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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 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Measurements of mixed harmonic cumulants in Pb–Pb collisions at √ s NN = 5.02 TeV

Correlations between moments of different flow coefficients are measured in Pb–Pb collisions at √ s NN = 5.02 TeV recorded with the ALICE detector. These new measurements are based on multiparticle mixed harmonic cumulants calculated using charged particles in the pseudorapidity region |η| < 0.8 with the transverse momentum range 0.2 < p T < 5.0 GeV/c. The centrality dependence of correlations between two flow coefficients as well as the correlations between three flow coefficients, both in terms of their second moments, are shown. In addition, a collection of mixed harmonic cumulants involving higher moments of v 2 and v 3 is measured for the first time, where the characteristic signature of negative, positive and negative signs of four-, six- and eight-particle cumulants are observed, respectively. The measurements are compared to the hydrodynamic calculations using iEBE-VISHNU with AMPT and TRENTo initial conditions. It is shown that the measurements carried out using the LHC Run 2 data in 2015 have the precision to explore the details of initial-state fluctuations and probe the nonlinear hydrodynamic response of v 2 and v 3 to their corresponding initial anisotropy coefficients and ε 2 and ε 3 . These new studies on correlations between three flow coefficients as well as correlations between higher moments of two different flow coefficients will pave the way to tighten constraints on initial-state models and help to extract precise information on the dynamic evolution of the hot and dense matter created in heavy-ion collisions at the LHC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Bridging confined phase behavior of CH 4 -CO 2 binary systems across scales

Phase behavior of confined fluids may deviate significantly from that of the bulk fluid due to the fluid-wall interactions being a significant portion of all intermolecular interactions under confinement. Despite recent advancements in understanding confined phase behavior of pure fluids, confined phase behavior of mixtures remains an understudied topic. In this work, we examine the confined phase behavior of a CH 4 -CO 2 binary system by combining Monte Carlo (MC) simulations, a cubic equation of state (EoS), and the lattice Boltzmann method (LBM). First, the effects of confinement on density and phase distribution in nano-size pores are established using Gibbs Ensemble MC calculations, which produce precise results of liquid and vapor confined pressures and account for the modification of the phase change location. By comparing the phase envelopes of bulk and confined mixtures at a fixed temperature, here it is observed that the phase envelopes shrink with reductions in pore size. Based on this observation, we extend a modified Peng-Robinson EoS, which was originally developed for pure fluids under confinement, to mixtures via van-der-Waals-type mixing rules and by accounting for shifts in the critical properties of confined CH 4 -CO 2 . The resulting phase envelopes are in good agreement with the MC data. In addition, a local density model is used in combination with the confined EoS to calculate adsorption isotherms of CH 4 -CO 2 mixtures and to characterize the behavior of confined matter in nanopores. Finally, we incorporate this EoS in a multicomponent multiphase LBM that uses a pseudopotential model to represent intermolecular forces. This workflow utilizes multiscale simulation techniques to bridge the behavior of multicomponent systems across scales and to shed light on the confined phase behavior of CH 4 -CO 2 binary systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Final Search for Short-Baseline Neutrino Oscillations with the PROSPECT-I Detector at HFIR

The PROSPECT experiment is designed to perform precise searches for antineutrino disappearance at short distances (7–9 m) from compact nuclear reactor cores. This Letter reports results from a new neutrino oscillation analysis performed using the complete data sample from the PROSPECT-I detector operated at the High Flux Isotope Reactor in 2018. The analysis uses a multiperiod selection of inverse beta decay neutrino interactions with reduced backgrounds and enhanced statistical power to set limits on electron neutrino disappearance caused by mixing with sterile neutrinos with 0.2–20 eV 2 mass splittings. Inverse beta decay positron energy spectra from six different reactor-detector distance ranges are found to be statistically consistent with one another, as would be expected in the absence of sterile neutrino oscillations. The data excludes at 95% confidence level the existence of sterile neutrinos in regions above 3 eV 2 previously unexplored by terrestrial experiments, including all space below 10 eV 2 suggested by the recently strengthened Gallium Anomaly. The best-fit point of the Neutrino-4 reactor experiment’s claimed observation of short-baseline oscillation is ruled out at more than 5 standard deviations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Flavoured warped axion

