Multi-scale Heterogeneity Research Articles

Upscaled permeability for gaseous microflows in porous media with arbitrary multiscale heterogeneities

Upscaled permeability for gaseous microflows in porous media with arbitrary multiscale heterogeneities

Tailoring smart hydrogels through manipulation of heterogeneous subdomains

The mechanical interactions among integrated cellular structures in soft tissues dictate the mechanical behaviors and morphogenetic deformations observed in living organisms. However, replicating these multifaceted attributes in synthetic soft materials remains a challenge. In this work, we develop a smart hydrogel system featuring engineered stiff cellular patterns that induce strain-driven heterogeneous subdomains within the hydrogel film. These subdomains arise from the distinct mechanical responses of the pattern and film domains under applied mechanical forces. Unlike previous studies that incorporate reinforced inclusions into soft matrices to tailor material properties, our method manipulates the localization, integration, and interaction of these subdomain building blocks within the soft film. This enables extensive tuning of both local and global behaviors. Notably, we introduce a subdomain-interface mechanism that allows for the concurrent customization and decoupling of mechanical properties and shape transformations within a single material system—an achievement rarely accomplished with current synthetic soft materials. Additionally, our use of in-situ imaging characterizations, including full-field strain mapping via digital imaging correlation and reciprocal-space patterns through fast Fourier transform analysis of real-space pattern domains, provides rapid real-time monitoring tools to uncover the underlying principles governing tailored multiscale heterogeneities and intricate behaviors.

Trajectory-centric framework TrajAtlas reveals multi-scale differentiation heterogeneity among cells, genes, and gene modules in osteogenesis.

Osteoblasts, the key cells responsible for bone formation and the maintenance of skeletal integrity, originate from a diverse array of progenitor cells. However, the mechanisms underlying osteoblast differentiation from these multiple osteoprogenitors remain poorly understood. To address this knowledge gap, we developed a comprehensive framework to investigate osteoblast differentiation at multiple scales, encompassing cells, genes, and gene modules. We constructed a reference atlas focused on differentiation, which incorporates various osteoprogenitors and provides a seven-level cellular taxonomy. To reconstruct the differentiation process, we developed a model that identifies the transcription factors and pathways involved in differentiation from different osteoprogenitors. Acknowledging that covariates such as age and tissue type can influence differentiation, we created an algorithm to detect differentially expressed genes throughout the differentiation process. Additionally, we implemented methods to identify conserved pseudotemporal gene modules across multiple samples. Overall, our framework systematically addresses the heterogeneity observed during osteoblast differentiation from diverse sources, offering novel insights into the complexities of bone formation and serving as a valuable resource for understanding osteogenesis.

Multi-scale model for evaluating stress fluctuation in shale gas reservoirs considering geomechanical heterogeneity

In this article, a numerical model considering multi-scale flow and heterogeneity of shale reservoirs is developed to analyze the spatiotemporal evolution of the stress field in shale gas production. After considering the geomechanical heterogeneity, the variation in the local rock mechanical parameters of the reservoir, and the increase in the effective stress of the reservoir will cause local stress fluctuations. In the hydraulic fracture control area, the average stress fluctuation coefficient is higher, indicating a stronger “stress heterogeneity.” When the homogeneity increases from 5 to 100, the fluctuation range of the minimum horizontal principal stress increases by 28.89 MPa, and the fluctuation range of the principal stress difference increases by 7.35 MPa. The presence of natural fractures can significantly impact the coupled hydraulic-mechanical processes of the reservoir, increasing the number of high-speed permeation channels penetrating the system. The greater the density and permeability, the smaller the minimum horizontal principal stress and the larger the principal stress difference. The angle of natural fractures directly influences the direction of stress drop, with an average minimum horizontal principal stress occurring when the angle of natural fractures is at 60°/120°.

