Coarse-grained Distribution Research Articles

On the convergence of phase space distributions to microcanonical equilibrium: dynamical isometry and generalized coarse-graining

Abstract This work explores the manner in which classical phase space distribution functions converge to the microcanonical distribution. We first prove a theorem about the lack of convergence, then define a generalization of the coarse-graining procedure that leads to convergence. We prove that the time evolution of phase space distributions is an isometry for a broad class of statistical distance metrics, implying that ensembles do not get any closer to (or farther from) equilibrium, according to these metrics. This extends the known result that strong convergence of phase space distributions to the microcanonical distribution does not occur. However, it has long been known that weak convergence can occur, such that coarse-grained distributions---defined by partitioning phase space into a finite number of cells---converge pointwise to the microcanonical distribution. We define a generalization of coarse-graining that removes the need for partitioning phase space into cells. We prove that our generalized coarse-grained distribution converges pointwise to the microcanonical distribution if the dynamics are strong mixing. As an example, we study an ensemble of triangular billiard systems.

Increased long-term stress-rupture life of a nickel-based superalloy with relatively homogeneous duplex grain size distributions

Effect of duplex grain size distributions on long-term stress-rupture life of Nimonic 80A had been investigated. Non-homogeneous duplex grain size distributions greatly reduce stress-rupture life. Regional distribution of coarse grains is not good for acquiring high stress-rupture life, the formation of micro-void and propagation of cracking can easily occur at coarse grain boundary especially when plate-like Cr23C6 precipitates at grain boundary. But relatively homogeneous duplex grain size distributions are of great significance in improving stress-rupture life, the samples even possess the life value up to more than 13000 h especially when hardly any plate-like Cr23C6 precipitates at grain boundaries. Slightly increased Ti/Al ratio from 1.65 to 1.80 is also beneficial to obtain a significantly longer stress-rupture life value. The γ′ phase is very stable and always exhibits a coherent orientation relationship with γ on {100} and {111} atomic planes. The grain boundary cracking will not easily appear at the early stage of stress-rupture test in the samples with relatively homogeneous grain size distribution, the coarse and adjacent fine grains possess better deformation adjustability, and the grain boundary cracking is apparently wider and the number of cracking is also getting more after fracture for the sample with longer stress-rupture life.

Effect of Grain Size Distribution on Pore Size Distribution Characteristics in a Conglomerate Reservoir from an Alluvial Fan Via Artificial Rock Approach

Summary Conglomerate is characterized by a multiscale grain stacking structure and various pore size distribution modes (PSDMs), significantly affecting multiphase fluid movement and transport in porous media. The multimodal structure and complicated PSDM are related to grain size distribution. However, the relationship between grain size distribution and pore structure characteristics remains unclear, which makes it hard to investigate using natural rocks affected by a single factor. Herein, a newly developed full-pore-scale artificial rock approach was used in this work to provide the ideal samples for experimental research. A bimodal distribution model was adopted to characterize the grain size distribution features quantitatively. Furthermore, the relationship between lithofacies, permeability, and PSDM was analyzed. The results demonstrate that grain size distribution includes coarse grain distribution (CGD) and fine grain distribution (FGD). As the average value of FGD increases, the permeability of conglomerate and sandstone have different decreasing trends. The increases in the grain size difference between CGD and FGD can decrease the most frequent and average pore radius, while the PSDM of conglomerate transforms from a steep peak shape to a hill shape. Furthermore, PSDM relates to permeability and lithofacies in an alluvial fan environment. The maximum permeability of sandstone with PSDM of hill shape is about 40 md while that of conglomerate is about 70 md. The grain and pore size distribution of artificial rocks is highly similar to that of natural rocks compared with natural rocks within the alluvial fan of Karamay conglomerate reservoirs. The findings are significant for robust determination in reservoir evaluation and development.

