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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Identification of Distorted Gamma-Ray Signature Patterns Using Digital Filtering and Auto-Associative Memory Implemented with a Hopfield Neural Network

The detection and identification of radioactive sources in search applications involve analyzing passive gamma-ray emissions from high-level radioactive materials. This process uses a mobile detector-spectrometer in a complex field test environment. Recently, the use of artificial intelligence for gamma-ray spectrum analysis has shown promising results. However, challenges persist in identifying isotopic signatures from spectral measurements that may be distorted due to source shielding, random variations in natural radioactive background, or insufficient measurement time to obtain clear spectral lines. Here, this paper presents a novel intelligent signature recognition method that combines digital filtering techniques with an artificial Hopfield Neural Network (HNN). The HNN leverages auto-associative memory to store training sample patterns and match them with incoming gamma spectra from distorted sources. It restores the testing sources’ measurements by finding the closest matching signature patterns in the spectral library. Before HNN recognition, the measured spectrum undergoes preprocessing with a digital image filter to reduce fluctuations. Performance of the proposed method is evaluated using a set of gamma-ray spectra measured with a sodium iodide detector. The data collected include measurements from six pure samples: 241 Am, 60 Co, 137 Cs, 192 Ir, 239 Pu, and 235 U, which are used for training and validation (i.e. six cases). Additionally, the data set contains 24 distorted synthesized sources with various fluctuating backgrounds. Test results demonstrate the potential of the proposed method to accurately recognize the correct isotope with high precision, achieving an accuracy rate exceeding 85%. Furthermore, the proposed method exhibits superior performance compared to the conventional multiple regression fitting and simple feedforward neural network methods.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Persistent structural distortion for anticipated improper ferroelectricity in ultrathin h-Lu 1− x Ca x MnO 3 films

Improper ferroelectricity in hexagonal rare-earth manganites (h-RMnO 3 , R = Ho–Lu, Y, Sc) arises from a geometric distortion as the primary order parameter, resilient to depolarizing fields and promising for ultrathin ferroelectric devices. However, the substrate-induced interface clamping effect, which suppresses the geometric distortion in the sub-nanometer regime, has thus far hindered the realization of two-dimensional improper ferroelectrics. This study demonstrates that doping with calcium can enhance ferroelectric structural distortion in h-LuMnO 3 thin films. Compressively strained h-Lu 1−x Ca x MnO 3 (x = 0.1, 0.2, 0.3, 0.4, 0.5) epitaxial thin films were stabilized on sapphire substrates using an h-ScFeO 3 buffer layer. We have found that the interface clamping effect is entirely overcome when the doping concentration reaches x ⩾ 0.2, establishing a potential quasi-2D ferroelectric system with a remarkably high estimated structural transition temperature of larger than 1200 K inferred indirectly from temperature-resolved reflection high-energy electron diffraction. This finding suggests a general strain engineering strategy to enhance improper ferroelectricity in hexagonal manganites.

hexagonal manganites↗
DOE OSTI2025

Interplay between electron localization, magnetic order, and Jahn-Teller distortion dictates LiMnO2 phase stability

The development of manganese (Mn)-rich cathodes for Li-ion batteries promises to alleviate potential supply chain bottlenecks in battery manufacturing. Fundamental challenges in Mn-rich cathodes arise from phenomena such as structural changes due to cooperative Jahn-Teller (JT) distortions of in octahedral environments, Mn migration, and phase transformations to spinel-like order, all of which affect the electrochemical performance. These physically complex phenomena motivate an re-examination of the Li-Mn-O rock-salt space, with a focus on the thermodynamics of the prototypical, polymorphs. It is found that the generalized gradient approximation (GGA-PBEsol) and meta-GGA ( ) density functionals with empirically fitted on-site Hubbard corrections yield spurious stable phases for , such as predicting a phase with -like order ( ) to be the ground state instead of the orthorhombic (Pmmn) phase, which is the experimentally known ground state. Accounting for antiferromagnetic order in each structure is shown to have a substantial effect on the total energies and resulting phase stability. By using hybrid-GGA (HSE06) and GGA with self-consistent Hubbard parameters (on-site and inter-site ) calculated from linear response theory, the experimentally observed phase stability trends are recovered. The calculated on-site between Mn- states in the experimentally observed orthorhombic, layered, and spinel phases are significantly smaller than in and disordered layered structures, by within GGA. The smaller values of are shown to be correlated with a collinear ordering of JT distortions, in which all orbitals are oriented in the same direction. This cooperative JT effect can lead to greater electron delocalization from Mn along the states due to increased Mn-O covalency, which contributes to the greater electronic stability compared to the phases with noncollinear JT arrangements. The structures with collinear ordering of JT distortions also generate greater vibrational entropy, which helps stabilize these phases at high temperature. These phases are shown to be strongly insulating with large calculated band gaps , which are computed using HSE06 and .