A Closer Look at Heritage Systems from Medieval Colors to Modern and Contemporary Artworks

This microreview, conducted by interdisciplinary teams, examines complex heritage material systems, such as medieval colors and modern and contemporary artworks. Our multi-analytical approach, a significant aspect of our research, is a means to this end. The conservation of works of art is our shared goal, as it ensures their accessibility and the transfer of cultural heritage to future generations. We seek to interpret the damage, usefulness, and innovation of the experimental design in this context. As Jan Wouters rightly points out, “The terminology used nowadays to describe the potential damage to objects caused by analysis should be refined beyond the destructiveness/non-invasiveness polarization. A terminology should include at least degree level intervention (low, medium, high), usefulness, and innovation”. Complementing micro- or sub-micro-sampling with the appropriate analytical methods is crucial, as exemplified in medieval, modern, and contemporary collections studies. Finally, a novel perspective for exploring the information contained in the multiscale heterogeneity of organic historical materials is envisaged, and it includes UV/Visible photoluminescence spectral imaging using a low-intensity ultraviolet synchrotron beam.

Soil organic carbon sequestration can be promoted through the improvement of landscape configuration heterogeneity in typical agricultural regions of northeast China

Landscape heterogeneity is considered a promising option for building resilient and sustainable agroecosystems. Understanding the relationships between farmland soil organic carbon (SOC) and landscape heterogeneity can support soil carbon sequestration and better serve food security and climate change. However, the influence extent and optimal scale of farmland landscape heterogeneity (i.e. landscape composition and landscape configuration heterogeneity) on SOC remains unclear. In this study, we established the relationships between multi-scale landscape heterogeneity and SOC in a typical grain-production county of northeast China. Stepwise regression results showed that when the buffer radius was 2000 m, the interpretation of SOC by landscape heterogeneity was the largest. The effects of landscape composition and landscape configuration on SOC were further decomposed by Variance Partitioning Analysis, and we found that independent interpretation ability of landscape configuration (8%) exceeded landscape composition (7%). The result of soil mapping combined with landscape indexes also showed that landscape configuration contributed more to the increased accuracy. Moreover, we found that correlation between configuration indexes and SOC at the class level was less related than that at the landscape level, among which the two most important indexes were Mean Fractal Dimension Index (FRAC_MN) and Number of Patches (NP). FRAC_MN was even more important than natural factors, indicating the validity of landscape as an indicator of human activities should not be ignored when considering farmland SOC. Overall, the results of this study revealed that the negative effects of agricultural intensification on SOC can be buffered to a certain extent by increasing the complexity of patch shape and reducing the degree of landscape fragmentation at the landscape level, providing hope for the sustainable development in intensive agricultural areas. In addition, due to the scale effect of landscape heterogeneity on farmland SOC, we suggest that decision makers should consider the spatial scale in landscape allocation and planning. This study provides a scientific reference for realizing the balance between grain production and ecological function in intensive agricultural areas.

A mechanism on multiscale heterogenous deformation of nickel-based single crystal superalloys unraveled by time-of-flight neutron diffraction technology

Time-of-flight (TOF) neutron diffraction technology is a powerful tool for acquiring rich diffraction information on the multiscale microstructures and stresses of nickel-based single crystal superalloys. In this study, the tensile deformation behaviors of DD426 superalloy at 760 °C were investigated by TOF neutron diffraction. Combined with electron backscatter diffraction technology, the multiscale deformation heterogeneity between γ/γ' phases and dendritic/interdendritic regions was simultaneously characterized for the first time. Our experiments revealed a significant misorientation difference and the existence of a long-range stress field in the adjacent area between the dendritic and interdendritic regions after tensile deformation at 760 °C. The misorientation angles of crystal planes along the loading direction between the dendritic and interdendritic regions in the deformed alloy was approximately 1.6 ± 0.6° This misorientation can be attributed to the geometrically necessary dislocations (GNDs) concentrated in the adjacent area between the two regions with densities of approximately 1014 m-2. In addition, the lattice strains of both γ' and γ showed a compressive–tensile transition from the dendritic to interdendritic regions, balanced with a long-range stress field. The pile-up GNDs in the adjacent area between the two regions contributed to the existence of long-range stress fields. This study highlights that TOF neutron diffraction technology may reveal well the heterogeneous deformation mechanisms via the formation of both GNDs and pile-up in the adjacent interdendritic/dendritic area of single crystal superalloys.