We consider a 5D extension of the DFSZ axion model that addresses both the axion quality and fermion mass hierarchy problems, and predicts flavour-dependent, off-diagonal axion-fermion couplings. The axion is part of a 5D complex scalar field charged under a U(1)PQ symmetry that is spontaneously broken in the bulk, and is insensitive to explicit PQ breaking on the UV boundary. Bulk Standard Model fermions interact with two Higgs doublets that can be localized on the UV boundary or propagate in the bulk to explain the fermion masses and mixings. When the Higgs doublets are localized on the UV boundary, they induce flavour diagonal couplings between the fermions and the axion. However, when the Higgs doublets propagate in the bulk, the overlap of the axion and fermion profiles generates flavour off-diagonal couplings. The effective scale of these off-diagonal couplings in both the quark and lepton sectors can be as small as 10 11 GeV, and therefore will be probed in future precision flavour experiments.

Global Symmetries↗
DOE OSTI2023

Titanium porous-transport layers for PEM water electrolysis prepared by tape casting

While the porous-transport layer (PTL) is a key component in PEM electrolyzers, it is one of the most underexplored due to limited available structures. In this work, we present a novel PTL design for PEM water electrolyzers enabled by a cost-effective, scalable tape-casting technique. Here, a precise control of the PTL pore structure is achieved by incorporating poreformers of various sizes, and by varying the titanium and poreformer ratio. The structures are characterized with SEM and synchrotron X-ray computed tomography imaging techniques. Comprehensive electrochemical performance analysis demonstrates that higher titanium loading provides improved contact at the catalyst-layer/PTL interface but suffers from severe mass-transport losses due to gas bubbles. We solve this mass-transport problem by mixing in large poreformer beads that produce a highly porous structure with excellent gas removal properties yet still maintaining mechanical integrity. The PTL fabricated with 60:40 Ti:PMMA ratio and 60 μm PMMA bead size outperformed the standard commercial Ti powder-based PTL by 62 mV at 4 A/cm 2 .

25 ENERGY STORAGE↗
DOE OSTI2020

Vaporizable endoskeletal droplets via tunable interfacial melting transitions

Liquid emulsion droplet evaporation is of importance for various sensing and imaging applications. The liquid-to-gas phase transformation is typically triggered thermally or acoustically by low–boiling point liquids, or by inclusion of solid structures that pin the vapor/liquid contact line to facilitate heterogeneous nucleation. However, these approaches lack precise tunability in vaporization behavior. Here, we describe a previously unused approach to control vaporization behavior through an endoskeleton that can melt and blend into the liquid core to either enhance or disrupt cohesive intermolecular forces. This effect is demonstrated using perfluoropentane (C 5 F 12 ) droplets encapsulating a fluorocarbon (FC) or hydrocarbon (HC) endoskeleton. FC skeletons inhibit vaporization, whereas HC skeletons trigger vaporization near the rotator melting transition. Our findings highlight the importance of skeletal interfacial mixing for initiating droplet vaporization. Tuning molecular interactions between the endoskeleton and droplet phase is generalizable for achieving emulsion or other secondary phase transitions, in emulsions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Dual dressed black holes as the end point of the charged superradiant instability in $\mathcal{N} = 4$ Yang Mills

Charged Black holes in AdS_5 × S^5 A d S 5 × S 5 suffer from superradiant instabilities over a range of energies. Hairy black hole solutions (constructed within gauged supergravity) have previously been proposed as endpoints to this instability. We demonstrate that these hairy black holes are themselves unstable to the emission of large dual giant gravitons. We propose that the endpoint to this instability is given by Dual Dressed Black Holes (DDBH)s; configurations consisting of one, two, or three very large dual giant gravitons surrounding a core AdS A d S black hole with one, two, or three SO(6) S O ( 6 ) chemical potentials equal to unity. The dual giants each live at AdS A d S radial coordinates of order \sqrt{N} N and each carry charge of order N^2 N 2 . The large separation makes DDBHs a very weakly interacting mix of their components and allows for a simple computation of their thermodynamics. We conjecture that DDBHs dominate the phase diagram of \mathcal{N}=4 𝒩 = 4 Yang-Mills over a range of energies around the BPS plane, and provide an explicit construction of this phase diagram, briefly discussing the interplay with supersymmetry. We develop the quantum description of dual giants around black hole backgrounds and explicitly verify that DDBHs are stable to potential tunneling instabilities, precisely when the chemical potentials of the core black holes equal unity. We also construct the 10-dimensional DDBH bulk solutions.

