physiological information for diagnostic purposes. However, no multiscale entropy analysis has been performed on LDF signals. The authors' goal is therefore to propose a first multiscale entropy study of LDF data recorded in healthy subjects. The LDF signals recorded in the forearm of seven healthy subjects are processed. Their period sampling is T=50 ms, and coarse-graining scales from T to 23T are studied. Also, for validation, the algorithm is first tested on synthetic signals of known theoretical multiscale entropy. The results reveal nonmonotonic evolution of the multiscale entropy of LDF signals, with a maximum at small scales around 7T and a minimum at longer scales around 18T, singling out in this way two distinctive scales where the LDF signals undergo specific changes from high to low complexity. This also marks a strong contrast with the HRV signals that usually display a monotonic increase in the evolution of the multiscale entropy. Multiscale entropy of LDF signals in healthy subjects shows variation with scales. Moreover, as the variation pattern observed appears similar for all the tested signals, multiscale entropy could potentially be a useful stationary signature for LDF signals, which otherwise are probe-position and subject dependent. Further work could now be conducted to evaluate possible diagnostic purposes of the multiscale entropy of LDF signals.

Well-behaved coarse-grained model of density-functional theory

A coarse-grained version of quantum density-functional theory featuring a limited spatial resolution is shown to model formal density-functional theory (DFT). This means that all densities are ensemble-$V$-representable (that is, by mixed states), the intrinsic energy functional $F$ is a continuous function of the density, and the representing external potential is the functional derivative of the intrinsic energy, in the sense of directional derivatives within the domain of $F$. The representing potential $v[\ensuremath{\rho}]$ also has a quasicontinuity property, specifically, $v[\ensuremath{\rho}]\ensuremath{\rho}$ is continuous as a function of $\ensuremath{\rho}$. Convergence of the intrinsic energy, coarse-grained densities, and representing potentials in the limit of coarse-graining scale going to zero are studied vis-\`a-vis Lieb's ${L}^{1}\ensuremath{\cap}{L}^{3}$ theory. The intrinsic energy converges monotonically to its fine-grained (continuum) value, and coarse-grainings of a density $\ensuremath{\rho}$ converge strongly to $\ensuremath{\rho}$. If a sequence of coarse-grained densities converges strongly to $\ensuremath{\rho}$ and their representing potentials converge weak-${}^{*}$, the limit is the representing potential for $\ensuremath{\rho}$. Conversely, ${L}^{3/2}+{L}^{\ensuremath{\infty}}$ representability implies the existence of such a coarse-grained sequence.

Cooperativity at different space and time scales in multiscale protein dynamics

A method proposed by Matsunaga [Phys. Rev. Lett. 99, 238103 (2007)] is applied to simple stochastic models and two model proteins composed of 46 amino beads with three different kinds of residues. The method, which is based on the combination of the principal component analysis and the finite size Lyapunov exponent, characterize the coarse-grained dynamics in different spatiotemporal hierarchies in protein dynamics. The application of the method to model proteins reveals that the low-indexed (large-variance) principal components carry less-divergent, regularized dynamics at the coarse-grained scales on a less-frustrated energy landscape, whereas this less-divergent nature is less pronounced for a protein model with a more frustrated energy landscape. It is also revealed that our technique can differentiate the collective motions on the projected principal component space inherent to the system and the apparent collective behavior which can appear even in high-dimensional stochastic systems.

A fully deterministic micro–macro simulation of complex flows involving reversible network fluid models

Micro–macro models associate the coarse-grained molecular scale of the kinetic theory to the macroscopic scale of continuum mechanics. The conservation equations are solved along with the microscopic equation or the so-called Fokker–Planck equation. In this paper, a micro–macro approach based on the separated representation introduced in [2,3] with the Stream-Tube method [10–12,21,22] is implemented to study the main features of fiber and polymer networks solutions in complex flows. The Fokker–Planck equation, that defines the fluid microstructure, is solved using a separated representation strategy and is coupled to the macroscopic equations through the macroscopic extra-stress tensor evaluated at the microscopic level. Then, the flow kinematics is solved by applying the Stream-Tube method.