Kam, Ronald L↗
DOE OSTI2025

Role of Computational Parameters on Predicting Self-Consistent Residual Stress and Distortion during Wire Arc Additive Manufacturing

Production of three-dimensional metallic parts through integration of an articulated robot and gas metal arc welding, also known as wire arc additive manufacturing (WAAM), can produce large-scale components with moderate geometrical complexity. This technology is particularly appealing due to its high deposition rates, scalability, and cost-effective feedstock compared to other AM processes. Despite its advantages, WAAM adoption is hindered by challenges in ensuring geometric conformity without extensive distortion, defect-free structures, and consistent mechanical properties. Finite element analysis (FEA) is often used to address the challenge of geometrical conformity. As the size of parts increases, the best practices for mesh size and temporal resolution known in the literature become computationally unviable. This research examined the effects of mesh and time-step resolutions during transient FEA of a large-scale (248 layers) metallic part. The impact of computational parameters on the thermal history, displacement, and residual stress distributions were evaluated. The results showed that predicted distortion was consistent across resolutions, while time-step length significantly affected predicted thermal history, and mesh size influenced residual stress distributions. To investigate this relationship further, directionally biased meshes were considered and analyzed. The results indicated that increasing mesh resolution perpendicular to the welding path yielded stress predictions that aligned closely with higher-resolution models while offering substantial computational savings. In conclusion, the significances of this research are related to verification and validation of WAAM models for widespread industrial adoption and pragmatic guidelines for optimizing computation parameters for balancing computational efficiency and predictive accuracy of residual stress and distortion.

Solsbee, Brandon [Univ. of Tennessee, Knoxville, T↗
DOE OSTI2024

Local lattice distortions and the structural instabilities in bcc Nb–Ta–Ti–Hf high-entropy alloys: An ab initio computational study

Local lattice distortions (LLD) and structural stability of body-centered cubic (bcc) Nb–Ta–Ti–Hf high-entropy alloys (HEAs) are studied as functions of composition employing ab initio density-functional theory calculations, with specific focus on the role of the relative concentrations of group IV (Ti and Hf) versus group V (Nb and Ta) elements. Calculated results are presented as a function of composition x in Nb x Ta 0.25 Ti (0.75-x)/2 Hf (0.75-x)/2 alloys, for elastic moduli, phonon spectral functions, LLD and structural energy differences for the bcc and competing hexagonal close-packed (hcp) and ω phases. The results highlight the important role of group V elements and LLD in stabilizing the bcc structure. They further reveal how composition x can be tuned to alter both the magnitude of the LLD and structural energy differences. Specifically, the magnitude of the structural energy differences, and elastic and dynamic stability of the bcc phase, are enhanced with increasing x, while the LLD increase in magnitude as this concentration is decreased. The results also show evidence of correlated LLD at lower values of x, reflecting local structural distortions towards the ω phase, but not hcp. The degree of ω-collapse is nevertheless partial i.e., transformation towards this phase is not observed to be complete due to the presence of Ta and Nb. At lower values of x we further find an energy landscape characterized by multiple, nearly degenerate local energy minima for different values of the LLD.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Electronic Structure Distortions in Chromium Chelates Impair Redox Kinetics in Flow Batteries