Experimental Study on the Effect of Coarse Grain Content on the Dilatancy and Particle Breakage Characteristics of Coarse-Grained Soils

The dilatancy deformation and particle breakage effects of coarse-grained soil have a significant influence on the safety and stability of high earth and rock-fill dams. To study the shear deformation and particle breakage characteristics of coarse-grained soil, four groups of soil sample with different coarse grain contents were to conduct consolidated drained triaxial compression tests by DJSZ-150 large-scale triaxial compression test machine. The results showed that the volume of coarse-grained soil changes significantly under deviation stress. The soil samples underwent positive dilatancy under the confining pressures of 200 kPa and 400 kPa but negative dilatancy under the confining pressures of 600 kPa and 800 kPa. When increasing the coarse grain contents in the soil sample under the same confining pressure, the positive dilatancy was more significant. A three-parameter dilatancy equation of coarse-grained soil considering confining pressure was established, in which the parameter L = 4 could serve as a criterion for whether the coarse-grained soil underwent positive dilatancy. Under the load, the coarse-grained soil showed three particle breakage modes: abrasion, attrition, and fracture. The coarse-grained soil particle size distribution before and after breakage conformed to the fractal characteristics, and the particle breakage rate increased significantly with larger soil particle size fractal dimension differences before and after the test. The coarse grain content and the confining pressure are two important factors affecting the mechanical properties of coarse-grained soil, and they control the shear deformation of soil.

Sequence stratigraphy and sedimentary processes since the last glacial maximum in Nha Phu Bay and adjacent shelf, central Vietnam

Three sedimentary systems tracts (LST, TST, and HST) have been identified in Nha Phu Bay and the adjacent shelf, Khanh Hoa Province, Vietnam. These have been deposited since the Last Glacial Maximum (LGM) and interpreted in this study via the analysis of high-resolution acoustic data and sediment cores. The lowstand systems tract (LST) comprises sandy sediments exposed at seabed on the outer shelf as sand ridges, and underlying the transgressive systems tract (TST) on the middle shelf. The LST developed under shallow-marine settings during the sea-level lowstand and early sea-level rise before 14.6 cal kyr BP. The TST comprises primarily fine-grained sediments deposited during the transgression between 14.6 and 8.0 cal kyr BP in an incised trough of the outer shelf, on the middle shelf, and in Nha Phu Bay. Erosion of the seaward portion of the TST on the middle shelf might occur during the late transgression (9.0–8.0 kyr BP). The highstand systems tract (HST) comprises sediments deposited during the sea-level highstand between 8.0 and 0.0 cal kyr BP and is distributed widely in the bay, on the inner-middle shelf, and partially on the outer shelf. A paleo-coast zone, located in 100–120 m present-day water depth, is recognized through the appearance of sand ridges and sandy sediments. The seafloor sediment distribution is mapped via four major acoustic echo types, combined with seabed sediment samples. The coarse-grained sediment distribution, subaqueous outcrops, and thin deglacial sediment thickness on the inner shelf indicate erosion-dominated processes under vigorous hydrodynamic conditions. Nha Phu Bay and the middle shelf are interpreted as the depocentres. The estimated sediment load deposited in Nha Phu Bay is 0.18 Mt./yr, accounting for 15–35% of the annual sediment discharge from the Dinh River. The seabed morphology, muddy sediment distribution, and deglacial sediment thickness reveal a dominant sediment-transport pathway, across the inner shelf to the middle shelf, near the northern shoreline of Nha Phu Bay under the influence of the southwest monsoon.

Scrambling and quantum chaos indicators from long-time properties of operator distributions

Scrambling is a key concept in the analysis of nonequilibrium properties of quantum many-body systems. Most studies focus on its characterization via out-of-time-ordered correlation functions (OTOCs), particularly through the early-time decay of the OTOC. However, scrambling is a complex process which involves operator spreading and operator entanglement, and a full characterization requires one to access more refined information on the operator dynamics at several timescales. In this work we analyze operator scrambling by expanding the target operator in a complete basis and studying the structure of the expansion coefficients treated as a coarse-grained probability distribution in the space of operators. We study different features of this distribution, such as its mean, variance, and participation ratio, for the Ising model with longitudinal and transverse fields, kicked collective spin models, and random circuit models. We show that the long-time properties of the operator distribution display common features across these cases, and discuss how these properties can be used as a proxy for the onset of quantum chaos. Finally, we discuss the connection with OTOCs and analyze the cost of probing the operator distribution experimentally using these correlation functions.

