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DOE OSTI2024

Structure and phase transitions in niobium and tantalum derived nanoscale transition metal perovskites, Ba(Ti,MV)O3, M=Nb,Ta

The prospect of creating ferroelectric or high permittivity nanomaterials provides motivation for investigating complex transition metal oxides of the form Ba(Ti, MV)O3, where M = Nb or Ta. Solid state processing typically produces mixtures of crystalline phases, rarely beyond minimally doped Nb/Ta. Using a modified sol-gel method, we prepared single phase nanocrystals of Ba(Ti, M)O3. Compositional and elemental analysis puts the empirical formulas close to BaTi0.5Nb0.5O3−δ and BaTi0.5Ta0.5O3−δ. For both materials, a reversible temperature dependent phase transition (non-centrosymmetric to symmetric) is observed in the Raman spectrum in the region 533–583 K (260–310 °C); for Ba(Ti, Nb)O3, the onset is at 543 K (270 °C); and for Ba(Ti, Ta)O3, the onset is at 533 K (260 °C), which are comparable with 390–393 K (117–120 °C) for bulk BaTiO3. The crystal structure was resolved by examination of the powder x-ray diffraction and atomic pair distribution function (PDF) analysis of synchrotron total scattering data. It was postulated whether the structure adopted at the nanoscale was single or double perovskite. Double perovskites (A2B′B″O6) are characterized by the type and extent of cation ordering, which gives rise to higher symmetry crystal structures. PDF analysis was used to examine all likely candidate structures and to look for evidence of higher symmetry. The feasible phase space that evolves includes the ordered double perovskite structure Ba2(Ti, MV)O6 (M = Nb, Ta) Fm-3m, a disordered cubic structure, as a suitable high temperature analog, Ba(Ti, MV)O3Pm-3m, and an orthorhombic Ba(Ti, MV)O3Amm2, a room temperature structure that presents an unusually high level of lattice displacement, possibly due to octahedral tilting, and indication of a highly polarized crystal.

Chemistry↗

NASA NTRSDate not supplied

Interlaminar R-Curve Effects in Thermoplastic Composites: Experiments and Model Correlations

The interlaminar fracture behavior of thermoplastic composites under Mode-I and Mode-II static loading is investigated in this research. The material system under consideration is a carbon fiber reinforced low melt semi-crystalline resin TC1225 LMPAEK T700G (T700/LMPAEK)†. Characterization experiments were conducted to measure the load-displacement response, peak load, and propagation of delamination from a pre-implanted Kapton® insert. The Mode-I response was characterized using a double cantilever beam (DCB) test according to the ASTM D5528-22 standard. It was observed that the propagation exhibited significant resistance to delamination growth, i.e., an R-Curve effect. The test data indicated that the steady-state fracture toughness, G SS I , was approximately twice the mean initiation fracture toughness, G Ic . The Mode-II response of an end notch flexure (ENF) specimen tested according to the ASTM D7905-19 standard exhibited an unexpected stable behavior upon attaining peak load. Prior to attaining peak load, the Mode-II response exhibited some non-linearity, which may be attributed to nonlinear bulk material response, e.g., hyper-elasticity, viscoelasticity, plasticity, etc., and potentially friction at the load/support rollers and R-Curve effects. Finite element models based on the Cohesive Zone Method (CZM) and the Virtual Crack Closure Technique (VCCT) were used to predict the DCB and ENF specimen responses. DCB analysis results obtained using G SS I predicted propagation consistent with experimental data. However, results obtained with the as characterized G Ic were inaccurate in predicting delamination growth onset and peak load. ENF analysis results obtained with the as-characterized Mode-II fracture toughness, G IIc , were inaccurate in predicting the peak load and propagation. Hence, R-Curve effects were included in both DCB and ENF simulations, which enabled improved predictions. The experimentally determined Mode-I R-Curve was used for the DCB simulations, whereas an R-Curve was derived for Mode-II assuming that the change in compliance of the specimen was associated with crack growth only.

