Search NASA⌕ Search

SEARCH · Search NASA

Results for “Closed form solution”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Formation of hierarchically structured martensites in pure iron with ultrahigh strength and stiffness

Strong steels are primarily fabricated by introducing spatial obstacles (e.g., stacking faults and precipitates) that inhibit dislocation slips under stress to achieve high strength. However, for most low-carbon steels, such obstacles are difficult to form mainly because the martensitic transition is kinetically unfavorable by conventional methods, which precludes the attainment of high-strength materials in these steels with low solute contents. Here, we report an innovative high-pressure preparation of martensitic pure Fe with involving nano-effect, which leads to the formation of ultrastrong bulk iron with exceptionally high yield strength, ultimate strength, and hardness of 2.9 GPa, 3.7 GPa, and 9.0 GPa, respectively, exceeding those of high-speed steels. Such extraordinary mechanical properties are closely attributed to its high-density martensites with unique multiscale hierarchical structures formed due to complex phase transitions under pressure.

Science & Technology - Other Topics↗
DOE OSTI2026

A Unified Design Theory for Multi-Port Polyphase Transformers Enabling Scalable Power-Multiplexed EV Fleet Charging Systems

This paper presents a unified analytical design theory for multi-port polyphase transformers, targeting scalable and isolated high-power Electric Vehicle (EV) fleet charging systems with power multiplexing capability. As fleet electrification accelerates, conventional one-to-one charger architectures face significant challenges in infrastructure cost, peak power demand, and low utilization of installed power electronics. Power-multiplexed charging architectures, which dynamically distribute power from a shared pool of converter modules across multiple vehicles, have emerged as a promising solution. However, such architectures require scalable, isolated multi-port power interfaces capable of routing energy among multiple inputs and outputs, whose design remains complex and dependent on iterative modeling. To address this gap, the proposed theory provides closed-form expressions for self-inductance, leakage inductance, and mutual coupling terms for arbitrary multi-phase, multi-port transformer structures. The formulation enables direct synthesis of isolated multi-input and multi-output resonant converter systems without reliance on geometry-specific finite-element analysis or extensive parameter extraction. This capability is particularly critical for power-multiplexed systems, where modular converter structures must interface with multiple vehicles while maintaining galvanic isolation and flexible power allocation. The effectiveness of the proposed framework is demonstrated through the design of a 360 kW multi-phase system operating over a 700–900 VDC input and 400–1250 VDC output range. PLECS simulation results confirm accurate prediction of system behavior and validate the applicability of the approach to multi-port, power-multiplexed charging scenarios. The proposed method significantly reduces design complexity while enabling scalable, cost-effective, and fully utilized EV fleet charging infrastructure.

Asa, Erdem [ORNL] (ORCID:0000000190884812)↗
DOE OSTI2023

Gauge constrained algorithm of variational discrete action theory at N = 3 for the multiorbital Hubbard model

The recently developed variational discrete action theory (VDAT) provides a systematic variational approach to the ground state of the quantum many-body problem, where the quality of the solution is controlled by an integer N, and increasing N monotonically approaches the exact solution. VDAT can be exactly evaluated in the d = ∞ multiorbital Hubbard model using the self-consistent canonical discrete action theory (SCDA), which requires a self-consistency condition for the integer time Green's functions. Previous work demonstrates that N = 3 accurately captures multiorbital Mott/Hund physics at a cost similar to the Gutzwiller approximation. Here we employ a gauge constraint to automatically satisfy the self-consistency condition of the SCDA at N = 3, yielding an even more efficient algorithm with enhanced numerical stability. We derive closed form expressions of the gauge constrained algorithm for the multiorbital Hubbard model with general density-density interactions, allowing VDAT at N = 3 to be straightforwardly applied to the seven-orbital Hubbard model. We present results and a performance analysis using N = 2 and N = 3 for the SU⁡(2⁢N orb ) Hubbard model in d = ∞ with N orb = 2–8, and compare to numerically exact dynamical mean-field theory solutions where available. Finally, the developments in this work will greatly facilitate the application of VDAT at N = 3 to strongly correlated electron materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Fundamental Thermodynamic, Kinetic, and Mechanical Properties of Lithium and Its Alloys