Misorientation Measurement in Tensile Test of Bimodal Harmonic Structured Stainless Steel by Diffraction Contrast Tomography Using Ultrabright Synchrotron Radiation X-ray

Austenitic stainless steel (JIS-SUS304L) with a bimodal harmonic structure, which is defined as a coarse-grained structure surrounded by a network of fine grains, was developed by powder metallurgy to improve both strength and ductility. In the present study, three-dimensional grain mapping for polycrystalline materials, called X-ray diffraction contrast tomography (DCT), was conducted at SPring-8, which is the brightest synchrotron radiation facility in Japan, to elucidate the deformation mechanism of harmonic structured JIS-SUS304L in tension. The average total misorientation tended to increase with stress in tensile tests; however, the total misorientation of the harmonic structured JIS-SUS304L was lower than that of JIS-SUS304L with a homogeneous distribution of coarse grains at comparable stress. Furthermore, the change in the crosssectional area of the harmonic structured JIS-SUS304L was also measured by refraction contrast tomography (RCT) imaging using SPring-8 in tensile tests.

The meaning distributions on different levels of granularity

The meaning distributions of certain linguistic forms generally follow a Zipfian distribution. However, since the meanings can be observed and classified on different levels of granularity, it is thus interesting to ask whether their distributions on different levels can be fitted by the same model and whether the parameters are the same. In this study, we investigate three quasi-prepositions in Shanghainese, a dialect of Wu Chinese, and test whether the meaning distributions on two levels of granularity can be fitted by the same model and whether the parameters are close. The results first show that the three models proposed by modern quantitative linguists can both achieve a good fit for all cases, while both the exponential (EXP) model and the right-truncated negative binomial (RTBN) models behave better than the modified right-truncated Zipf-Alekseev distribution (MRTZA), in terms of the consistency of the goodness of fit, parameter change, rationality, and simplicity. Second, the parameters of the distributions on the two levels and the curves are not exactly the same or even close to each other. This has supported a weak view of the concept of ‘scaling’ in complex sciences. Finally, differences are found to lie between the distributions on the two levels. The fine-grained meaning distributions are more right-skewed and more non-linear. This is attributed to the openness of the categories of systems. The finer semantic differentiation behaves like systems with open set of categories, while the coarse-grained meaning distribution resembles those having a close set of few categories.

CSEA: A Fine-Grained Framework of Climate-Season-Based Energy-Aware in Cloud Storage Systems

Abstract Continuous data scale growth increases energy consumption and operating cost that cannot be ignored in cloud storage systems. Previous studies have shown that analyzing the characteristics of I/O access and mining data features is effective for reasonable data distribution in storage systems. The granularity and criterion of classification are the key factors in determining the data distribution. To decrease energy consumption and operating cost, this paper puts forward a fine-grained framework of the climatic-season-based energy-aware in cloud storage system called CSEA. The framework concludes the following three aspects: (i) data feature mining. CSEA discovers potential data features by analyzing data access to provide help with data classification. (ii) K-means clustering algorithm. CSEA uses an unsupervised data classification algorithm in machine learning to divide data into categories based on seasonal characteristics by gathering real I/O access. (iii) data distribution of fine-grained. On the basis of seasonal features, CSEA fuses regional features to further refine the data distribution granularity to save on energy consumption and operating cost. Simulation experiments using extended CloudSimDisk and the constructed mathematical models indicate that CSEA reduces the energy consumption and operating cost compared with the single data classification standard and coarse-grained data distribution.

Deep coarse-grained potentials via relative entropy minimization.

Neural network (NN) potentials are a natural choice for coarse-grained (CG) models. Their many-body capacity allows highly accurate approximations of the potential of mean force, promising CG simulations of unprecedented accuracy. CG NN potentials trained bottom-up via force matching (FM), however, suffer from finite data effects: They rely on prior potentials for physically sound predictions outside the training data domain, and the corresponding free energy surface is sensitive to errors in the transition regions. The standard alternative to FM for classical potentials is relative entropy (RE) minimization, which has not yet been applied to NN potentials. In this work, we demonstrate, for benchmark problems of liquid water and alanine dipeptide, that RE training is more data efficient, due to accessing the CG distribution during training, resulting in improved free energy surfaces and reduced sensitivity to prior potentials. In addition, RE learns to correct time integration errors, allowing larger time steps in CG molecular dynamics simulation, while maintaining accuracy. Thus, our findings support the use of training objectives beyond FM, as a promising direction for improving CG NN potential's accuracy and reliability.

