Coarse-grained Scale Research Articles

Multi-scale comparison of topographic complexity indices in relation to plant species richness

Topographic complexity is a key component of habitat, which has been linked to increased species richness in many ecological communities. It can be measured in various ways and it is unclear whether these different measurements are mutually comparable when they relate to plant species richness at different spatial scales. Using a densely sampled set of observations for Rhododendrons (406 species and 13,126 georeferenced records) as a test case, we calculated eight topographic complexity indices from a 250-m resolution digital elevation model and examined their correlations with Rhododendron species richness in China at seven spatial scales: grain sizes 0.05°, 0.1°, 0.25°, 0.5°, 1.0°, 1.5°, and 2.0°. Our results showed that the eight topographic complexity indices were moderately to highly correlated with each other, and the relations between each pair of indices decreased with increasing grain size. However, with an increase in grain size, there was a higher correlation between topographic complexity indices and Rhododendron species richness. At finer scales (i.e. grain size≤1°), the standard deviation of elevation and range of elevation had significantly stronger correlations with Rhododendron species richness than other topographic complexity indices. Our findings indicate that different topographic complexity indices may have positive correlations with plant species richness. Moreover, the topographic complexity–species richness associations could be scale-dependent. In our case, the correlations between topographic complexity and Rhododendron species richness tended to be stronger at coarse-grained macro-habitat scales. We therefore suggest that topographic complexity index may serve as good proxy for studying the pattern of plant species richness at continental to global levels. However, choosing among topographic complexity indices must be undertaken with caution because these indices respond differently to grain sizes.

Finite-Ncorrections to Vlasov dynamics and the range of pair interactions

We explore the conditions on a pair interaction for the validity of the Vlasov equation to describe the dynamics of an interacting N-particle system in the large N limit. Using a coarse graining in phase space of the exact Klimontovich equation for the N-particle system, we evaluate, neglecting correlations of density fluctuations, the scalings with N of the terms describing the corrections to the Vlasov equation for the coarse-grained one-particle phase space density. Considering a generic interaction with radial pair force F(r), with F(r)∼1/r(γ) at large scales, and regulated to a bounded behavior below a "softening" scale ɛ, we find that there is an essential qualitative difference between the cases γ<d and γ>d, i.e., depending on the the integrability at large distances of the pair force. In the former case, the corrections to the Vlasov dynamics for a given coarse-grained scale are essentially insensitive to the softening parameter ɛ, while for γ>d the amplitude of these terms is directly regulated by ɛ, and thus by the small scale properties of the interaction. This corresponds to a simple physical criterion for a basic distinction between long-range (γ≤d) and short-range (γ>d) interactions, different from the canonical one (γ≤d+1 or γ>d+1) based on thermodynamic analysis. This alternative classification, based on purely dynamical considerations, is relevant notably to understanding the conditions for the existence of so-called quasistationary states in long-range interacting systems.

Dielectric and Viscoelastic Behavior of Star-Branched Polyisoprene: Two Coarse-Grained Length Scales in Dynamic Tube Dilation

cis-Polyisoprene (PI) chain has the type A dipole parallel along the backbone so that its large-scale (global) motion results in not only viscoelastic but also dielectric relaxation. Utilizing this feature of PI, this paper examined dielectric and viscoelastic behavior of star PI probe chains (arm molecular weight 10–3Ma = 9.5–23.5, volume fraction υ1 = 0.1) blended in a matrix of long linear PI (M = 1.12 × 106). The constraint release (CR)/dynamic tube dilation (DTD) mechanism was quenched for those dilute probes entangled with the much longer matrix, as evidenced from coincidence of the frequency dependence of the dielectric and viscoelastic losses of the probe in the blend. Comparison of the probe data in the blend and in monodisperse bulk revealed that the star probe relaxation is retarded and broadened on blending and the retardation/broadening is enhanced exponentially with Ma. This result in turn demonstrates significant CR/DTD contribution to the dynamics of star PI in bulk. The magnitude of retardation was quantitatively analyzed within the context of the tube model, with the aid of the dielectrically evaluated survival fraction of the dilated tube, φ′(t), and the literature data of CR time, τCR. In the conventional molecular picture of partial-DTD, the tube is assumed to dilate laterally, but not coherently along the chain backbone. The corresponding lateral partial-DTD relationship between φ′(t) and the normalized viscoelastic relaxation function μ(t), μ(t) = φ′(t)/β(t) with β(t) being the number of entanglement segments per laterally dilated segment (that was evaluated from the φ′(t) and τCR data), held for the μ(t) and φ′(t) data of star PI in bulk. Nevertheless, the observed retardation of the star probe relaxation on blending was less significant compared to the retardation expected for the arm motion (retraction) along the laterally dilated tube in bulk PI. This result suggests that the relaxation time of the probe in bulk is governed by the longitudinal partial-DTD that occurs coherently along the chain backbone. In fact, the magnitude of retardation evaluated from the φ′(t) and τCR data on the basis of this longitudinal partial-DTD picture was close to the observation. These results strongly suggest that the star PI chains in monodisperse bulk have two different coarse-grained length scales: the diameter of laterally dilated tube that determines the modulus level and the diameter of longitudinally dilated tube that reflects the path length for the arm retraction and determines the relaxation time. Thus, the star PI chains in bulk appear to move along the longitudinally dilated tube that wriggles in the laterally dilated tube. This molecular scenario is consistent with the previous finding for bulk linear PI [Matsumiya et al. Macromolecules 2013, 46, 6067].