Prabhakar M Rao↗

NASA NTRSDate not supplied

Interlaminar R-Curve Effects in Thermoplastic Composites: Experiments and Model Correlations

Prabhakar Rao↗

DOE OSTI2024

Sputter-Coated TiO 2 Films as Passivation and Hole Transfer Layers for Improved Energy Conversion with Solar Fuel WO 3 /CuWO 4 Photoanodes

Atomic layer deposited (ALD) “leaky” TiO 2 have gained interest as charge-selective protection layers for semiconductor solar fuel electrodes. Here we demonstrate the use of sputter-deposited TiO 2 layers as hole selective contacts for WO 3 /CuWO 4 type 2 heterojunction water oxidation photoanodes for the first time. TiO 2 protection layers with varying thicknesses (2 to 128 nm) were deposited using the RF magnetron sputtering technique. The resulting TiO 2 films are amorphous based on Raman spectroscopy and powder XRD. Photoelectrochemical scans and Vibrating Kelvin probe photovoltage spectroscopy show that 2-8 nm TiO 2 layers nearly double the photocurrent to 0.97 mA cm -2 under AM 1.5 illumination (19% AQE at 350 nm), increase the surface photovoltage signal by 25%, and increase the WO 3 /CuWO 4 bandgap. These effects can be attributed to the selectivity of TiO 2 for photoholes. Additionally, SPV data suggest that TiO 2 overlayers suppress copper-based surface recombination defects. Reduced photocurrent and the photovoltage are seen in thicker TiO 2 films (16 to 128 nm) as a result of an increasing hole transfer resistance and because of light shading effects according to photoaction spectra. The TiO 2 films also improve the stability of the WO 3 /CuWO 4 photoelectrodes, allowing nearly constant O 2 evolution over 3 hours after an initial 20-35% loss. Overall, this work establishes RF magnetron sputtering as a useful method to install amorphous TiO 2 passivation layers for improved WO 3 /CuWO 4 solar fuel photoelectrodes. Furthermore, we show how the combination of PEC with SPV measurements provides insight into the function of the TiO 2 coatings.

CuWO4↗

DOE OSTI2021

D-Band EPR and ENDOR Spectroscopy of 15 N-Labeled Photosystem I

For billions of years, nature has optimized the photosynthetic machinery that converts light energy into chemical energy. Key primary reactions of photosynthesis occur in large membrane protein-cofactor complexes. The light-induced sequential electron transfer reactions occur through a chain of donor/acceptor cofactors embedded in the protein matrix resulting in a long-lived transmembrane charge-separated state. EPR is the method of choice to study electron transfer and the interaction of protein environment with redox-active cofactors. However, the spectra of organic cofactor radicals typically are not fully resolved and severely overlap at conventional X-band EPR. Even at Q-band EPR, this overlap is present and often a serious problem. As a result, there is a large variation of the reported EPR data and limited understanding of electronic structures of several redox-active cofactors. These serious problems can often be overcome by the excellent spectral resolution provided by high-frequency EPR (HF EPR). In this work, we study the electronic structure of the primary electron donor P 700 and the secondary electron acceptor A 1 of Photosystem I (PSI) using 130 GHz (D-band) EPR and Electron-Nuclear-Double-Resonance (ENDOR) spectroscopy. PSI was isotopically labeled with 15 N (I = $\frac{1/2}$) to avoid quadrupolar interactions in the most abundant nitrogen isotope 14 N (I = 1) and simplify the ENDOR spectra. ENDOR spectroscopy is central for determining the hyperfine coupling of nitrogen atoms of the two chlorophyll molecules comprising oxidized P 700 and the involvement of protein nitrogen atoms with reduced A 1 . While HF ENDOR of A 1 - allows identification of two nitrogen atoms, HF ENDOR of P 700 + still does not permit unique assignment of the recorded hyperfine couplings.

