Mesoscopic Field Research Articles

29th Annual Computational Neuroscience Meeting: CNS*2020

P38 Priors based on abstract rules modulate the encoding of pure tones in the subcortical auditory pathwayAlejandro Tabas1, Glad Mihai1, Stefan Kiebel2, Robert Trampel3, Katharina von Kriegstein4 1Max Planck Institute for Human Cognitive and Brain Sciences, Research Group in Neural Mechanisms of Human Communication, Leipzig, Germany; 2Technische Univerität Dresden, Chair of Neuroimage, Dresden, Germany; 3Max Planck Institute for Human Cognitive and Brain Sciences, Department of Neurophysics, Leipzig, Germany; 4Technische Univerität Dresden, Chair of Cognitive and Clinical Neuroscience, Dresden, Germany Correspondence: Alejandro Tabas (alextabas@gmail.com)BMC Neuroscience 2020, 21(Suppl 1):P38Sensory pathways efficiently transmit information by adapting the neural responses to the local statistics of the sensory input. The predictive coding framework suggests that sensory neurons constantly match the incoming stimuli against an internal prediction derived from a generative model of the sensory input. Although predictive coding is generally accepted to underlay cortical sensory processing, the role of predictability in subcortical sensory coding is still unclear. Several studies have shown that single neurons and neuronal ensembles of the subcortical sensory pathway nuclei exhibit stimulus specific adaptation (SSA), a phenomenon where neurons adapt to frequently occurring stimuli (standards) yet show restored responses to a stimulus with deviating characteristics from the standard (deviant). Although neurons showing SSA are often interpreted as encoding prediction error, computational models to date have successfully explained SSA in terms of local network effects based on synaptic fatigue.Here, we first introduce a novel experimental paradigm where abstract rules are used to manipulate predictability. 19 human participants listened to sequences of pure tones consisting on seven standards and one deviant while we recorded mesoscopic responses in auditory thalamus and auditory midbrain using 7-Tesla functional MRI. In each sequence, the deviant was constrained to occur once and only once, and always in locations 4, 5 or 6. Although the three locations were equiprobable at the beginning of the trial, the conditional probability of hearing a deviant in location n after hearing n-1 standards is 1/3, 1/2, and 1, for deviant locations 4, 5, and 6, respectively.This paradigm yields different outcomes for habituation and predictive coding: if adaptation is driven by local habituation only, the three deviants should elicit similar neuronal responses; however, if it is predictive coding that entails adaptation, the neuronal responses to each deviant should depend on their abstract predictability. Our data showed that the responses to the deviants were strongly driven by abstract expectations, indicating that predictive coding is the main mechanism underlying mesoscopic SSA in the subcortical pathway. These results are robust even at the single-subject level.Next, we developed a new model of pitch encoding for pure tones following the main directives of predictive coding. The model comprises two layers whose dynamics reflect two different levels of abstraction. The lower layer receives its inputs from the auditory nerve and makes use of the finite bandwidth of the peripheral filters to decode pitch fast and robustly. The second layer holds a sparse representation that integrates the activity in the first layer only once the pitch decision has been made. Top-down afferents from the upper layer reinforce the pitch decision and accept the inclusion of priors that facilitate the decoding of predictable tones.Without the inclusion of priors, the model explains the key elements of SSA in animal recordings at the single-neuron level, as well as the main phenomenology of its mesoscopic representation. The inclusion of priors reflecting the abstract rules described in our paradigm facilitates the decoding of tones according to their predictability, effectively modulating the responses at the mesoscopic level. This modulation affects the mesoscopic fields generated during pitch encoding, fully explaining our experimental data.Fig. 1Top: z-scores of the BOLD responses to standards and deviants in the left auditory thalamus. Similar responses were recorded in the right auditory thalamus and bilateral auditory midbrain. Bottom: average model predictions under the habituation only (without informed priors) and predictive coding (with informed priors) scenariosFull size image

Manipulating Complex Hybrid Entanglement and Testing Multipartite Bell Inequalities in a Superconducting Circuit.

