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Applications of Fuzzy Set Theory to Satellite Soundings

The introduction of an appropriate fuzzy setting for satellite soundings and its application to clustering methods via unimodal fuzzy sets in the future is proposed. Methods of hard clustering analysis and fuzzy partitioned clustering were applied on simulated data with very encouraging results. The proposed clustering technique is discussed. The notion of a unimodal fuzzy set was chosen to represent the partition of a data set for two reasons: (1) it detects all the locations in the vector space where highly concentrated clusters of points exist; and (2) the notion is general enough to represent clusters that exhibit quite general distributions of points. The technique detects all of the existing unimodal fuzzy sets and realizes the maximum separation among them. It is economical in memory space and computational time requirements and also detects groups that are fairly generally distributed in the feature space.

Munteanu, M. J.↗

Dynamics of cD clusters of galaxies. II: Analysis of seven Abell clusters

We have investigated the dynamics of the seven Abell clusters A193, A399, A401, A1795, A1809, A2063, and A2124, based on redshift data reported previously by us (Hill & Oegerle, (1993)). These papers present the initial results of a survey of cD cluster kinematics, with an emphasis on studying the nature of peculiar velocity cD galaxies and their parent clusters. In the current sample, we find no evidence for significant peculiar cD velocities, with respect to the global velocity distribution. However, the cD in A2063 has a significant (3 sigma) peculiar velocity with respect to galaxies in the inner 1.5 Mpc/h, which is likely due to the merger of a subcluster with A2063. We also find significant evidence for subclustering in A1795, and a marginally peculiar cD velocity with respect to galaxies within approximately 200 kpc/h of the cD. The available x-ray, optical, and galaxy redshift data strongly suggest that a subcluster has merged with A1795. We propose that the subclusters which merged with A1795 and A2063 were relatively small, with shallow potential wells, so that the cooling flows in these clusters were not disrupted. Two-body gravitational models of the A399/401 and A2063/MKW3S systems indicate that A399/401 is a bound pair with a total virial mass of approximately 4 x 10(exp 15) solar mass/h, while A2063 and MKW3S are very unlikely to be bound.

Oegerle, William R.↗

Cluster Method Analysis of K. S. C. Image

Information obtained from satellite-based systems has moved to the forefront as a method in the identification of many land cover types. Identification of different land features through remote sensing is an effective tool for regional and global assessment of geometric characteristics. Classification data acquired from remote sensing images have a wide variety of applications. In particular, analysis of remote sensing images have special applications in the classification of various types of vegetation. Results obtained from classification studies of a particular area or region serve towards a greater understanding of what parameters (ecological, temporal, etc.) affect the region being analyzed. In this paper, we make a distinction between both types of classification approaches although, focus is given to the unsupervised classification method using 1987 Thematic Mapped (TM) images of Kennedy Space Center.

Rodriguez, Joe, Jr.↗

Rapid subsurface analysis of frequency-domain thermoreflectance images with K-means clustering

K-means clustering analysis is applied to frequency-domain thermoreflectance (FDTR) hyperspectral image data to rapidly screen the spatial distribution of thermophysical properties at material interfaces. Performing FDTR while raster scanning a sample consisting of 8.6 μm of doped-silicon (Si) bonded to a doped-Si substrate identifies spatial variation in the subsurface bond quality. Routine thermal analysis at select pixels quantifies this variation in bond quality and allows assignment of bonded, partially bonded, and unbonded regions. Performing this same routine thermal analysis across the entire map, however, becomes too computationally demanding for rapid screening of bond quality. To address this, K-means clustering was used to reduce the dimensionality of the dataset from more than 20 000 pixel spectra to just K = 3 component spectra. The three component spectra were then used to express every pixel in the image through a least-squares minimized linear combination providing continuous interpolation between the components across spatially varying features, e.g., bonded to unbonded transition regions. Fitting the component spectra to the thermal model, thermal properties for each K cluster are extracted and then distributed according to the weighting established by the regressed linear combination. Thermophysical property maps are then constructed and capture significant variation in bond quality over 25 μm length scales. The use of K-means clustering to achieve these thermal property maps results in a 74-fold speed improvement over explicit fitting of every pixel.

