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At least 127 records · Page 7

Spin-orbital correlations from complex orbital order in MgV 2⁢ O 4

MgV 2 ⁢O 4 is a spinel based on magnetic V 3+ ions, which host both spin (𝑆 = 1) and orbital (𝑙 eff = 1) moments. Owing to the underlying pyrochlore coordination of the magnetic sites, the spins in MgV 2 ⁢O 4 only antiferromagnetically order once the frustrating interactions imposed by the 𝐹⁡𝑑⁢$\overline{3}$⁢𝑚 lattice are broken through an orbitally-driven structural distortion at T 𝑆 ≃ ⁢60 K. Consequently, a Néel transition occurs at T 𝑁 ≃ ⁢40 K. Low-temperature spatial ordering of the electronic orbitals is fundamental to both the structural and magnetic properties; however, considerable discussion on whether it can be described by complex or real orbital ordering is ambiguous. We apply neutron spectroscopy to resolve the nature of the orbital ground state and characterize hysteretic spin-orbital correlations using x-ray and neutron diffraction. Neutron spectroscopy finds multiple excitation bands and we parametrize these in terms of a multilevel (or excitonic) theory based on the orbitally degenerate ground state. Meaningful for the orbital ground state, we report an “optical-like” mode at high energies that we attribute to a crystal-field-like excitation from the spin-orbital 𝑗 eff = 2 ground-state manifold to an excited 𝑗 eff =1 energy level. We parametrize the magnetic excitations in terms of a Hamiltonian with spin-orbit coupling and local crystalline electric field distortions resulting from deviations from perfect octahedra surrounding the V 3+ ions. We suggest that this provides compelling evidence for complex orbital order in MgV 2⁢ O 4 . We then apply the consequences of this model to understand hysteretic effects in the magnetic diffuse scattering where we propose that MgV 2⁢ O 4 displays a high-temperature orbital memory of the low-temperature spin order.

Frustrated magnetism↗

VpROM: a novel variational autoencoder-boosted reduced order model for the treatment of parametric dependencies in nonlinear systems

Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction, such as Proper Orthogonal Decomposition. The limitation of the linear nature of such operators is typically tackled via a library of local reduction subspaces, which requires the assembly of numerous local ROMs to address parametric dependencies. Our work attempts to define a more generalisable mapping between parametric inputs and reduced bases for the purpose of generative modeling. We propose the use of Variational Autoencoders (VAEs) in place of the typically utilised clustering or interpolation operations, for inferring the fundamental vectors, termed as modes, which approximate the manifold of the model response for any and each parametric input state. The derived ROM still relies on projection bases, built on the basis of full-order model simulations, thus retaining the imprinted physical connotation. However, it additionally exploits a matrix of coefficients that relates each local sample response and dynamics to the global phenomena across the parametric input domain. The VAE scheme is utilised for approximating these coefficients for any input state. This coupling leads to a high-precision low-order representation, which is particularly suited for problems where model dependencies or excitation traits cause the dynamic behavior to span multiple response regimes. Moreover, the probabilistic treatment of the VAE representation allows for uncertainty quantification on the reduction bases, which may then be propagated to the ROM response. The performance of the proposed approach is validated on an open-source simulation benchmark featuring hysteresis and multi-parametric dependencies, and on a large-scale wind turbine tower characterised by nonlinear material behavior and model uncertainty.