15N↗

DOE OSTI2020

Performance of an atomic mean-field spin–orbit approach within exact two-component theory for perturbative treatment of spin–orbit coupling

The paper reports development of an atomic mean-field (AMF) spin–orbit approach within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e), a new relativistic quantum-chemical method for treating spin-orbit coupling in molecules. The effective one-electron spin–orbit integral matrix in the four-component representation is assembled as a direct sum of one-centre spin–orbit integral matrices with the mean-field two-electron contributions evaluated using atomic SFX2C-1e Hartree–Fock density matrices. It is then transformed into two-component representation using analytic SFX2C-1e energy derivative formulation. The resulting two-component spin–orbit integral matrix is by design suitable for use in perturbative calculations of spin–orbit coupling, treating SFX2C-1e wavefunctions as unperturbed states. The accuracy of the present AMF approach has been demonstrated using benchmark calculations of spin–orbit splittings for representative diatomic radicals at the equation-of-motion coupled-cluster singles and doubles level. In conclusion, to demonstrate the applicability and accuracy of the present perturbative spin–orbit scheme in calculations of challenging heavy-element containing systems, a thorough computational investigation of six low-lying electronic states of ThO+ is reported.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

Statistical Validation of Multiple Related Data Sets—Case Study Using Interstellar Boundary Explorer Satellite Data

Abstract Space scientists often face the question of whether data collected by different instruments are measurements of the same source population. This paper proposes a statistical validation method for evaluating the agreement between such related data sets. It offers a detailed case study focused on validating a new data set from the Interstellar Boundary Explorer (IBEX) mission, which serves as a practical how-to guide for similar analyses. Since 2008, the IBEX satellite has been gathering data on heliospheric energetic neutral atoms (ENAs) while being exposed to various sources of background noise, such as cosmic rays and solar energetic particles. The IBEX mission initially released only a qualified triple-coincidence (qABC) data product, which was designed to provide observations of ENAs free of background contamination. Further measurements revealed that the qABC data were in fact susceptible to contamination, having relatively low ENA counts and high background rates. To mitigate this issue, the mission team recently considered releasing a certain qualified double-coincidence (qBC) data product, which has roughly twice the detection rate of the qABC data product. This paper presents a simulation-based validation of the new qBC data product against the already-released qABC data product. The results show that the qBCs can plausibly be said to be measuring the same source population as the qABCs up to an average absolute deviation of 3.6%. Visual diagnostics provide additional confirmation of source rate coherence across data products. The framework introduced here is general and can be applied to other validation problems both within and outside the field of space physics.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Mixed-precision numerics in scientific applications: survey and perspectives

The explosive demand for artificial intelligence (AI) workloads has led to a significant increase in silicon area dedicated to lower-precision computations on recent high-performance computing hardware designs. However, mixed-precision capabilities, which can achieve performance improvements of up to 8x compared to double-precision in extreme compute-intensive workloads, remain largely untapped in most scientific applications. A growing number of efforts have shown that mixed-precision algorithmic innovations can deliver superior performance without sacrificing accuracy. These developments should prompt computational scientists to seriously consider whether their scientific modeling and simulation applications could benefit from the acceleration offered by new hardware and mixed-precision algorithms. In this survey, we (1) review progress across diverse scientific domains—fluid dynamics, weather and climate, quantum chemistry, and computational genomics—that have begun adopting mixed-precision strategies; (2) examine state-of-the-art algorithmic techniques such as iterative refinement, splitting and emulation schemes, and adaptive precision solvers; (3) assess their implications for accuracy, performance, and resource utilization; and (4) survey the emerging software ecosystem that enables mixed-precision methods at scale. We conclude with perspectives and recommendations on cross-cutting opportunities, domain-specific challenges, and the role of co-design between application scientists, numerical analysts, and computer scientists. Collectively, this survey underscores that mixed-precision numerics can reshape computational science by aligning algorithms with the evolving landscape of hardware capabilities.