Choi, Sunjin (ORCID:0000000283310199)↗
DOE OSTI2026

Bayesian Fit to NOvA Data Subsamples for Three Flavor Oscillation Analysis

NOvA (NuMI Off-Axis $\nu_e$ Appearance) is a long baseline neutrino experiment designed to measure the oscillation of muon neutrinos to electron neutrinos over a distance of 810 km. NOvA uses a near and far detector to observe $\nu_\mu$ disappearance and $\nu_e$ appearance of neutrinos produced by the NuMI beam at Fermilab. NOvA uses a Bayesian analysis framework in addition to its Frequentist method to measure neutrino oscillation parameters such as the mixing angles, mass ordering, and CP-violating phase. We report preliminary results of Bayesian fits to representative NOvA datasets. Comparison of fits to $\nu_\mu$ disappearance and $\nu_e$ appearance enables a cross-check of NOvA results with reactor $\bar{\nu_e}$ disappearance measurements. NOvA also searches for violation of Lorentz invariance by analyzing fits of forward horn current (FHC) versus reverse horn current (RHC) samples. The results validate and advance NOvA's contributions to precision measurements of neutrino properties.

Zhao, Larry [Fermilab]↗
DOE OSTI2021

Understanding the Stabilization and Tunability of Divalent Europium 2.2.2B Cryptates

Lanthanides such as europium with more accessible divalent states are useful for studying redox stability afforded by macrocyclic organic ligands. Substituted cryptands, such as 2.2.2B cryptand, that increase the oxidative stability of divalent europium also provide coordination environments that support synthetic alterations of Eu(II) cryptate complexes. Two single crystal structures were obtained containing nine-coordinate Eu(II) 2.2.2B cryptate complexes that differ by a single coordination site, the occupation of which is dictated by changes in reaction conditions. A crystal structure containing a [Eu(2.2.2B)Cl] + complex is obtained from a methanol–THF solvent mixture, while a methanol–acetonitrile solvent mixture affords a [Eu(2.2.2B)(CH 3 OH)] 2+ complex. While both crystals exhibit the typical blue emission observed in most Eu(II) containing compounds as a result of 4f 6 5d 1 to 4f 7 transitions, computational results show that the substitution of a Cl– anion in the place of a methanol molecule causes mixing of the 5d excited states in the Eu(II) 2.2.2B cryptate complex. Additionally, magnetism studies reveal the identity of the capping ligand in the Eu(II) 2.2.2B cryptate complex may also lead to exchange between Eu(II) metal centers facilitated by π-stacking interactions within the structure, slightly altering the anticipated magnetic moment. Finally, the synthetic control present in these systems makes them interesting candidates for studying less stable divalent lanthanides and the effects of precise modifications of the electronic structures of low valent lanthanide elements.

Anions↗
DOE OSTI2021

Diversifying Composition Leads to Hierarchical Composites with Design Flexibility and Structural Fidelity

