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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 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Potential-specific structure at the hematite-electrolyte interface

The atomic-scale structure of interfaces between metal oxides and aqueous electrolytes controls their catalytic, geochemical, and corrosion behavior. Measurements that probe these interfaces in situ provide important details of ion and solvent arrangements, but atomically precise structural models do not exist for common oxide-electrolyte interfaces far from equilibrium. Using a novel cell, we measured the structure of the hematite (a-Fe 2 O 3 ) (110$\bar{2}$)-electrolyte interface under controlled electrochemical bias using synchrotron crystal truncation rod X ray scattering. At increasingly cathodic potentials, charge-compensating protonation of surface oxygen groups increases the coverage of specifically bound water while adjacent water layers displace outwardly and became disordered. Returning to open circuit potential leaves the surface in a persistent metastable protonation state. The flux of current and ions at applied potential is thus regulated by a unique interfacial electrolyte environment, suggesting that electrical double layer models should be adapted to the dynamically changing interfacial structure far from equilibrium.

electrochemistry↗
DOE OSTI2023

Study of beyond nearest-neighbor environment and intermediate-range order in a sodium aluminosilicate geopolymer using Reverse Monte Carlo modeling

A large scale three-dimensional structural model of a geopolymer with an approximate composition of NaAlSi 2 O 6 .5.5H 2 O obtained by Reverse Monte Carlo (RMC) modeling based on experimental high-energy x-ray diffraction is presented for the first time in order to obtain information regarding beyond nearest-neighbor environment and intermediate-range order (IRO). RMC model exhibits a three-dimensional network consisting of randomly cross-linked AlO 4 and SiO 4 tetrahedral units with uniformly distributed Na atoms and H 2 O molecules. The bond angle distributions, i.e. T-O-T, O-T-O and Na-O-Na angles, are somewhat distorted with lower values compared to analogous crystal systems. The origin of the first peak in the structure factor indicating IRO is investigated using the partial structure factors; Na-Na, Si-Na, Al-Si, O-H, and H-H atom pairs are found to be the main contributors. Ring size distribution analysis demonstrates that the structure mainly involves 6-, 7- and 8-membered rings. Finally, the coherence length of these IRO characteristics is ~10.3 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Chasing the open-state structure of pentameric ligand-gated ion channels

Remarkable advances have been made toward the structural characterization of ion channels in the last two decades. However, the unambiguous assignment of well-defined functional states to the obtained structural models has proved challenging. In the case of the superfamily of nicotinic-receptor channels (also referred to as pentameric ligand-gated ion channels [pLGICs]), for example, two different types of model of the open-channel conformation have been proposed on the basis of structures solved to resolutions better than 4.0 Å. At the level of the transmembrane pore, the open-state models of the proton-gated pLGIC from Gloeobacter violaceus (GLIC) and the invertebrate glutamate-gated Cl – channel (GluCl) are very similar to each other, but that of the glycine receptor (GlyR) is considerably wider. Indeed, the mean distances between the axis of ion permeation and the Cα atoms at the narrowest constriction of the pore (position -2') differ by ~2 Å in these two classes of model, a large difference when it comes to understanding the physicochemical bases of ion conduction and charge selectivity. Here, we take advantage of the extreme open-channel stabilizing effect of mutations at pore-facing position 9'. We find that the I9'A mutation slows down entry into desensitization of GLIC to the extent that macroscopic currents decay only slightly by the end of pH 4.5 solution applications to the extracellular side for several minutes. We crystallize (at pH 4.5) two variants of GLIC carrying this mutation and solve their structures to resolutions of 3.12 Å and 3.36 Å. Furthermore, we perform all-atom molecular dynamics simulations of ion permeation and picrotoxinin block, using the different open-channel structural models. On the basis of these results, we favor the notion that the open-channel structure of pLGICs from animals is much closer to that of the narrow models (of GLIC and GluCl) than it is to that of the GlyR.