Lithium alloying reactions are beneficial in promoting uniform plating and stripping of lithium metal in all-solid-state batteries. First-principles calculations are performed to predict thermodynamic, kinetic, and mechanical properties of lithium and several important Li–M alloys (M = Mg, Ag, Zn, Al, Ga, In, Sn, Sb, and Bi). While the Li–Mg binary system forms a solid solution, most other lithium–metal alloys prefer stoichiometric intermetallic compounds with common local motifs that enable fast Li diffusion. Lithium and Li-rich alloys exhibit an unusually flat energy landscape along paths that connect BCC to close-packed structures like FCC and HCP, with important implications for mechanical properties. Very low migration barriers for Li diffusion that rival those of superion conductors are predicted, both in pure Li and in Li–M intermetallics. However, vacancy concentration, which is crucial for substitutional diffusion, is predicted to be low in metallic Li and most Li–M intermetallics. Compounds such as B32 LiAl and LiGa as well as D0 3 Li 3 Sb and Li 3 Bi exhibit structural vacancies at higher ends of their voltage windows, which together with low migration barriers leads to exceptionally high Li mobilities. In the Li–Mg solid solution, the addition of Mg is found to decrease the vacancy tracer diffusion coefficient by an order of magnitude.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A Decade of Innovative Approaches to Treating and Dispositioning Radioactive Waste at the Savannah River Site - 20620

This year marks the 70. anniversary of the U.S. Department of Energy's (DOE) Savannah River Site (SRS), located near Aiken, South Carolina. SRS is a key industrial complex responsible for environmental stewardship, environmental cleanup, waste management, and disposition of nuclear materials. SRS also continues to have a role in critical defense-related activities and the reprocessing of used reactor fuel. The SRS encompasses 803 square kilometers (310 square miles) in parts of Aiken, Barnwell, and Allendale counties. The Liquid Waste Mission starts with the safe receipt and storage of radioactive liquid waste in the waste tanks, which principally includes Cold War legacy waste, but also waste from support of National Aeronautics Space Administration missions, medical isotope production, and research activities. This 133,000 cubic meters (m{sup 3}) (35 million gallons [Mgal]) of high-level radioactive waste (HLW) is currently held in 43 large underground waste tanks. The capacity of each of these tanks range from 2,800 m{sup 3} to 5,000 m{sup 3} (0.75 to 1.33 Mgal) and were placed in operation between 1954 and 1986. In July 2009, the DOE awarded a stand-alone contract to execute the Liquid Waste Mission at SRS. The Liquid Waste Contractor selected was Savannah River Remediation LLC1 (SRR), which is responsible for receipt, storage, retrieval and treatment of all HLW, disposal of the decontaminated low-activity waste fraction, as well as operationally closing cleaned HLW tanks. Since July 2009, SRR has successfully grouted and operationally closed six large underground tanks, poured 1,476 canisters of vitrified HLW (a stable glass waste form), treated approximately 34,200 m{sup 3} (9.0 Mgal) of HLW, and dispositioned over 41,200 m{sup 3} (10.9 Mgal) of decontaminated salt solution as low-level waste (LLW) into the Saltstone Disposal Units (SDUs) being constructed by SRR on site. The innovative work performed by SRR in the LLW portion of its mission has earned it the Richard S. Hodes Award. The work conducted by SRR is the same work championed by the late Richard S. Hodes, a respected physician, statesmen, and Chairman of the Southeast Compact Commission for Low-Level Radioactive Waste Management. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Influence of voids on the thermal and light stability of perovskite solar cells

The formation of voids in perovskite films close to the buried interface has been reported during film deposition. These voids are thought to limits the efficiency and stability of perovskite solar cells (PSCs). Here, we studied the voids formed during operation in perovskite films that were optimized during the solution deposition process to avoid voids. New voids formed during operation are found to assemble along grain boundaries at the bottom interface, caused by the loss of residual solvent and conversion of amorphous phase to crystalline phase. Unexpectedly, the formation of these voids did not negatively affect the stability of PSCs. Decreasing the amorphous region in perovskites by thermal annealing decreased the positive iodide interstitial density, and improved the light stability of PSCs. The annealed devices maintained 90% of their initial efficiency and light soaking for 1900 hours at open circuit condition under 1-sun illumination at 50°C.