Quantum correlations in observables of multiple systems not only are of fundamental interest, but also play a key role in quantum information processing. As a signature of these correlations, the violation of Bell inequalities has not been demonstrated with multipartite hybrid entanglement involving both continuous and discrete variables. Here we create a five-partite entangled state with three superconducting transmon qubits and two photonic qubits, each encoded in the mesoscopic field of a microwave cavity. We reveal the quantum correlations among these distinct elements by joint Wigner tomography of the two cavity fields conditional on the detection of the qubits and by test of a five-partite Bell inequality. The measured Bell signal is 8.381±0.038, surpassing the bound of 8 for a four-partite entanglement imposed by quantum correlations by 10 standard deviations, demonstrating the genuine five-partite entanglement in a hybrid quantum system.

Influence of Interface Proximity on Precipitation Thermodynamics

The formation of coherent precipitates is often accompanied by large elastic mismatch stresses, which suppress phase separation. We discuss the presence of interfaces as a mechanism for stress relaxation, which can lead to preferred zones of precipitation. In particular, we discuss the proximity of free surfaces and shear-coupled grain boundaries, for which we can obtain a substantial local energy reduction and predict the influence on the local precipitation thermodynamics. The latter case is accompanied by morphological changes of the grain boundary, which are less suitable for large-scale descriptions. For that purpose, we develop an effective description through an elastic softening inside the grain boundary and map the microscopic grain boundary relaxation to a mesoscopic elastic and phase field model, which also allows generalizing the description to multi-phase situations.

Sparse scattered high performance computing data driven artificial neural networks for multi-dimensional optimization of buoyancy driven heat and mass transfer in porous structures

An artificial intelligence (AI) enhanced optimization framework is developed to reduce computational costs for evaluating transport performance of buoyancy driven heat and mass transfer in porous structures. The present optimization framework integrates prediction with artificial neural networks (ANNs), optimization with the weighted objective function, and physics-based simulations with high performance computing (HPC). Multi-dimensional governing parameters and objectives are investigated by ANNs with sparse scattered training data obtained from HPC with controllable structure generation scheme (CSGS) and parallel non-dimensional lattice Boltzmann method (P-NDLBM). The macroscopic prediction results based on ANNs are validated by comparison with HPC results. Full maps of the objective function values versus structure and physical parameters are illustrated. The maximum objective function value subjected to constraints is obtained together with the corresponding optimal structure and physical parameters. The optimal parameters are further applied in HPC to obtain mesoscopic physical fields. The underlying mechanism is also revealed by comparing the physical fields with optimal and off-optimal parameters.

Statistical Volume Elements for the Characterization of Angle-Dependent Fracture Strengths in Anisotropic Microcracked Materials

Abstract Statistical volume elements (SVEs) are used to homogenize fracture strength of rock, based on the microcrack statistics of a real-world Yuen-Long marble sample. The small size of SVEs enables maintaining inhomogeneities in fracture properties with lower computational cost compared to methods that explicitly model microcracks at macroscale. Maintaining inhomogeneity is important to capture realistic fracture patterns in rock as a quasi-brittle material. Uniaxial tensile, uniaxial compressive, and shear strengths are derived for arbitrary angle for loading and orientation of a single crack by using the linear elastic fracture mechanics (LEFM) method and incorporating frictional effects. Mesoscopic fracture strength fields are generated for different strengths and angle of loading by traversing the spatial domain with circular SVEs. Increasing the SVE size smoothens the spatial inhomogeneity and angular anisotropy of homogenized strengths. Spatial and angular covariance functions of the random fields are obtained to demonstrate how fracture strength varies in space and by changing the angle of loading. Two isotropic and anisotropic rock domains are studied and shown to have very different single- and two-point statistics. Macroscopic fracture simulations by an asynchronous spacetime discontinuous Galerkin (aSDG) method demonstrate that most macroscopic cracks for the anisotropic domain are aligned with the weakest strength planes.

