HSR Lattice Model in the Hadron Beam Direction Featuring High-Order Dipole Field Harmonics
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73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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Identifying Differential Equations in Fourier Domain (FourierIdent)
We investigate identifying differential equations in the frequency domain. Fourier analysis is an important tool in theoretical analysis and numerical solvers of differential equations, yet there is limited work in exploring this connection in the identification of differential equations. This paper aims to identify the underlying differential equation in the frequency domain, from a given single realization of the differential equation perturbed by noise. Such setting imposes difficulties which are different from other identification methods where computation is carried out in the physical domain. We propose several ways to mitigate the challenges arising from noise in data and large differences in the magnitudes of frequency responses. The main takeaways are that identifying differential equations solely in the frequency domain is challenging, the method we propose is based on a form of domain partitions in the frequency domain, and this method shows benefits for complex data even with high level of noise. We introduce a Fourier feature denoising, and define the meaningful data region and the core regions of features to reduce the effect of noise in the frequency domain and to enhance the accuracy in coefficient identification. The proposed method is tested on various differential equations with linear, nonlinear, and high-order derivative feature terms, and shows advantages on complex data with many frequency modes, even under high level of noise.
97 MATHEMATICS AND COMPUTING↗
Bayesian inference of anisotropic 2D small-angle scattering from sparse measurement
Here, we present a Bayesian inference framework for reconstructing anisotropic two-dimensional small-angle scattering (2D SAS) patterns from sparse, noisy, or partially missing data. The method combines a symmetry-aware angular basis with radial Gaussian process priors to enable accurate, training-free interpolation and denoising. Computational benchmarks demonstrate reliable recovery of both isotropic and high-order anisotropic features under severe data reduction. Experimental validations on stretched polymers, sheared wormlike micelles, and carbon fibers show improved fidelity and resolution compared to raw measurements, achieving comparable accuracy with up to 50-fold fewer detected neutrons. This approach enables quantitative structural analysis under low-flux, time-limited, or single-shot conditions, extending the applicability of 2D SAS techniques to compact neutron sources and mechanically driven soft matter systems undergoing transient structural changes.
Tung, Chi-Huan [Oak Ridge National Laboratory (ORN↗
A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow
High order essentially non-oscillatory (ENO) schemes, originally designed for compressible flow and in general for hyperbolic conservation laws, are applied to incompressible Euler and Navier-Stokes equations with periodic boundary conditions. The projection to divergence-free velocity fields is achieved by fourth order central differences through Fast Fourier Transforms (FFT) and a mild high-order filtering. The objective of this work is to assess the resolution of ENO schemes for large scale features of the flow when a coarse grid is used and small scale features of the flow, such as shears and roll-ups, are not fully resolved. It is found that high-order ENO schemes remain stable under such situations and quantities related to large-scale features, such as the total circulation around the roll-up region, are adequately resolved.
Weinan, E.↗
High-Order Mesh r-Adaptivity with Tangential Relaxation and Guaranteed Mesh Validity
High-order meshes are crucial for achieving optimal convergence rates in curvilinear domains, preserving symmetry, and aligning with key flow features in moving mesh simulations [1], but their quality is challenging to control. In prior work, we have developed techniques based on Target-Matrix Optimization Paradigm (TMOP) to adapt a given high-order mesh to the geometry and solution of the partial differential equation (PDE) [2, 3]. Here, we extend this framework to address two key gaps in the literature for highorder mesh 𝑟-adaptivity. First, we introduce tangential relaxation on curved surfaces using solely the discrete mesh representation, eliminating the need for access to underlying geometry (e.g., CAD model). Second, we ensure a continuously positive Jacobian determinant throughout the domain. This determinant positivity is essential for using the high-order mesh resulting from 𝑟-adaptivity with arbitrary quadrature schemes in simulations. The proposed approach is demonstrated to be robust using a variety of numerical experiments.