Although significant progress has been made in the self-assembly of nanostructures, present successes heavily rely on precision in building block design, composition, and pair interactions. These requirements fundamentally limit our ability to synthesize macroscopic materials where the likelihood of impurity inclusion escalates and, more importantly, to access molecular-to-nanoscopic-to-microscopic-to-macroscopic hierarchies, since the types and compositions of building blocks vary at each stage. Inspired by biological blends and high-entropy alloys, we hypothesize that diversifying the blend’s composition can overcome these limitations. Increasing the number of components increases mixing entropy, leading to the dispersion of different components and, as a result, enhances interphase miscibility, weakens the dependence on specific pair interactions, and enables long-range cooperativity. This hypothesis is validated in complex blends containing small molecules, block copolymer-based supramolecules, and nanoparticles/colloidal particles. Hierarchically structured composites can be obtained with formulation flexibility in the filler selection and blend composition. It is worth noting that, by adding small molecules, we can solve the size constraint that plagues traditional block copolymer/nanoparticle blends. Detailed characterization and simulation further confirm that each component is distributed to locally mediate unfavorable interactions, cooperatively mitigate composition fluctuations, and retain structural fidelity. Furthermore, the blends have sufficient mobility to access tunable microstructures without compromising the order of the nanostructure. Besides establishing a kinetically viable pathway to release current constraints in the composite design and to navigate uncertainties during structure formation over multiple length scales, the present study demonstrates that entropy-driven behaviors can be realized in systems beyond high-entropy alloys despite inherent differences between metal alloys and organic/inorganic hybrids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Deterministic Fabrication of Large-Area, High-Crystallinity Oxide Moiré Superlattices

Oxide twistronics extends moiré engineering beyond van der Waals materials, offering a promising platform for accessing emergent interfacial phenomena arising from the strong coupling of lattice, charge, and orbital degrees of freedom in complex oxides. However, deterministic fabrication of high-crystallinity oxide moiré superlattices over large lateral dimensions remains challenging due to the three-dimensional bonding network of oxides. Here, we demonstrate a scalable, generalized fabrication strategy that enables the formation of high-crystallinity oxide moiré superlattices with clean, chemically bonded interfaces and precisely controlled twist angles down to nominal values of 0.1°, achieving subdegree twist-angle accuracy across large contiguous lateral dimensions approaching the millimeter scale. Using NaNbO3 as a model system, we show that the resulting interlayer coupling drives pronounced structural reconstruction that modifies both the phase structure and ferroelectric domain configuration. Synchrotron-based X-ray 3D reciprocal space mapping reveals the emergence of a single-phase state in twisted bilayers, in contrast to the mixed-phase structure observed in single-layer membranes prior to twist assembly. The structural signatures are further consistent with gradual lattice rotation distributed along the thickness direction that may accommodate interfacial shear strain, distinct from reconstruction observed in van der Waals moiré systems which primarily occurs through in-plane stacking rearrangement. This collective lattice response is correlated with twist-dependent nanoscale electromechanical modulations observed by piezoresponse force microscopy. These results establish a scalable materials platform for oxide twistronics and support the implementation of twist-engineered functionalities in practical, macroscale device architectures.

Ghanbari, Reza [North Carolina State University (N↗
DOE OSTI2021

VFA Biorefinery Design for Informed Production of Ground and Aviation Fuels

The rising demand for low-carbon intensity fuel options requires evaluation of a system which can support their production economically and sustainably. Volatile fatty acids (VFAs) ranging from C2 to C8 can be derived in high yield from arrested anaerobic digestion of biomass. This talk provides an overview of our work in which we upgrade wet waste-derived VFAs using ketonization to elongate their carbon backbone to reach a range relevant to jet or diesel fuels. Kinetic models were used to predict ketone profiles from varying VFA profiles, thereby informing potential carbon flow to either (a) mixed paraffins for use in diesel or aviation fuel, or (b) ethers for use in diesel fuel. To do this, the anticipated products were screened for critical fuel characteristics using predictive tools. The criteria for neat and blended bioblendstocks were chosen based on conventional petrofuel requirements, and they were applied to inform fuel targets, identify limiting characteristics, and guide conversion development. While paraffins can serve as either diesel or aviation fuels, the latter has stringent criteria which include a precise distillation curve range tied to carbon distribution. Fuels which fall outside this range typically fail to meet other property metrics, and as such flashpoint and viscosity were identified as potentially limiting properties of this VFA aviation fuel. However, paraffin fractions which fall outside aviation criteria may meet diesel fuel requirements, which are looser except for the flashpoint minimum. Flashpoint was also a concern for smaller VFA diesel ethers, which posed an additional oxygenate risk of high water solubility. This fuel-informed conversion design process was demonstrated through production of paraffins with reduced sooting as compared to petrodiesel (~34%), and increased renewable aviation fuel blend levels (>70%). VFA-derived ethers improved petrodiesel by increasing fuel autoignition quality by 56% and reducing sooting by 86%. These VFA aviation and diesel fuels could enable greenhouse gas (GHG) reductions of over 165% and 50%, respectively, relative to their purely fossil-derived counterparts. Collectively, this work provides (i) an overview of how we leveraged the flexibility of VFAs for fuel production; and (ii) insight into the potential of a VFA biorefinery to accommodate varied feed and fuel applications, while also considering the merit of tailored fuel production pathways and GHG reduction potential.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2024

