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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 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Self-consistent dispersal puts tight constraints on the spatiotemporal organization of species-rich metacommunities

Dispersal can be critical to the maintenance of ecosystems as it allows local communities to be recolonized after extinction. However, it remains unclear whether the extinction-mitigating effect of dispersal persists when the number of competing species is large. Based on a spatially explicit mathematical description of metacommunities, we show that when many species coexist, each species operates near its extinction threshold, barely surviving due to dispersal. This has general consequences for spatiotemporal abundance patterns. For short-range dispersal, species organize into fractal spatiotemporal extinction patterns characteristic of a directed percolation phase transition. As species approach their extinction threshold, biodiversity is very sensitive to perturbation, suggesting that dispersal within a metacommunity puts tight constraints on the robustness and evolution of species-rich metacommunities. Biodiversity is often attributed to a dynamic equilibrium between the immigration and extinction of species. This equilibrium forms a common basis for studying ecosystem assembly from a static reservoir of migrants—the mainland. Yet, natural ecosystems often consist of many coupled communities (i.e., metacommunities), and migration occurs between these communities. The pool of migrants then depends on what is sustained in the ecosystem, which, in turn, depends on the dynamic migrant pool. This chicken-and-egg problem of survival and dispersal is poorly understood in communities of many competing species, except for the neutral case—the “unified neutral theory of biodiversity.” Employing spatiotemporal simulations and mean-field analyses, we show that self-consistent dispersal puts rather tight constraints on the dynamic migration–extinction equilibrium. When the number of species is large, species are pushed to the edge of their global extinction, even when competition is weak. As a consequence, the overall diversity is highly sensitive to perturbations in demographic parameters, including growth and dispersal rates. When dispersal is short range, the resulting spatiotemporal abundance patterns follow broad scale-free distributions that correspond to a directed percolation phase transition. The qualitative agreement of our results for short-range and long-range dispersal suggests that this self-organization process is a general property of species-rich metacommunities. Our study shows that self-sustaining metacommunities are highly sensitive to environmental change and provides insights into how biodiversity can be rescued and maintained.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Mineralized sclerites in the gorgonian coral Leptogorgia chilensis as a natural jamming system

The soft corals (Cnidaria, Octocorallia), a diverse group of colonial marine invertebrates, can reversibly tune their body stiffness in response to external stimuli. This capability is attributed to their dynamic skeletal systems, which consist of thousands of mineralized skeletal elements, called sclerites, embedded within a gel-like matrix that swells/deswells and unjams/jams the sclerites, thus modulating skeletal stiffness. While sclerite morphology is widely used for species identification, its role in the mechanical performance of a soft coral’s skeletal system is largely unknown. Here, we investigated structure-jamming relationships in sclerite-based skeletal architectures using the red gorgonian octocoral Leptogorgia chilensis as a model system. The sclerites of L. chilensis exhibit a shaft-like geometry with two axial branches and two sets of triradiate side branches, which are aligned with the crystallographic symmetry of the constituent magnesium-containing calcite. By combining multiscale three-dimensional (3D) structural characterization, parametric geometrical modeling, 3D printing, mechanical testing, and discrete element simulations, we demonstrate how sclerite geometry achieves a balanced jamming performance in terms of stiffness, weight, strength, and fracture resistance in comparison to alternative geometries parametrically modified from the native sclerites (e.g., changes in the length and number of side branches). Here, we also found that these performance metrics are achieved through the effective interlocking among side and axial branches, which is further enhanced by the fractal-like microscopic spikes on the branch tips. The findings in this natural jamming system offer insights for designing synthetic mechanotunable material architectures for a wide range of applications, from soft robotics to mechanical dampeners.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Airborne Release Fractions from Surrogate Nuclear Waste Fires Containing Lanthanide Nitrates and Depleted Uranium Nitrate in 30% Tributyl Phosphate in Kerosene