Gonzalez-Gutierrez, Giovanni↗
DOE OSTI2025

Building molecular model series from heterogeneous CryoEM structures using Gaussian mixture models and deep neural networks

Cryogenic electron microscopy (CryoEM) produces structures of macromolecules at near-atomic resolution. However, building molecular models with good stereochemical geometry from those structures can be challenging and time-consuming, especially when many structures are obtained from datasets with conformational heterogeneity. Here we present a model refinement protocol that automatically generates series of molecular models from CryoEM datasets, which describe the dynamics of the macromolecular system and have near-perfect geometry scores. This method makes it easier to interpret the movement of the protein complex from heterogeneity analysis and to compare the structural dynamics observed from CryoEM data with results from other experimental and simulation techniques.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Structure Based Prediction of Neoantigen Immunogenicity

The development of immunological therapies that incorporate peptide antigens presented to T cells by MHC proteins is a long sought-after goal, particularly for cancer, where mutated neoantigens are being explored as personalized cancer vaccines. Although neoantigens can be identified through sequencing, bioinformatics and mass spectrometry, identifying those which are immunogenic and able to promote tumor rejection remains a significant challenge. Here we examined the potential of high-resolution structural modeling followed by energetic scoring of structural features for predicting neoantigen immunogenicity. After developing a strategy to rapidly and accurately model nonameric peptides bound to the common class I MHC protein HLA-A2, we trained a neural network on structural features that influence T cell receptor (TCR) and peptide binding energies. The resulting structurally-parameterized neural network outperformed methods that do not incorporate explicit structural or energetic properties in predicting CD8 + T cell responses of HLA-A2 presented nonameric peptides, while also providing insight into the underlying structural and biophysical mechanisms governing immunogenicity. Our proof-of-concept study demonstrates the potential for structure-based immunogenicity predictions in the development of personalized peptide-based vaccines.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Renewable Energy and Efficiency Technologies in Scenarios of U.S. Decarbonization in Two Types of Models: Comparison of GCAM Modeling and Sector-Specific Modeling

Energy system projections from quantitative models inform actions ranging from short-term and local decisions, such as those about technology and infrastructure deployment, and global and long-term negotiations and targets. Computational limits require model designers to balance coverage and resolution (i.e., breadth versus depth). Some models, such as the Global Change Analysis Model (GCAM), represent all energy sources and uses with less resolution than models that focus on a single sector's energy use. GCAM balances global supply and demand of all energy carriers projecting prices using internal calculations for energy sources and costs of greenhouse gas mitigation while capturing interlinkages between the energy system, water, agriculture and land use, the economy, and the climate. This globally comprehensive model was used to frame the Long-Term Strategy of the United States: Pathways to Net-Zero Greenhouse Gas Emissions by 2050, which the White House released in 2021 and has been used to inform national and global economy-wide climate change mitigation discussions and strategy development for decades. Unlike GCAM, sectoral models focus on a portion of the energy sector and with greater detail and resolution. The Regional Energy Deployment System (ReEDS) electricity-sector model, for example, projects electricity system capacity expansion and operation with high-fidelity representation of emerging technologies for deep decarbonization, such as variable renewable energy and energy storage, and integration of these technologies into the electric grid. The Transportation Energy and Mobility Pathway Options (TEMPO) transportation-sector model enables analysis of household choices, with a focus on adoption, charging, and use of electric vehicles. The Scout buildings-sector model supports detailed consideration of the policies and markets that can accelerate the adoption of electrification and energy conservation measures in buildings. Such sector-specific models are instrumental in informing technology research, sectoral planning strategies, and sector-specific aspects of greenhouse gas mitigation strategies in the United States. The integrated multisector and sector-specific modeling approaches represented by GCAM and these sectoral models are complementary. The integrated multisector approach calculates energy pricing and resource allocation within the model, which is important for consistency when future conditions substantially diverge from current conditions in transformative scenarios. The sector-specific approach facilitates representation of granular details across spatial, temporal, technological, and market dimensions that enable exploration of particular interactions and trade-offs. This report presents the results of recent work to explore the differences and trade-offs between these approaches by comparing GCAM with the sector-specific ReEDS, TEMPO, and Scout models. The report compares both model structures and results, and it addresses their potential relevance and applications.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2015

On the mesoscopic origins of high viscosities in some polyelectrolyte-surfactant mixtures