A multi-scale model for texture development in Zr/Nb nanolayered composites processed by accumulative roll bonding

Recently it has been demonstrated that nanolayered hcp/bcc Zr/Nb composites can be fabricated with a severe plastic deformation technique called accumulative roll bonding (ARB) [1]. The final layer thickness averaged to approximately 90 nm for both phases. Interestingly, the texture measurements show that the textures in each phase correspond to those of rolled single-phase rolled Zr and Nb for a wide range of layer thickness from the micron to the nanoscales. This is in remarkable contrast to fcc/bcc Cu/Nb layered composites made by the same ARB technique, which developed textures that strongly deviated from theoretical rolling textures of Cu or Nb alone when the layers were refined to submicron and nanoscale dimensions. To model texture evolution and reveal the underlying deformation mechanisms, we developed a 3D multiscale model that combines crystal plasticity finite element with a thermally activated dislocation density based hardening law [2]. For systematic study, the model is applied to a two-phase Zr/Nb polycrystalline laminate and to the same polycrystalline Zr and polycrystalline Nb as single-phase metals. Consistent with the measurement, the model predicts that texture evolution in the phases in the composite and the relative activities of the hcp slip modes are very similar to those in the phases in monolithic form. In addition, the two-phase model also finds that no through-thickness texture gradient develops. This result suggests that neither the nanoscale grain sizes nor the bimetal Zr/Nb interfaces induce deformation mechanisms different from those at the coarse-grain scale.

Complexity of human postural control in subjects with unilateral peripheral vestibular hypofunction

Complexity is a new measure for identifying the adaptability of a complex system to meet possible challenges. For a center of pressure (COP) time series, the complexity measure represents the stability of postural control. In this study, multiscale entropy (MSE) was used to evaluate the complexity of COP time series in six test conditions of sensory organization test (SOT). Complexity index (CI) is defined as the summation of entropies with coarse-graining scales 1–20 by MSE. A total of 51 subjects belonging to 3 groups – healthy-young, healthy-elderly and dizzy – were recruited in this study. The COP signals in both anteroposterior (AP) and mediolateral (ML) directions were analyzed respectively. According to our results, the CI of AP-direction COP time series is significantly correlated to the equilibrium score, which represents the stability of postural control in SOT. The AP-direction sway is significant larger than the ML-direction sway, particularly in the test conditions with sway-surface. In additions, the CI of AP-direction COP for the healthy-elderly and dizzy groups are significantly lower than those for the healthy young group in the test conditions 1–4. The CI of ML-direction COP for the healthy-elderly group is significantly lower than those for the healthy-young and dizzy groups under test conditions 3 and 6. These results show that the complexity loss is a common status of AP-direction COP time series for both healthy-elderly and dizzy groups, and the complexity of ML-direction COP time series for subjects with unilateral vestibular dysfunction is higher than that for the healthy-elderly group specifically under test conditions 3 and 6.

Scanning tunneling macroscopy, black holes and AdS/CFT bulk locality

We establish resolution bounds on reconstructing a bulk field from boundary data on a timelike hypersurface. If the bulk only supports propagating modes, reconstruction is complete. If the bulk also supports evanescent modes, local reconstruction is not achievable unless one has exponential precision in knowledge of the boundary data. Without exponential precision, for a Minkowski bulk, one can reconstruct a spatially coarse-grained bulk field, but only out to a depth set by the coarse-graining scale. For an asymptotically AdS bulk, reconstruction is limited to a spatial coarse-graining proper distance set by the AdS scale. AdS black holes admit evanescent modes. We study the resolution bound in the large AdS black hole background and provide a dual CFT interpretation. Our results demonstrate that, if there is a black hole of any size in the bulk, then sub-AdS bulk locality is no longer well-encoded in boundary data in terms of local CFT operators. Specifically, in order to probe the bulk on sub-AdS scales using only boundary data in terms of local operators, one must either have such data to exponential precision or make further assumptions about the bulk state.