Airborne contaminants from fires containing nuclear waste represent significant health hazards and shape the design and operation of nuclear facilities. Much of the data used to formulate DOE-HDBK-3010-94, “Airborne Release Fractions/Rates and Respirable Fractions for Nonreactor Nuclear Facilities,” from the U.S. Department of Energy, were taken over 40 years ago. The objectives of this study were to reproduce experiments from Pacific Northwest Laboratories conducted in June 1973 employing current aerosol measurement methods and instrumentation, develop an enhanced understanding of particulate formation and transport from fires containing nuclear waste, and provide modeling and experimental capabilities for updating current standards and practices in nuclear facilities. A special chamber was designed to conduct small fires containing 25 mL of flammable waste containing lutetium nitrate, ytterbium nitrate, or depleted uranium nitrate. Carbon soot aerosols showed aggregates of primary particles ranging from 20 to 60 nm in diameter. In scanning electron microscopy, ~200-nm spheroidal particles were also observed dispersed among the fractal aggregates. The 200-nm spherical particles were composed of metal phosphates. Airborne release fractions (ARFs) were characterized by leaching filter deposits and quantifying metal concentrations with mass spectrometry. The average mass-based ARF for 238 U experiments was 1.0 × 10 -3 with a standard deviation of 7.5 × 10 -4 . For the original experiments, DOE-HDBK-3010-94 states, “Uranium ARFs range from 2 × 10 -4 to 3 × 10 -3 , an uncertainty of approximately an order of magnitude.” Therefore, current measurements were consistent with DOE-HDBK-3010-94 values. ARF values for lutetium and ytterbium were approximately one to two orders of magnitude lower than 238 U. Furthermore, metal nitrate solubility may have varied with elemental composition and temperature, thereby affecting ARF values for uranium surrogates (Yb and Lu). In addition to ARF data, solution boiling temperatures and evaporation rates can also be deduced from experimental data.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Multi-modal chemical characterization of highly viscous submicrometer organic particles

Distinguishing highly viscous organic particles within complex mixtures of atmospheric aerosol and accurate descriptions of their composition, size distributions, and mixing states are challenges at the forefront of aerosol measurement science and technology. Here, we present results obtained from complementary single-particle measurement techniques employed for the in-depth characterization of highly viscous particles. In this study, we demonstrate advantages and synergy of this multi-modal particle characterization approach based on the analysis of individual viscous particles formed in the air-discharged waste produced by a common sewer pipe rehabilitation technology. Using oil immersion flow microscopy, we investigate particle size distributions and morphology of colloidal components present in field-collected aqueous waste condensates. We compare these results with corresponding measurements of viscous particles formed in drying droplets of the aerosolized discharged waste. The colloidal components and viscous particles were found to be approximately 10 µm and 0.5 µm, respectively. The aerosolized viscous particles exhibited a spherical morphology, while the colloidal particles appeared noticeably fractal, resembling fragments of a cured composite material. Chemical imaging of the viscous particles collected on substrates was performed using scanning electron microscopy and soft X-ray spectro-microscopy techniques. Through these methods, comprehensive description of these particles emerged, confirming their high solid-like viscosity, wide-ranging sizes, diverse carbon speciation with high degrees of oxygenation, and high organic volume fractions. The aerosolized viscous particles were further characterized using high-throughput single particle mass spectrometry. This technique provides real-time measurements of composition, size, and morphological metrics for large numbers of individual particles, enabling the identification of their distinct mass spectrometric signatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Surface structure of mass-selected niobium oxide nanoclusters on Au(111)

The structures formed by the deposition of mass-selected niobium oxide clusters, Nb 3 O y ( y = 5, 6, 7), onto Au(111) were studied by scanning tunneling microscopy. The as-deposited Nb 3 O 7 clusters assemble into large dendritic structures that grow on the terraces as well as extend from the top and bottom of step edges. The Nb 3 O 6 cluster also forms dendritic assemblies but they are generally much smaller in size. The assemblies are composed of smaller discrete structures (<1 nm) which are likely to be single clusters. Furthermore, the dendritic assemblies for both the Nb 3 O 7 and Nb 3 O 6 clusters have fractal dimensions of about 1.7 which is very close to that expected for simple diffusion limited aggregation. Annealing the Nb 3 O 7,6 /Au(111) surfaces up to 550 K results in changes in assembly sizes and increases in heights, while heating to 700 results in the disruption of the assemblies into smaller structures. By contrast, the as-deposited Nb 3 O 5 /Au(111) surface at RT exhibits compact cluster structures which become 3D nanoparticles when annealed above 550 K. Differences in the observed surface structures and thermal stability are attributed to differences in metal-oxygen stoichiometry which can influence cluster binding energies, mobility and inter-cluster interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