Impact of multi-scale microstructural heterogeneities on the mechanical behavior of additively manufactured and post-processed Nb-based C103 alloy

Laser powder-bed fusion (LPBF) processed Nb-based alloy C103 (Nb-10Hf-1Ti wt.%) develops a complex, hierarchical microstructure comprising a fine-scale solidification cell structure, overlaid with a dense dislocation-network outlining the cell boundaries, within the primary grains. Additionally, sub-grain boundaries and a fine-scale dispersion of nano-sized hafnium oxide precipitates, possibly forming during solidification, decorate the solidification cell boundaries as well as exist within the cells. This complex hierarchical microstructure results in impressive tensile mechanical properties. Post-build stress-relieving annealing and hot isostatic pressing (HIP) largely annihilates the solidification cell structure and associated dislocation network, lowering the strength but with substantial recovery of tensile ductility. Nevertheless, the resulting microstructure offers higher strengths as compared to their wrought counterparts.

Characterizing preferential infiltration of loess using geostatistical electrical resistivity tomography

Preferential infiltration is prevalent in loess and is pivotal in disasters such as landslides. However, the inherent multi-scale heterogeneity of loess makes traditional in-situ monitoring techniques challenging for characterizing the preferential infiltration process. This study employed the Geostatistical Electrical Resistivity Tomography (GERT) to examine the spatial distribution of mass water content (ωs) in loess strata to understand the preferential infiltration processes in loess. This study improved stimulus-response data quality and used GERT to characterize the spatial-temporal distribution of electrical conductivity (σ) and estimate ωs through the σ-ωs relationship. This study indicates that the surface loess layer has higher ωs than deeper layers, rapidly declining as depth increases. Under preferential infiltration, early-stage water forms a spherical saturated zone, transforming into an ellipsoid as it descends. Using equivalent homogeneous parameters as prior information effectively improved σ estimation. This study found a 15.9% error in the total change in water content based on the GERT survey compared to the known amount of injected water. It explores the possible impacts of the uncertainty of the unknown relationship between σ and ωs, its spatial variability, and the accuracy of the survey on the error. The formation of an electric double-layer structure within the loess as the saturation increases, which reduces the sensitivity of GERT to changes in water content, is likely another cause. Finally, these areas are essential for advancing future studies on applying geophysical tools to accurately estimate water distributions in loess formations.

Multi-scale structural heterogeneity promoting hydrogen embrittlement in additively manufactured pure nickel

In this study, how physical differences in the microstructure of additively manufactured (AM) pure Ni affect its susceptibility to hydrogen embrittlement (HE) are investigated. The presence of high-density dislocation cells (DCs) and grain boundaries in AM Ni could absorb more hydrogen therein, with the DC boundaries serving as reversible hydrogen trapping sites. The DC boundaries overlapped with the grain boundaries might lead to an enhanced hydrogen diffusion therein for AM Ni. Consequently, an increased depth of hydrogen-affected region and accelerated failure process were observed in AM Ni during tensile testing due to intergranular cracking. Furthermore, the HE resistance can be slightly improved by a dislocation-cell elimination heat treatment for AM Ni-800, but it remains lower than that of traditionally manufactured Ni, primarily due to the residue of bi-modal grains with small grains along the molten pool boundaries. The underlying HE mechanism based on the structural heterogeneities at different scales for pure Ni is discussed.

Multiscale heterogeneity of white matter morphometry in psychiatric disorders.

Inter-individual variability in neurobiological and clinical characteristics in mental illness is often overlooked by classical group-mean case-control studies. Studies using normative modelling to infer person-specific deviations of grey matter volume have indicated that group means are not representative of most individuals. The extent to which this variability is present in white matter morphometry, which is integral to brain function, remains unclear. We applied Warped Bayesian Linear Regression normative models to T1-weighted magnetic resonance imaging data and mapped inter-individual variability in person-specific white matter volume deviations in 1,294 cases (58% male) diagnosed with one of six disorders (attention-deficit/hyperactivity, autism, bipolar, major depressive, obsessive-compulsive and schizophrenia) and 1,465 matched controls (54% male) recruited across 25 scan sites. We developed a framework to characterize deviation heterogeneity at multiple spatial scales, from individual voxels, through inter-regional connections, specific brain regions, and spatially extended brain networks. The specific locations of white matter volume deviations were highly heterogeneous across participants, affecting the same voxel in fewer than 8% of individuals with the same diagnosis. For autism and schizophrenia, negative deviations (i.e., areas where volume is lower than normative expectations) aggregated into common tracts, regions and large-scale networks in up to 35% of individuals. The prevalence of white matter volume deviations was lower than previously observed in grey matter, and the specific location of these deviations was highly heterogeneous when considering voxel-wise spatial resolution. Evidence of aggregation within common pathways and networks was apparent in schizophrenia and autism but not other disorders.