36 MATERIALS SCIENCE↗

Study on Closely Related Citrus CMMs based on Chemometrics and Prediction of Components-Targets-Diseases Network by Ingenuity Pathway Analysis

As the representatives of closely related Chinese medicinal materials (CMMs) originated from Rutaceae family, Aurantii fructus immaturus (AFI), Aurantii fructus (AF), Citri reticulatae pericarpium viride (CRPV), and Citri reticulatae pericarpium (CRP) have better functions in regulating qi and promoting gastrointestinal motility. However, differences in the quality of closely related Citrus CMMs have not yet been revealed until now. Herein, this study focused on the systematic differentiation and in-depth understanding of closely related Citrus CMMs by a strategy integrating chemometrics and network pharmacology. Determined by ultra performance liquid chromatography, the content of nine flavonoids showed obvious fluctuations in the decoction pieces from different species (Citrus aurantium Linnaeus and Citrus reticulate Blanco) with decreasing levels in the samples of ripe fruits. Decoction pieces from the different species and ripening stages were well distinguished by orthogonal projection to latent structure-discriminate analysis (OPLS-DA) and cluster analysis. As a result, four active components including narirutin, naringenin, hesperidin, and 3,5,6,7,8,3′,4′-heptemthoxyflavone were filtered out by variable importance for the projection (VIP) value (VIP > 1.0), which were regarded as chemotaxonomic markers. Furthermore, a components-targets-diseases network was constructed via ingenuity pathway analysis (IPA), and the correlations were predicted between four chemotaxonomic markers, 223 targets, and three diseases including colitis, breast cancer, and colorectal cancer. The obtained results will be of great significance for identifying closely related Citrus CMMs and conduce to improving the resource utilization of CMMs.

Mu, Qixuan↗

Clustering High-dimensional Toxicogenomics Data with Rare Signals

Toxicogenomics studies the gene and protein activities to drug treatments or toxic exposures. As the drugs and genes are numerous, toxicogenomics data are naturally high dimensional, with dimension sizes up to millions. In addition, the distribution of toxicogenomics data is oftentimes skewed, and they contain rare but important signals representing a cell or organism’s response to toxicity. The combination of high dimension and extremely skewed distribution of toxicogenomics data makes clustering analysis extremely challenging.We present our study of clustering toxicogenomics data using classical approaches such as principal component analysis as well as deep learning approaches such as auto-encoders. Our experiments show that these approaches fail to preserve rare signals and produce high-quality clusters. We then explore augmenting matrix factorization with deep learning techniques such as attention mechanism to produce latent representations for clustering. Our technique is able to better preserve rare signals after dimensionality reduction than prior approaches. Furthermore, we combine our augmented matrix factorization with a mechanism similar to autoencoder to balance separable clusters and low regeneration errors. Our experiments demonstrate better clustering with our proposed approach.

Cong, Guojing↗

Stability of Cool Cores during Galaxy Cluster Growth: A Joint Chandra/SPT Analysis of 67 Galaxy Clusters along a Common Evolutionary Track Spanning 9 Gyr

We present the results of a joint analysis of Chandra X-ray and South Pole Telescope (SPT) Sunyaev–Zel’dovich (SZ) observations targeting the first sample of galaxy clusters at 0.3 < z < 1.3, selected to be the progenitors of well-studied nearby clusters based on their expected accretion rate. We develop a new procedure in order to tackle the analysis challenge that is estimating the intracluster medium (ICM) properties of low-mass and high-redshift clusters with ~150 X-ray counts. One of the dominant sources of uncertainty on the ICM density profile estimated with a standard X-ray analysis with such shallow X-ray data is due to the systematic uncertainty associated with the ICM temperature obtained through the analysis of the background-dominated X-ray spectrum. We show that we can decrease the uncertainty on the density profile by a factor varying between 2 and 8 with a joint deprojection of the X-ray surface brightness profile measured by Chandra and the SZ-integrated Compton parameter available in the SPT cluster catalog. We apply this technique to the whole sample of 67 clusters in order to track the evolution of the ICM core density during cluster growth. We confirm that the evolution of the gas density profile is well modeled by the combination of a fixed core and a self-similarly evolving non-cool-core profile. We show that the fraction of cool cores in this sample is remarkably stable with redshift although clusters have gained a factor of ~4 in total mass over the past ~9 Gyr.