Oppositely charged polyelectrolyte (PE) surfactant mixtures allow the control of rheological parameters of a solution even at fairly low concentrations. For example, addition of 0.3 wt. % of anionic surfactant to a 1 wt. % solution of the polycation JR 400 increases the viscosity by 4 orders of magnitude. Recently, we could show that this increase is related to the formation of mixed, rod-like PE/surfactant aggregates which interconnect several polyelectrolyte chains [Hoffmann et al., Europhys. Lett. 104, 28001 (2013)]. In this paper, we refine our structural model of the aggregates to obtain a more consistent picture of their internal structure for different anionic surfactants. Combining small angle neutron scattering (SANS) and neutron spin-echo (NSE) allows us to determine the size of the aggregates. By comparing different contrasts, the internal structure of the aggregates can be elucidated and it is seen that the PE in the aggregates retains a relatively high freedom of movement. We proceeded to investigate the influence of the surfactant concentration and the surfactant type on structure and dynamics of the mixed aggregates. It is seen that the structural parameters of the aggregates depend very little on the surfactant concentration and headgroup. However, it is crucial to incorporate a sufficient amount of PE in the aggregates to increase the viscosity of the aggregates. By comparing viscous samples at 1 wt. % PE concentration with samples at a PE concentration of 0.3 wt. %, where no significant increase in viscosity is observed, we find that similar aggregates are formed already at this lower PE concentrations. However, the amount of PE incorporated in them is insufficient to interconnect several PE chains and therefore, they do not increase viscosity. So, our detailed investigation combining contrast variation SANS and NSE does not only allow to explain the viscosity behavior but also to deduced detailed information regarding the structures and the dynamics especially of the polyelectrolyte within the complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

First-principle calculation of core level binding energies of Li{sub x}PO{sub y}N{sub z} solid electrolyte

We present first-principle calculations of core-level binding energies for the study of insulating, bulk phase, compounds, based on the Slater-Janak transition state model. Those calculations were performed in order to find a reliable model of the amorphous Li{sub x}PO{sub y}N{sub z} solid electrolyte which is able to reproduce its electronic properties gathered from X-ray photoemission spectroscopy (XPS) experiments. As a starting point, Li{sub 2}PO{sub 2}N models were investigated. These models, proposed by Du et al. on the basis of thermodynamics and vibrational properties, were the first structural models of Li{sub x}PO{sub y}N{sub z}. Thanks to chemical and structural modifications applied to Li{sub 2}PO{sub 2}N structures, which allow to demonstrate the relevance of our computational approach, we raise an issue concerning the possibility of encountering a non-bridging kind of nitrogen atoms (=N{sup −}) in Li{sub x}PO{sub y}N{sub z} compounds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Short- and medium-range order in Sb–Se glasses

Neutron diffraction measurements were performed to investigate the structure of Sb{sub x}Se{sub 100−x} bulk glasses with x=5, 10, 15, 20 and 25 at% Sb. The total pair distribution functions show two peaks at 2.36 Å and 2.64 Å, which are attributed to Se–Se and Sb–Se bonds, respectively. The coordination numbers calculated from these peaks indicate that Sb atoms are three-coordinated and Se atoms are two-coordinated for all the above compositions. However, the composition dependences of the first two peaks in the structure factors show an obvious change between 15 and 20 at% Sb, indicating that the medium-range structure is changed in this range of Sb content. In order to elucidate the medium-range structure, reverse Monte Carlo simulation was used with coordination number constraints. The structure models consisting of a mixture of the SbSe{sub 3/2} network and Se{sub n} chain clusters were in good agreement with neutron diffraction data for Se-rich glass (5, 10 and 15 at% Sb). On the other hand, a better fit was obtained for Sb{sub 25}Se{sub 75} glass with a model based on the network structure formed by connected SbSe{sub 3} units. - Graphical abstract: A 50 Å slice of the RMC configuration for Sb{sub 15}Se{sub 85} glass. - Highlights: • Sb atoms are three-coordinated and Se atoms are two-coordinated. • The medium-range structure changes between 15 and 20 at%. • The phase-separation tendency is observed in Se-rich glasses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Enumeration as a Tool for Structure Solution: A Materials Genomic Approach to Solving the Cation-Ordered Structure of Na 3 V 2 (PO 4 ) 2 F 3