Effects of standard heat treatment on micro-to nanostructure heterogeneities in a Rene 65 Ni-based superalloy billet

Advancements in the manufacturing of aeroengine components with superior mechanical properties rely on the microstructure homogeneity of industrially forged Ni-based superalloys. Billets often contain microstructural heterogeneities that can persist throughout the process, potentially compromising the integrity of the final product. Rene 65 is a relatively new superalloy with high-temperature mechanical properties superior to those of Alloy 718. However, systematic studies on its microstructure-property relationships are scarce. Here, we correlate the microstructural evolution with the hardness of a Rene 65 billet subjected to industrial processing and standard heat treatments. Multiscale microstructural heterogeneities, including grain size, geometrically necessary dislocations, twin boundary density, and the multimodal distribution of γʹ precipitates, are characterised. Grain growth occurs near the billet centre. Precipitation varies with radial position, showing up to a two-fold change in primary and secondary γʹ fractions. Tertiary γʹ precipitates exhibit variations in morphology and chemical composition, with Cr and Co enrichment near the billet surface. These heterogeneities arise from varying strain distributions and cooling rates during radial forging. Sub-solvus annealing and ageing are shown to mitigate these heterogeneities by promoting recrystallisation, recovery, and homogeneous precipitation of tertiary γʹ. A strengthening model elucidates the active mechanisms in as-received and heat-tread conditions, predicting hardness with a deviation of <8 %. Analyses of grain boundaries and γ/γʹ interfaces reveal strong segregation of Mo, W, Nb, C and B before and after heat treatment, with Mo and B showing the highest interfacial excess values. Insights into the microstructural evolution and its impact on properties could guide the development of next-generation aerospace parts.

A preoperative radiogenomic model based on quantitative heterogeneity for predicting outcomes in triple-negative breast cancer patients who underwent neoadjuvant chemotherapy

BackgroundTriple-negative breast cancer (TNBC) is highly heterogeneous, resulting in different responses to neoadjuvant chemotherapy (NAC) and prognoses among patients. This study sought to characterize the heterogeneity of TNBC on MRI and develop a radiogenomic model for predicting both pathological complete response (pCR) and prognosis.Materials and methodsIn this retrospective study, TNBC patients who underwent neoadjuvant chemotherapy at Fudan University Shanghai Cancer Center were enrolled as the radiomic development cohort (n = 315); among these patients, those whose genetic data were available were enrolled as the radiogenomic development cohort (n = 98). The study population of the two cohorts was randomly divided into a training set and a validation set at a ratio of 7:3. The external validation cohort (n = 77) included patients from the DUKE and I-SPY 1 databases. Spatial heterogeneity was characterized using features from the intratumoral subregions and peritumoral region. Hemodynamic heterogeneity was characterized by kinetic features from the tumor body. Three radiomics models were developed by logistic regression after selecting features. Model 1 included subregional and peritumoral features, Model 2 included kinetic features, and Model 3 integrated the features of Model 1 and Model 2. Two fusion models were developed by further integrating pathological and genomic features (PRM: pathology-radiomics model; GPRM: genomics-pathology-radiomics model). Model performance was assessed with the AUC and decision curve analysis. Prognostic implications were assessed with Kaplan‒Meier curves and multivariate Cox regression.ResultsAmong the radiomic models, the multiregional model representing multiscale heterogeneity (Model 3) exhibited better pCR prediction, with AUCs of 0.87, 0.79, and 0.78 in the training, internal validation, and external validation sets, respectively. The GPRM showed the best performance for predicting pCR in the training (AUC = 0.97, P = 0.015) and validation sets (AUC = 0.93, P = 0.019). Model 3, PRM and GPRM could stratify patients by disease-free survival, and a predicted nonpCR was associated with poor prognosis (P = 0.034, 0.001 and 0.019, respectively).ConclusionMultiscale heterogeneity characterized by DCE-MRI could effectively predict the pCR and prognosis of TNBC patients. The radiogenomic model could serve as a valuable biomarker to improve the prediction performance.