Particle interspacing effects on the mechanical behavior of a Fe\u2013TiB2 metal matrix composite using FFT-based mesoscopic field dislocation mechanics

This paper presents an application to metal matrix composites (MMCs) of an enhanced elasto-viscoplastic Fast Fourier Transform (EVP-FFT) formulation coupled with a phenomenological continuum Mesoscale Field Dislocation Mechanics (MFDM) theory. Contrary to conventional crystal plasticity, which only accounts for plastic flow and hardening induced by statistically stored dislocations (SSDs), MFDM-EVP-FFT also describes the evolution of polarized geometrically necessary dislocation (GND) density and its effect on both plastic flow and hardening. Numerical results for a Fe–TiB2 MMC made of a ferrite matrix (α-Fe) and elastic ceramic particles (TiB2) are presented. Full-field simulations are performed using synthetic periodic unit cells representative of the MMC, with single-crystalline and polycrystalline matrix, for different particle interspacing distances. A strong dependence of the predicted equivalent stress, cumulated plastic strain and GND density fields with particle interspacing distance is observed, in contrast with conventional crystal plasticity. Correlations between these mechanical fields and microstructural features, and their influence on local and global mechanical behavior are examined for the different MMC microstructures.

A two-dimensional lattice model for simulating the failure and fracture behavior of wood

A two-dimensional lattice model consisting of truss elements was developed in this study to characterize the failure behavior under arbitrary loading and fracture behavior of wood. The characteristic of this model is to use the integral analytical procedure to determine the elastic stiffness and ultimate strengths of bonds based on energy and strength criteria, respectively, instead of using the trial-and-error method adopted by the current scholars in the field of timber. To prove the feasibility of the lattice model, the tension test, compression test, shear test, and off-axis test on Korean pine were carried out, and two types of fracture tests of Pinus pinaster were cited. The properties of the truss elements were determined from the basic mechanical parameters of wood. The simulated results from using the proposed lattice model were compared with the experimental data, and good agreements including deformation and stress–strain curves were observed. The lattice model in this paper can accurately simulate the failure and fracture behavior of heterogeneous wood, and this method can promote the use of lattice models in the wood mesoscopic and microscopic fields.

Quantum Rabi Oscillations in Coherent and in Mesoscopic Cat Field States.

The simple resonant Rabi oscillation of a two-level system in a single-mode coherent field reveals complex features at the mesoscopic scale, with oscillation collapses and revivals. Using slow circular Rydberg atoms interacting with a superconducting microwave cavity, we explore this phenomenon in an unprecedented range of interaction times and photon numbers. We demonstrate the efficient production of cat states, which are the quantum superposition of coherent components with nearly opposite phases and sizes in the range of few tens of photons. We measure cuts of their Wigner functions revealing their quantum coherence and observe their fast decoherence. This experiment opens promising perspectives for the rapid generation and manipulation of nonclassical states in cavity and circuit quantum electrodynamics.

Statistical volume element averaging scheme for fracture of quasi-brittle materials

To capture the randomness and inhomogeneity of rock at microscale, a statistical volume element (SVE) averaging approach is proposed. The microcrack statistics of a real-world Yuen-Long marble sample is used to realize 2D microcracked domains. The size effect, i.e. the decrease of the mean and variation of homogenized strength field by increasing SVE size, is analyzed. Increasing the crack density is shown to have a similar effect. While smaller SVEs maintain a greater level of inhomogeneity and are preferred for fracture analysis, it is shown that low density of microcracks pose a lower limit on the SVE size. Beside the actual power-law distribution of microcrack length, by varying the Weibull model shape parameter m other domains are created with different microcrack distribution shapes. Macroscopic fracture simulations, by the asynchronous Spacetime Discontinuous Galerkin (aSDG) method, study the effect of m for a uniaxial tensile problem. By increasing m from 0.5 to 4, the length distribution of microcracks become more uniform; this corresponds to a more uniform and stronger mesoscopic strength field, which results to about 3 and 6 times increase to macroscopic tensile strength and toughness, respectively. However, the more uniform length distribution of microcracks is shown to reduce rock brittleness.

Driving driven lattice gases to identify their universality classes.