Conditional VAEs↗

Exact-two-component block-localized wave function: A simple scheme for the automatic computation of relativistic ΔSCF

Block-localized wave function is a useful method for optimizing constrained determinants. In this article, we extend the generalized block-localized wave function technique to relativistic two-component framework. Optimization of excited state determinants for two-component wave functions presents a unique challenge because the excited state manifold is often quite dense with degenerate states. Furthermore, we test the degree to which certain symmetries result naturally from the ΔSCF optimization such as time reversal symmetry and symmetry with respect to the total angular momentum operator on a series of atomic systems. Variational optimizations may often break symmetry in order to lower the overall energy, just as unrestricted Hartree-Fock breaks spin symmetry. Overall, we demonstrate that time reversal symmetry is roughly maintained when using Hartree-Fock, but less so when using Kohn-Sham density functional theory. Additionally, maintaining total angular momentum symmetry appears to be system dependent and not guaranteed. Finally, we were able to trace the breaking of total angular momentum symmetry to the relaxation of core electrons.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Studies of the Virgo Cluster. I - Photometry of 109 galaxies near the cluster center to serve as standards

Attention is given to the technical aspects of photometric measurements of 109 galaxies near the center of the Virgo Cluster, noting various types of radii and surface brightness for about 50 E and dE galaxies in the sample that range in absolute magnitude from -20 to -12. These data are combined with data from the literature for giant E and dwarf E galaxies in the Local Group to study the systematic properties of E galaxies over a range of one million luminosities. The radial intensity profiles derived are fitted to the manifold of King (1978) models to derive model-dependent central surface brightness, core radii, and cutoff radii.

Sandage, A.↗

Efficient manifolds tracing for planar maps

Here, we present an exact calculation method and an approximation technique for tracing the invariant manifolds of unstable periodic orbits of planar maps. The exact approach relies on an adaptive refinement procedure that prevents redundant calculations occurring in other approaches, and the approximated method relies on a novel interpolation approach based on normal displacement functions. The resulting approximated manifold is precise when compared to the exact one, and its relative computational cost falls like the inverse of the manifold length. To present the tracing method, we obtain the invariant manifolds of the Chirikov-Taylor map, and as an application we illustrate the transition from homoclinic to heteroclinic chaos in the Duffing oscillator that leads from localized chaos to global chaotic motion.

74 ATOMIC AND MOLECULAR PHYSICS↗

Canonical Transformation of Potential Model Hamiltonian Mechanics to Geometrical Form I

Using the methods of symplectic geometry, we establish the existence of a canonical transformation from potential model Hamiltonians of standard form in a Euclidean space to an equivalent geometrical form on a manifold, where the corresponding motions are along geodesic curves. The advantage of this representation is that it admits the computation of geodesic deviation as a test for local stability, shown in recent previous studies to be a very effective criterion for the stability of the orbits generated by the potential model Hamiltonian. We describe here an algorithm for finding the generating function for the canonical transformation and describe some of the properties of this mapping under local diffeomorphisms. We give a convergence proof for this algorithm for the one-dimensional case, and provide a precise geometric formulation of geodesic deviation which relates the stability of the motion in the geometric form to that of the Hamiltonian standard form. We apply our methods to a simple one-dimensional harmonic oscillator and conclude with a discussion of the relation of bounded domains in the two representations for which Morse theory would be applicable.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Airflow Model Testing to Determine the Distribution of Hot Gas Flow and O/F Ratio Across the Space Shuttle Main Engine Main Injector Assembly

Engine 0209, the certification engine for the new Phase 2+ Hot Gas Manifold (HGM), showed severe deterioration of the Main Combustion Chamber (MCC) liner during hot fire tests. One theory on the cause of the damage held that uneven local distribution of the fuel rich hot gas flow through the main injector assembly was producing regions of high oxidizer/fuel (O/F) ratio near the wall of the MCC liner. Airflow testing was proposed to measure the local hot gas flow rates through individual injector elements. The airflow tests were conducted using full scale, geometrically correct models of both the current Phase 2 and the new Phase 2+ HGMs. Different main injector flow shield configurations were tested for each HGM to ascertain their effect on the pressure levels and distribution of hot gas flow. Instrumentation located on the primary faceplate of the main injector measured hot gas flow through selected injector elements. These data were combined with information from the current space shuttle main engine (SSME) power balances to produce maps of pressure, hot gas flow rate, and O/F ratio near the main injector primary plate. The O/F distributions were compared for the different injector and HGM configurations.