On the non-existence of stepped-pressure equilibria far from symmetry

The Stepped Pressure Equilibrium Code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502) has been successful in the construction of equilibria in 3D configurations that contain a mixture of flux surfaces, islands and chaotic magnetic field lines. In this model, the plasma is sliced into sub-volumes separated by ideal interfaces, and in each volume the magnetic field is a Beltrami field. In the cases where the system is far from possessing a continuous symmetry, such as in stellarators, the existence of solutions to a stepped-pressure equilibrium with given constraints, such as a multi-region relaxed MHD minimum energy state, is not guaranteed but is often taken for granted. Using SPEC, we have studied two different scenarios in which a solution fails to exist in a slab with analytic boundary perturbations. Here we found that with a large boundary perturbation, a certain interface becomes fractal, corresponding to the break up of a Kolmogorov–Arnold–Moser (KAM) surface. Moreover, an interface can only support a maximum pressure jump while a solution of the magnetic field consistent with the force balance condition can be found. An interface closer to break-up can support a smaller pressure jump. We discovered that the pressure jump can push the interface closer to being non-smooth through force balance, thus significantly decreasing the maximum pressure it can support. Our work shows that a convergence study must be performed on a SPEC equilibrium with interfaces close to break-up. These results may also provide insights into the choice of interfaces and have applications in finding out the maximum pressure a machine can support.

3D equilibrium↗
DOE OSTI2023

Fungal drops: a novel approach for macro- and microscopic analyses of fungal mycelial growth

Abstract This study presents an inexpensive approach for the macro- and microscopic observation of fungal mycelial growth. The ‘fungal drops’ method allows to investigate the development of a mycelial network in filamentous microorganisms at the colony and hyphal scales. A heterogeneous environment is created by depositing 15–20 µl drops on a hydrophobic surface at a fixed distance. This system is akin to a two-dimensional (2D) soil-like structure in which aqueous-pockets are intermixed with air-filled pores. The fungus (spores or mycelia) is inoculated into one of the drops, from which hyphal growth and exploration take place. Hyphal structures are assessed at different scales using stereoscopic and microscopic imaging. The former allows to evaluate the local response of regions within the colony (modular behaviour), while the latter can be used for fractal dimension analyses to describe the hyphal network architecture. The method was tested with several species to underpin the transferability to multiple species. In addition, two sets of experiments were carried out to demonstrate its use in fungal biology. First, mycelial reorganization of Fusarium oxysporum was assessed as a response to patches containing different nutrient concentrations. Second, the effect of interactions with the soil bacterium Pseudomonas putida on habitat colonization by the same fungus was assessed. This method appeared as fast and accessible, allowed for a high level of replication, and complements more complex experimental platforms. Coupled with image analysis, the fungal drops method provides new insights into the study of fungal modularity both macroscopically and at a single-hypha level.