Graphics processing units↗

DOE OSTI2024

Thermally Insulating Transparent Barrier (THINNER) coatings on single pane windows

Conventional silica aerogel monoliths can provide remarkable thermal insulation but the presence of large pores (> 30 nm) tends to scatter visible light and render the material opaque or translucent instead of transparent. In addition, they are prone to cracking during synthesis and handling which makes them difficult to integrate in products and in particular in window solutions. This project developed two new solgel synthesis methods using silica precursors or preformed silica nanoparticles and ambient drying to produce mesoporous organo-silica monoliths. The monoliths were (i) thermally insulating, (ii) optically transparent, (iii) flexible, and (iv) hydrophobic. They feature porosity ranging from 50% to 90% with narrow pore size distribution with pore less than 20 nm resulting in excellent optical clarity (haze < 2%) and very low thermal conductivity (< 30 mW/mK). Interestingly, not only porosity but also pore size and mass fractal dimension were found to affect the thermal conductivity of the mesoporous silica. The superior transparency of the monoliths was shown to be attributed to dependent scattering among silica nanoparticles. Flexibility was achieved through trimethylchlorosilane surface modification. Furthermore, process scale-up and integration of the ambigel monoliths into window solutions using optically clear adhesives were also demonstrated in 6”x6” double-pane windows. The aerogel and the window solution were shown to be durable to accelerated aging under UV, moisture, and/or temperature gradient and thermal cycling. Overall, the window solution achieved the technical performance and the cost target of $10/sqft set for the SHIELD program. However, scaling to industry relevant scale (> 10’x10’) remains a challenge due to requirements on the drying process and fume hood size and to the propensity of large aerogel slab to crack during drying.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

NASA NTRS1993

Reduction in size and unsteadiness of a VTOL ground vortex by ground fences

A ground vortex, produced when a jet impinges on the ground in the presence of cross flow, is encountered by V/STOL aircraft hovering near the ground and is known to be hazardous to the aircraft. The objective of this research was to identify a ground-based technique by which both the mean size and fluctuation in size of the ground vortex could be reduced. A simple passive method was identified and examined in the laboratory. Specifically, one or two fine wire mesh screens (ground fences) bent in a horseshoe shape and located on the ground in front of the jet impingement point proved to be very effective. The ground fences work by decreasing the momentum of the upstream-traveling wall jet, effectively causing a higher freestream-to-jet velocity ratio (V(sub infinity)/V(sub j)) and thus, a ground vortex smaller in size and unsteadiness. At(V(sub infinity)/V(sub j)) = 0.15, the addition of a single ground fence resulted in a 70 percent reduction in mean size of the ground vortex. With two ground fences, the mean size decreased by about 85 percent. Fluctuations in size decreased nearly in proportion to the mean size, for both the single and double fence configurations. These results were consistent over a wide range of jet Reynolds number (10(exp 4) less than Re(sub jet) less than 10(exp 5)); further development and full-scale Reynolds number testing are required, however, to determine if this technique can be made practical for the case of actual VTOL aircraft.

Cimbala, John M.↗

NASA NTRS2014

Obtaining Stokes Parameters from the SUMI Experiment

A sounding rocket experiment designed at the Marshall Space Flight Center, named the Solar Ultraviolet Magnetograph Investigation, had its second launch in July of 2012 to test the feasibility of measuring polarization signals of the ionized magnesium resonance doublet near 280 nm, originating from the transition region. The rocket housed a telescope at the front end and an imaging system at the rear end. Placed at the focal point of the self‐filtering telescope, a wave plate rotated through 12 predefined angular orientations to restrict the measurements to specific combinations of circular and linear polarization. Coupled with a double Wollaston analyzer, the linearly polarized ordinary and extraordinary beams were measured for the 12 combinations, each containing different fractions of the Stokes parameters (I, Q, U, V). A thorough analysis of the data has allowed us to come to several conclusions regarding the design of the experiment. 1) We are confident that polarization can be measured. A sunspot region was determined to exhibit similar results over multiple pixels. 2) Measurements are limited by resolution, i.e. regions smaller than the angular resolution per pixel cannot be resolved with any certainty. 3) Temporal evolution of magnetic features must be considered in future experimental designs. Measurements need to be taken in repeated cycles as opposed to a single cycle over the duration of the experiment. In our presentation, we will provide a summary of the observations along with the methods of our analysis, including the limitations that we've encountered.

