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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Polariton Condensation in Gap-Confined States of Photonic Crystal Waveguides

Here, the development of patterned multiquantum well heterostructures in GaAs/AlGaAs waveguides has recently made it possible to achieve exciton-polariton condensation in a topologically protected bound state in the continuum (BIC). Polariton condensation was shown to occur above a saddle point of the two-dimensional polariton dispersion in a one-dimensional photonic crystal waveguide. A rigorous analysis of the condensation phenomenon in these systems, as well as the role of the BIC, is still missing. In the present Letter, we theoretically and experimentally fill this gap by showing that polariton confinement resulting from the negative effective mass and the photonic energy gap in the dispersion play a key role in enhancing the relaxation toward the condensed state. In fact, our results show that low-threshold polariton condensation is achieved within the effective trap created by the exciting laser spot, regardless of whether the resulting confined mode is long-lived (polariton BIC) or short-lived (lossy mode). In both cases, the spatial quantization of the polariton condensate and the threshold differences associated to the corresponding state lifetime are measured and characterized. For a given negative mass, a slightly lower condensation threshold from the polariton BIC mode is found and associated to its reduced radiative losses, as compared to the lossy one.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Depinning, melting, and sliding of generalized Wigner crystals in Moiré systems

We numerically examine the depinning, sliding, and melting of commensurate and incommensurate Wigner crystals on two-dimensional hexagonal periodic substrates near fillings of 1 / 3 , 1 / 2 , and 2 / 3 to model the dynamics of generalized Wigner crystals in moiré heterostructures. At low temperatures where thermal fluctuations are irrelevant, for commensurate fillings we find a strongly pinned state that depins into a sliding crystal, while at incommensurate fillings the depinning threshold is strongly reduced. For fillings below 1 / 2 , the depinning occurs in a two-step process. Above the first depinning threshold, there is an extended range of drives where the conduction occurs via the sliding of antikinks along the charge stripes, followed by a second threshold where all the charges begin to slide. At finite temperatures, the external driving reduces the effective melting temperature at commensurate fillings and enhances creep at incommensurate fillings. We show that depinning into different sliding states, such as moving fluids or moving crystals, produces nonlinear features in the transport curves. We also show that transport is asymmetric on either side of a commensurate filling due to the different dynamics for interstitials versus holes in the commensurate structure. A variety of sliding states should be accessible for generalized Wigner crystals at finite temperatures even for low drives. If experiments can realize sliding dynamics in moiré systems, it would open another class of commensurate and incommensurate phases for study. Additionally, the sliding dynamics and antikink flow could provide unique functionalities for charge transport in moiré heterostructures. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Rare events and Griffiths phases in topological quantum error correction

The performance of quantum error correcting (QEC) codes is often studied under the assumption of spatiotemporally uniform error rates. On the other hand, experimental implementations almost always produce heterogeneous error rates, in either space or time, as a result of effects such as imperfect fabrication and/or cosmic rays. It is therefore important to understand if and how their presence can affect the performance of QEC in qualitative ways. Here, in this work, we study the effects of nonuniform error rates in the representative examples of the 1D repetition code and the 2D toric code, focusing on when they have extended spatiotemporal correlations; these may arise, for instance, from rare events (such as cosmic rays) that temporarily elevate error rates over the entire code patch. These effects can be described in the corresponding statistical mechanics models for decoding, where long-range correlations in the error rates lead to extended rare regions of weaker coupling. For the 1D repetition code where the rare regions are linear, we find two distinct decodable phases: a conventional ordered phase in which logical failure rates decay exponentially with the code distance, and a rare-region dominated Griffiths phase in which failure rates are parametrically larger and decay as a stretched exponential. In particular, the latter phase is present when the error rates in the rare regions are above the bulk threshold. For the 2D toric code where the rare regions are planar, we find no decodable Griffiths phase: rare events which boost error rates above the bulk threshold lead to an asymptotic loss of threshold and failure to decode. Unpacking the failure mechanism implies that techniques for suppressing extended sequences of repeated rare events (which, without intervention, will be statistically present with high probability) will be crucial for QEC with the toric code.