While powder diffraction methods are routinely utilized to optimize structural models for compounds whose crystal structures are known, the determination of unknown structures is far more challenging. When the unknown structure is large, structure solution can become a virtually intractable problem using standard structure solution methodologies, especially when the space group cannot be unambiguously resolved. One such system is the promising Na-ion battery cathode material Na 3 V 2 (PO 4 ) 2 F 3 whose high temperature and room temperature structures were previously solved, but whose more complex low-temperature structure could not be determined. Here, a novel materials genomic approach is demonstrated for the solution of the unknown 100 K structure of Na 3 V 2 (PO 4 ) 2 F 3 in which enumeration methods are first used to generate a large number (~3,000) of trial structures based on plausible orderings of Na ions and then automated Rietveld refinements are carried out to optimize each of these trial structures. Based on both the analysis of the ensemble of optimized trial structures and the density functional theory energy minimization of selected trial structures, the 100 K structure of Na 3 V 2 (PO 4 ) 2 F 3 is best described as belonging to the space group A2 1 am with unit cell dimensions of a = 9.01928(4), b = 27.1379(1), c = 10.73307(5). The 100 K unit cell has a large volume of 2627.07(2) Å 3 with Z = 12 and 33 independent crystallographic sites (9 Na, 3 V, 3 P, 12 O, and 6 F) that is 3x and 6x larger than the room- and high-temperature polymorphs of this phase, respectively. Finally, the novel methods described here will be generally applicable for the solution of the complex cation-ordered structures that commonly occur for battery materials.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Impacts of irrigation expansion on moist-heat stress based on IRRMIP results

Irrigation rapidly expanded during the 20 th century, affecting climate via water, energy, and biogeochemical changes. Previous assessments of these effects predominantly relied on a single Earth System Model, and therefore suffered from structural model uncertainties. Here we quantify the impacts of historical irrigation expansion on climate by analysing simulation results from six Earth system models participating in the Irrigation Model Intercomparison Project (IRRMIP). Results show that irrigation expansion causes a rapid increase in irrigation water withdrawal, which leads to less frequent 2-meter air temperature heat extremes across heavily irrigated areas (≥4 times less likely). However, due to the irrigation-induced increase in air humidity, the cooling effect of irrigation expansion on moist-heat stress is less pronounced or even reversed, depending on the heat stress metric. In summary, this study indicates that irrigation deployment is not an efficient adaptation measure to escalating human heat stress under climate change, calling for carefully dealing with the increased exposure of local people to moist-heat stress.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Ultrahigh-pressure crystallographic passage towards metallic hydrogen

The structural evolution of molecular hydrogen H 2 under multi-megabar compression and its relation to atomic metallic hydrogen is a key unsolved problem in condensed-matter physics. Although dozens of crystal structures have been proposed by theory, only one, the simple hexagonal-close-packed (hcp) structure of only spherical disordered H 2 , has been previously confirmed in experiments. Through advancing nano-focused synchrotron X-ray probes, here we report the observation of the transition from hcp H 2 to a post-hcp structure with a six-fold larger supercell at pressures above 212 GPa, indicating the change of spherical H 2 to various ordered configurations. Theoretical calculations based on our XRD results found a time-averaged structure model in the space group $P\bar{6}2c$ with alternating layers of spherically disordered H 2 and new graphene-like layers consisting of H 2 trimers (H 6 ) formed by the association of three H 2 molecules. Here, this supercell has not been reported by any previous theoretical study for the post-hcp phase, but is close to a number of theoretical models with mixed-layer structures. The evidence of a structural transition beyond hcp establishes the trend of H 2 molecular association towards polymerization at extreme pressures, giving clues about the nature of the molecular-to-atomic transition of metallic hydrogen. Considering the spectroscopic behaviours that show strong vibrational and bending peaks of H 2 up to 400 GPa, it would be prudent to speculate the continuation of hydrogen molecular polymerization up to its metallization.

Ji, Cheng [Center for High Pressure Science and Te↗
DOE OSTI2013

Climate change effects on agriculture: Economic responses to biophysical shocks

Agricultural production is sensitive to weather and will thus be directly affected by climate change. Plausible estimates of these climate change impacts require combined use of climate, crop, and economic models. Results from previous studies vary substantially due to differences in models, scenarios, and data. This paper is part of a collective effort to systematically integrate these three types of models. We focus on the economic component of the assessment, investigating how nine global economic models of agriculture represent endogenous responses to seven standardized climate change scenarios produced by two climate and five crop models. These responses include adjustments in yields, area, consumption, and international trade. We apply biophysical shocks derived from the IPCC’s Representative Concentration Pathway that result in end-of-century radiative forcing of 8.5 watts per square meter. The mean biophysical impact on crop yield with no incremental CO2 fertilization is a 17 percent reduction globally by 2050 relative to a scenario with unchanging climate. Endogenous economic responses reduce yield loss to 11 percent, increase area of major crops by 12 percent, and reduce consumption by 2 percent. Agricultural production, cropland area, trade, and prices show the greatest degree of variability in response to climate change, and consumption the lowest. The sources of these differences includes model structure and specification; in particular, model assumptions about ease of land use conversion, intensification, and trade. This study identifies where models disagree on the relative responses to climate shocks and highlights research activities needed to improve the representation of agricultural adaptation responses to climate change.