Buffi, Matteo↗
DOE OSTI2022

Entanglement phases in large- N hybrid Brownian circuits with long-range couplings

Here, we develop solvable models of large-N hybrid quantum circuits on qubits and fermions with tunable long-range power-law interactions and continuous local monitoring. These models provide analytical access to the entanglement phase diagram and error-correcting properties of many-body entangled nonequilibrium states generated by such dynamics. In one dimension, the long-range couplings are irrelevant for α > 3/2, where α is the power-law exponent, and the models exhibit a conventional measurement-induced phase transition between volume- and area-law entangled phases. For 1/2 < α < 3/2, the long-range couplings become relevant, leading to a nontrivial dynamical exponent at the measurement-induced phase transition. More interestingly, for α < 1, the entanglement pattern receives a subvolume correction for both area-law and volume-law phases, indicating that the phase realizes a quantum error correcting code whose code distance scales as L 2–2α . While the entanglement phase diagram is the same for both the interacting qubit and fermionic hybrid Brownian circuits, we find that long-range free-fermionic circuits exhibit a distinct phase diagram with two different fractal entangled phases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Deep learning Hamiltonians from disordered image data in quantum materials

The capabilities of image probe experiments are rapidly expanding, providing new information about quantum materials on unprecedented length- and timescales. Many such materials feature inhomogeneous electronic properties with intricate pattern formation on the observable surface. This rich spatial structure contains information about interactions, dimensionality, and disorder—a spatial encoding of the Hamiltonian driving the pattern formation. Image recognition techniques from machine learning are an excellent tool for interpreting information encoded in the spatial relationships in such images. Here, we develop a deep learning framework for using the rich information available in these spatial correlations in order to discover the underlying Hamiltonian driving the patterns. We first vet the method on a known case, scanning near-field optical microscopy on a thin film of V⁢O 2 . We then apply our trained convolutional neural network architecture to new optical microscope images of a different V⁢O 2 film as it goes through the metal-insulator transition. We find that a two-dimensional Hamiltonian with both interactions and random field disorder is required to explain the intricate, fractal intertwining of metal and insulator domains during the transition. This detailed knowledge about the underlying Hamiltonian paves the way for using the model to control the pattern formation via, e.g., tailored hysteresis protocols. Finally, we also introduce a distribution-based confidence measure on the results of a multilabel classifier, which does not rely on adversarial training. In addition, we propose a machine-learning-based criterion for diagnosing a physical system's proximity to criticality.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Chaotic saddles and interior crises in a dissipative nontwist system

Here, we consider a dissipative version of the standard nontwist map. Nontwist systems present a robust transport barrier, called the shearless curve, that becomes the shearless attractor when dissipation is introduced. This attractor can be regular or chaotic depending on the control parameters. Chaotic attractors can undergo sudden and qualitative changes as a parameter is varied. These changes are called crises, and at an interior crisis the attractor suddenly expands. Chaotic saddles are nonattracting chaotic sets that play a fundamental role in the dynamics of nonlinear systems; they are responsible for chaotic transients, fractal basin boundaries, and chaotic scattering, and they mediate interior crises. In this work we discuss the creation of chaotic saddles in a dissipative nontwist system and the interior crises they generate. We show how the presence of two saddles increases the transient times and we analyze the phenomenon of crisis induced intermittency.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Sierpinski Structure and Electronic Topology in Bi Thin Films on InSb(111)B Surfaces

Deposition of Bi on InSb(111)B reveals a striking Sierpinski-triangle (ST)-like structure in Bi thin films. Such a fractal geometric topology is further shown to turn off the intrinsic electronic topology in a thin film. Relaxation of a huge misfit strain of about 30 to 40% between Bi adlayer and substrate is revealed to drive the ST-like island formation. A Frenkel-Kontrova model is developed to illustrate the enhanced strain relief in the ST islands offsetting the additional step energy cost. Besides a sufficiently large tensile strain, forming ST-like structures also requires larger adlayer-substrate and intra-adlayer elastic stiffnesses, and weaker intra-adlayer interatomic interactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Critical Scaling of Solid Fragmentation at Quasistatic and Finite Strain Rates

Here, using two-dimensional simulations of sheared, brittle solids, we characterize the resulting fragmentation and explore its underlying critical nature. Under quasistatic loading, a power-law distribution of fragment masses emerges after fracture which grows with increasing strain. With increasing strain rate, the maximum size of a grain decreases and a shallower distribution is produced. We propose a scaling theory for distributions based on a fractal scaling of the largest mass with system size in the quasistatic limit or with a correlation length that diverges as a power of rate in the finite-rate limit. Critical exponents are measured using finite-size scaling techniques.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Topological Phenomena in Artificial Quantum Materials Revealed by Local Chern Markers