Mathematics and Computing↗
Two-phase ultraviolet spectrophotometry of the pulsating white dwarf ZZ Piscium
Spectra of the pulsating white dwarf ZZ Psc (= G29-38) were obtained using the International Ultraviolet Explorer. By using a multiple-exposure technique in conjunction with simultaneous ground-based exposure-metering photometry, it was possible to obtain mean on-pulse and off-pulse spectra in the 1950-1310 A wavelength range. The ratio of the time-averaged on-pulse to off-pulse spectra is best fitted by a temperature variation that is in phase with the optical light variation. This result is consistent with the hypothesis that the observed variation is due to a high-order nonradial pulsation. Conventional ultraviolet spectra of ZZ Psc showed broad absorption features at 1390 and 1600 A. These features are also found in the spectra of the cool DA-type white dwarfs G226-29 and G67-23, and appear to increase in strength with decreasing temperature. A possible explanation for the 1600 A feature is absorption by the satellite band of resonance-broadened hydrogen Ly-alpha. Such absorption would also help explain a discrepancy between the observed pulsation amplitude shortward of 1650 A and the predicted amplitudes based on model atmospheres.
Bond, H. E.↗
Lacunarity and intermittency in fluid turbulence
It is shown that oscillations in the high-order moments of turbulent velocity fields are inherent to the fractal character of intermittent turbulence and are a feature of the lacunarity of fractal sets. Oscillations in simple Cantor sets are described, and a single parameter to measure lacunarity is identified. The connection between oscillations in fractals and in the turbulent velocity correlations is discussed using the phenomenological beta model of intermittent turbulence (Frisch et al., 1978).
Smith, L. A.↗
Basalts of Mars: Constraints on Volatile Evolution
The mineralogy of relatively unweathered rocks on Mars place important constraints on models of planetary oxidation state, volcanism and associated outgassing, accretion and associated volatile inventory, and geochemical changes over time. Reflectance spectra (300 to 2500 nm) provide direct mineralogic information about the surface materials. Spectra measured using Earth-based telescopes were analyzed by a multiple high-order derivative spectroscopy technique. Nine areas, measured during the 1978 opposition, were analyzed by the technique. Each contained suites of well-defined absorption bands. These bands can be interpreted in terms of constituent mineralogy by the technique of Adams. Among the features extracted from the spectra were bands attributed to iron oxides. Other bands can be attributed to silicates within chemically unweathered rocks/fines. Absorption features suggest the presence of Mg-olivine and plagioclase feldspar.
Huguenin, R. L.↗
Multiscale Modeling Framework Using Element‐Based Galerkin Methods for Moist Atmospheric Limited‐Area Simulations
This paper presents a multiscale modeling framework (MMF) to model moist atmospheric limited-area weather. The MMF resolves large-scale convection using a coarse grid while simultaneously resolving local features through numerous fine local grids and coupling them seamlessly. Both large- and small-scale processes are modeled using the compressible Navier-Stokes equations within the Nonhydrostatic Unified Model of the Atmosphere (NUMA), and are discretized using a continuous element-based Galerkin method (spectral elements) with high-order basis functions. Consequently, the large-scale and small-scale models share the same dynamical core but have the flexibility to be adjusted individually. The proposed MMF method is tested in 2D and 3D idealized limited-area weather problems involving storm clouds produced by squall line and supercell simulations. Numerical results from the MMF showed enhanced representation of cloud processes compared to the coarse model.