The critical behaviors of driven lattice gas models have been studied for decades as a paradigm to explore nonequilibrium phase transitions and critical phenomena. However, there exists a long-standing controversy in their universality classes. This is of paramount importance as it implies the question of whether or not a microscopic model and its mesoscopic field theory may possess different symmetries in nonequilibrium critical phenomena in contrast to their equilibrium counterparts. Here, we heat with finite rates two generic models of driven lattice gases across their respective nonequilibrium critical points into further nonequilibrium situations. Employing the theory of finite-time scaling, we are able to unambiguously discriminate the universality classes between the two models. In particular, the infinitely driven lattice gas and the randomly driven lattice gas models belong to different universality classes. These results show that finite-time scaling is effective even in nonequilibrium phase transitions.

In vivo measurements of irreversible and reversible transverse relaxation rates in human basal ganglia at 7 T: making inferences about the microscopic and mesoscopic structure of iron and calcification deposits

The goal of this study was to measure irreversible and reversible transverse relaxation rates in the globus pallidus and putamen at 7T, and to use these rates to make inferences about the sub-voxel structure of iron and calcification deposits. Gradient Echo Sampling of a Spin Echo (GESSE) data were acquired at 7T on eighteen volunteers spanning a large range of ages (23-85years), with calcifications in the globus pallidus incidentally observed in one volunteer. Maps of transverse relaxation rates were derived from the GESSE data, and the mean value of these rates in globus pallidus and putamen was estimated for each volunteer. Both irreversible and reversible transverse relaxation rates increased with the expected age-dependent iron content in these structures, except for the individual with calcifications for whom extremely large reversible relaxation rates but normal irreversible relaxation rates were found in the globus pallidus. Given the sensitivity of irreversible and reversible transverse relaxation rates to microscopic and mesoscopic field variations, respectively, our findings suggest that joint consideration of these rates may yield information not only about the amount of iron and calcification deposited in the brain, but also about the sub-voxel structure of these deposits, perhaps revealing certain aspects of their geometry and cellular distribution.

Mesoscopic continuum theory for liquid crystals

A summary of the mesoscopic theory of liquid crystals is presented. Mesoscopic field quantities are defined on the enlarged space of position, time and orientation. An orientation distribution function is defined as the fraction of the mesoscopic mass density over the total mass density. For the mesoscopic field quantities of mass, momentum, angular momentum and energy balance equations on the enlarged domain are formulated. They allow the derivation of a differential equation for the orientation distribution function. Measurable quantities are macroscopic ones. They are obtained from the mesoscopic quantities by averaging with the orientation distribution function. In addition to the usual macroscopic fields, alignment tensors are obtained by the averaging procedure. These tensors of successive order are a measure of the orientational order, present on the mesoscopic level. For these alignment tensors equations of motion are derived here. They form a set of coupled equations for infinitely many alignment tensors, and a closure is needed. At the lowest level, only the alignment tensor of second order is an independent variable, and the fourth order tensor is substituted by an algebraic closure relation. At this level of approximation Landau theory of phase transitions can be recovered in case of vanishing flow field. In a refined approach, the second and the fourth order alignment tensor are considered as independent variables, and the sixth order tensor is eliminated by an algebraic closure relation. This refined alignment tensor dynamics is considered in detail in the case of a uniaxial orientation distribution function.

Mesoscopic quantitative chemical analyses using STEM-EDX in current and next generation polycrystalline Ni-based superalloys

Quantitative chemical analyses of Ni3Al based hardening precipitates (γ′) in polycrystalline Ni based superalloys have been conducted using energy dispersive X-ray spectroscopy (EDX), coupled with a scanning transmission electron microscope (STEM). The aim of the current investigation is (1) to evaluate the accuracy of calibration (k factor determinations and absorption corrections using a combination of differential X-ray absorption (DXA) and convergent beam electron diffraction (CBED)) by comparing with thermodynamic calculations and (2) to demonstrate the importance of the EDX chemical analysis by taking advantage of its unique capabilities to analyse sub-micron scale chemistries within a mesoscopic field of view under STEM. Our experimental findings show good agreement with the mole fraction ratio of γ′ to the disordered γ matrix predicted using the Lever rule on a thermodynamically stabilised unimodal superalloy, RR1000. The significance of analysing a statistically viable number of samples in thermodynamically metastable superalloys and the chemical fluctuations found in coarse γ′, sized above 200 nm on a scale of a few hundred nanometres in the context of solving a complex morphological evolution of γ′ particles is demonstrated.