Fayock, Brian↗

DOE OSTI2023

Growth phase estimation for abundant bacterial populations sampled longitudinally from human stool metagenomes

Longitudinal sampling of the stool has yielded important insights into the ecological dynamics of the human gut microbiome. However, human stool samples are available approximately once per day, while commensal population doubling times are likely on the order of minutes-to-hours. Despite this mismatch in timescales, much of the prior work on human gut microbiome time series modeling has assumed that day-to-day fluctuations in taxon abundances are related to population growth or death rates, which is likely not the case. Here, we propose an alternative model of the human gut as a stationary system, where population dynamics occur internally and the bacterial population sizes measured in a bolus of stool represent a steady-state endpoint of these dynamics. We formalize this idea as stochastic logistic growth. We show how this model provides a path toward estimating the growth phases of gut bacterial populations in situ. We validate our model predictions using an in vitro Escherichia coli growth experiment. Finally, we show how this method can be applied to densely-sampled human stool metagenomic time series data. We discuss how these growth phase estimates may be used to better inform metabolic modeling in flow-through ecosystems, like animal guts or industrial bioreactors.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

A dual high-energy radiography platform with 15 μ m resolution at the National Ignition Facility

To study matter at extreme densities and pressures, we need mega laser facilities such as the National Ignition Facility as well as creative methods to make observations during timescales of a billionth of a second. To facilitate this, we developed a platform and diagnostic to characterize a new point-projection radiography configuration using two micro-wires irradiated by a short pulse laser system that provides a large field of view with up to 3.6 ns separation between images. In this work, we used tungsten-carbide solid spheres as reference objects and inferred characteristics of the back-lighter source using a forward-fitting algorithm. The resolution of the system is inferred to be 15 μm (using 12.5 μm diameter wires). The bremsstrahlung temperature of the source is 70–300 keV, depending on laser energy and coupling efficiency. By adding the images recorded on multiple stacked image plates, the signal-to-noise of the system is nearly doubled. The imaging characterization technique described here can be adapted to most point-projection platforms where the resolution, spectral contrast, and signal-to-noise are important.

47 OTHER INSTRUMENTATION↗

NASA NTRS2006

New Propellants and Cryofuels

The proposed research will investigate the stability and cryogenic properties of solid propellants that are critical to NASA s goal of realizing practical propellant designs for future spacecraft. We will determine the stability and thermal properties of a solid hydrogen-liquid helium stabilizer in a laboratory environment in order to design a practical propellant. In particular, we will explore methods of embedding atomic species and metallic nano-particulates in hydrogen matrices suspended in liquid helium. We will also measure the characteristic lifetimes and diffusion of atomic species in these candidate cryofuels. The most promising large-scale advance in rocket propulsion is the use of atomic propellants; most notably atomic hydrogen stabilized in cryogenic environments, and metallized-gelled liquid hydrogen (MGH) or densified gelled hydrogen (DGH). The new propellants offer very significant improvements over classic liquid oxygen/hydrogen fuels because of two factors: (1) the high energy-release, and (ii) the density increase per unit energy release. These two changes can lead to significant reduced mission costs and increased payload to orbit weight ratios. An achievable 5 to 10 percent improvement in specific impulse for the atomic propellants or MGH fuels can result in a doubling or tripling of system payloads. The high-energy atomic propellants must be stored in a stabilizing medium such as solid hydrogen to inhibit or delay their recombination into molecules. The goal of the proposed research is to determine the stability and thermal properties of the solid hydrogen-liquid helium stabilizer. Magnetic resonance techniques will be used to measure the thermal lifetimes and the diffusive motions of atomic species stored in solid hydrogen grains. The properties of metallic nano-particulates embedded in hydrogen matrices will also be studied and analyzed. Dynamic polarization techniques will be developed to enhance signal/noise ratios in order to be able to detect low concentrations of the introduced species. The required lifetimes for atomic hydrogen and other species can only be realized at low temperatures to avoid recombination of atoms before use as a fuel.