14 SOLAR ENERGY↗
DOE OSTI2024

Unified wavefront singularity characterization of three-dimensional elastodynamic time-domain half-space Green's function under impulsive boundary and internal loads

Founded on a novel analytical formulation that led to a rigorous yet compact path-integral representation of the time-domain elastodynamic half-space Green's function, a unified analysis of the possible occurrence of different singular wavefront behaviour in the response under arbitrary impulsive internal or surface point loads at arbitrary source-receiver locations is presented. With the decomposition of the general solution into distinct initiating and reflected wave group integrals that share a common factored format and simple contour definitions, the mathematical framework is shown to allow a straightforward identification of the specific conditions and the particular wave groups that are responsible for the singular wavefront phenomena without resorting to advanced analytic function theories or asymptotic methods. Analytic characterizations of the nature, strength and direction of all intrinsic singular wavefront behaviours of the three-dimensional Green's function in three canonical cases of source-receiver configurations are given in a dual integral-closed form format to facilitate their theoretical understanding as well as computational applications. Graphical illustrations of their variation with the source-receiver configuration and the medium's Poisson's ratio together with relevant comparison and clarifications of some classical treatments are included.

Green’s functions↗
DOE OSTI2022

Tree-inspired lignin microrods-based composite heterogeneous nanochannels for ion transport and osmotic energy harvesting

One of the key processes of tree lignification is that lignin penetrates into the cell wall and fills in the cell wall framework, thereby increasing the hardness and hydrophobic of the tree channels, which is beneficial to consolidate and support the tree cell wall and water transport. Inspired by this natural process, we demonstrated a lignin-based nanofluidic heterogeneous membrane that closely mimics the channels in tree, which can realize ion transport function and effectively capture reverse electrodialysis. The membrane was synthesized by heating dealkaline lignin and PVA at 200 °C and this formed fusiform microrods and a closed-packed membrane. Simultaneously, this membrane composited with anodized aluminum (AAO) channels membrane at 200 °C to form asymmetric heterogeneous nanochannels membrane, which can transport counter-ions and harvest osmotic energy. This membrane implements ion current rectification in 0.1 M KCl electrolyte solution at pH 3 due to the confinement of pores and opposite surface charges in lignin-based heterogeneous nanochannel. An output power density of 0.97 W m- 2 is obtained under a 50-fold salinity gradient, which can be further improved to 1.19 W m -2 by increasing the salinity gradient from 50-fold to 500-fold. Accordingly, this nanofluidic membranes were prepared by using lignin, the key component in tree, which not only mimicked a crucial process of the water and ionic transport process of channels in tree, but also had the prospect in the field of osmotic energy harvesting.

09 BIOMASS FUELS↗
DOE OSTI2023

Amorphous 1-D nanowires of calcium phosphate/pyrophosphate: A demonstration of oriented self-growth of amorphous minerals

Amorphous inorganic solids are traditionally isotropic, thus, it is believed that they only grow in a non-preferential way without the assistance of regulators, leading to the morphologies of nanospheres or irregular aggregates of nanoparticles. However, in the presence of (ortho)phosphate (Pi) and pyrophosphate ions (PPi) which have synergistic roles in biomineralization, the highly elongated amorphous nanowires (denoted ACPPNs) form in a regulator-free aqueous solution (without templates, additives, organics, etc). Based on thorough characterization and tracking of the formation process (e.g., Cryo-TEM, spherical aberration correction high resolution TEM, solid state NMR, high energy resolution monochromated STEM-EELS), the microstructure and its preferential growth behavior are elucidated. In ACPPNs, amorphous calcium orthophosphate and amorphous calcium pyrophosphate are distributed at separated but close sites. The ACPPNs grow via either the preferential attachment of ~2 nm nanoclusters in a 1-dimension way, or the transformation of bigger nanoparticles, indicating an inherent driving force-governed process. Here, we propose that the anisotropy of ACPPNs microstructure, which is corroborated experimentally, causes their oriented growth. This study proves that, unlike the conventional view, amorphous minerals can form via oriented growth without external regulation, demonstrating a novel insight into the structures and growth behaviors of amorphous minerals.