Quantifying carrier density in monolayer MoS 2 by optical spectroscopy

The successful design and device integration of nanoscale heterointerfaces hinges upon precise manipulation of both ground- and excited-state charge carrier (electron and hole) densities. However, it is particularly challenging to quantify these charge carrier densities in nanoscale materials, leading to uncertainties in the mechanisms of many carrier density-dependent properties and processes. Here, we demonstrate a method that utilizes steady-state and transient absorption spectroscopies to correlate monolayer MoS 2 electron density with the easily measured metric of excitonic optical absorption quenching in a variety of mixed-dimensionality s-SWCNT/MoS 2 heterostructures. By employing a 2D phase-space filling model, the resulting correlation elucidates the relationship between charge density, local dielectric environment, and concomitant excitonic properties. The phase-space filling model is also able to describe existing trends from the literature on transistor-based measurements on MoS 2 , WS 2 , and MoSe 2 monolayers that were not previously compared to a physical model, providing additional support for our method and results. The findings provide a pathway to the community for estimating both ground- and excited-state carrier densities in a wide range of TMDC-based systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

One-Component, Vinyl-Functional Fluorosilicone Pastes for Direct Ink Write Additive Manufacturing

In this study, one-component (“all-in-one”) fluorosilicone pastes specifically designed for application in direct ink write (DIW) additive manufacturing (AM) have been developed. They consist of vinyl-functional, methyltrifluoropropyl-containing (MeTfpS) terpolysiloxane base polymer(s), hydrosilyl-functional cross-linker(s), UV-sensitive hydrosilylation catalyst, thixotropic additive, and trimethylsilylated fumed silica filler, with other additives that are optional. Their base polymers were completely amorphous and linear, with molecular weights (M n ) ranging from approximately 7000 to 50,000 and specifically targeted for the viscosity range ideal for DIW. These polymers were prepared by anionic ring-opening polymerizations (A-ROP) of appropriate mixtures of cyclic siloxanes initiated by oligomeric, difunctional tetramethylammonium silanolate in the presence of a difunctional tetramethyldivinyldisiloxane end-blocker and molecular weight regulator. Two series of these terpolymers were prepared: one containing 5 mol % MeTfpS repeat units but varying degrees of polymerization (DP) from 80 to 600 and the other containing 5, 10, and 15 mol % MeTfpS at a constant DP of 600. All polymers contained mostly random distributions of MeTfpS repeat units. The pastes were prepared by speed-mixing, ready for use in DIW, they exhibited ideal thixotropy, long-term (over a year) rheological stability, and can be quickly (within seconds) and permanently cured by room-temperature, UV-activated hydrosilylation in air. The resulting elastomers showed base polymer molecular weight- and composition-dependent stress-induced crystallization (SIC) at higher molecular weights and lower trifluoropropyl contents and tunable Shore A hardness (30A–40A) typical for soft polysiloxane rubbers. Preliminary DIW tests indicated excellent printability with high precision of printed shapes and clearly present these one-component pastes as prime candidates for simple and practical printing of silicone elastomer objects.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Multi-cation perovskites prevent carrier reflection from grain surfaces