Palasezski, Bryan↗

DOE OSTI2022

Assessing Raindrop Breakup Parameterizations Using Disdrometer Observations

In this work, an intercomparison of raindrop mean diameter frequency distribution (RDFD) is performed for numerical simulations of precipitating cloud systems using an array of models and microphysics schemes. This includes results from the Regional Atmospheric Modeling System (RAMS) double-moment microphysics, the Hebrew University Cloud Model bin microphysics (HUCM) interfaced to the RAMS parent model, and the Weather Research and Forecasting (WRF) Model with the Thompson, Morrison, double-moment 6-class (WDM6), and National Severe Storms Laboratory (NSSL) double-moment schemes. Simulations are examined with respect to the raindrop size distribution (DSD) volume-number mean diameter (D m ) and intercept parameter (N w ). When compared to a suite of disdrometer observations, the RDFD resulting from each microphysics scheme exhibits varying degrees of mean drop size constraints and peaks in the frequency distribution of D m . A more detailed investigation of the peaked RDFD from the RAMS simulations suggests that the parameterization of raindrop collisional breakup can impose strong limitations on the evolution of simulated drop growth. As such, a summary and comparison of the drop breakup parameterizations among the aforementioned microphysics schemes is presented. While some drop breakup parameterizations are adjusted toward the observations by modifying the threshold diameter for the onset of breakup, this study explores the use of a modified maximum breakup efficiency. This method permits the parameterization to retain its threshold breakup diameter, while limiting the strength of drop breakup and permitting a broader range of drop sizes. As a result, the simulated mean drop sizes are in better agreement with observations.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1996

Waveguides in Thin Film Polymeric Materials

Results on the fabrication of integrated optical components in polymeric materials using photo printing methods will be presented. Optical waveguides were fabricated by spin coating preoxidized silicon wafers with organic dye/polymer solution followed by soft baking. The waveguide modes were studied using prism coupling technique. Propagation losses were measured by collecting light scattered from the trace of a propagation mode by either scanning photodetector or CCD camera. We observed the formation of graded index waveguides in photosensitive polyimides after exposure of UV light from a mercury arc lamp. By using a theoretical model, an index profile was reconstructed which is in agreement with the profile reconstructed by the Wentzel-Kramers-Brillouin calculation technique using a modal spectrum of the waveguides. Proposed mechanism for the formation of the graded index includes photocrosslinking followed by UV curing accompanied with optical absorption increase. We also developed the prototype of a novel single-arm double-mode interferometric sensor based on our waveguides. It demonstrates high sensitivity to the chance of ambient temperature. The device can find possible applications in aeropropulsion control systems.