Mahorter, L.↗

TiAl Scramjet Inlet Flap Subelement Designed and Fabricated

Next-generation launch vehicles are being designed with turbine-based combined cycle (TBCC) propulsion systems having very aggressive thrust/weight targets and long lives. Achievement of these goals requires advanced materials in a wide spectrum of components. TiAl has been identified as a potential backstructure material for maintainable composite panel heat exchangers (HEX) in the inlet, combustor, and nozzle section of a TBCC propulsion system. Weight reduction is the primary objective of this technology. Design tradeoff studies have assessed that a TiAl structure, utilizing a high-strength, hightemperature TiAl alloy called Gamma MET PX,1 reduce weight by 41 to 48 percent in comparison to the baseline Inconel 718 configuration for the TBCC propulsion system inlet, combustor, and nozzle. A collaborative effort between the NASA Glenn Research Center, Pratt & Whitney, Engineering Evaluation & Design, PLANSEE AG (Austria), and the Austrian Space Agency was undertaken to design, manufacture, and validate a Gamma-MET PX TiAl structure for scramjet applications. The TiAl inlet flap was designed with segmented flaps to improve manufacturability, to better control thermal distortion and thermal stresses, and to allow for maintainable HEX segments. The design philosophy was to avoid excessively complicated shapes, to minimize the number of stress concentrations, to keep the part sizes reasonable to match processing capabilities, and to avoid risky processes such as welding. The conceptual design used a standard HEX approach with a double-pass coolant concept for centrally located manifolds. The flowpath side was actively cooled, and an insulation package was placed on the external side to save weight. The inlet flap was analyzed structurally, and local high-stress regions were addressed with local reinforcements.

Draper, Susan L.↗

Aspects of AdS 2 classification in M-theory: solutions with mesonic and baryonic charges

We construct necessary and sufficient geometric conditions for a class of AdS 2 solutions of M-theory with, at least, minimal supersymmetry to exist. We generalize previous results in the literature for N = (2,0) supersymmetry in AdS 2 to N = (1,0). When the solution can be locally described as AdS 2 × Σ g × SE 7 with Σ g a Riemann surface of genus g and SE 7 a seven-dimensional Sasaki-Einstein manifold, we clarify and unify various solutions present in the literature. In the case of SE 7 = Q 1,1,1 we find a new solution with baryonic and mesonic charges turned on simultaneously.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Automated and efficient local adaptive regression for principal component-based reduced-order modeling of turbulent reacting flows

Principal Component Analysis can be used to reduce the cost of Computational Fluid Dynamics simulations of turbulent reacting flows by reducing the dimensionality of the transported variables through projection of the thermochemical state onto a lower-dimensional manifold. However, because of the nonlinearity of the principal component source terms, nonlinear regression techniques must be utilized for the source terms in terms of the principal components. Unfortunately, widely available and utilized nonlinear regression techniques can have prohibitive computational requirements and/or accuracy that is highly dependent on user experience in ad hoc tuning of model architecture and hyperparameters. Here, in this work, a new nonlinear regression approach is proposed that is both computationally efficient and automated so does not require any user input. The approach is evaluated through a priori prediction of principal component source terms using data from a Direct Numerical Simulation of a turbulent nonpremixed n-heptane/air jet flame. In particular, the proposed framework consists of local regressions whose complexity is adapted according to the local nonlinearity of the data: local linear regression when accurate enough and local Artificial Neural Networks when nonlinear regression is required. The number of local clusters for local regression is determined automatically using the Davies-Bouldin index. In addition, Bayesian optimization is utilized for model training (i.e., to select the best architectures and hyperparameters of the nonlinear regressions in an unsupervised fashion), eliminating ad hoc hand-tuning and/or expensive grid searches. Overall, compared to a single, global neural network, the new local adaptive regression approach is shown to have comparable accuracy but 69% less training time due to the utilization of local linear regression and faster training of local neural networks.