Diffusive evolution of experimental braided rivers

Water flowing over a loose granular bed organizes into a braided river, a network of ephemeral and interacting channels. The temporal and spatial evolution of this network of braided channels is not yet quantitatively understood. In ∼ 1 m-scale experiments, we found that individual channels exhibit a self-similar geometry and near-threshold transport conditions. Measurements of the rate of growth of topographic correlation length scales, the time scale of system-slope establishment, and the random spatial decorrelation of channel locations indicate together that the evolution of the braided river system may be diffusive in nature. This diffusion is due to the separation of scales between channel formation and network evolution, and the random motion of interacting channels when viewed at a coarse-grained scale.

Coarse Graining in Hydrodynamics and Effects of Fluctuations

We address the physical meaning of coarse graining scale and the hidden statistical ensemble in event by event analysis in hydrodynamic approach to heavy-ion collisions. It is shown that these features are appropriately understood in the frame work of variational formulation and pointed out that the local thermal equilibrium does not necessarily play a critical role in the description of the collective flow patterns. We further discuss that the effect of viscosity is also formlated in the form of the variational method including fluctuations.

Plasticity of Crystals with Disordered Microstructure: Scale-dependent Fluctuations of Stress and Strain

ABSTRACTA generic model of bulk crystal plasticity with stochastic evolution of the local microstructure is formulated. The evolution of local fluctuations of internal stress and plastic strain, as well as the cross correlation between these variables, is investigated for different loading modes (stress control vs. displacement control) as a function of the coarse graining scale, and the spatial structure of the respective correlation functions is determined. The investigations demonstrate that, after an initial transient characterized by uncorrelated initiation of plasticity in different sample locations, nontrivial long range correlations emerge both within the strain pattern and between the internal stress and plastic strain patterns. The internal stresses, on the other hand, remain short range correlated throughout. Implications of our findings for larger-scale plasticity models are discussed.

Efficient solvent-free dissipative particle dynamics for lipid bilayers.

We rigorously derived effective potentials for solvent-free DPD simulation of lipid bilayers. The derivation relies on an earlier developed hybrid particle/field method and is based on the idea that the solvent is always in local equilibrium on a coarse-grained time scale, given the instantaneous templates set by the self-assembly structure. By relating the parameters in the effective implicit-solvent potentials directly to the lipid-solvent interactions and membrane properties for the explicit solvent DPD model, we constitute an efficient and general procedure for reformulating any DPD membrane model in an implicit-solvent form. Here, we determined these membrane properties for two existing DPD models, via an analysis of membrane fluctuation spectra. Equivalent single-processor implicit- and explicit-solvent calculations show the trade-mark of implicit solvent simulation: a 20-fold reduction of the total simulation time for a system containing 92% solvent. This increased efficiency enabled us to realistically simulate the spontaneous formation of a ∼20 nm diameter vesicle on a single processor overnight. We believe that this work will contribute to an enhanced computational study of large vesicles and thus a better understanding of experimental liposome dynamics.

Temperature-dependent defect dynamics in the network glass SiO2

We investigate the long time dynamics of a strong glass former, SiO(2), below the glass transition temperature by averaging single-particle trajectories over time windows which comprise roughly 100 particle oscillations. The structure on this coarse-grained time scale is very well defined in terms of coordination numbers, allowing us to identify ill-coordinated atoms, which are called defects in the following. The most numerous defects are O-O neighbors, whose lifetimes are comparable to the equilibration time at low temperature. On the other hand, SiO and OSi defects are very rare and short lived. The lifetime of defects is found to be strongly temperature dependent, consistent with activated processes. Single-particle jumps give rise to local structural rearrangements. We show that in SiO(2) these structural rearrangements are coupled to the creation or annihilation of defects, giving rise to very strong correlations of jumping atoms and defects.

Peak-background split, renormalization, and galaxy clustering

We present a derivation of two-point correlations of general tracers in the peak-background split (PBS) framework by way of a rigorous definition of the PBS argument. Our expressions only depend on connected matter correlators and "renormalized" bias parameters with clear physical interpretation, and are independent of any coarse-graining scale. This result should be contrasted with the naive expression derived from a local bias expansion of the tracer number density with respect to the matter density perturbation \delta_L coarse-grained on a scale R_L. In the latter case, the predicted tracer correlation function receives contributions of order <\delta_L^n> at each perturbative order n, whereas, in our formalism, these are absorbed in the PBS bias parameters at all orders. Further, this approach naturally predicts both a scale-dependent bias ~ k^2 such as found for peaks of the density field, and the scale-dependent bias induced by primordial non-Gaussianity in the initial conditions. The only assumption made about the tracers is that their abundance at a given position depends solely on the matter distribution within a finite region around that position.