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

Micropolar Elastoplasticity Using a Fast Fourier Transform‐Based Solver

ABSTRACT This work presents a micromechanical spectral formulation for obtaining the full‐field and homogenized response of elastoplastic micropolar composites. A closed‐form radial‐return mapping is derived from thermodynamics‐based micropolar elastoplastic constitutive equations to determine the increment of plastic strain necessary to return the generalized stress state to the yield surface, and the algorithm implementation is verified using the method of numerically manufactured solutions. Then, size‐dependent material response and micro‐plasticity are shown as features that may be efficiently simulated in this micropolar elastoplastic framework. The computational efficiency of the formulation enables the generation of large datasets in reasonable computing times.

42 ENGINEERING↗
DOE OSTI2020

Strings in Ramond-Ramond backgrounds from the Neveu-Schwarz-Ramond formalism

We treat RR flux backgrounds of type II string theory in the framework of closed superstring field theory based on the NSR formalism, focusing on two examples: (1) the pp-wave background supported by 5-form flux, and (2) AdS 3 × S 3 × M 4 supported by mixed 3-form fluxes. In both cases, we analyze the classical string field solution perturbatively, and compute the correction to the dispersion relation of string states to quadratic order in the RR flux. In the first example, our result is in a delicate way consistent with that obtained from lightcone quantization of the Green-Schwarz string. In the second example, we will obtain numerically the mass corrections to pulsating type IIB strings in AdS 3 × S 3 × M 4 . Our results, valid at finite AdS radius, agree with previously known answers in the semiclassical limit and in the BMN limit respectively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Scattering-based structural inversion of soft materials via Kolmogorov–Arnold networks

Small-angle scattering techniques are indispensable tools for probing the structure of soft materials. However, traditional analytical models often face limitations in structural inversion for complex systems, primarily due to the absence of closed-form expressions of scattering functions. To address these challenges, we present a machine learning framework based on the Kolmogorov–Arnold Network (KAN) for directly extracting real-space structural information from scattering spectra in reciprocal space. This model-independent, data-driven approach provides a versatile solution for analyzing intricate configurations in soft matter. By applying the KAN to lyotropic lamellar phases and colloidal suspensions—two representative soft matter systems—we demonstrate its ability to accurately and efficiently resolve structural collectivity and complexity. Here, our findings highlight the transformative potential of machine learning in enhancing the quantitative analysis of soft materials, paving the way for robust structural inversion across diverse systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Ab initio molecular dynamics (AIMD) simulations of NaCl, UCl 3 molten salts

Ab initio molecular dynamics (AIMD) simulations are used to calculate select thermophysical and thermodynamic properties of NaCl, UCl and NaCl-UCl 3 molten salts. Following established approaches, the AIMD simulations include a model for Van der Waals interactions. The Langreth & Lundqvist (vDW-DF2), DFT-D3, and density-dependent energy correction (DFT-dDsC) dispersion models are first tested for molten NaCl in order to assess their accuracy for density and heat capacity predictions across a range of temperatures. Based on the NaCl results, the vdW-DF2 and DFT-dDsC methods are extended to the UCl 3 system and compared to available experimental data. Next, mixtures of NaCl-UCl 3 are investigated and analyzed with respect to the deviation from ideal solution behavior. For the DFT-dDsC simulations, density deviates by up to 2% from an ideal mixture, with the maximum occurring close to the eutectic composition. The mixing energy also deviates from an ideal solution and exhibits a minimum of about -0.074 to eV per formula unit, again close to the eutectic composition. Finally, the compressibility and species diffusivity of the pure and mixed salt systems are calculated. The diffusivities are slightly reduced in the mixed compared to the pure systems and the compressibilities loosely follow a linear correlation as a function of the UCl 3 composition. The trends observed for mixing properties are rationalized by correlating them to the coordination chemistry, which emphasizes the importance of maintaining the extended network formed by U and Cl ions as the NaCl concentration increases. The concentration at which breakdown of the extended network occurs, roughly coincides with the minimum of both the mixing energy and the deviation from ideal solution behavior for density.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Filling the gap with a bulky diaryl boron group: fluorinated and non-fluorinated copper pyrazolates fitted with a dimesityl boron moiety on the backbone