42 ENGINEERING↗

Templates for Risk Informed Assurance with Curvature Embeddings (TRACE)

We investigate recovery of geometric structure from networks embedded in manifolds with spatially varying curvature, extending the constant-curvature framework of Lubold et al. (2023). Our work supports cascade risk assessment in critical infrastructure through the Templates for Risk-informed Assurance with Curvature Embeddings (TRACE) framework. Simulations on a bi-modal Gaussian surface show that constant-curvature methods yield weighted averages shaped by clique patterns, while hierarchical clustering identifies distinct regimes. Localized estimation, however, reveals boundary contamination in transitional regions. To address heterogeneity, we develop distance metrics for graphs with edge and node features, proving their metric validity, and validate them via deterministic graph generation from canonical tilings. We further propose a diffusion-based anomaly detection approach that treats networks as glued manifolds, using curvature discontinuities to detect structural anomalies. Employing the carré-du-champ operator and scalar curvature, we achieve robust anomaly discrimination, demonstrated on the Singapore Water Treatment (SWaT) dataset with joint network-traffic and sensor features. Integration with TRACE reveals how curvature shapes cascade dynamics: positive curvature impedes, while negative curvature accelerates propagation. This geometric perspective provides interpretable risk metrics and visualization tools for critical infrastructure managers. While full validation remains ongoing, our contributions establish a rigorous foundation for geometric analysis of network resilience and cascade vulnerability.

97 MATHEMATICS AND COMPUTING↗

Advances in Hyperspectral Image Classification Methods for Vegetation and Agricultural Cropland Studies

Hyperspectral data are becoming more widely available via sensors on airborne and unmanned aerial vehicle (UAV) platforms, as well as proximal platforms. While space-based hyperspectral data continue to be limited in availability, multiple spaceborne Earth-observing missions on traditional platforms are scheduled for launch, and companies are experimenting with small satellites for constellations to observe the Earth, as well as for planetary missions. Land cover mapping via classification is one of the most important applications of hyperspectral remote sensing and will increase in significance as time series of imagery are more readily available. However, while the narrow bands of hyperspectral data provide new opportunities for chemistry-based modeling and mapping, challenges remain. Hyperspectral data are high dimensional, and many bands are highly correlated or irrelevant for a given classification problem. For supervised classification methods, the quantity of training data is typically limited relative to the dimension of the input space. The resulting Hughes phenomenon, often referred to as the curse of dimensionality, increases potential for unstable parameter estimates, overfitting, and poor generalization of classifiers. This is particularly problematic for parametric approaches such as Gaussian maximum likelihood–based classifiers that have been the backbone of pixel-based multispectral classification methods. This issue has motivated investigation of alternatives, including regularization of the class covariance matrices, ensembles of weak classifiers, development of feature selection and extraction methods, adoption of nonparametric classifiers, and exploration of methods to exploit unlabeled samples via semi-supervised and active learning. Data sets are also quite large, motivating computationally efficient algorithms and implementations. This chapter provides an overview of the recent advances in classification methods for mapping vegetation using hyperspectral data. Three data sets that are used in the hyperspectral classification literature (e.g., Botswana Hyperion satellite data and AVIRIS airborne data over both Kennedy Space Center and Indian Pines) are described in Section 3.2 and used to illustrate methods described in the chapter. An additional high-resolution hyperspectral data set acquired by a SpecTIR sensor on an airborne platform over the Indian Pines area is included to exemplify the use of new deep learning approaches, and a multiplatform example of airborne hyperspectral data is provided to demonstrate transfer learning in hyperspectral image classification. Classical approaches for supervised and unsupervised feature selection and extraction are reviewed in Section 3.3. In particular, nonlinearities exhibited in hyperspectral imagery have motivated development of nonlinear feature extraction methods in manifold learning, which are outlined in Section 3.3.1.4. Spatial context is also important in classification of both natural vegetation with complex textural patterns and large agricultural fields with significant local variability within fields. Approaches to exploit spatial features at both the pixel level (e.g., co-occurrence–based texture and extended morphological attribute profiles [EMAPs]) and integration of segmentation approaches (e.g., HSeg) are discussed in this context in Section 3.3.2. Recently, classification methods that leverage nonparametric methods originating in the machine learning community have grown in popularity. An overview of both widely used and newly emerging approaches, including support vector machines (SVMs), Gaussian mixture models, and deep learning based on convolutional neural networks is provided in Section 3.4. Strategies to exploit unlabeled samples, including active learning and metric learning, which combine feature extraction and augmentation of the pool of training samples in an active learning framework, are outlined in Section 3.5. Integration of image segmentation with classification to accommodate spatial coherence typically observed in vegetation is also explored, including as an integrated active learning system. Exploitation of multisensor strategies for augmenting the pool of training samples is investigated via a transfer learning framework in Section 3.5.1.2. Finally, we look to the future, considering opportunities soon to be provided by new paradigms, as hyperspectral sensing is becoming common at multiple scales from ground-based and airborne autonomous vehicles to manned aircraft and space-based platforms.