79 ASTRONOMY AND ASTROPHYSICS↗

Orthopyroxenes as recorders of diogenite petrogenesis: Major and minor element systematics

As a part of our research to better understand magmatic processes in the Eucrite Parent Body, we have initiated an ambitious program of study of major, minor and trace elements in orthopyroxene from diogenites. This paper reports preliminary results for major and minor elements in orthopyroxenes for a suite of 13 diogenites: Aioun El Atrouss, ALH 84001, ALH A 77256, EET 87530, Ellemeet, Garland, Ibbenburen, Johnstown, Manegoan, peckelsheim, Roda, Shalka, and Tatahouine. A companion paper by Shearer et al. reports new trace element data for ALH 84001, ALH A 77256, Ibbenburen, and Tatahouine. We have presently collected over 800 high quality pyroxene microprobe analyses for Si, Al, Ca, Na, Mn, Fe, Mg, Cr, and Ti. The chemical systematics observed for these orthopyroxenes reflect original magmatic mineral/melt partitioning plus later trapped liquid/mineral equilibration, subsolids, exsolution, and mineral/mineral metamorphic reactions. We have therefore avoided, at this point, any attempt to use statistical analysis to group (e.g. factor or cluster analysis) these orthopyroxenes chemically.

Papike, J. J.↗

Analysis of SETI data collected in the parasitic mode

A system for performing SETI observations continuously as part of non-SETI observations at a radio observatory is presented, and the analysis of results obtained by the parasitic system is discussed. The system, designated SERENDIP, is a real-time microprocessor-controlled spectrum analyzer with algorithms for performing statistical operations and recording those spectra with characteristics presumed to be typical of intelligent rather than astrophysical origin. Programs also exist for the post-acquisition analysis of signal autocorrelation, power spectra, time behavior and positional coordinates, and for a generalized cluster analysis to detect clusters of signal detections. In a recent run of 35 days, the SERENDIP system detected 4000 narrowband spectra exceeding a preset threshold, of which 98% were determined to be of instrumental origin. The remaining class of detections is also believed to be instrumental, although not as well organized as the first signals, and means are currently being sought for eliminating them.

Bowyer, S.↗

Investigating Covalent Bonding in f-elements using Gas-phase Ion Chemistry

Introduction In the reprocessing of f-elements present in used nuclear fuels, a variety of diglycolamides (DGA’s) are used as extractants for actinide partitioning. In particular, the Actinide-Lanthanide Separation (ALSEP) process typically utilizes either the N,N,N’,N’-tetraoctyl diglycolamide (TODGA) or N,N,N',N'-tetra-2-ethylhexyl diglycolamide (T2EHDGA) extractant ligands following the partitioning of uranium and plutonium from used nuclear fuel. To better understand fundamental interactions in these processes, covalent bonding of several f-elements with diglycolamides, primarily TODGA, is investigated in the gas phase using nanospray ionization and a quadrupole time-of-flight mass spectrometer. Further, analysis of the identity and relative strength of the cluster is enabled by MS2 isolation and collision induced dissociation. Methods Metal ion cluster analysis was completed using a Bruker mircOTOF-Q II quadrupole time-of-flight mass spectrometer equipped with a CaptiveSpray nanospray ion source. Metal:ligand solutions were prepared as 30 µM europium nitrate, samarium nitrate, cerium nitrate, or holmium nitrate and 3 µM DGA in acetonitrile or a 50:50 mixture of acetonitrile: isopropanol. Cluster mass spectra and collision-induced dissociation experiments were conducted in positive mode. Preliminary data To examine the patterns and relative strength of lanthanide: DGA interactions, MS2 experiments were completed with each lanthanide species listed above. Preliminary analyses of samarium and europium TODGA clusters suggest several combinations of TODGA and nitrate forming. The samarium cluster experiments yielded Sm(TODGA)x clusters with a samarium:TODGA ratio of up to 1:7 able to be isolated and evidence of greater ratios present in the mass spectrum. This is surprising, as metal clusters are not expected to have a coordination space able to accommodate this many ligands as large as TODGA. MS2 experiments show that, at higher ratios and with sufficient collision energy, entire TODGA ligands are removed instead of being fragmented. These experiments show that a lower collision energy is required to remove ligands as the number of bound TODGA’s increases, suggesting that in larger clusters, ligands are more delicately complexed to the metal. In addition to Sm(TODGA)x, several clusters were observed with nitrate ions bound to the metal in addition to TODGA. With a single nitrate ion, clusters with up to six TODGA’s were able to be isolated. In a similar pattern to the samarium clusters with only TODGA, less collision energy is required to eliminate one or more TODGA’s with increasing size. MS2 experiments suggest clusters with one nitrate appear to be of an equivalent or greater stability to clusters which replace the nitrate with a TODGA, as more collision energy is required to remove a TODGA ligand. These species with one nitrate are also in a higher abundance than the equivalent TODGA only cluster. With two nitrate ions, only clusters with a single TODGA were able to be isolated. Analogous europium experiments resulted in very similar clusters. Ratios of up to 1:7 Eu:TODGA were able to be isolated, and clusters with one nitrate and up to five TODGAs were isolated. In clusters with two nitrate ions, one or two TODGA’s could also be bound to the metal. MS2 experiments suggested, similarly to samarium, that larger clusters required less collision energy to eliminate TODGA. Europium clusters with one nitrate are in greater abundance and are stronger than the equivalent cluster which replaces the nitrate with TODGA. Similar analysis with cerium and holmium is ongoing, as well as analysis with other DGA ligands to compare relative strengths of the lanthanide metals with various extractant ligands.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Empowering Machine Learning Forecasting of Labquake Using Event‐Based Features and Clustering Characteristics