Successful synthesis has been reported of 4-Mes 2 B-3,5-(CF 3 ) 2 PzH and 4-Mes 2 B-3,5-(CF 3 ) 2 PzH bearing sterically demanding diarylboron moieties at the pyrazole ring 4-position, and their corresponding copper(I) pyrazolate complexes. They show visible blue photoluminescence in solution. The X-ray crystal structures revealed that the fluorinated {[4-BMes 2 -3,5-(CF 3 ) 2 Pz]Cu} 3 crystallizes as discrete trinuclear molecules whereas as the non-fluorinated {[4-BMes 2 -3,5-(CH 3 ) 2 Pz]Cu} 3 forms dimers of trimers with two close inter-trimer Cu···Cu separations. The solid {[4-BMes 2 -3,5-(CF 3 ) 2 Pz]Cu} 3 featuring a sterically confined Cu 3 N 6 core displays bright blue phosphorescence while {[4-BMes 2 -3,5-(CH 3 ) 2 Pz]Cu} 3 , which is a dimer of a trimer, is a red phosphor at room temperature. Here, this work illustrates the modulation of photo-physical properties of metal pyrazolates by adjusting the supporting ligand steric features and introducing secondary diarylboron luminophores. Computational analysis of the structures and photophysical properties of copper complexes are also presented.

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

LightMAT - Continuous fiber malleable thermoset composites with sub-1-minute dwell times; validation of impact performance and evaluation of the efficacy of the compression forming process (CRADA 409 Final Report)

In spite of carbon fiber composite materials’ significant impact on light-weighting, performance, and efficiency in the aerospace industry, adoption of these materials has been slow in high-volume industries such as automotive. Two major barriers to adoption are cost and cycle-time. Current approaches to thermoset composite part production are dependent on in-mold curing of thermosets which are not optimal for high volume, high throughput production due to limitations and inefficiencies associated with the in-mold cure itself. In addition, ancillary activities, such as transport and storage of shelf-life-limited uncured, or B-staged prepreg materials typically necessitate refrigerated transport and storage which significantly impacts the economic and energy costs associated with manufacturing. Furthermore, limited out-life means that trimmings cannot typically be used as they partially cure during initial production leading to high scrap rates (+20% is common). Finally, the need to cure in-mold drives cycle times to multiple minutes in the best cases, and 10’s of minutes to hours in most cases. Mallinda is developing polyimine malleable thermoset prepreg composite materials which have excellent mechanical properties (100 GPa tensile modulus, 2 GPA tensile strength, 2.4% elongation at break) and high operating temperatures (Tg>200°C). At scale, polyimine resins are commensurate in price with commodity epoxy resins. What distinguishes malleable thermoset prepreg from traditional thermoset prepreg materials, is that they are fully cured during Mallinda’s roll-to-roll production of prepreg laminate. This results in 5 key value-differentiating benefits. First, it simplifies manufacturing logistics by enabling ambient transportation and storage, and by significantly extending out-life and shelf-life almost indefinitely. Second, elimination of autoclave curing reduces the economic and energy costs to the customer. Third, scrap rates can be reduced as malleable thermoset prepreg materials are directly reusable. Fourth, the manufacturing consolidation step can be roughly 10x faster than traditional thermosets, because the resin is already cured. Parts can be made via compression forming by the application of heat and pressure to quickly vitrify and consolidate a multilayer part – easily leading to sub 3-minute cycle times (at lab scale we have demonstrated a 20 second dwell time, with room for further optimization). Finally, the closed-loop cradle-to-cradle solution-based recyclability of malleable thermoset composites can also contribute significantly to the future of sustainable lightweight materials. The focus of this project was the development, optimization and validation of malleable thermoset composite materials which exhibit manufacturing cycle times of 3-minute or less, high speed impact performance on par with incumbent technologies, and defect-free consolidation of 3 dimensional parts. Government funding is required on this project because Mallinda is a start-up company whose focus is the development and scale-up of the described technology for introduction to the transportation segment. Unlike incumbent industry players, Mallinda is bringing a completely new and highly relevant malleable thermoset technology to bear on the problem of high throughput composites. As a small business, Mallinda relies on a combination of government R&D funding and private capital to perform development work.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Continuous fiber malleable thermoset composites with sub-1-minute dwell times; validation of impact performance and evaluation of the efficacy of the compression forming process. CRADA Final Report