Bypassing backmapping: Coarse-grained electronic property distributions using heteroscedastic Gaussian processes.

We employ deep kernel learning electronic coarse-graining (DKL-ECG) with approximate Gaussian processes as a flexible and scalable framework for learning heteroscedastic electronic property distributions as a smooth function of coarse-grained (CG) configuration. The appropriateness of the Gaussian prior on predictive CG property distributions is justified as a function of CG model resolution by examining the statistics of target distributions. The certainties of predictive CG distributions are shown to be limited by CG model resolution with DKL-ECG predictive noise converging to the intrinsic physical noise induced by the CG mapping operator for multiple chemistries. Further analysis of the resolution dependence of learned CG property distributions allows for the identification of CG mapping operators that capture CG degrees of freedom with strong electron-phonon coupling. We further demonstrate the ability to construct the exact quantum chemical valence electronic density of states (EDOS), including behavior in the tails of the EDOS, from an entirely CG model by combining iterative Boltzmann inversion and DKL-ECG. DKL-ECG provides a means of learning CG distributions of all-atom properties that are traditionally "lost" in CG model development, introducing a promising methodological alternative to backmapping algorithms commonly employed to recover all-atom property distributions from CG simulations.

Model-Based Analysis of SARS-CoV-2 Infections, Hospitalization and Outcome in Germany, the Federal States and Districts.

The coronavirus disease 2019 (COVID-19) pandemic challenged many national health care systems, with hospitals reaching capacity limits of intensive care units (ICU). Thus, the estimation of acute local burden of ICUs is critical for appropriate management of health care resources. In this work, we applied non-linear mixed effects modeling to develop an epidemiological SARS-CoV-2 infection model for Germany, with its 16 federal states and 400 districts, that describes infections as well as COVID-19 inpatients, ICU patients with and without mechanical ventilation, recoveries, and fatalities during the first two waves of the pandemic until April 2021. Based on model analyses, covariates influencing the relation between infections and outcomes were explored. Non-pharmaceutical interventions imposed by governments were found to have a major impact on the spreading of SARS-CoV-2. Patient age and sex, the spread of variant B.1.1.7, and the testing strategy (number of tests performed weekly, rate of positive tests) affected the severity and outcome of recorded cases and could reduce the observed unexplained variability between the states. Modeling could reasonably link the discrepancies between fine-grained model simulations of the 400 German districts and the reported number of available ICU beds to coarse-grained COVID-19 patient distribution patterns within German regions.

Entropy growth during free expansion of an ideal gas

To illustrate Boltzmann’s construction of an entropy function that is defined for a microstate of a macroscopic system, we present here the simple example of the free expansion of a one dimensional gas of non-interacting point particles. The construction requires one to define macrostates, corresponding to macroscopic variables. We define a macrostate M by specifying the fraction of particles in rectangular boxes ΔxΔv of the single particle position-velocity space {x, v}. We verify that when the number of particles is large the Boltzmann entropy, S B(t), of a typical microstate of a nonequilibrium ensemble coincides with the Gibbs entropy of the coarse-grained time-evolved one-particle distribution associated with this ensemble. S B(t) approaches its maximum possible value for the dynamical evolution of the given initial state. The rate of approach depends on the size of Δv in the definition of the macrostate, going to zero at any fixed time t when Δv → 0. Surprisingly the different curves S B(t) collapse when time is scaled with Δv as: t ∼ τ/Δv. We find an explicit expression for S B(τ) in the limit Δv → 0. We also consider a different, more hydrodynamical, definition of macrostates for which S B(t) is monotone increasing, unlike the previous one which has small decaying oscillations near its maximum value. Our system is non-ergodic, non-chaotic and non-interacting; our results thus illustrate that these concepts are not as relevant as sometimes claimed, for observing macroscopic irreversibility and entropy increase. Rather, the notions of initial conditions, typicality, large numbers and coarse-graining are the important factors. We demonstrate these ideas through extensive simulations as well as analytic results.