Abstract Following recent advances of machine learning (ML), we present a novel approach to extract spatiotemporal seismo‐mechanical features from Acoustic Emission (AE) catalogs to empower ML‐based forecasting. The AE data were recorded during laboratory stick‐slip experiments on granite samples cut by rough faults. Based on the features computed for a past time window, a random forest (RF) classifier is used to forecast the occurrence of a large magnitude event ( M AE > 3.5) in the next time window. Event‐based features allow us to associate informative time‐space characteristics to each feature and nearest‐neighbor clustering analysis enables us to separate background and clustered seismicity and train individual models. The results show that the separation of AEs enhances the forecasting accuracy from 73.2% for the entire catalog up to 82.1% and 89.0% if background and clustered events are used separately. The presented new approach may be upscaled for applications to forecast tectonic earthquakes.

Karimpouli, Sadegh↗

Proteogenomic characterization of difficult-to-treat breast cancer with tumor cells enriched through laser microdissection

Abstract Background Breast cancer (BC) is the most commonly diagnosed cancer and the leading cause of cancer death among women globally. Despite advances, there is considerable variation in clinical outcomes for patients with non-luminal A tumors, classified as difficult-to-treat breast cancers (DTBC). This study aims to delineate the proteogenomic landscape of DTBC tumors compared to luminal A (LumA) tumors. Methods We retrospectively collected a total of 117 untreated primary breast tumor specimens, focusing on DTBC subtypes. Breast tumors were processed by laser microdissection (LMD) to enrich tumor cells. DNA, RNA, and protein were simultaneously extracted from each tumor preparation, followed by whole genome sequencing, paired-end RNA sequencing, global proteomics and phosphoproteomics. Differential feature analysis, pathway analysis and survival analysis were performed to better understand DTBC and investigate biomarkers. Results We observed distinct variations in gene mutations, structural variations, and chromosomal alterations between DTBC and LumA breast tumors. DTBC tumors predominantly had more mutations inTP53,PLXNB3, Zinc finger genes, and fewer mutations inSDC2,CDH1,PIK3CA,SVIL, andPTEN. Notably, Cytoband 1q21, which contains numerous cell proliferation-related genes, was significantly amplified in the DTBC tumors. LMD successfully minimized stromal components and increased RNA–protein concordance, as evidenced by stromal score comparisons and proteomic analysis. Distinct DTBC and LumA-enriched clusters were observed by proteomic and phosphoproteomic clustering analysis, some with survival differences. Phosphoproteomics identified two distinct phosphoproteomic profiles for high relapse-risk and low relapse-risk basal-like tumors, involving several genes known to be associated with breast cancer oncogenesis and progression, includingKIAA1522,DCK,FOXO3,MYO9B,ARID1A,EPRS,ZC3HAV1, andRBM14. Lastly, an integrated pathway analysis of multi-omics data highlighted a robust enrichment of proliferation pathways in DTBC tumors. Conclusions This study provides an integrated proteogenomic characterization of DTBC vs LumA with tumor cells enriched through laser microdissection. We identified many common features of DTBC tumors and the phosphopeptides that could serve as potential biomarkers for high/low relapse-risk basal-like BC and possibly guide treatment selections.