A striking example of frustration in physics is Hofstadter’s butterfly, a fractal structure that emerges from the competition between a crystal’s lattice periodicity and the magnetic length of an applied field. Current methods for predicting the topological invariants associated with Hofstadter’s butterfly are challenging or impossible to apply to a range of materials, including those that are disordered or lack a bulk spectral gap. Here, in this work, we demonstrate a framework for predicting a material’s local Chern markers using its position-space description and validate it against experimental observations of quantum transport in artificial graphene in a semiconductor heterostructure, inherently accounting for fabrication disorder strong enough to close the bulk spectral gap. By resolving local changes in the system’s topology, we reveal the topological origins of antidot-localized states that appear in artificial graphene in the presence of a magnetic field. Moreover, we show the breadth of this framework by simulating how Hofstadter’s butterfly emerges from an initially unpatterned 2D electron gas as the system’s potential strength is increased and predict that artificial graphene becomes a topological insulator at the critical magnetic field. Overall, we anticipate that a position-space approach to determine a material’s Chern invariant without requiring prior knowledge of its occupied states or bulk spectral gaps will enable a broad array of fundamental inquiries and provide a novel route to material discovery, especially in metallic, aperiodic, and disordered systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Analytical desmearing of Bonse–Hart ultra-small-angle neutron scattering data via truncated Abel inversion

A non-iterative analytical framework based on the truncated Abel inversion is developed for desmearing Bonse–Hart ultra-small-angle neutron scattering (USANS) data. The method directly inverts the slit-averaged intensity without empirical extrapolation or iterative regularization, establishing a closed-form relationship between the measured and intrinsic scattering profiles. Numerical benchmarks on representative models, including a rigid-line form factor, a Lorentzian function and a fractal structural model, demonstrate quantitative recovery of the ground-truth intensity across the full Q range. Application to a deuterated polystyrene/poly(2-vinylpyridine) blend further confirms that the approach yields smooth continuous profiles consistent with companion small-angle neutron scattering data. The truncated Abel inversion thus provides a stable, model-independent and physically transparent route for accurate desmearing of Bonse–Hart USANS measurements.

Huang, Guan-Rong [National Tsing Hua University, T↗
DOE OSTI2022

Diffuse X-ray scattering from polished silicon: application of the distorted wave Born approximation

Measured diffuse X-ray scattering data for a `smooth' as well as for a `rough' silicon sample were fit to theoretical expressions within the distorted wave Born approximation (DWBA). Data for the power spectral density (PSD) for both samples were also obtained by means of atomic force microscopy and optical interferometry. The Fourier transforms of trial correlation functions were fit to the PSD data and then applied to the DWBA formalism. The net correlation functions needed to fit the PSD data for each sample comprised the sum of two terms with different cutoff lengths and different self-affine fractal exponents. At zero distance these correlation functions added up to yield net values of σ 2 = (2) 2 and (71) 2 Å 2 for the smooth and rough samples, respectively. X-ray scattering data were obtained at beamline 1-BM of the Advanced Photon Source. Data and fits at values of q z = 0.05 and 0.10 Å −1 for the smooth sample are reported. Good fits for the smooth sample were obtained at both q z values simultaneously, that is, identical fitting parameters were applied at both values of q z . The smooth sample also exhibited weak Yoneda wings and a clear distinction between the strong specular scattering and the weak diffuse scattering. Data for the rough sample were qualitatively different and exhibited very weak scattering at the specular condition in contrast to extremely large Yoneda wings. Fits for the rough sample are reported for q z = 0.04, 0.05, and 0.06 Å −1 . Although the large Yoneda wings could be fit quite well in both position and amplitude, scattering near the specular condition could not be equally well fit by applying the same fitting parameters at all values of q z . Albeit imperfect, best-fitting results at the specular condition were obtained by invoking only diffuse scattering, that is, without including a separate theoretical expression for specular scattering.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Physical properties, internal structure, and the three‐dimensional petrography of CI chondrites