Aminopolycarboxylate chelates are emerging as a promising class of electrolyte materials for aqueous redox flow batteries, offering tunable redox potentials, solubility, and pH stability through careful selection of ligands and transition metal ions. Despite their potential, the impact of molecular structure modifications on the electronic and electrochemical properties of these chelates remains underexplored. Here, in this study, we examine how introducing a hydroxyl group, often employed for its solubilizing properties, to the backbone of CrPDTA, a reference chelate material, significantly changes the thermodynamics and kinetics of the chelate's redox process. We correlate changes in molecular and electronic structures to different electrochemical responses resulting from the hydroxyl addition and show that the introduction of this functional group leads to a distortion in the octahedral coordination of chromium. Furthermore, increased anisotropic spin density and nonintegral oxidation state changes in the Cr metal center result in a larger barrier for electron transfer in CrPDTA‐OH. It is demonstrated that preserving a hexacoordinate chelate structure across a broad pH range is crucial for efficient flow battery application and it is emphasized that ligand modifications must avoid distorting the octahedral coordination of the transition metal.

25 ENERGY STORAGE↗
DOE OSTI2025

Portable Distortion Free Large Solid Angle Coverage Detector

Neutron single crystal diffractometers require large solid angle coverage for optimum performance. This can be achieved by tiling flat detectors in a cylindrical or spherical geometry, but results in large gaps in detector coverage and parallax distortion. The detector edges exhibit degraded resolution, distortion, and gamma rejection. Since the detector edge regions are a significant fraction of the detector active area, they must be removed from the experimental data set, requiring extra beam time to collect enough analysis data. A spherical detector with a continuous surface would effectively address this issue while eliminating most boundary ‘dead’ areas. Here we report on the development of a novel hemispherical shaped neutron detector using seamlessly tiled readout modules to form the desired shape. The heart of the detector is a specially developed curved neutron scintillator coupled to high resolution silicon photomultiplier (SiPM) Anger cameras via custom made fiber optic tapers (FOTs). The detector has been assembled and initial tests have been conducted at the High Flux Isotope Reactor (HFIR) beamlines at Oak Ridge National Laboratory (ORNL). Here, in this work, we describe details of the scintillator design, fabrication and characterization, evaluation of individual detector modules, the details of the detector design implementation, and evaluation of the assembled detector at ORNL beamlines.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Exploring the Links between Structural Distortions, Orbital Ordering, and Multipolar Magnetic Ordering in Double Perovskites Containing Re(VI) and Os(VII)

A combination of high-resolution powder diffraction techniques and solid-state NMR has been employed to explore the links between crystal structure, orbital ordering, and magnetism in three isostructural double perovskites containing transition metal ions with a 5d 1 configuration. In Ba 2 ZnReO 6 , both neutron and synchrotron X-ray powder diffraction data reveal a cubic-to-tetragonal transition at 23 K that breaks the degeneracy of the t 2g orbitals and leads to a pattern of orbital ordering that stabilizes magnetic ordering when the sample is cooled below 16 K. Similar behavior is observed in Ba 2 MgReO 6 , with an orbital ordering temperature of 33 K and a magnetic ordering temperature of 18 K. Prior theoretical works suggest that the pattern of orbital order seen in the P42/mnm space group is needed to stabilize the heavily canted antiferromagnetism of these compounds. Unfortunately, powder diffraction data is not sensitive enough to differentiate between the I4/mmm and P42/mnm structural models, as the distortions are too subtle to be unambiguously identified from either neutron or synchrotron X-ray powder diffraction methods. In contrast, both diffraction and 7 Li NMR data indicate that Ba 2 LiOsO 6 retains the cubic structure down to 1.7 K. The antiferromagnetic ground state and lack of any sign of orbital ordering in Ba 2 LiOsO 6 provide compelling evidence that the electronically driven tetragonal distortion seen in Ba2ZnReO6, and Ba2MgReO6 is intimately linked to the magnetic ordering seen in those compounds. The absence of magnetic reflections in high intensity neutron powder diffraction data collected on Ba 2 MgReO 6 strongly suggests ordering of multipolar moments on Re(VI), likely ferro-octupolar ordering.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Node Distortions in UiO-66 Inform Negative Thermal Expansion Mechanisms: Kinetic Effects, Frustration, and Lattice Hysteresis