classical statistical mechanics↗
DOE OSTI2026

Saturation of magnetized plasma turbulence by propagating zonal flows

Strongly driven ion-scale turbulence in tokamak plasmas is shown to be regulated by a new propagating zonal flow mode, the toroidal secondary mode, which is nonlinearly supported by the turbulence. The mode grows and propagates due to the combined effects of zonal flow shearing and advection by the magnetic drift. Above a threshold in the turbulence level, small-scale toroidal secondary modes become unstable and shear apart turbulent eddies, forcing the turbulence level to remain near the threshold. This threshold condition is used to derive scaling laws for the turbulent heat flux, fluctuation spectra, and zonal flow amplitude, which are validated in nonlinear gyrokinetic simulations and explain previous experimental observations.

Nies, Richard [Princeton Univ., NJ (United States)↗
DOE OSTI2026

Toward an AI-Powered Software Pipeline for Real-Time Tracking and Analysis of Wildfire and Smoke

Real-time tracking of wildfires and smoke is crucial for effective response, minimizing damage, protecting lives, and efficiently managing resources during fire emergencies. We develop a web-based AI-powered pipeline that detects wildfires in aerial video and estimates deployment-relevant behavior metrics, including cumulative burned area, burned-area growth rate, fire spread direction, and smoke dispersion. The system combines a YOLO-based detector with YCbCr-based fire segmentation, HSV-based smoke segmentation, Farneback optical flow, and centroid-based spatiotemporal tracking. Using ground sampling distance (GSD), pixel-level fire masks are converted to physical burned-area measurements by correlating fire pixel counts with camera altitude and tilt angle. We benchmark YOLO variants and non-YOLO baselines (GoogLeNet, CNN, DBN, Autoencoder, U-Net, and AlexNet) on the IEEE FLAME dataset and a newly created aerial frame dataset, Wildfire-DB. Cross-dataset evaluation uses a strict threshold-transfer protocol: decision thresholds are selected on FLAME validation and transferred unchanged to Wildfire-DB to quantify generalization under domain shift. YOLOv6 achieves the strongest cross-dataset frame-level fire detection on Wildfire-DB (ROC-AUC 0.8200, PR-AUC 0.8044, and transferred-threshold F1 0.7596). For tracking-oriented deployment requiring oriented localization, YOLO11-OBB provides the most reliable cross-dataset behavior among OBB-capable models while remaining computationally feasible. To analyze the feasibility of UAV deployment, we further measure inference efficiency using synchronized GPU and CPU power logs on a fixed workload of 1569 frames. YOLO-family models process the video in 5.73–12.47 seconds with net energy of 1247.28–1775.39 J, substantially lower latency and energy than heavier classification and reconstruction baselines. Overall, model optimality depends on operational objectives: YOLOv6 is best for cross-dataset detection robustness, whereas YOL...

Color segmentation↗
DOE OSTI2023

Incorporating Operational Uncertainties into the Dispatch of an Integrated Solar and Storage System

The economic assessment of hybrid energy systems (HES) pairing battery energy storage systems (BESSs) and photovoltaics (PV) is highly important for advancing their deployment in power systems. This paper presents an innovative assessment framework, including an optimal control policy for dispatch under uncertainty and procedures for exploring control parameters that maximize economic benefits. The proposed dispatch policy consists of two steps using system forecast information. The first step is to determine whether a BESS will be used within an operational scheduling time frame based on the probability of events and their thresholds. Once the dispatch of BESS is triggered, a model predictive control (MPC) is carried out in the second step for scheduling using the expected value of system information. By exercising this policy with different thresholds, one can explore the trade-offs between short-term benefits and battery lifetime, and identify an optimal threshold that maximizes the total economic benefits within the battery lifetime. An evaluation study in a real-world HES project is presented to illustrate the proposed framework. Compared with traditional optimal dispatch algorithms, the proposed method can significantly improve the economic benefits of an HES scheduled under forecast uncertainties.