physical properties and the nature of their breccation, we investigated nine samples of the Ivuna and Orgueil CI chondrites ranging in size from 1 mm to 4 cm in approximate diameter. The combined mass of unique material investigated in this work is 113 g. For our investigations, we use ideal gas pycnometry, 3-D laser scanning, x-ray computed microtomography (μCT), and accompanying digital data extraction techniques. We found that the bulk density of the samples ranged from 1.61 to 2.10 g cm −3 . Larger samples tend to have a lower bulk density. Grain density (ranging from 2.44 to 2.55 g cm −3 ) is significantly less variable than the bulk density in our samples and the quantity of porosity (ranging from 14.6% to 33.8%) is the dominant factor in determining the bulk density of CI chondrite material. Our μCT results show that the visible porosity across all sizes of our CI chondrite samples is in the form of cracks, but these cracks can account for less than two-thirds of the porosity in the CI chondrites. Other porosity is not visible, even at μCT resolutions of 2.7 μm voxel edge −1 and we conclude that it is sub-micron in nature. It is not clear if the cracks seen in our samples are indigenous to the chondrites or are a result of terrestrial processes. We also find that the CI chondrites are excellent examples of the fractal-like nature of brecciation, where clasts can be observed at all scales we imaged. The breccias are composed of sub-equant-shaped and sub-rounded-textured clasts like melt-free impact breccias on other solar system bodies. From our μCT volume and digital data extraction, we determine that the Ivuna CI chondrite breccia is organized: the mostly sub-equant clasts within our ~2 cm chunk of Ivuna have a mean diameter of 1.33 mm and their aligned longest axes define a lineation structure. We speculate that the lineation was imparted after fragmentation of the clasts by slight shear on the parent asteroid which could be the result of seismic-related granular flow or mild non-axial impact-related compaction. These data will help to place returned asteroidal material from asteroids 162173 Ryugu and 101955 Bennu and the CI chondrites into a mutual geological context.

CI chondrite↗
DOE OSTI2020

Direct observation of minibands in a twisted graphene/WS 2 bilayer

Stacking two-dimensional (2D) van der Waals materials with different interlayer atomic registry in a heterobilayer causes the formation of a long-range periodic superlattice that may bestow the heterostructure with properties such as new quantum fractal states or superconductivity. Recent optical measurements of transition metal dichalcogenide (TMD) heterobilayers have revealed the presence of hybridized interlayer electron-hole pair excitations at energies defined by the superlattice potential. The corresponding quasiparticle band structures, so-called minibands, have remained elusive, and no such features have been reported for heterobilayers composed of a TMD and another type of 2D material. We introduce a new x-ray capillary technology for performing microfocused angle-resolved photoemission spectroscopy with a spatial resolution of ~1 μm, and directly observe minibands at certain twist angles in mini Brillouin zones (mBZs). We discuss their origin in terms of initial and final state effects by analyzing their dispersion in distinct mBZs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Nanoscale chromatin imaging and analysis platform bridges 4D chromatin organization with molecular function

Extending across multiple length scales, dynamic chromatin structure is linked to transcription through the regulation of genome organization. However, no individual technique can fully elucidate this structure and its relation to molecular function at all length and time scales at both a single-cell level and a population level. Here, we present a multitechnique nanoscale chromatin imaging and analysis (nano-ChIA) platform that consolidates electron tomography of the primary chromatin fiber, optical super-resolution imaging of transcription processes, and label-free nano-sensing of chromatin packing and its dynamics in live cells. Using nano-ChIA, we observed that chromatin is localized into spatially separable packing domains, with an average diameter of around 200 nanometers, sub-megabase genomic size, and an internal fractal structure. The chromatin packing behavior of these domains exhibits a complex bidirectional relationship with active gene transcription. Furthermore, we found that properties of PDs are correlated among progenitor and progeny cells across cell division.

59 BASIC BIOLOGICAL SCIENCES↗