Pasolli, Edoardo↗

Flow instabilities in non-uniformly heated helium jet arrays used for divertor PFCs

In this study, due to a lack of prototypical experimental data, little is known about the off-normal behavior of recently proposed divertor jet cooling concepts. This article describes a computational fluid dynamics (CFD) study on two jet array designs to investigate their susceptibility to parallel flow instabilities induced by non-uniform heating and large increases in the helium outlet temperature. The study compared a single 25-jet helium-cooled modular divertor (HEMJ) thimble and a micro-jet array with 116 jets. Both have pure tungsten armor and a total mass flow rate of 10 g/s at a 600 °C inlet temperature. We investigated flow perturbations caused by a 30 MW/m 2 off-normal heat flux applied over a 25 mm 2 area in addition to the nominal 5 MW/m 2 applied over a 75 mm 2 portion of the face. The micro-jet array exhibited lower temperatures and a more uniform surface temperature distribution than the HEMJ thimble. We also investigated the response of a manifolded nine-finger HEMJ assembly using the nominal heat flux and a 274 mm 2 heated area. For the 30 MW/m2 case, the micro-jet array absorbed 750 W in the helium with a maximum armor surface temperature of 1280 °C and a fluid/solid interface temperature of 801 °C. The HEMJ absorbed 750 W with a maximum armor surface temperature of 1411 °C and a fluid/solid interface temperature of 844 °C. For comparison, both the single HEMJ finger and the micro-jet array used 5-mm-thick tungsten armor. The ratio of maximum to average temperature and variations in the local heat transfer coefficient were lower for the micro-jet array compared to the HEMJ device. Although high heat flux testing is required to validate the results obtained in these simulations, the results provide important guidance in jet design and manifolding to increase heat removal while providing more even temperature distribution and minimizing non-uniformity in the gas flow and thermal stresses at the armor joint.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A comment on the construction of the maximal globally hyperbolic Cauchy development

Under mild assumptions, we remove all traces of the axiom of choice from the construction of the maximal globally hyperbolic Cauchy development in general relativity. The construction relies on the notion of direct union manifolds, which we review. The construction given is very general: any physical theory with a suitable geometric representation (in particular all classical fields), and such that a strong notion of “local existence and uniqueness” of solutions for the corresponding initial value problem is available, is amenable to the same treatment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Probing polariton dynamics in trapped ions with phase-coherent two-dimensional spectroscopy