Ma, Xu↗
DOE OSTI2020

Application of Chebyshev’s Inequality in Online Anomaly Detection Driven by Streaming PMU Data

The day-to-day operation of modern power systems is highly reliant on prompt and adequate situational-awareness. This can be achieved via various system monitoring functions such as anomaly detection, in which static thresholds are commonly utilized to distinguish the normal and the abnormal system states. However, a predetermined static threshold usually lacks the flexibility to adapt to unobserved scenarios. In this paper, we propose two self-adaptive synchrophasor data driven anomaly detection approaches based on Chebyshev’s Inequality. The proposed approaches have been evaluated with Kundur’s 2area system and Mini-WECC system. Experimental results verify that the proposed approaches can dynamically adapt to unprecedented scenarios, and detect anomalous events with lower false alarm rate compared to static threshold based detection.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Electromagnetic Properties of Aluminum-based Bilayers for Kinetic Inductance Detectors

The complex conductivity of a superconducting thin film is related to the quasiparticle density, which depends on the physical temperature and can also be modified by external pair breaking with photons and phonons. This relationship forms the underlying operating principle of Kinetic Inductance Detectors (KIDs), where the detection threshold is governed by the superconducting energy gap. We investigate the electromagnetic properties of thin-film aluminum that is proximitized with either a normal metal layer of copper or a superconducting layer with a lower T-C, such as iridium, in order to extend the operating range of KIDs. Using the Usadel equations along with the Nam expressions for complex conductivity, we calculate the density of states and the complex conductivity of the resulting bilayers to understand the dependence of the pair breaking threshold, surface impedance, and intrinsic quality factor of superconducting bilayers on the relative film thicknesses. The calculations and analyses provide theoretical insights in designing aluminum-based bilayer kinetic inductance detectors for detection of microwave photons and athermal phonons at the frequencies well below the pair breaking threshold of a pure aluminum film.

complex conductivity↗
DOE OSTI2022

Surface temperatures reveal the patterns of vegetation water stress and their environmental drivers across the tropical Americas

Vegetation is a key component in the global carbon cycle as it stores ~450 GtC as biomass, and removes about a third of anthropogenic CO2 emissions. However, in some regions, the rate of plant carbon uptake is beginning to slow, largely because of water stress. Here, we develop a new observation-based methodology to diagnose vegetation water stress and link it to environmental drivers. We used the ratio of remotely sensed land surface to near surface atmospheric temperatures (LST/Tair) to represent vegetation water stress, and built regression tree models (random forests) to assess the relationship between LST/Tair and the main environmental drivers of surface energy fluxes in the tropical Americas. We further determined ecosystem traits associated with water stress and surface energy partitioning, pinpointed critical thresholds for water stress, and quantified changes in ecosystem carbon uptake associated with crossing these critical thresholds. Additionally, we found that the top drivers of LST/Tair, explaining over a quarter of its local variability in the study region, are (1) radiation, in 58% of the study region; (2) water supply from precipitation, in 30% of the study region; and (3) atmospheric water demand from vapor pressure deficits (VPD), in 22% of the study region. Regions in which LST/Tair variation is driven by radiation are located in regions of high aboveground biomass or at high elevations, while regions in which LST/Tair is driven by water supply from precipitation or atmospheric demand tend to have low species richness. Carbon uptake by photosynthesis can be reduced by up to 80% in water-limited regions when critical thresholds for precipitation and air dryness are exceeded simultaneously, that is, as compound events. Our results demonstrate that vegetation structure and diversity can be important for regulating surface energy and carbon fluxes over tropical regions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Geostatistical Mapping of Salinity Conditioned on Borehole Logs, Montebello Oil Field, California

We present a geostatistics-based stochastic salinity estimation framework for the Montebello Oil Field that capitalizes on available total dissolved solids (TDS) data from groundwater samples as well as electrical resistivity (ER) data from borehole logging. Data from TDS samples (n = 4924) was coded into an indicator framework based on falling below four selected thresholds (500, 1000, 3000, and 10,000 mg/L). Collocated TDS-ER data from the surrounding groundwater basin were then employed to produce a kernel density estimator to establish conditional probabilities for ER data (n = 8 boreholes) falling below the selected TDS thresholds within the Montebello Oil Field area. Directional variograms were estimated from these indicator coded data, and 500 TDS realizations from conditional indicator simulation were generated for the subsurface region above the Montebello Oil Field reservoir. Simulations were summarized as 3D maps of median TDS, most likely salinity class, and probability for exceeding each of the specified TDS thresholds. Results suggested TDS was below 500 mg/L in most of the study area, with a trend toward higher values (500 to 1000 mg/L) to the southwest; consistent with the average regional groundwater flow direction. Discrete localized zones of TDS greater than 1000 mg/L were observed, with one of these zones in the greater than 10,000 mg/L range; however, these areas were not prevalent. The probabilistic approach used here is adaptable and is readily modified to include additional data and types and can be employed in time-lapse salinity modeling through Bayesian updating.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Development and Validation of Passive Yaw in the Open-Source WEC-Sim Code