Numerical Simulation of Tectonic Stress State Considering The Multiscale Heterogeneity of Geological Structures

Numerical Simulation of Tectonic Stress State Considering The Multiscale Heterogeneity of Geological Structures

Prediction of arsenic retention in vadose zone based on empirical relationship between soil properties and segmented retardation factors

Arsenic (As) is a widespread environmental contaminant that poses a significant threat to ecosystems and human health. Although previous studies have qualitatively revealed the effects of individual soil properties on the transport and fate of As in the vadose zone, their integrated impacts remain obscure. Moreover, studies investigating the retardation factor therein, which is a key parameter for comprehending As transport in the vadose zone, are extremely limited. In this study, we investigated the interplay of soil properties with As transport and retention within the vadose zone, while focusing on the retardation factor of As. We employed steady-state unsaturated water-flow soil column experiments coupled with a mobile–immobile model and multiple linear regression analysis to elucidate the dependence of As retardation factors on the soil properties. In the mobile water zone, iron and organic matter contents emerged as the two most influential properties that impedes As mobility. Whereas, in the immobile water zone, the coefficient of uniformity and bulk density were the most influential factors that enhanced As retention. Finally, we derived an empirical equation for calculating the As retardation factors in each zone, offering a valuable tool for describing and predicting As behavior to protect the groundwater resources underneath.

Time-frequency relationship between heterogeneous uncertainties and stock market extreme risk: new evidence from China

ABSTRACT We empirically investigate the dynamic correlation between different uncertainties and stock market extreme risk across multiple time-frequency domains, providing novel evidence for the multiscale heterogeneity of popular uncertainty measures. Our findings reveal a more significant short-term relationship between the observable news-based economic uncertainty proposed by Baker et al. (2016) and China’s stock market extreme risk, while the latent economic uncertainty suggested by Jurado et al. (2015) dominates the long-term time horizon. Moreover, financial uncertainty is also a crucial source of stock market extreme risk that cannot be ignored.

Three-dimensional geological modeling applied to multiscale heterogeneity of a reservoir analog: Paleocoastal deposits from the Rio Bonito formation, Paraná Basin

Coastal sandstones have high permoporosity and contain significant hydrocarbon reserves, although they present variable flow heterogeneities. The goal of this paper is to understand the distribution of potential reservoir-flow units in the Rio Bonito Formation (early Permian, Paraná Basin) and to investigate heterogeneities on multiscale. We use stratigraphic, sedimentological, 3D model, and petrological data to evaluate reservoir heterogeneities. System tracts were modeled by sectioning the entire succession into five zones. Eleven facies associations were modeled separately within each zone, using geostatistical analysis and different algorithms. The 3D model was validated by jackknife procedure, and the distribution of facies associations adequately represented both depositional and stratigraphic frameworks. The results are adequate in a curve of accommodation changes similar to previous proposal for the study area. Tidal sand bar facies association presents as elongated (parallel to depositional dip) to sheetlike geobodies according to amalgamation grade, while upper and middle shoreface one is mostly elongated (parallel to depositional strike) to sheetlike. Besides, fluvial channel facies association occurs mainly elongated parallel to depositional dip, forming multilateral and multistory geobodies. Modeled depositional geometries were distinguished along the succession, showing similarities to Rio Bonito Formation outcrops, recent environments, and other deposits around the world, such as estuarine strata from Oriente Basin and shoreface ones from Gulf of Mexico Basin. Using a detailed petrological analysis, eleven reservoir petrofacies were defined and classified into good-, medium-, and low-quality reservoirs or non-reservoirs. Tidal sand bar, upper-middle shoreface, and fluvial channel deposits were categorized as the main reservoir-flow units. This study provides predictive scenarios for heterogeneities in reservoirs and may be applied in petroleum fields.