climate change adaptation model intercomparison in↗
DOE OSTI2019

Constraining spectroscopic factors near the r -process path using combined measurements: Kr 86 ( d , p ) 87 Kr

Background: Current nuclear structure models indicate that the shell structure near the valley of stability, with well-established shell closures at N=50, for example, changes in very neutron-rich nuclei far from stability. Single-particle properties of nuclei away from stability can be probed in single-neutron (d,p) transfer reactions with beams of rare isotopes. The interpretation of these data requires reaction theories with various effective interactions. Often, approximations made to the final bound-state potential introduce a large uncertainty in the extracted single-particle properties, in particular the spectroscopic factor. Purpose: Mitigate this uncertainty using a combined measurement method to constrain the shape of the bound-state potential and to reliably extract the spectroscopic factor. Methods: The 2 H( 86 Kr,p) 87 Kr reaction was measured at 33 MeV/u at the National Superconducting Cyclotron Laboratory (NSCL) as a test of the combined method. The reaction protons were detected with the Oak Ridge Rutgers University Barrel Array (ORRUBA) of position sensitive silicon strip detectors, the first implementation of ORRUBA coupled to the S800 spectrograph with fast beams at NSCL. Results: These measurements at 33 MeV/u are combined with previous studies of the 86 Kr(d,p) reaction at 5.5 MeV/u to demonstrate a successful case of the combined method to constrain the shape of the single-particle potential and deduce asymptotic normalization coefficients and spectroscopic factors. In particular, the single-particle asymptotic normalization coefficient for the ground state of 87 Kr was constrained to b d5/2 =6.46$^{+1.12}_{–0.57}$ fm –1/2 , and therefore the deduced spectroscopic factor is S=0.44$^{+0.09}_{–0.13}$ with uncertainties dominated by experimental statistics. Conclusions: By combining measurements at two very different beam energies, single-particle asymptotic normalization coefficients, at least for low angular momentum transfers, can be constrained. Thus, spectroscopic factors can be deduced with uncertainties dominated by experimental uncertainties, rather than limited knowledge of bound-state potential parameters.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2014

Bioenergy crop productivity and potential climate change mitigation from marginal lands in the United States: An ecosystem modeling perspective

Growing biomass feedstocks from marginal lands is becoming an increasingly attractive choice for producing biofuel as an alternative energy to fossil fuels. Here, we used a biogeochemical model at ecosystem scale to estimate crop productivity and greenhouse gas (GHG) emissions from bioenergy crops grown on marginal lands in the United States. Two broadly tested cellulosic crops, switchgrass, and Miscanthus, were assumed to be grown on the abandoned land and mixed crop–vegetation land with marginal productivity. Production of biomass and biofuel as well as net carbon exchange and nitrous oxide emissions were estimated in a spatially explicit manner. We found that, cellulosic crops, especially Miscanthus could produce a considerable amount of biomass, and the effective ethanol yield is high on these marginal lands. For every hectare of marginal land, switchgrass and Miscanthus could produce 1.0–2.3 kl and 2.9–6.9 kl ethanol, respectively, depending on nitrogen fertilization rate and biofuel conversion efficiency. Nationally, both crop systems act as net GHG sources. Switchgrass has high global warming intensity (100–390 g CO 2 eq l –1 ethanol), in terms of GHG emissions per unit ethanol produced. Miscanthus , however, emits only 21–36 g CO 2 eq to produce every liter of ethanol. To reach the mandated cellulosic ethanol target in the United States, growing Miscanthus on the marginal lands could potentially save land and reduce GHG emissions in comparison to growing switchgrass. Furthermore, the ecosystem modeling is still limited by data availability and model deficiencies, further efforts should be made to classify crop–specific marginal land availability, improve model structure, and better integrate ecosystem modeling into life cycle assessment.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Representation of U.S. Warm Temperature Extremes in Global Climate Model Ensembles