(Invited) Mechanical and Gas Transport Properties of Pristine and Cross-Linked Carbon Nanotube Materials

Carbon nanotubes (CNTs) have a unique combination of mechanical properties, including extremely high elastic modulus, large strength, and relatively low bending rigidity. The porous CNT materials also have a potential for application as membranes for gas separation, purification, and sensing. The load transfer in networks of pristine CNT, however, is weak and CNT materials exhibit much smaller stiffness and strength than it can be anticipated based on properties of individual CNTs. Weak mechanical properties prevent CNT materials from using in multiple emerging applications. Covalent cross-linking via irradiation by energetic ion or electron beams, as well as chemical functionalization, allow one to enhance stability of CNT materials and improve their elastic and inelastic properties. In this work, the mechanical and gas transport properties of pristine and cross-linked CNT materials are studies theoretically based on a mesoscopic computational model. This model is capable of predicting the mechanical loading of CNT films and aerogels and gas transport in these materials in large-scale simulations involving thousands of nanotubes. In the mesoscopic model, every nanotube is represented by a chain of cylindrical mesoscopic segments. The mesoscopic force field accounts for the stretching, bending, and buckling of nanotubes, van der Waals interaction between CNTs, and presence of cross-links. Discrete cross-links between nanotubes are described by a model based on the Morse potential function for an individual cross-link and a geometrical model of the effective cross-link bond. The molecular dynamics simulations of pulling-out of a CNT from a cross-linked CNT bundle are performed in order to characterize the effect of cross-links on the shear load transfer between CNTs. The obtained results in the form of force-displacement curves and rates of cross-link breaking and reformation are used to parameterize the mesoscopic model of cross-links. The developed atomistic and mesoscopic models as well as novel continuum-level model of cross-linked CNT bundles are first applied to study the shear lag effect during pulling-out of CNTs from long nanotube bundles. The results of pull-out tests obtained with these models agree with each other and reveal a strong shear lag effect, when the effective sheaf force is limited by stretching of individual nanotubes. This effect is found to be a factor that puts limits on improving the shear load transfer by covalent cross-links. The developed mesoscopic model is then applied to study mechanical properties of thin quasi-two-dimensional films and isotropic three-dimensional aerogels composed of single-walled nanotubes. The in silico generated material samples with the entangled network of bundles of nanotubes are prepared by self-assembly of initially dispersed CNTs in dynamic mesoscopic simulations. The equilibrated films and aerogels are subjected to compressive and stretching loading. The simulations show a few distinct modes of compression of CNT films, including the wrinkling mode, and reveal the mechanisms responsible for irreversible material deformation and fracture by means of cross-link breaking and re-arrangement of nanotubes. In addition to quasi-static loading, elastic wave propagation through the CNT films with a size up to a few micrometers is studied in order to calculate the acoustic speed in CNT network materials. The elastic moduli, ultimate strength, and acoustic speed in CNT films are found as functions of the material and cross-link densities, CNT length, and strain rate. The study of gas diffusion through CNT network materials is based on a hybrid model, including the mesoscopic model for CNTs and a molecular dynamics-type approach based on direct solution of equations of motion for individual gas molecules. This hybrid approach is used to study self-diffusion of argon inside CNT networks and simulate gas permeability of CNT materials placed in between low- and high-pressure gas reservoirs. The simulations reveal the strong effect of porous structure and density of the CNT materials on gas self-diffusivity and the material effective permeability. This work is supported by NASA through an Early Stage Innovations grant from NASA’s Space Technology Research Grants Program (project NNX16AD99G) and by NSF (CAREER project CMMI-1554589). Computational support is provided by the Alabama Supercomputer Center and NASA's Advanced Supercomputing (NAS) Division.