Coarse-grained local and objective continuum description of three-dimensional granular flows down an inclined surface

Dry, frictional, steady-state granular flows down an inclined, rough surface are studied with discrete particle simulations. From this exemplary flow situation, macroscopic fields, consistent with the conservation laws of continuum theory, are obtained from microscopic data by time-averaging and spatial smoothing (coarse-graining). Two distinct coarse-graining length scale ranges are identified, where the fields are almost independent of the smoothing length w. The smaller, sub-particle length scale, w ≪ d, resolves layers in the flow near the base boundary that cause oscillations in the macroscopic fields. The larger, particle length scale, w ≈ d, leads to smooth stress and density fields, but the kinetic stress becomes scale-dependent; however, this scale-dependence can be quantified and removed. The macroscopic fields involve density, velocity, granular temperature, as well as strain-rate, stress, and fabric (structure) tensors. Due to the plane strain flow, each tensor can be expressed in an inherently anisotropic form with only four objective, coordinate frame invariant variables. For example, the stress is decomposed as: (i) the isotropic pressure, (ii) the “anisotropy” of the deviatoric stress, i.e., the ratio of deviatoric stress (norm) and pressure, (iii) the anisotropic stress distribution between the principal directions, and (iv) the orientation of its eigensystem. The strain rate tensor sets the reference system, and each objective stress (and fabric) variable can then be related, via discrete particle simulations, to the inertial number, I. This represents the plane strain special case of a general, local, and objective constitutive model. The resulting model is compared to existing theories and clearly displays small, but significant deviations from more simplified theories in all variables – on both the different length scales.

Overdamped Dynamics of Folded Protein Domains within a Locally Harmonic Basin Using Coarse Graining Based on a Partition of Compact Flexible Clusters

A coarse-graining method based on the partitioning of atoms into compact flexible clusters is used to formulate the dynamics of the nonequilibrium response of a protein to ligand dissociation. The α-carbon positions are used as the degrees of freedom. The net stiffness between each pair of neighboring α-carbons is calculated for the quasi-static, overdamped regime within the harmonic (quadratic potential energy surface) using the equivalent stiffness matrix of the network of atoms occupying the intervening space within the locally interacting region. This localized approach realizes a divide and conquer strategy that results in a substantial reduction in computational complexity while accurately predicting relaxations under general loading conditions. A close correlation between the shapes and time scales of the relaxation curves of the coarse-grained and all-atom instances of two medium-sized proteins, T4 lysozyme and ferric binding protein (each of which having known apo and holo structures), was observed for the holo to the apo transitions. Furthermore, for both proteins the dominant modes of motion and the decay rates of the temporal relaxation profiles monitoring the separation distance between select amino acid pairs were found to be nearly identical when calculated on the coarse-grained and all-atom scales.

Homogenised model linking microscopic and macroscopic dynamics of a biofilm: Application to growth in a plug flow reactor

We propose a new “hybrid” model for the simulation of biofilm growth in a plug flow bioreactor, that combines information from three scales: a microscopic one for the individual bacteria, a mesoscopic or “coarse-grained” one that homogenises at an intermediate scale the quantities relevant to the attachment/detachment process, and a macroscopic one in terms of substrate concentration. In contrast to existing partial differential equations models, this approach is based on a description of biological mechanisms at the individual scale, thus bringing in a biological justification of the attachment/detachment process responsible of the macroscopic behaviour. We found that compared to purely individual based or purely macroscopic models,•the approximate coarse-grained scale simplifies the change of scales from micro to macro, and speeds up the computation,•additional information about the stochasticity of the solution, especially at small populations, is revealed compared with the numerical simulations of partial differential equations models. Furthermore, the coarse-grained model can be much more easily adapted to various attachment/detachment hypotheses, that are at the core of the biofilm development.

Coarse-graining scale and effectiveness of hydrodynamic modeling

Some basic questions about the hydrodynamical approach to relativistic heavy ion collisions are discussed aiming to clarify how far we can go with such an approach to extract useful information on the properties and dynamics of the QCD matter created. We emphasize the importance of the coarse-graining scale required for the hydrodynamic modeling which determines the space-time resolution and the associated limitations of collective flow observables. We show that certain kinds of observables can indicate the degree of inhomogeneity of the initial condition under less stringent condition than the local thermal equilibrium subjected to the coarse-graining scale compatible to the scenario.