In metal–organic frameworks (MOFs) the interplay between the dynamics of individual components and how these are constrained by the extended lattice can yield unusual emergent phenomena. For the archetypal Zr-MOF, UiO-66, we explore the cooperative dynamics of a Zr-node transformation that gives rise to negative thermal expansion (NTE). Here, using in situ synchrotron X-ray scattering, with powder diffraction and pair distribution function (PDF) analyses, we identify lattice hysteresis and a thermal ramp-rate-dependence of the thermal expansion. Specifically, kinetic trapping of distorted node states formed at high temperature, leads to broad variability in the apparent thermal expansion which ranges from large positive to large negative thermal expansion with coefficients of thermal expansion (CTE) from +45 to –80 × 10 –6 K –1 . Time-resolved relaxation studies at selected temperatures suggest that when equilibrated UiO-66 is intrinsically NTE, with a CTE of –35 × 10 –6 K –1 . Kinetic trapping of the node-distorted state following high temperature activation has broad implications for characterization and applications of these Zr-MOFs; the nonequilibrium node state depends on the thermal history of the sample with quench vs slow cooling likely to impact gas binding, pore volume, and accessible catalytic sites.

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

Conduction band convergence and local structure distortion for superior thermoelectric performance of GaSb-doped n-type PbSe thermoelectrics

Achieving high-stability thermoelectric materials with excellent average power factor and figure of merit is crucial for maximizing the output power density and conversion efficiency of thermoelectric devices. In this study, GaSb is added to PbSe as an n-type dopant to form stable solid solutions. Doping with GaSb flattens the conduction band and reduces the energy difference between the Σ and L conduction bands, thereby significantly improving the Seebeck coefficient. Herein, the Ga and Sb atoms co-occupy the vacant Pb sites, unlike in the case of traditional single-element doping, as is verified by density functional theory calculations. The resultant structural distortion is confirmed via transmission electron microscopy. This local structure distortion caused by GaSb doping reduces the lattice thermal conductivity. Consequently, the Pb 0.99875 (GaSb) 0.00125 Se sample exhibits a record-high average power factor of ~22.37 μW cm −1 K −2 and a high average figure of merit of ~0.94 in the temperature range of 300‒873 K. Furthermore, the introduction of interstitial Cu and discordant Zn atoms further reduces the lattice thermal conductivity. The Pb 0.99875 (GaSb) 0.00125 Zn 0.01 Se 1.01 -0.3%Cu sample exhibits a low lattice thermal conductivity of ~0.4 W m −1 K −1 at 873 K and a record-high average figure of merit of ~1.01 in the temperature range of 300‒873 K.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Local lattice distortions drive the transition of BaIrO 3 into a ferromagnetic insulator state

Using variable temperature total and resonant x-ray scattering at the K edge of Ir species, we study the “bad metal” to insulator transition in BaIrO 3 , a canonical third transition series oxide. The usage of advanced experimental techniques and large-scale computer modeling helps us show that, contrary to the widely accepted view, charge disproportionation leading to the formation of Ir-trimers with a different number of 5d valence electrons already exists at room temperature. The charge disbalance between the trimers does not evolve much with decreasing temperature while local lattice distortions do, suggesting that the latter and not the former make a key contribution to the emergence of the enigmatic ferromagnetic insulator state of BaIrO 3 . The conclusion is supported by DFT calculations based on unmodified experimental structure data. Our work calls for a reconsideration of the role of lattice distortions in determining the electronic properties of third transition series oxides. It also charts a path to assessing these properties on a realistic and not assumed crystal structure basis.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Emergence of heavy-fermion behavior and distorted square nets in partially vacancy-ordered Y 4 Fe x Ge 8 (1.0 ≤ x ≤ 1.5)