Multiscale pore‐network reconstruction of a fine‐textured heterogeneous soil

AbstractDigital samples offer many opportunities to study subsurface fluid flow and contaminant transport processes. The pore size distribution of especially fine‐textured porous media often covers many orders of magnitude in the length scale, which makes accurate microCT scanning and modeling of the underlying processes difficult. When a single‐resolution image is not capable of capturing all relevant details of a sample, one should scan the sample, or selected parts of it, at different resolutions. Combining multiple resolutions into one single sample for subsequent pore‐scale modeling is generally not possible due to limitations in computer memory and speed, thus making it necessary to create a simpler sample containing relevant information from the parent networks. We imaged four samples using different resolutions to capture the multiscale heterogeneity of a fine‐textured soil and combined them into one overall digital sample based on the original pore networks. The parent networks were characterized using their geometrical properties, correlations between these properties, and connectivity functions describing the network topologies. Our approach creates stochastic networks of arbitrary size with the same flow properties as the parent network. The method, implemented using the PoreStudio pore network model, repeatedly integrates information at two subsequent scales, with the resulting digital sample having the same hydraulic properties as the original samples. The procedure leads to more useful three‐dimensional digital models, facilitating basic analyses of underlying pore size distributions. Porosity calculations were compared with direct measurements, while those for the hydraulic conductivity were compared with estimates based on the particle size distribution and nearby field data.

Synergistic Effect of Surface Thermal Heterogeneity in Phase With Topography on Deep Moist Convection

AbstractUsing large eddy simulation, we investigate the combined effect of terrain and surface sensible heat flux (SHF) heterogeneity on the development of afternoon deep moist convection (DMC). We implement an analytically derived, two‐dimensional terrain and SHF variations transformed from a κ−3 (where κ is the wavenumber) spectrum spanning wavelengths from 32 to 0.2 km. By separately coupling multiscale terrain with a homogeneous SHF field and the multiscale SHF field with flat terrain, we discern the individual impacts of these κ−3‐spectrum forcings on DMC. Our specific forcing configuration demonstrates that the multiscale terrain had a greater influence on DMC development compared to the multiscale SHF field. While the solely surface SHF heterogeneity forcing results in a wider pool of high relative humidity above the boundary layer, its significance is relatively lower in the mountainous terrain cases due to the shorter interaction time between highly buoyant thermals and the surrounding environment. However, when the multiscale terrain and SHF field are synchronized, DMC develops rapidly within a time frame of 4.5 hr, which is facilitated by enhanced surface buoyancy fluxes, the presence of highly buoyant thermals, and the persistence of mesoscale structures such as near‐surface convergence and mesoscale updrafts. Our study highlights the importance of the synergistic effects between multiscale terrain and surface SHF heterogeneity in DMC development. Additionally, our multiscale analyses of atmospheric variables reveal distinct atmospheric regimes between the pre‐storm and DMC periods. These findings contribute to a better understanding of the complex dynamics involved in the formation of afternoon DMC.

K-nearest-neighbors induced topological PCA for single cell RNA-sequence data analysis

Single-cell RNA sequencing (scRNA-seq) is widely used to reveal heterogeneity in cells, which has given us insights into cell–cell communication, cell differentiation, and differential gene expression. However, analyzing scRNA-seq data is a challenge due to sparsity and the large number of genes involved. Therefore, dimensionality reduction and feature selection are important for removing spurious signals and enhancing downstream analysis. Traditional PCA, a main workhorse in dimensionality reduction, lacks the ability to capture geometrical structure information embedded in the data, and previous graph Laplacian regularizations are limited by the analysis of only a single scale. We propose a topological Principal Components Analysis (tPCA) method by the combination of persistent Laplacian (PL) technique and L2,1 norm regularization to address multiscale and multiclass heterogeneity issues in data. We further introduce a k-Nearest-Neighbor (kNN) persistent Laplacian technique to improve the robustness of our persistent Laplacian method. The proposed kNN-PL is a new algebraic topology technique which addresses the many limitations of the traditional persistent homology. Rather than inducing filtration via the varying of a distance threshold, we introduced kNN-tPCA, where filtrations are achieved by varying the number of neighbors in a kNN network at each step, and find that this framework has significant implications for hyper-parameter tuning. We validate the efficacy of our proposed tPCA and kNN-tPCA methods on 11 diverse benchmark scRNA-seq datasets, and showcase that our methods outperform other unsupervised PCA enhancements from the literature, as well as popular Uniform Manifold Approximation (UMAP), t-Distributed Stochastic Neighbor Embedding (tSNE), and Projection Non-Negative Matrix Factorization (NMF) by significant margins. For example, tPCA provides up to 628%, 78%, and 149% improvements to UMAP, tSNE, and NMF, respectively on classification in the F1 metric, and kNN-tPCA offers 53%, 63%, and 32% improvements to UMAP, tSNE, and NMF, respectively on clustering in the ARI metric.