Collective non-equilibrium dynamics at surfaces and the spatio-temporal edge

Symmetries represent a fundamental constraint for physical systems and relevant new phenomena often emerge as a consequence of their breaking. An important example is provided by space- and time-translational invariance in statistical systems, which hold at a coarse-grained scale in equilibrium and are broken by spatial and temporal boundaries, the former being implemented by surfaces —unavoidable in real samples— the latter by some initial condition for the dynamics which causes a non-equilibrium evolution. While the separate effects of these two boundaries are well understood, we demonstrate here that additional, unexpected features arise upon approaching the effective edge formed by their intersection. For this purpose, we focus on the classical semi-infinite Ising model with spin-flip dynamics evolving out of equilibrium at its critical point. Considering both subcritical and critical values of the coupling among surface spins, we present numerical evidence of a scaling regime with universal features which emerges upon approaching the spatio-temporal edge and we rationalise these findings within a field-theoretical approach.

Comparing normal modes across different models and scales: Hessian reduction versus coarse‐graining

Dimension reduction is often necessary when attempting to reach longer length and time scales in molecular simulations. It is realized by constraining degrees of freedom or by coarse-graining the system. When evaluating the accuracy of a dimensional reduction, there is a practical challenge: the models yield vectors with different lengths, making a comparison by calculating their dot product impossible. This article investigates mapping procedures for normal mode analysis. We first review a horizontal mapping procedure for the reduced Hessian techniques, which projects out degrees of freedom. We then design a vertical mapping procedure for the "implosion" of the all-atom (AA) Hessian to a coarse-grained scale that is based upon vibrational subsystem analysis. This latter method derives both effective force constants and an effective kinetic tensor. Next, a series of metrics is presented for comparison across different scales, where special attention is given to proper mass-weighting. The dimension-dependent metrics, which require prior mapping for proper evaluation, are frequencies, overlap of normal mode vectors, probability similarity, Hessian similarity, collectivity of modes, and thermal fluctuations. The dimension-independent metrics are shape derivatives, elastic modulus, vibrational free energy differences, heat capacity, and projection on a predefined basis set. The power of these metrics to distinguish between reasonable and unreasonable models is tested on a toy alpha helix system and a globular protein; both are represented at several scales: the AA scale, a Gō-like model, a canonical elastic network model, and a network model with intentionally unphysical force constants.

Multiscale Modeling of Microtubules and Actin Filaments

AbstractComputational methods, as Molecular Dynamics (MD) simulations, have been used for years to gain insight into the properties of small fractions of microtubules (MTs) and actin filaments (F-actins). However, when considering an entire cytoskeleton filament, MD simulations lack of sufficient sampling of the phase space. In order to acquire adequate amount of data with statistical validity, a faster sampling technique is here developed and the bending stiffness of entire MTs and F-actins is computed. Our approach allows to propagate the information obtained at a fine-grained atomistic scale to a coarse grained (CG) scale. We perform MD simulations on representative units of the MT and F-actin. Then, we describe each monomer of these representative units with few interacting grains and employ them to build CG filaments: (1) entire MTs with lengths from ~300 nm to ~1.5 μm and (2) an entire actin filament of ~500 nm. The dynamics of these CG systems is analyzed using Brownian Dynamics (BD) simulations, allowing to achieve time and length scales hundreds of times higher than MD simulations. For our BD simulations an ad hoc force field is used, that matches MD atomistic fluctuations on the interaction potentials between pairs of CG beads. Results from the here proposed combination of atomistic MD simulations with coarse grained BD simulations are in agreement with experimental finding, providing more informative proofs of concept on how thermal fluctuations change interaction potentials among beads and on how the molecular rearrangements affect MT and F-actin rigidities.

Local Anisotropy in Globally Isotropic Granular Packings

We report on two-dimensional computer simulations of frictionless granular packings at various area fractions φ above the jamming point φ(c). We measure the anisotropy in coarse-grained stress ε(s) and shear modulus ε(m) as functions of coarse-graining scale, R. ε(s) can be collapsed onto a master curve after rescaling R by a characteristic length scale ξ and ε(s) by an anisotropy magnitude A. Both A and ξ accelerate as φ→φ(c) from above, consistent with a divergence at φ(c). ε(m) shows no characteristic length scale and has a nontrivial power-law form, ε(m)~R(-0.62), over almost the entire range of R at all φ. These results suggest that the force chains present in the spatial structure of the quenched stress may be governed by different physics than the anomalous elastic response near jamming.