Disorders in intermetallic systems belonging to the CeNiSi 2 -family are frequently overlooked. Even compounds presumed to be stoichiometric, such as YFeGe 2 , can be misidentified. Here, in this study, we report a series of Y 4 Fe x Ge 8 (1.0 ≤ x ≤ 1.5) compounds and show, using high-resolution synchrotron X-ray diffraction, that they feature asymmetrical structural distortions in the Fe and Ge sites that lead to a superstructure with partially ordered Fe vacancies and distorted Ge square-net in the triclinic crystal system, space group P[1 with combining macron] with a = 11.4441(3) Å, b = 32.7356(7) Å, c = 11.4456(3) Å, α = 79.6330(10)°, β = 88.3300(10)°, and γ = 79.6350 (10)°. The unit cell is 16 times the conventional orthorhombic cell with the space group Cmcm. We identified the lower and upper limits for Fe in Y 4 Fe x Ge 8 (1.0 ≤ x ≤ 1.5). Our physical property measurements yielded a Sommerfeld coefficient γ = 39.8 mJ mole −1 K −2 , a Kadowaki–Woods ratio of 1.2 × 10 −5 μΩ cm mole 2 K 2 mJ −2 , and a Wilson ratio of 1.83, suggesting heavy fermion behavior in the absence of f electrons, a rather rare case. Furthermore, we observed strong spin frustration and noted findings indicating possible superconductivity associated with the Fe content.

Zhao, Hengdi [Argonne National Laboratory (ANL), A↗
DOE OSTI2025

Dome-like pressure-temperature phase diagram of the cooperative Jahn–Teller distortion in NaNiO 2

NaNiO 2 is a Ni 3+ -containing layered material consisting of alternating triangular networks of Ni and Na cations, separated by octahedrally-coordinated O anions. At ambient pressure, it features a collinear Jahn–Teller distortion below $T^{JT}_{onset} ≈ 480$ K, which disappears in a first-order transition on heating to $T^{JT}_{onset} ≈ 500$ K, corresponding to the increase in symmetry from monoclinic to rhombohedral. It was previously studied by variable-pressure neutron diffraction (Nagle-Cocco et al 2022 ACS Inorg. Chem. 61 4312) and found to exhibit an increasing $T^{JT}_{onset}$ with pressure up to ∼5 GPa. In this work, powdered NaNiO 2 was studied via variable-pressure synchrotron x-ray diffraction up to pressures of ∼67 GPa at 294 K and 403 K. Suppression of the collinear Jahn–Teller ordering is observed via the emergence of a high-symmetry rhombohedral phase, with the onset pressure occurring at ∼18 GPa at both studied temperatures. Further, a discontinuous decrease in unit cell volume is observed on transitioning from the monoclinic to the rhombohedral phase. These results taken together suggest that in the vicinity of the transition, application of pressure causes the Jahn–Teller transition temperature, $T^{JT}_{onset}$, to decrease rapidly. We conclude that the pressure-temperature phase diagram of the cooperative Jahn–Teller distortion in NaNiO 2 is dome-like.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Local lattice distortions and electronic phases in perovskite manganite Pr 0.5 Sr 0.5 MnO 3

We use variable temperature and magnetic field total x-ray scattering to study the crystal structure of the strongly correlated Pr 0.5 Sr 0.5 MnO 3 perovskite, which is a paramagnetic insulator at room temperature, becomes a ferromagnetic metal at 272 K and, upon further decreasing the temperature, turns into an antiferromagnetic insulator at 105 K. We find that a model featuring a monoclinic symmetry captures the structure and its temperature and field evolution well, eliminating the need to evoke a phase segregation scenario as done in prior studies. It appears that coupled variations in Mn–oxygen bonding distances and angles from their values in an undistorted perovskite lattice, i.e., coupled local lattice distortions, assist the phase transitions in Pr 0.5 Sr 0.5 MnO 3 , contributing to its unique physical properties. Local structural distortions thus emerge as an important degree of freedom in strongly correlated systems, in particular perovskite manganates, and, therefore, they should be fully accounted for when their fascinating physics is considered.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Magnetic excitations from the hexagonal spin clusters in the 𝑆 = $\frac{1}{2}$ distorted honeycomb lattice antiferromagnet Cu 2 ⁢(pymca)⁢ 3 ⁢(ClO 4 )