Oncology↗

Structuring Nutrient Yields throughout Mississippi/Atchafalaya River Basin Using Machine Learning Approaches

To minimize the eutrophication pressure along the Gulf of Mexico or reduce the size of the hypoxic zone in the Gulf of Mexico, it is important to understand the underlying temporal and spatial variations and correlations in excess nutrient loads, which are strongly associated with the formation of hypoxia. This study’s objective was to reveal and visualize structures in high-dimensional datasets of nutrient yield distributions throughout the Mississippi/Atchafalaya River Basin (MARB). For this purpose, the annual mean nutrient concentrations were collected from thirty-three US Geological Survey (USGS) water stations scattered in the upper and lower MARB from 1996 to 2020. Eight surface water quality indicators were selected to make comparisons among water stations along the MARB over the past two decades. Principal component analysis (PCA) was used to comprehensively evaluate the nutrient yields across thirty-three USGS monitoring stations and identify the major contributing nutrient loads. The results showed that all samples could be analyzed using two main components, which accounted for 81.6% of the total variance. The PCA results showed that yields of orthophosphate (OP), silica (SI), nitrate–nitrites (NO 3 -NO 2 ), and total suspended sediment (TSS) are major contributors to nutrient yields. It also showed that land-planted crops, density of population, domestic and industrial discharges, and precipitation are fundamental causes of excess nutrient loads in MARB. These factors are of great significance for the excess nutrient load management and pollution control of the Mississippi River. It was found that the average nutrient yields were stable within the sub-MARB area, but the large nitrogen yields in the upper MARB and the large phosphorus yields in the lower MARB were of great concern. t-distributed stochastic neighbor embedding (t-SNE) revealed interesting nonlinear and local structures in nutrient yield distributions. Clustering analysis (CA) showed the detailed development of similarities in the nutrient yield distribution. Moreover, PCA, t-SNE, and CA showed consistent clustering results. This study demonstrated that the integration of dimension reduction techniques, PCA, and t-SNE with CA techniques in machine learning are effective tools for the visualization of the structures of the correlations in high-dimensional datasets of nutrient yields and provide a comprehensive understanding of the correlations in the distributions of nutrient loads across the MARB.

54 ENVIRONMENTAL SCIENCES↗

The composite sequential clustering technique for analysis of multispectral scanner data

The clustering technique consists of two parts: (1) a sequential statistical clustering which is essentially a sequential variance analysis, and (2) a generalized K-means clustering. In this composite clustering technique, the output of (1) is a set of initial clusters which are input to (2) for further improvement by an iterative scheme. This unsupervised composite technique was employed for automatic classification of two sets of remote multispectral earth resource observations. The classification accuracy by the unsupervised technique is found to be comparable to that by traditional supervised maximum likelihood classification techniques. The mathematical algorithms for the composite sequential clustering program and a detailed computer program description with job setup are given.

Su, M. Y.↗

Oleaginous Yeast Biology Elucidated With Comparative Transcriptomics

ABSTRACT Extremophilic yeasts have favorable metabolic and tolerance traits for biomanufacturing‐ like lipid biosynthesis, flavinogenesis, and halotolerance – yet the connection between these favorable phenotypes and strain genotype is not well understood. To this end, this study compares the phenotypes and gene expression patterns of biotechnologically relevant yeasts Yarrowia lipolytica , Debaryomyces hansenii , and Debaryomyces subglobosus grown under nitrogen starvation, iron starvation, and salt stress. To analyze the large data set across species and conditions, two approaches were used: a “network‐first” approach where a generalized metabolic network serves as a scaffold for mapping genes and a “cluster‐first” approach where unsupervised machine learning co‐expression analysis clusters genes. Both approaches provide insight into strain behavior. The network‐first approach corroborates that Yarrowia upregulates lipid biosynthesis during nitrogen starvation and provides new evidence that riboflavin overproduction in Debaryomyces yeasts is overflow metabolism that is routed to flavin cofactor production under salt stress. The cluster‐first approach does not rely on annotation; therefore, the coexpression analysis can identify known and novel genes involved in stress responses, mainly transcription factors and transporters. Therefore, this work links the genotype to the phenotype of biotechnologically relevant yeasts and demonstrates the utility of complementary computational approaches to gain insight from transcriptomics data across species and conditions.