Extreme temperature events can have considerable negative impacts on sectors such as health, agriculture, and transportation. Observational evidence indicates the severity and frequency of warm extremes are increasing over much of the United States, but there are sizeable challenges both in estimating extreme temperature changes and in quantifying the relevant associated uncertainties. This study provides a simple statistical framework using a block maxima approach to analyze the representation of warm temperature extremes in several recent global climate model ensembles. Uncertainties due to structural model differences, grid resolution, and internal variability are characterized and discussed. Results show that models and ensembles differ greatly in the representation of extreme temperature over the United States, and variability in tail events is dependent on time and anthropogenic warming, which can influence estimates of return periods and distribution parameter estimates using generalized extreme value (GEV) distributions. These effects can considerably influence the uncertainty of model hindcasts and projections of extremes. Several idealized regional applications are highlighted for evaluating ensemble skill and trends, based on quantile analysis and root-mean-square errors in the overall sample and the upper tail. The results are relevant to regional climate assessments that use global model outputs and that are sensitive to extreme warm temperature. Accompanying this manuscript is a simple toolkit using the R statistical programming language for characterizing extreme events in gridded datasets.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Network Scale Travel Time Prediction using Deep Learning

In recent years, deep learning models have been receiving increased attention within the artificial intelligence (AI) community because of their high prediction accuracy. In this paper, two deep learning models, long short-term memory (LSTM) and convolutional neural network (CNN), are proposed to predict travel time in a road network. One major advantage of using deep learning for travel time prediction is that it can make accurate predictions for all the segments in the transportation network with a single model structure, instead of building customized models for each segment separately. The proposed models were evaluated on a transportation network in the City of Saint Louis, Missouri. The prediction results show that deep learning can provide accurate prediction for both congested and uncongested traffic conditions, and can successfully capture the traffic dynamics of unexpected incidents or special events. The study findings show that deep learning offers a promising approach to real-time prediction of travel times on a network scale.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

Dark matter halo mass functions and density profiles from mass and energy cascade

Abstract Halo abundance and structure play a central role for modeling structure formation and evolution. Without relying on a spherical or ellipsoidal collapse model, we analytically derive the halo mass function and cuspy halo density (inner slope of −4/3) based on the mass and energy cascade theory in dark matter flow. The hierarchical halo structure formation leads to halo or particle random walk with a position-dependent waiting time $$\tau _g$$ τ g . First, the inverse mass cascade from small to large scales leads to the halo random walk in mass space with $$\tau _g\propto m_h^{-\lambda }$$ τ g ∝ m h - λ , where $$m_h$$ m h is the halo mass and $$\lambda$$ λ is a halo geometry parameter with predicted value of 2/3. The corresponding Fokker-Planck solution for halo random walk in mass space gives rise to the halo mass function with a power-law behavior on small scale and exponential decay on large scale. This can be further improved by considering two different $$\lambda$$ λ for haloes below and above a critical mass scale $$m_h^*$$ m h ∗ , i.e. a double- $$\lambda$$ λ halo mass function. Second, a double- $$\gamma$$ γ density profile can be derived based on the particle random walk in 3D space with a position-dependent waiting time $$\tau _g \propto \Phi (r)^{-1} \propto r^{-\gamma }$$ τ g ∝ Φ ( r ) - 1 ∝ r - γ , where $$\Phi$$ Φ is the gravitational potential and r is the particle distance to halo center. Theory predicts $$\gamma =2/3$$ γ = 2 / 3 that leads to a cuspy density profile with an inner slope of −4/3, consistent with the predicted scaling laws from energy cascade. The Press-Schechter mass function and Einasto density profile are just special cases of proposed models. The small scale permanence can be identified due to the scale-independent rate of mass and energy cascade, where density profiles of different halo masses and redshifts converge to the $$-4/3$$ - 4 / 3 scaling law ( $$\rho _h \propto r^{-4/3}$$ ρ h ∝ r - 4 / 3 ) on small scales. Theory predicts the halo number density scales with halo mass as $$\propto m_h^{-1.9}$$ ∝ m h - 1.9 , while the halo mass density scales as $$\propto m_h^{4/9}$$ ∝ m h 4 / 9 . Results were compared against the Illustris simulations. This new perspective provides a theory for nearly universal halo mass functions and density profiles.

79 ASTRONOMY AND ASTROPHYSICS↗