Dynamical fluctuations in dense granular flows

We have made measurements of force and velocity fluctuations in a variety of dense, gravity-driven granular flows under flow conditions close to the threshold of jamming. The measurements reveal a microscopic state that evolves rapidly from entirely collisional to largely frictional, as the system is taken close to jamming. On coarse-grained time scales, some descriptors of the dynamics-such as the probability distribution of force fluctuations, or the mean friction angle-do not reflect this profound change in the micromechanics of the flow. Other quantities, such as the frequency spectrum of force fluctuations, change significantly, developing low-frequency structure in the fluctuations as jamming is approached. We also show evidence of spatial structure, with force fluctuations being organized into local collision chains. These local structures propagate rapidly in the flow, with consequences far away from their origin, leading to long-range correlations in velocity fluctuations.

Ultraweak excitations of the quantum vacuum as physical models of gravity

It has been argued by several authors that the spacetime curvature observed in gravitational fields, and the same idea of forms of physical equivalence different from the Lorentz group, might emerge from the dynamical properties of the physical flat-space vacuum in a suitable hydrodynamic limit. To explore this idea, one could start by representing the physical vacuum as a Bose condensate of elementary quanta and look for vacuum excitations that, on a coarse grained scale, resemble the Newtonian potential. In this way, it is relatively easy to match the weak-field limit of classical general relativity or of some of its possible variants. The idea that Bose condensates can provide various forms of gravitational dynamics is not new. Here, I want to emphasize some genuine quantum field theoretical aspects that can help to understand (i) why infinitesimally weak, 1/r interactions can indeed arise from the same physical vacuum of electroweak and strong interactions and (ii) why, on a coarse-grained scale, their dynamical effects can be reabsorbed into an effective curved metric structure.

Inversion of radial distribution functions to pair forces by solving the Yvon–Born–Green equation iteratively

We develop a new method to invert the target profiles of radial distribution functions (RDFs) to the pair forces between particles. The target profiles of RDFs can be obtained from all-atom molecular dynamics (MD) simulations or experiments and the inverted pair forces can be used in molecular simulations at a coarse-grained (CG) scale. Our method is based on a variational principle that determines the mean forces between CG sites after integrating out the unwanted degrees of freedom. The solution of this variational principle has been shown to correspond to the Yvon-Born-Green (YBG) equation [Noid et al., J. Phys. Chem. B 111, 4116 (2007)]. To invert RDFs, we solve the YBG equation iteratively by running a CG MD simulation at each step of iteration. A novelty of the iterative-YBG method is that during iteration, CG forces are updated according to the YBG equation without imposing any approximation as is required by other methods. As a result, only three to ten iterations are required to achieve convergence for all cases tested in this work. Furthermore, we show that not only are the target RDFs reproduced by the iterative solution; the profiles of the three-body correlation function in the YBG equation computed from all-atom and CG simulations also have a better agreement. The iterative-YBG method is applied to compute the CG forces of four molecular liquids to illustrate its efficiency and robustness: water, ethane, ethanol, and a water/methanol mixture. Using the resulting CG forces, all of the target RDFs observed in all-atom MD simulations are reproduced. We also show that the iterative-YBG method can be applied with a virial constraint to expand the representability of a CG force field. The iterative-YBG method thus provides a general and robust framework for computing CG forces from RDFs and could be systematically generalized to go beyond pairwise forces and to include higher-body interactions in a CG force field by applying the aforementioned variational principle to derive the corresponding YBG equation for iterative solution.

Normal mode analysis of biomolecular structures: functional mechanisms of membrane proteins.

Normal mode analysis of biomolecular structures: functional mechanisms of membrane proteins.