We devise a phase-coherent three-pulse protocol to probe the polariton dynamics in a trapped-ion quantum simulation. In contrast to conventional nonlinear signals, the presented scheme does not change the number of excitations in the system, allowing for the investigation of the dynamics within an N-excitation manifold. In the particular case of a filling factor one (N excitations in an N-ion chain), the proposed interaction induces coherent transitions between a delocalized phonon superfluid and a localized atomic insulator phase. Numerical simulations of a two-ion chain demonstrate that the resulting two-dimensional spectra allow for the unambiguous identification of the distinct phases, and the two-dimensional line shapes efficiently characterize the relevant decoherence mechanism.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Discrete quantum geometry and intrinsic spin Hall effect

We show that the quantum geometry of the Fermi surface can be numerically described by a three-dimensional discrete quantum manifold. This approach not only avoids singularities in the Fermi sea, but it also enables the precise computation of the intrinsic Hall conductivity resolved in spin, as well as any other local properties of the Fermi surface. The method assures numerical accuracy when the Fermi level is arbitrarily close to singularities, and it remains robust when Kramers degeneracy is protected by symmetry. Furthermore, the approach is demonstrated by calculating the anomalous Hall and spin Hall conductivities of a two-band lattice model of a Weyl semimetal and a full-band ab initio model of zinc-blende GaAs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Exceptional Radiation Absorption in a Pentagon-Based Si Allotrope

Excellent photovoltaic performance is predicted in a pentagonal covalent network of Si in a hollow structure exhibiting both thermal and dynamical stability. Consisting of a combination of sp 2 and sp 3 hybridized Si atomic orbitals, the GW0 computed band structure shows an indirect band gap near the zone edge and also a manifold of directly absorbing transitions at frequencies in the window of visible light, in distinction with conventional Si. Hydrogenation of a single sp 2 site is predicted to lead to a robust local magnetic moment. In this study, we find a low formation energy at low pressure that is compatible with other experimentally known phases, suggesting that a stable phase might be obtained.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Vibronic coupling in asymmetric bichromophores: Experimental investigation of diphenylmethane-d{sub 5}

Vibrationally and rotationally resolved electronic spectra of diphenylmethane-d{sub 5} (DPM-d{sub 5}) are reported in the isolated-molecule environment of a supersonic expansion. While small, the asymmetry induced by deuteration of one of the aromatic rings is sufficient to cause several important effects that change the principle mechanism of vibronic coupling between the close-lying S{sub 1} and S{sub 2} states, and spectroscopic signatures such coupling produces. The splitting between S{sub 1} and S{sub 2} origins is 186 cm{sup −1}, about 50% greater than its value in DPM-d{sub 0} (123 cm{sup −1}), and an amount sufficient to bring the S{sub 2} zero-point level into near-resonance with the v = 1 level in the S{sub 1} state of a low-frequency phenyl flapping mode, ν{sub R} = 191 cm{sup −1}. Dispersed fluorescence spectra bear clear evidence that Δv(R) = 1 Herzberg-Teller coupling dominates the near-resonant internal mixing between the S{sub 1} and S{sub 2} manifolds. The fluorescence into each pair of Franck-Condon active ring modes shows an asymmetry that suggests incorrectly that the S{sub 1} and S{sub 2} states may be electronically localized. From rotationally resolved studies, the S{sub 0} and S{sub 1} states have been well-fit to asymmetric rotor Hamiltonians while the S{sub 2} state is perturbed and not fit. The transition dipole moment (TDM) orientation of the S{sub 1} state is nearly perpendicular to the C{sub 2} symmetry axes with 66(2)%:3(1)%:34(2)% a:b:c hybrid-type character while that of the S{sub 2} origin contains 50(10)% a:c-type (S{sub 1}) and 50(10)% b-type (S{sub 2}) character. A model is put forward that explains qualitatively the TDM compositions and dispersed emission patterns without the need to invoke electronic localization. The experimental data discussed here serve as a foundation for a multi-mode vibronic coupling model capable of being applied to asymmetric bichromophores, as presented in the work of B. Nebgen and L. V. Slipchenko [“Vibronic coupling in asymmetric bichromophores: Theory and application to diphenylmethane-d{sub 5},” J. Chem. Phys. (submitted)].

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