Layer-Specific Physiological Features and Interlaminar Interactions in the Primary Visual Cortex of the Mouse

SummaryThe relationship between mesoscopic local field potentials (LFPs) and single-neuron firing in the multi-layered neocortex is poorly understood. Simultaneous recordings from all layers in the primary visual cortex (V1) of the behaving mouse revealed functionally defined layers in V1. The depth of maximum spike power and sink-source distributions of LFPs provided consistent laminar landmarks across animals. Coherence of gamma oscillations (30–100 Hz) and spike-LFP coupling identified six physiological layers and further sublayers. Firing rates, burstiness, and other electrophysiological features of neurons displayed unique layer and brain state dependence. Spike transmission strength from layer 2/3 cells to layer 5 pyramidal cells and interneurons was stronger during waking compared with non-REM sleep but stronger during non-REM sleep among deep-layer excitatory neurons. A subset of deep-layer neurons was active exclusively in the DOWN state of non-REM sleep. These results bridge mesoscopic LFPs and single-neuron interactions with laminar structure in V1.

Fatigue Life Prediction of Welded Joint by Microstructure-based Simulation

This paper proposes a numerical framework to predict fatigue life on welded joints by integrating several computational techniques. The framework consists of five steps: i) materials properties estimation; ii) welding simulation using thermo-mechanical finite element method; iii) macroscopic stress field analysis under cyclic loading; iv) mesoscopic stress field analysis using crystal plasticity finite element method (CPFEM); v) analysis of fatigue crack growth. The total number of cycles to failure is eventually obtained by the sum of initiation life calculated by CPFEM and propagation life calculated by X-FEM. A fatigue life of butt joint is evaluated by the proposed method. The results demonstrated the possibility of evaluating the fatigue life and its scattering by the proposed framework.

Sharp-wave ripple features in macaques depend on behavioral state and cell-type specific firing.

Sharp‐wave ripples (SWRs) are spontaneous, synchronized neural population events in the hippocampus widely thought to play a role in memory consolidation and retrieval. They occur predominantly in sleep and quiet immobility, and in primates, they also appear during active visual exploration. Typical measures of SWRs in behaving rats include changes in the rate of occurrence, or in the incidence of specific neural ensemble activity contained within the categorical SWR event. Much less is known about the relevance of spatiotemporal SWR features, though they may index underlying activity of specific cell types including ensemble‐specific internally generated sequences. Furthermore, changes in SWR features during active exploratory states are unknown. In this study, we recorded hippocampal local‐field potentials and single‐units during periods of quiescence and as macaques performed a memory‐guided visual search task. We observed that (a) ripples during quiescence have greater amplitudes and larger postripple waves (PRW) compared to those in task epochs, and (b) during “remembered” trials, ripples have larger amplitudes than during “forgotten” trials, with no change in duration or PRWs. We further found that spiking activity influences SWR features as a function of cell type and ripple timing. As expected, larger ripple amplitudes were associated with putative pyramidal or putative basket interneuron (IN) activity, even when the spikes in question exceed the duration of the ripple. In contrast, the PRW was attenuated with activity from low firing rate cells and enhanced with activity from high firing rate cells, with putative IN spikes during ripples leading to the most prominent PRW peaks. The selective changes in SWR features as a function of time window, cell type, and cognitive/vigilance states suggest that this mesoscopic field event can offer additional information about the local network and animal's state than would be appreciated from SWR event rates alone.

A multi-scale analysis method for the simulation of tunnel excavation in sandy cobble stratum