Sakisov, Sergey↗

NASA NTRS1998

Tropospheric Wind Profile Measurements with a Direct Detection Doppler Lidar

Research has established the importance of global tropospheric wind measurements for large scale improvements in numerical weather prediction. In addition, global wind measurements provide data that are fundamental to the understanding and prediction of global climate change. These tasks are closely linked with the goals of the NASA Earth Science Enterprise and Global Climate Change programs. NASA Goddard has been actively involved in the development of direct detection Doppler lidar methods and technologies to meet the wind observing needs of the atmospheric science community. In this paper we describe a recently developed prototype wind lidar system using a direct detection Doppler technique for measuring wind profiles from the surface through the troposphere. This system uses a pulsed ND:YAG laser operating at 1064 nm as the transmitter. The laser pulse is directed to the atmosphere using a 40 cm diameter scan mirror. The portion of the laser energy backscattered from aerosols and molecules is collected by a 40 cm diameter telescope and coupled via fiber optics into the Doppler receiver. Single photon counting APD's are used to detect the atmospheric backscattered signal. The principle element of the receiver is a dual bandpass tunable Fabry Perot etalon which analyzes the Doppler shift of the incoming laser signal using the double edge technique. The double edge technique uses two high resolution optical filters having bandpasses offset relative to one another such that the 'edge' of the first filter's transmission function crosses that of the second at the half power point. The outgoing laser frequency is located approximately at the crossover point. Due to the opposite going slopes of the edges, a Doppler shift in the atmospheric backscattered laser frequency produces a positive change in signal for one filter and a negative change in the second filter. Taking the ratio of the two edge channel signals yields a result which is directly proportional to the component of the wind along the line-of-sight of the laser. Measuring the radial wind in several directions provides sufficient information to determine the true wind speed and direction. The lidar has operated from our laboratory at Goddard since June, 1997. Wind profiles have been obtained to altitudes of 12 km with a vertical resolution of 330 in. Vector wind data are obtained by rotating the scan mirror to measure line-of-sight wind profiles for at least two azimuth angles at an elevation angle of 45 degrees. The precision of the data as determined from the standard deviation of multiple independent lidar profiles is in the range of 1 to 3 m/sec up to 10 km. Good agreement is obtained when the lidar data are compared with the upper air rawinsonde soundings taken at Dulles airport. Examples of the wind lidar data will be presented along with a description of the instrument and future developments.

Gentry, Bruce M.↗

DOE OSTI2025

PAC in DESI. I. Galaxy stellar mass function into the 10 6 M ⊙ frontier

The Photometric objects Around Cosmic webs (PAC) method integrates cosmological photometric and spectroscopic surveys, offering valuable insights into galaxy formation. PAC measures the excess surface density of photometric objects, $\bar{n}_2w_{{\rm {p}}}$, with specific physical properties around spectroscopic tracers. In this study, we improve the PAC method to make it more rigorous and eliminate the need for redshift bins. We apply the enhanced PAC method to the DESI Y1 BGS Bright spectroscopic sample and the deep Dark Energy Camera Legacy Survey (DECaLS) photometric sample, obtaining $\bar{n}_2w_{{\mathrm {p}}}$ measurements across the complete stellar mass range, from $10^{5.3}$ to $10^{11.5}\,{\rm M}_{\odot }$ for blue galaxies, and from $10^{6.3}$ to $10^{11.9}\,{\rm M}_{\odot }$ for red galaxies. We combine $\bar{n}_2w_{{\rm {p}}}$ with $w_{{\rm {p}}}$ measurements from the BGS sample, which is not necessarily complete in stellar mass. Assuming that galaxy bias is primarily determined by stellar mass and colour, we derive the galaxy stellar mass functions (GSMFs) down to $10^{5.3}\,{\rm M}_{\odot }$ for blue galaxies and $10^{6.3}\,{\rm M}_{\odot }$ for red galaxies, while also setting lower limits for smaller masses. The blue and red GSMFs are well described by single and double Schechter functions, respectively, with low-mass end slopes of $\alpha _{\rm {blue}}=-1.54^{+0.02}_{-0.02}$ and $\alpha _{\rm {red}}=-2.50^{+0.08}_{-0.08}$, resulting in the dominance of red galaxies below $10^{7.6}\,{\rm M}_{\odot }$. Stage-IV cosmological photometric surveys, capable of reaching 2–3 mag deeper than DECaLS, present an opportunity to explore the entire galaxy population in the local universe with PAC. This advancement allows us to address critical questions regarding the nature of dark matter, the physics of reionization, and the formation of dwarf galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