Mallinda is developing polyimine malleable thermoset prepreg composite materials which have excellent mechanical properties (100 GPa tensile modulus, 2 GPA tensile strength, 2.4% elongation at break) and high operating temperatures (Tg>200°C). At scale, polyimine resins are commensurate in price with commodity epoxy resins. What distinguishes malleable thermoset prepreg from traditional thermoset prepreg materials, is that they are fully cured during Mallinda’s roll-to-roll production of prepreg laminate. This results in 5 key value-differentiating benefits. First, it simplifies manufacturing logistics by enabling ambient transportation and storage, and by significantly extending out-life and shelf-life almost indefinitely. Second, elimination of autoclave curing reduces the economic and energy costs to the customer. Third, scrap rates can be reduced as malleable thermoset prepreg materials are directly reusable. Fourth, the manufacturing consolidation step can be roughly 10x faster than traditional thermosets, because the resin is already cured. Parts can be made via compression forming by the application of heat and pressure to quickly vitrify and consolidate a multilayer part – easily leading to sub 3-minute cycle times (at lab scale we have demonstrated a 20 second dwell time, with room for further optimization). Finally, the closed-loop cradle-to-cradle solution-based recyclability of malleable thermoset composites can also contribute significantly to the future of sustainable lightweight materials. The focus of this project was the development, optimization and validation of malleable thermoset composite materials which exhibit manufacturing cycle times of 3-minute or less, high speed impact performance on par with incumbent technologies, and defect-free consolidation of 3 dimensional parts.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Modeling ethanol/water adsorption in all-silica zeolites using the real adsorbed solution theory

A comprehensive set of single-component and binary isotherms were collected for ethanol/water adsorption into the siliceous forms of 185 known zeolites using grand-canonical Monte Carlo simulations. Using these data, a systematic analysis of ideal/real adsorbed-solution theory (IAST/RAST) was conducted and activity coefficients were derived for ethanol/water mixtures adsorbed in different zeolites based on RAST. It was found that activity coefficients of ethanol are close to unity while activity coefficients of water are larger in most zeolites, indicating a positive excess free energy of the mixture. This observation can be attributed to water/ethanol interactions being less favorable than water/water interactions in the single-component adsorption of water at comparable loadings. The deviation from ideal behavior can be highly structure-dependent but no clear correlation with pore diameters was identified. Furthermore, our analysis also demonstrates the following: (1) accurate unary isotherms in the low-loading regime are critical for obtaining physically sensible activity coefficients; (2) the global regression scheme to solve for activity model parameters performs better than fitting activity models to activity coefficients calculated locally at each binary state point; and (3) including the dependence on adsorption potential offers only a minor benefit for describing binary adsorption at the lowest fugacities. Finally, the Margules activity model was found incapable of capturing the non-ideal adsorption behavior over the entire range of fugacities and compositions in all zeolites, but for conditions typical of solution-phase adsorption, RAST predictions using zeolite-specific or even bulk Margules parameters provide an improved description compared to IAST.

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

Boson star normal modes

Boson stars are gravitationally bound objects that arise in ultralight dark matter models and form in the centers of galactic halos or axion miniclusters. We systematically study the excitations of a boson star, taking into account the mixing between positive and negative frequencies introduced by gravity. We show that the spectrum contains zero-energy modes in the monopole and dipole sectors resulting from spontaneous symmetry breaking by the boson star background. We analyze the general properties of the eigenmodes and derive their orthogonality and completeness conditions which have non-standard form due to the positive-negative frequency mixing. The eigenvalue problem is solved numerically for the first few energy levels in different multipole sectors and the results are compared to the solutions of the Schrödinger equation in fixed boson star gravitational potential. The two solutions differ significantly for the lowest modes, but get close for higher levels. We further confirm the normal mode spectrum in 3D wave simulations where we inject perturbations with different multipoles. As an application of the normal mode solutions, we compute the matrix element entering the evaporation rate of a boson star immersed in a hot axion gas. The computation combines the use of exact wavefunctions for the low-lying bound states and of the Schrödinger approximation for the high-energy excitations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