Cu 2 ⁢(pymca) ⁢3 (ClO 4 ) (pymca: pyrimidine-2-carboxylate) consists of a slightly distorted honeycomb lattice of Cu 2+ spins, which shows no long-range magnetic order down to 0.6 K. A magnetization study revealed 1/3 and 2/3 plateau phases [A. Okutani et al., J. Phys. Soc. Jpn. 88, 013703 (2019)], which is not expected for regular honeycomb antiferromagnets. Inelastic neutron scattering experiments were performed using a powder sample to investigate the exchange interactions of this material. The spin excitations from the singlet ground state to the first three triplet states, predicted from the antiferromagnetic hexagonal spin cluster interacting with 3.9 meV, were observed. Using the exact diagonalization methods, the intercluster coupling was estimated from the excitation peak width to be about 20% of the intracluster interaction, which is consistent with the previously reported value. Finally, our exchange path model explains the anisotropic exchange interactions in the distorted honeycomb plane.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Compensating for Sintering Distortion in Additively Manufactured Shaped Charge Liners using Physics-Informed Machine Learning

Copper is a challenging material to process using laser-based additive manufacturing due to its high reflectivity and high thermal conductivity. Sintering-based processes can produce solid copper parts without the processing challenges and defects associated with laser melting; however, sintering can also cause distortion in copper parts, especially those with thin walls. In this study, we use physics-informed Gaussian process regression to predict and compensate for sintering distortion in thin-walled copper parts produced using a Markforged Metal X bound powder extrusion (BPE) additive manufacturing system. Through experimental characterization and computational simulation of copper’s viscoelastic sintering behavior, we can predict sintering deformation. We can then manufacture, simulate, and test parts with various compensation scaling factors to inform Gaussian process regression and predict a compensated as-printed (pre-sintered) part geometry that produces the desired final (post-sintered) part.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Neutron Positioning and Geometric Distortion Correction on the SNS SiPM Anger Camera

Neutron Anger cameras are scintillator-based thermal neutron detectors that utilize pixelated photosensors to read out visible light signals and position neutrons accurately They are versatile detectors that can cover large areas for diffraction instruments and offer high efficiency and sub-millimeter spatial resolution. Photomultiplier Tube (PMT) based cameras are installed on three instruments at Spallation Neutron Source (SNS). The next generation camera uses Silicon Photomultipliers (SiPMs) instead of PMTs, which allows for a more compact design and higher spatial resolution. In this report, the Gaussian least-squares position fitting method is described in detail, as well as the method used to correct for geometric distortions across the face of the camera. Results from neutron camera tests before and after the distortion correction are shown and the spatial resolution is quantified.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Distortion of a Relativistic Jet Echoing a Magnetic Flux Eruption

Magnetized accretion onto spinning black holes (BHs) can accumulate a large magnetic flux across the event horizon and launch a pair of relativistic jets via the Blandford–Znajek mechanism. In the magnetically saturated (arrested) state, excess magnetic flux is ejected from the BH in episodic magnetic flux eruptions, which result in a significant yet temporary reduction of jet power. We analyze results of a high-resolution 3D general-relativistic magnetohydrodynamic numerical simulation of geometrically thick magnetically saturated accretion onto a high-spin Kerr BH for a single cycle of magnetic flux eruption and accumulation. We show that following an eruption, a weakened jet develops a strong helical distortion with a distinct structure of magnetic fields—the poloidal field along the jet core is unaffected by the eruption; while toroidal field lines, ejected from the BH during the eruption and later readvected onto it, form poloidal “bypasses” along the inner jet sheath. Such a distortion may appear in sources fed by geometrically thick accretion flows as an asymmetric superluminal knot, strongly interacting with the jet sheath along an oblique working surface. The jet section repowered by magnetic flux reaccumulated on the BH is tilted by a few degrees, implying significant variations in radiation boost towards observers of BL Lac blazars. The intrinsic structure of the jet spine is consistent with axisymmetric semi-analytical models.

79 ASTRONOMY AND ASTROPHYSICS↗