A passive yaw implementation is developed, validated, and explored for the WEC-Sim, an open-source wave energy converter modeling tool that works within MATLAB/Simulink. The Reference Model 5 (RM5) is selected for this investigation, and a WEC-Sim model of the device is modified to allow yaw motion. A boundary element method (BEM) code was used to calculate the excitation force coefficients for a range of wave headings. An algorithm was implemented in WEC-Sim to determine the equivalent wave heading from a body’s instantaneous yaw angle and interpolate the appropriate excitation coefficients to ensure the correct time-domain excitation force. This approach is able to determine excitation force for a body undergoing large yaw displacement. For the mathematically simple case of regular wave excitation, the dynamic equation was integrated numerically and found to closely approximate the results from this implementation in WEC-Sim. A case study is presented for the same device in irregular waves. In this case, computation time is increased by 32x when this interpolation is performed at every time step. To reduce this expense, a threshold yaw displacement can be set to reduce the number of interpolations performed. A threshold of 0.01° was found to increase computation time by only 22x without significantly affecting time domain results. Similar amplitude spectra for yaw force and displacements are observed for all threshold values less than 1°, for which computation time is only increased by 2.2x.

50 EE - Wind and Water Power Program - Water (EE-4↗
DOE OSTI2020

Evidence for anti-synergism between ion-assisted etching and in-plasma photoassisted etching of silicon in a high-density chlorine plasma

Etching of p-Si in 60 mTorr 10%Cl2/90%Ar Faraday-shielded inductively coupled high density plasmas was investigated under both ionassisted etching (IAE) and photoassisted etching (PAE) conditions. Real-time etching rates and after-etching Si surface chemical compositions were obtained by laser interferometry and vacuum-transfer x-ray photoelectron spectroscopy (XPS), respectively. Precisely controlled ion energy distributions (IEDs) were generated by applying pulsed negative DC bias on the conductive sample stage. Above a 36 eV threshold at a total flow rate of 250 SCCM, the IAE rate increased with the square root of the ion energy. In contrast to the DC bias, etching under RF bias did not exhibit a threshold ion energy because of the wide IED. XPS spectra revealed that the surface layer under PAE conditions had a significantly lower chlorine content, composed of only SiCl. Under IAE conditions, however, silicon dangling bonds (Si•), SiCl 2 , and SiCl 3 were found on the surface, in addition to SiCl, with a relative abundance of SiCl > SiCl 2 , and SiCl 3 . The absence of higher chlorides and Si• under PAE conditions suggested that vacuum ultraviolet photons and above threshold-energy ions interact with the surface very differently. By varying the duty cycle of the pulsed DC bias, it was found that the IAE rate scaled with the energetic ion dose, but only for low duty cycles. For higher duty cycles, the apparent IAE yield fell off with an increasing Cl coverage on the surface, as the duty cycle went up, which pointed to a negative synergy (antisynergism) between PAE and IAE as the explanation. This antisynergism was further supported by the observed decrease of the total etching rate with an increasing period of the pulsed DC bias. A plausible mechanism is that increasing the pulsing period causes more near-surface damage, creating more recombination centers that lead to a higher loss rate of electron-hole pairs through recombination, thereby reducing the PAE rate.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

$J/\psi $-p scattering length from the total and differential photoproduction cross sections