Sandy cobble stratum is a kind of heterogeneous geological body. A further study on the safety of wall rocks and underground structure demands developing suitable analysis method to simulate tunnel excavation in such a formation. Macro-scale simulations assume the sandy cobble soil to be homogeneous in numerical models. They get more efficient computing, but have difficulties in capturing enough information about the meso-scopic fields needed. Meso-scale simulations explicitly represent the individual components of the heterogeneous internal material structure in numerical models, e.g. the shape and the spatial distribution of rocks. They achieve high accuracy, but large computational cost would be needed. To reduce the numerical effort with the precision guaranteed, a multi-scale analysis method for simulating tunnel excavation in sandy cobble strata is proposed. In this method, the numerical model is divided into two regions, involving the meso-scale region and macro-scale region. The meso-scale region is a critical sub-domain disturbed by tunnel excavation, in it, the rocks and soil are considered as separate constituents. In the macro domain, the sand gravel soil was regarded as homogeneous materials whose effective material parameters were determined using an equivalent homogenization method. Three critical issues in the multi-scale method are explored, including: (i) the determination of meso domain and macro domain, (ii) the determination of rock maximum size that can be homogenized in the meso domain and iii) the determination of effective material parameters of soil-rock mixture during the equivalent process. By comparing with simulation results predicted by macro-scale and meso-scale simulation methods, the validation of the proposed multi-scale simulation method was carried out. The result indicates that the proposed multi-scale analysis method has a high efficiency without loosening accuracy on the simulation of tunnel excavation in sandy cobble stratum.

Determination of the diffusivity, dispersion, skewness and kurtosis in heterogeneous porous flow. Part II: Lattice Boltzmann schemes with implicit interface

Abstract A simple local two-relaxation-time Lattice Boltzmann numerical formulation (TRT-EMM) of the extended method of moments (EMM) is proposed for analysis of the spatial and temporal Taylor dispersion in d-dimensional streamwise-periodic stationary mesoscopic velocity field resolved in a piecewise-continuous porous media. The method provides an effective diffusivity, dispersion, skewness and kurtosis of the mean concentration profile and residence time distribution. The TRT-EMM solves a chain of steady-state heterogeneous advection–diffusion equations with the pre-computed space-variable mass-source and automatically undergoes diffusion-flux jump on the abrupt-porosity streamwise-normal interface. The temporal and spatial systems of moments are computed within the same run; the symmetric dispersion tensor can be restored from independent computations performed for each periodic mean-velocity axis; the numerical algorithm recursively extends for any order moment. We derive an exact form of the bulk equation and implicit closure relations, construct symbolic TRT-EMM solutions and determine specific relation between the equilibrium and the collision degrees of freedom viewing an exact parameterization by the physical non-dimensional numbers in two alternate situations: “parallel” fracture/matrix flow and “perpendicular” Darcy flow through porous blocks in “series”. Two-dimensional simulations in linear Brinkman flow around solid and through porous obstacles validate the method in comparison with the two heterogeneous direct LBM-ADE schemes with different anti-numerical-diffusion treatment which are proposed and examined in parallel. On the coarse grid, accuracy of the three moments is essentially determined by the free-tunable collision rate in all schemes, and especially TRT-EMM. However, operated within a single periodic cell, the TRT-EMM is many orders of magnitude faster than the direct solvers, numerical-diffusion free, more robust and much more capable for accuracy improving, high Peclet range and free-parameter influence reduction with the mesh refinement. The method is an efficient predicting tool for the Taylor dispersion, asymmetry and peakedness; moreover, it allows for an optimal analysis between the mutual effect of the flow regime, Peclet number, porosity, permeability and obstruction geometry.

Measuring solid\u2013liquid interfacial energy fields: diffusion-limited patterns

The Leibniz–Reynolds transport theorem yields an omnimetric interface energy balance, i.e., one valid over all continuum length scales. The transport theorem, moreover, indicates that solid–liquid interfaces support capillary-mediated redistributions of energy capable of modulating an interface’s motion—a thermodynamic phenomenon not captured by Stefan balances that exclude capillarity. Capillary energy fields affect interfacial dynamics on scales from about 10 nm to several mm. These mesoscopic fields were studied using entropy density multiphase-field simulations. Energy rate distributions were exposed and measured by simulating equilibrated solid–liquid interfaces configured as stationary grain boundary grooves (GBGs). Negative rates of energy distributed over GBGs were measured as residuals, by subtracting the linear potential distribution contributed by applied thermal gradients constraining the GBGs from the nonlinear distributions actually developed along their solid–liquid interface. Rates of interfacial cooling revealed numerically confirm independent predictions based on sharp-interface thermodynamics, variational calculus, and field theory. This study helps answer a long-standing question: What creates patterns for diffusion-limited transformations in nature and in material microstructures?