The composition of perovskite has been optimized combinatorially such that it often contains six components (A x B y C 1-x-y PbX z Y 3-z ) in state-of-art perovskite solar cells. Questions remain regarding the precise role of each component, and the lack of a mechanistic explanation limits the practical exploration of the large and growing chemical space. Here, aided by transient photoluminescence microscopy, we find that, in perovskite single crystals, carrier diffusivity is in fact independent of composition. In polycrystalline thin films, the different compositions play a crucial role in carrier diffusion. In this work, we report that methylammonium (MA)-based films show a high carrier diffusivity of 0.047 cm 2 s -1 , while MA-free mixed caesium-formamidinium (CsFA) films exhibit an order of magnitude lower diffusivity. Elemental composition studies show that CsFA grains display a graded composition. This curtails electron diffusion in these films, as seen in both vertical carrier transport and surface potential studies. Incorporation of MA leads to a uniform grain core-to-edge composition, giving rise to a diffusivity of 0.034 cm 2 s -1 in CsMAFA films. A model that invokes competing crystallization processes allows us to account for this finding, and suggests further strategies to achieve homogeneous crystallization for the benefit of perovskite optoelectronics.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Hydrogen underground storage for grid electricity storage: An optimization study on techno-economic analysis

Here, this study performs a techno-economic analysis of hydrogen underground storage systems for grid electricity storage, evaluating their economic viability at the plant scale using dynamic optimization. It explores the feasibility of various system configurations and revenue models in the context of volatile electricity prices and the necessity for multiple revenue streams. The hypothesis tested is that large-scale hydrogen storage, despite its low round-trip efficiency, can be economically viable with the right mix of revenue streams. This study uses scenario-based analysis to assess the impacts of different system configurations, including engaging in time-shifting arbitrage, ancillary service markets and blending hydrogen with natural gas. Results indicate potential annual net cash flows of up to $\$$1.5 million from ancillary services integration and $\$$5.2 million from natural gas blending, contingent on specific system sizes. The study concludes that hydrogen underground storage for grid electricity storage can be profitable, and emphasizes that proper system design and precise electricity price forecasting are crucial for optimizing system performance and economic returns. This research sets the stage for further investigations into the scalability of hydrogen storage systems and their broader implications for grid electricity storage and energy market dynamics.

25 ENERGY STORAGE↗
DOE OSTI2020

Ultracompact 3D microfluidics for time-resolved structural biology

To advance microfluidic integration, we present the use of two-photon additive manufacturing to fold 2D channel layouts into compact free-form 3D fluidic circuits with nanometer precision. We demonstrate this technique by tailoring microfluidic nozzles and mixers for time-resolved structural biology at X-ray free-electron lasers (XFELs). We achieve submicron jets with speeds exceeding 160 ms -1 , which allows for the use of megahertz XFEL repetition rates. By integrating an additional orifice, we implement a low consumption flow-focusing nozzle, which is validated by solving a hemoglobin structure. Also, aberration-free in operando X-ray microtomography is introduced to study efficient equivolumetric millisecond mixing in channels with 3D features integrated into the nozzle. Such devices can be printed in minutes by locally adjusting print resolution during fabrication. This technology has the potential to permit ultracompact devices and performance improvements through 3D flow optimization in all fields of microfluidic engineering.

3-D reconstruction↗
DOE OSTI2024

The Cauchy Problem for Boltzmann Bi-linear Systems: The Mixing of Monatomic and Polyatomic Gases

Abstract From a unified vision of vector valued solutions in weighted Banach spaces, this paper establishes the existence and uniqueness for space homogeneous Boltzmann bi-linear systems with conservative collisional forms arising in complex gas dynamical structures. This broader vision is directly applied to dilute multi-component gas mixtures composed of both monatomic and polyatomic gases. Such models can be viewed as extensions of scalar Boltzmann binary elastic flows, as much as monatomic gas mixtures with disparate masses and single polyatomic gases, providing a unified approach for vector valued solutions in weighted Banach spaces. Novel aspects of this work include developing the extension of a general ODE theory in vector valued weighted Banach spaces, precise lower bounds for the collision frequency in terms of the weighted Banach norm, energy identities, angular or compact manifold averaging lemmas which provide coerciveness resulting into global in time stability, a new combinatorics estimate for p -binomial forms producing sharper estimates for the k -moments of bi-linear collisional forms. These techniques enable the Cauchy problem improvement that resolves the model with initial data corresponding to strictly positive and bounded initial vector valued mass and total energy, in addition to only a $$2^+$$ 2 + moment determined by the hard potential rates discrepancy, a result comparable in generality to the classical Cauchy theory of the scalar homogeneous Boltzmann equation.

Physics↗