The J/ψ-p scattering length, αJ/ψp, can be extracted from the J/ψ photoproduction cross section near threshold using the Vector Meson Dominance (VMD) model to relate the reaction γp→J/ψp to J/ψp→J/ψp. Such estimates based on experimental data result in values for |αJ/ψp|, which are much lower than most of the theoretical predictions. In this work, we study the relations between the different results, depending on the use of the total or the differential cross sections, and the method of extrapolating the data to threshold in the case of a low-statistics data sample, such as the near threshold J/ψ photoproduction dataset. We estimate a range for |αJ/ψp| of 0.003–0.025 fm as extracted from experimental data within the VMD model and discuss possible reasons for such lower values compared to the theoretical results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Future Circular Collider Feasibility Study Report

In response to the 2020 Update of the European Strategy for Particle Physics , the Future Circular Collider (FCC) Feasibility Study was launched as an international collaboration hosted by CERN. This report describes the FCC integrated programme , which consists of two stages: an electron-positron collider (FCC-ee) in the first phase, serving as a high-luminosity Higgs, top, and electroweak factory; followed by a proton-proton collider (FCC-hh) at the energy frontier in the second phase. The FCC-ee is designed to operate at four key centre-of-mass energies: the Z pole, the WW pair production threshold, the ZH production peak, and the top/anti-top production threshold—each delivering the highest possible luminosities to four experiments. Over 15 years of operation, FCC-ee will produce more than 6 trillion Z bosons, 200 million WW pairs, nearly 3 million Higgs bosons, and 2 million top anti-top pairs. Precise energy calibration at the Z pole and WW threshold will be achieved through frequent resonant depolarisation of pilot bunches. The sequence of operation modes between the Z, WW, and ZH substages remains flexible. The FCC-hh will operate at a centre-of-mass energy of approximately 85 TeV—nearly an order of magnitude higher than the LHC—and is designed to deliver 5 to 10 times the integrated luminosity of the upcoming High-Luminosity LHC. Its mass reach for direct discovery extends to several tens of TeV. In addition to proton-proton collisions, the FCC-hh is capable of supporting ion-ion, ion-proton, and lepton-hadron collision modes. This second volume of the Feasibility Study Report presents the complete design of the FCC-ee collider, its operation and staging strategy, the full-energy booster and injector complex, required accelerator technologies, safety concepts, and technical infrastructure. It also includes the design of the FCC-hh hadron collider, development of high-field magnets, hadron injector options, and key technical systems for FCC-hh.

Benedikt, M. [European Organization for Nuclear Re↗
DOE OSTI2022

The Influence of Shear on Deep Convection Initiation. Part II: Simulations

Abstract This study evaluates a hypothesis for the role of vertical wind shear in deep convection initiation (DCI) that was introduced in Part I by examining behavior of a series of numerical simulations. The hypothesis states, “Initial moist updrafts that exceed a width and shear threshold will ‘root’ within a progressively deeper steering current with time, increase their low-level cloud-relative flow and inflow, widen, and subsequently reduce their susceptibility to entrainment-driven dilution, evolving toward a quasi-steady self-sustaining state.” A theoretical model that embodied key elements of the hypothesis was developed in Part I, and the behavior of this model was explored within a multidimensional environmental parameter space. Remarkably similar behavior is evident in the simulations studied here to that of the theoretical model, both in terms of the temporal evolution of DCI and in the sensitivity of DCI to environmental parameters. Notably, both the simulations and theoretical model experience a bifurcation in outcomes, whereby nascent clouds that are narrower than a given initial radius R 0 threshold quickly decay and those above the R 0 threshold undergo DCI. An important assumption in the theoretical model, which states that the cloud-relative flow of the background environment V CR determines cloud radius R , is scrutinized in the simulations. It is shown that storm-induced inflow is small relative to V CR beyond a few kilometers from the updraft edge, and V CR therefore plays a predominant role in transporting conditionally unstable air to the updraft. Thus, the critical role of V CR in determining R is validated.