Weintraub, Sarah J. [Department of Bioinformatics ↗

Global Weather States and Their Properties from Passive and Active Satellite Cloud Retrievals

In this study, the authors apply a clustering algorithm to International Satellite Cloud Climatology Project (ISCCP) cloud optical thickness-cloud top pressure histograms in order to derive weather states (WSs) for the global domain. The cloud property distribution within each WS is examined and the geographical variability of each WS is mapped. Once the global WSs are derived, a combination of CloudSat and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) vertical cloud structure retrievals is used to derive the vertical distribution of the cloud field within each WS. Finally, the dynamic environment and the radiative signature of the WSs are derived and their variability is examined. The cluster analysis produces a comprehensive description of global atmospheric conditions through the derivation of 11 WSs, each representing a distinct cloud structure characterized by the horizontal distribution of cloud optical depth and cloud top pressure. Matching those distinct WSs with cloud vertical profiles derived from CloudSat and CALIPSO retrievals shows that the ISCCP WSs exhibit unique distributions of vertical layering that correspond well to the horizontal structure of cloud properties. Matching the derived WSs with vertical velocity measurements shows a normal progression in dynamic regime when moving from the most convective to the least convective WS. Time trend analysis of the WSs shows a sharp increase of the fair-weather WS in the 1990s and a flattening of that increase in the 2000s. The fact that the fair-weather WS is the one with the lowest cloud radiative cooling capability implies that this behavior has contributed excess radiative warming to the global radiative budget during the 1990s.

histograms↗

Combinatorial Exploration and Mapping of Phase Transformation in a Ni–Ti–Co Thin Film Library

Combinatorial synthesis and high-throughput characterization of a Ni–Ti–Co thin film materials library are reported for exploration of reversible martensitic transformation. The library was prepared by magnetron co-sputtering, annealed in vacuum at 500 °C without atmospheric exposure, and evaluated for shape memory behavior as an indicator of transformation. Composition, structure, and transformation behavior of the 177 pads in the library were characterized using high-throughput wavelength dispersive spectroscopy (WDS), X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD), and four-point probe temperature-dependent resistance (R(T)) measurements. A new, expanded composition space having phase transformation with low thermal hysteresis and Co > 10 at. % is found. Unsupervised machine learning methods of hierarchical clustering were employed to streamline data processing of the large XRD and XPS data sets. Through cluster analysis of XRD data, we identified and mapped the constituent structural phases. Finally, composition–structure–property maps for the ternary system are made to correlate the functional properties to the local microstructure and composition of the Ni–Ti–Co thin film library.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modal analysis of the behavior of inertial particles in turbulence subjected to Stokes drag

The clustering of small heavy inertial particles subjected to Stokes drag in turbulence, which is the concern of present study, is known to be minimal at small and large Stokes number and substantial at St = $\textit{O}$(1). This nonmonotonic trend, which has been shown computationally and experimentally, is yet to be explained analytically. In this study, we obtain an analytical expression for the Lyapunov exponents that quantitatively predicts this trend. The sum of the exponents, which is the normalized rate of change of the signed volume of a small cloud of particles, is correctly predicted to be negative and positive at small and large Stokes numbers, respectively, asymptoting to $\textit{τQ}$ as $\textit{τ}$ → 0 and $τ^{–1/2}|Q|^{1/4}$ as $\textit{τ} → ∞$, where $\textit{τ}$ is the particle relaxation time and $\textit{Q(τ)}$ is the difference between the norm of the rotation- and strain-rate tensors computed along the particle trajectory, which remains negative at all $\textit{τ}$ in turbulent flows. Additionally, the trajectory crossing is predicted only in hyperbolic flows where Q < 0 for sufficiently inertial particles with a $\textit{τ}$ that scales with $|Q|^{–1/2}$. Following the onset of crossovers, a transition from clustering to dispersion is predicted correctly. We show these behaviors are not unique to three-dimensional isotropic turbulence and can be reproduced closely by a one-dimensional mono-harmonic flow, which appears as a fundamental canonical problem in the study of particle clustering. Analysis of this one-dimensional canonical flow shows that the rate of clustering, quantified as the product of the Lyapunov exponent and particle relaxation time, is bounded by –1/2, behaving with extreme nonlinearity in the hyperbolic flows and always remaining positive in the elliptic flows. Finally, this model problem also confirms that dispersion in a hyperbolic flow will occur only if particles' trajectory cross. These findings, which stem from our analysis, are corroborated by the direct numerical simulations.

42 ENGINEERING↗