Kinetic theory of collisionless relaxation for systems with long-range interactions

We develop the kinetic theory of collisionless relaxation for systems with long-range interactions in relation to the statistical theory of Lynden-Bell. We treat the multi-level case. We make the connection between the kinetic equation obtained from the quasilinear theory of the Vlasov equation and the relaxation equation obtained from a maximum entropy production principle. We propose a method to close the infinite hierarchy of kinetic equations for the phase level moments and obtain a kinetic equation for the coarse-grained distribution function in the form of a generalized Landau, Lenard–Balescu or Kramers equation associated with a generalized form of entropy (Chavanis, 2004). This allows us to go beyond the two-level case associated with a Fermi–Dirac-type entropy. We discuss the numerous analogies with two-dimensional turbulence. We also mention possible applications of the present formalism to fermionic and bosonic dark matter halos.

Systematic bottom-up molecular coarse-graining via force and torque matching using anisotropic particles.

We derive a systematic and general method for parameterizing coarse-grained molecular models consisting of anisotropic particles from fine-grained (e.g., all-atom) models for condensed-phase molecular dynamics simulations. The method, which we call anisotropic force-matching coarse-graining (AFM-CG), is based on rigorous statistical mechanical principles, enforcing consistency between the coarse-grained and fine-grained phase-space distributions to derive equations for the coarse-grained forces, torques, masses, and moments of inertia in terms of properties of a condensed-phase fine-grained system. We verify the accuracy and efficiency of the method by coarse-graining liquid-state systems of two different anisotropic organic molecules, benzene and perylene, and show that the parameterized coarse-grained models more accurately describe properties of these systems than previous anisotropic coarse-grained models parameterized using other methods that do not account for finite-temperature and many-body effects on the condensed-phase coarse-grained interactions. The AFM-CG method will be useful for developing accurate and efficient dynamical simulation models of condensed-phase systems of molecules consisting of large, rigid, anisotropic fragments, such as liquid crystals, organic semiconductors, and nucleic acids.

Prediction of the overall mechanical response of gradient nano-grained materials based on grain size distribution profile

Inspired by the gradient structure of biological materials, various gradient nano-grained (GNG) materials, inside which grain size spans several orders of magnitude, have been manufactured in recent years. This kind of material often exhibits extra hardening ability and ultimately achieves synergetic strength and ductility. The extra hardening of GNG materials is closely related to the strain gradient formed during deformation. However, the analytical relation between the structural gradient, strain gradient is still unexplored. Besides, the previous works focused on only one type of GNG material, and the understanding of the effect of different kinds of microstructures is limited. This paper explores the analytical relations between the strain gradient and the average grain size, as well as the grain size gradient in GNG materials. The overall mechanical responses of GNG interstitial-free (IF) steel and GNG Ni are well predicted. The results verify that the extra hardening of GNG materials is dependent on their unique microstructures. The strength and ductility of GNG materials can be improved by adjusting the composition and distribution of coarse grains and nano-grains.

CRS-CONT: A Well-Trained General Encoder for Facial Expression Analysis.

Existing facial expression recognition (FER) methods train encoders with different large-scale training data for specific FER applications. In this paper, we propose a new task in this field. This task aims to pre-train a general encoder to extract any facial expression representations without fine-tuning. To tackle this task, we extend the self-supervised contrastive learning to pre-train a general encoder for facial expression analysis. To be specific, given a batch of facial expressions, some positive and negative pairs are firstly constructed based on coarse-grained labels and a FER-specified data augmentation strategy. Secondly, we propose the coarse-contrastive (CRS-CONT) learning, where the features of positive pairs are pulled together, while pushed away from the features of negative pairs. Moreover, one key event is that the excessive constraint on the coarse-grained feature distribution will affect fine-grained FER applications. To address this, a weight vector is designed to control the optimization of the CRS-CONT learning. As a result, a well-trained general encoder with frozen weights could preferably adapt to different facial expressions and realize the linear evaluation on any target datasets. Extensive experiments on both in- the-wild and in- the-lab FER datasets show that our method provides superior or comparable performance against state-of-the-art FER methods, especially on unseen facial expressions and cross-dataset evaluation. We hope that this work will help to reduce the training burden and develop a new solution against the fully-supervised feature learning with fine-grained labels. Code and the general encoder will be publicly available at https://github.com/hangyu94/CRS-CONT.