58 GEOSCIENCES↗
DOE OSTI2022

The Influence of Shear on Deep Convection Initiation. Part I: Theory

Abstract This article introduces a novel hypothesis for the role of vertical wind shear (“shear”) in deep convection initiation (DCI). In this hypothesis, initial moist updrafts that exceed a width and shear threshold will “root” within a progressively deeper steering current with time, increase their low-level cloud-relative flow and inflow, widen, and subsequently reduce their susceptibility to entrainment-driven dilution, evolving toward a quasi-steady self-sustaining state. In contrast, initial updrafts that do not exceed the aforementioned thresholds experience suppressed growth by shear-induced downward pressure gradient accelerations, will not root in a deep-enough steering current to increase their inflow, will narrow with time, and will succumb to entrainment-driven dilution. In the latter case, an externally driven lifting mechanism is required to sustain deep convection, and deep convection will not persist in the absence of such lifting mechanism. A theoretical model is developed from the equations of motion to further explore this hypothesis. The model indicates that shear generally suppresses DCI, raising the initial subcloud updraft width that is necessary for it to occur. However, there is a pronounced bifurcation in updraft growth in the model after the onset of convection. Sufficiently wide initial updrafts grow and eventually achieve a steady state. In contrast, insufficiently wide initial updrafts shrink with time and eventually decay completely without external support. A sharp initial updraft radius threshold discriminates between these two outcomes. Thus, consistent with our hypothesis and observations, shear inhibits DCI in some situations, but facilitates it in others.

42 ENGINEERING↗
DOE OSTI2025

Wide bandgap photoconductor (SiC:V)-based optically addressed light valve for high fluence operation

Optically addressable light valves based on wide bandgap 4H- and 6H-SiC as photoconductors were designed to withstand higher operational laser fluences than the state of-the-art bismuth silicon oxide (BSO; Bi 12 SiO 20 ) based devices. Vanadium-doped SiC was selected as the photoconductors due to their reasonable photoresponsivity while many fold improvement in laser induced damage threshold as compared to BSO. The laser induced damage threshold values of the materials were measured after exposing ~ 200 sites on the samples to increasing levels of fluence of a gaussian pulsed Nd: YAG laser system (1064 nm) with a 5 Hz repetition rate. The measured damage threshold values for BSO, 4H- and 6H-SiC were 0.4 J/cm 2 , 1.75 J/cm 2 and 1.8 J/cm 2 , respectively. Photoconductive switches based on 4H and 6H-SiC samples were characterized at wavelengths of 380 nm, 405 nm, and 447 nm. The peak photoresponsivity values of the 4H- and 6H-SiC materials were measured to be under 380 nm and 405 nm, respectively. The photoconductor was bonded to a BK7 optical window with 5 μm diameter microspheres as spacers. A twisted nematic type E7 liquid crystal (LC) was filled in the 5 μm gap in a vacuum chamber. The desired alignment of the liquid crystal was achieved by mutually orthogonal orientation of LC alignment layers on the two mating faces (SiC and BK7). The fabricated devices were modulated using address beams of wavelengths 380 nm, 405 nm, and 447 nm. In conclusion, required transmission levels of > 90% was achieved for the fabricated OALVs for a sinusoidal voltage waveform that meets the lifetime requirement of the device.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Exploring numerical blow-up phenomena for the Keller–Segel–Navier–Stokes equations

The Keller–Segel–Navier–Stokes system governs chemotaxis in liquid environments. This system is to be solved for the organism and chemoattractant densities and for the fluid velocity and pressure. It is known that if the total initial organism density mass is below 2π there exist globally defined generalised solutions, but what is less understood is whether there are blow-up solutions beyond such a threshold and its optimality. Motivated by this issue, a numerical blow-up scenario is investigated. Approximate solutions computed via a stabilised finite element method founded on a shock capturing technique are such that they satisfy a priori bounds as well as lower and L 1 (Ω) bounds for the organism and chemoattractant densities. In particular, these latter properties are essential in detecting numerical blow-up configurations, since the non-satisfaction of these two requirements might trigger numerical oscillations leading to non-realistic finite-time collapses into persistent Dirac-type measures. Our findings show that the existence threshold value 2π encountered for the organism density mass may not be optimal and hence it is conjectured that the critical threshold value 4π may be inherited from the fluid-free Keller–Segel equations. Additionally it is observed that the formation of singular points can be neglected if the fluid flow is intensified.

97 MATHEMATICS AND COMPUTING↗