Local elasticity map and plasticity in a model Lennard-Jones glass

In this work we calculate the local elastic moduli in a weakly polydispersed two-dimensional Lennard-Jones glass undergoing a quasistatic shear deformation at zero temperature. The numerical method uses coarse-grained microscopic expressions for the strain, displacement, and stress fields. This method allows us to calculate the local elasticity tensor and to quantify the deviation from linear elasticity (local Hooke's law) at different coarse-graining scales. From the results a clear picture emerges of an amorphous material with strongly spatially heterogeneous elastic moduli that simultaneously satisfies Hooke's law at scales larger than a characteristic length scale of the order of five interatomic distances. At this scale, the glass appears as a composite material composed of a rigid scaffolding and of soft zones. Only recently calculated in nonhomogeneous materials, the local elastic structure plays a crucial role in the elastoplastic response of the amorphous material. For a small macroscopic shear strain, the structures associated with the nonaffine displacement field appear directly related to the spatial structure of the elastic moduli. Moreover, for a larger macroscopic shear strain we show that zones of low shear modulus concentrate most of the strain in the form of plastic rearrangements. The spatiotemporal evolution of this local elasticity map and its connection with long term dynamical heterogeneity as well as with the plasticity in the material is quantified. The possibility to use this local parameter as a predictor of subsequent local plastic activity is also discussed.

Hybrid particle-field molecular dynamics simulations for dense polymer systems

We propose a theoretical scheme for a hybrid simulation technique where self-consistent field theory and molecular dynamics simulation are combined (MD-SCF). We describe the detail of the main implementation issues on the evaluation of a smooth three-dimensional spatial density distribution and its special gradient based on the positions of particles. The treatments of our multiscale model system on an atomic scale or on a specific coarse-grained scale are carefully discussed. We perform a series of test simulations on this hybrid model system and compare the structural correlations on the atomic scale with those of classical MD simulations. The results are very encouraging and open a way to an efficient strategy that possess the main advantages common to the SCF and the atomistic approaches, while avoiding the disadvantages of each of the treatments.

Phenotypic plasticity in response to fine‐grained environmental variation in predation

Summary 1 In nature, organisms experience environmental variability at coarse-grained (inter-generational) and fine-grained (intra-generational) scales and a common response to environmental variation is phenotypic plasticity. The emphasis of most empirical work on plasticity has been on examining coarse-grained variation with the goal of understanding the costs and benefits of plastic responses in response to a particular environment. 2 In this study, we investigated the effects of fine-grained variation in predation on the inducible defences of larval wood frogs (Rana sylvatica) by widely altering the density and feeding schedule of caged predators (Dytiscus spp.) while holding average predation constant. 3 We found that predator cues induced change in tadpole behaviour, morphology, and mass. Surprisingly, however, temporal variation in predation did not cause the tadpoles to alter their activity (compared to a constant predation treatment) or mass. Temporal variation in predation did alter tadpole tail depth, but only when experiencing our most extreme variation treatment in which the predators were fed once every 8 days. Under these conditions, the predator-induced tadpole tail was less extreme compared to environments containing constant predation. 4 While a number of previous studies have examined behavioural responses of prey to temporal variation in predation risk without holding average predation constant, this appears to be the first test of temporal variation per se. As in previous studies of organism responses to temporal variation in resources, our results suggest that fine-grained environmental variability can affect the expression of phenotypically plastic traits, but our tadpoles appear to be generally unresponsive to this fine-grained variation for many of their traits.

Dielectric properties of solids in the regular and split-charge equilibration formalisms

We investigate the generic dielectric properties of solids in the split-charge equilibration (SQE) formalism, which contains the regular charge equilibration (QE) method as a limiting case, but augments it with a bond hardness term. It is shown that QE always mimics ideal conductors, while any positive bond hardness used in SQE turns the solid into a dielectric. Crystals with simple cubic and rocksalt structure are considered explicitly. For these symmetries, we solve the continuum limit of the SQE formalism analytically. As a result, we provide simple analytical expressions for how dielectric constant and penetration depth of the electrostatic field depend on atomic hardness, bond hardness, and lattice constant. This mapping may prove useful not only for force field parametrization but also for solving dielectric responses on coarse-grained scales. Successful comparison of numerical data to analytical solutions is made, including those containing discretization corrections.