A Continuous Taxi Pickup Path Recommendation under The Carbon Neutrality Context

In the context of the carbon neutrality target, carbon reduction in the daily operation of the transportation system is more important than that in productive activities. There are few travel services that can quantify low-carbon travel, with a lack of effective low-carbon travel tools to guide transportation behavior. On-demand access to taxi services can effectively reduce the additional carbon emissions caused by cruising, which in turn increases efficiency in urban mobility with a reduced taxi fleet scale. For individual taxis, they lack macroscopic horizon in their choice of passenger pickup paths. The selected travel path based on personal operational experience or real-time location is limited by local optimization when making path decisions. In this work, we proposed a macro-path recommendation method to assist the taxi pickup path selection to accelerate the transformation of the taxi system towards low-carbon sharing. First, an adaptive learning spatiotemporal neural network was used to predict the coarse-grained distribution of potential trips. Next, the trajectory sharing graph was constructed based on the potential trips distribution to reallocate the taxi orders for the continuous pickup path optimization. As a result, the continuous pickup path balanced the relation between travel demands and taxi supply, improving the economic and environmental benefits of taxi operation and contributing to the goal of carbon neutrality. We conducted experiments on the Chengdu city ride-hailing dataset. Compared with the current status of taxi operations, the solution shows improvements in both the scale of taxi services and order gain.

Composition and provenance analysis of beach sands in an almost isolated sedimentary system – A field study of the Galápagos Archipelago

The Galápagos Archipelago is the surface expression of an active hotspot or long-lived mantle plume. The Archipelago consists of a group of 13 main islands which are located in the eastern central Pacific Ocean about 1,000 km west of the northern edge of the South American continent, east of the East Pacific Rise and south of the Galápagos spreading center. Because of the large distance to the nearest continental land mass, Galapagos can be seen as an almost isolated sedimentary system. A provenance study conducted on samples collected from seventeen beaches on eleven islands, demonstrates that mineral grains and particles were derived from weathering of predominantly basaltic rocks and were transported within the islands, between the islands or inside the coastal area around the Archipelago. The exclusion of external sources allows advanced studies about erosion processes, transport pathways of particles and the accumulation of autochthonous sediments. The combined usage of optical particle size and shape analysis with RAMAN spectroscopy allows a successful spatial delimitation of host rocks and a reconstruction of transport pathways. The analyzed samples can be subdivided into three groups: 1) Type-A sediments: fine-grained and sampled on beaches of the oldest islands in the eastern part of Galápagos. The composition of volcanic minerals corresponds to the alkaline character of the basaltic source rocks. 2) Type-B: well sorted sediments characterized by medium-grained olivine, pyroxene, plagioclase and even a small amount of quartz grains. The islands of this group are located in the central region of the Archipelago. 3) Type-C samples: olivine and pyroxene are the predominant volcanic minerals. These samples indicate bimodal, coarse-grained size distributions and large proportions of pumice and are found in Floreana in the south and the youngest islands Isabela and Fernandina in the west of Galápagos.

On the stochastic representation and Markov approximation of Hamiltonian systems.

We study the coarse-grained distribution of a Hamiltonian system on the space partition determined by the initial measurement inaccuracies. Using methods of coding theory, introduced by Shannon and further researchers, Kolmogorov treated the stationary case for a discretized time, when the microscopic system is initially uniformly distributed. Following his work, we consider the non-stationary mesoscopic process induced by the Hamiltonian evolution from an inhomogeneous initial distribution. In general, this process has an infinite memory, but we show that its memory fades out with time: with any finite accuracy a, it can be approximated by a process with a memory limited to the n past events, n depending only on a. As a result, under suitable hypotheses, the mesoscopic process obeys an approximate Markov equation on groups of n successive states. More roughly, one obtains an ordinary Markov system by introducing a time coarse-graining on n successive elementary time steps. So, in a generic case, the system eventually tends to equilibrium for any initial mesoscopic distribution.