Kang, Soonpil [Naval Postgraduate School, Monterey↗
A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation
Here, this paper formulates a new particle-in-cell method for the Vlasov–Maxwell system. Under the Lorenz gauge condition, Maxwell’s equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The use of potentials for the fields motivates the adoption of a Hamiltonian formulation for particles that employs the generalized (conjugate) momentum. A notable advantage offered by the Hamiltonian formulation is the elimination of time derivatives in the Lorenz gauge formulation that are required by the standard Newton–Lorentz treatment of the particles. This allows the fields to retain the full time-accuracy guaranteed by the field solver. The resulting updates for particles require only knowledge of the fields and their spatial derivatives. An analytical method for constructing these spatial derivatives is presented that exploits the underlying integral solution used in the field solver for the wave equations. Moreover, these derivatives are demonstrated to converge at the same rate as the fields in both time and space. The Method of Lines Transpose field solver we consider in this work is globally first-order accurate in time and high-order accurate in space (e.g., fourth- and fifth-order) and belongs to a larger class of methods which are unconditionally stable, can address geometry, and leverage $\mathcal {O}(N)$ fast summation methods for efficiency. We demonstrate the method on several well-established benchmark problems on bounded domains, including a plasma sheath as well as a relativistic particle beam. The efficacy of the proposed formulation is established by comparing with a second-order accurate finite-difference time-domain method that employs a leapfrog time advance for particles and a charge conserving map suitable for bounded domains. The new method shows mesh-independent numerical heating properties even in cases where the plasma Debye length is smaller than the grid spacing. This is an important feature of the new method for problems defined on bounded domains, because it permits the use of coarser grids in space in the representation of the fields. Such a capability has significant implications for the simulation of plasmas in bounded domains with complex geometry, where the ratio between the largest and smallest cells can vary significantly. The use of high-order spatial approximations in the new method also means that fewer grid points are required in order to achieve a fixed accuracy. Our results also suggest that the new method can be used with fewer simulation particles per cell compared to the benchmark explicit method, which permits further computational savings.
97 MATHEMATICS AND COMPUTING↗
Real-Time Multiprocessor Programming Language (RTMPL) user's manual
A real-time multiprocessor programming language (RTMPL) has been developed to provide for high-order programming of real-time simulations on systems of distributed computers. RTMPL is a structured, engineering-oriented language. The RTMPL utility supports a variety of multiprocessor configurations and types by generating assembly language programs according to user-specified targeting information. Many programming functions are assumed by the utility (e.g., data transfer and scaling) to reduce the programming chore. This manual describes RTMPL from a user's viewpoint. Source generation, applications, utility operation, and utility output are detailed. An example simulation is generated to illustrate many RTMPL features.
Arpasi, D. J.↗
General trends of superconducting pairing and magnetic correlations in the Ruddlesden-Popper nickelate 𝑚-layered superconductors La 𝑚+1 Ni 𝑚 O 3𝑚+1
Here, we report a comprehensive theoretical analysis of the Ruddlesden-Popper layered nickelates La 𝑚+1 Ni 𝑚 O 3𝑚+1 (𝑚 = 1 to 6) under pressure. These materials have recently received significant attention due to the discovery of superconductivity in some nickelates under pressure. Our results suggest that, while these Ruddlesden-Popper layered nickelates display many similarities, they also show noticeable differences. One of the common features of La 𝑚+1 Ni 𝑚 O 3𝑚+1 is that the electronic states near the Fermi level are mainly contributed by Ni 3𝑑 orbitals, slightly hybridized with O 2𝑝 orbitals. The Ni 𝑑 3𝑧 2 −𝑟 2 orbitals display bonding-antibonding, or bonding-antibonding-nonbonding, characteristic splittings, depending on the even or odd number of stacking layers 𝑚. In addition, the ratio of the in-plane interorbital hopping between 𝑑 3𝑧 2 −𝑟 2 and 𝑑 𝑥 2 −𝑦 2 orbitals and in-plane intraorbital hopping between 𝑑 𝑥 2 −𝑦 2 orbitals was found to be large in La 𝑚+1 Ni 𝑚 O 3𝑚+1 (𝑚 = 1 to 6), and this ratio increases from 𝑚 = 1 to 𝑚 = 6, suggesting that the in-plane hybridization will increase as the layer number 𝑚 increases. In contrast to the dominant 𝑠 ± -wave state driven by spin fluctuations in the bilayer La 3 Ni 2 O 7 and trilayer La 4 Ni 3 O 10 , two nearly degenerate 𝑑 𝑥 2 −𝑦 2 -wave and 𝑠 ± -wave leading states were obtained in the four-layer stacking La 5 Ni 4 O 13 and five-layer stacking La 6 Ni 5 O 16 . The leading 𝑠 ± -wave state was recovered in the six-layer material La 7 Ni 6 O 19 with slightly higher calculated pairing strength 𝜆 than that of the 𝑑 𝑥 2 −𝑦 2 -wave state. All this evidence suggests that both 𝑠 ± -wave and 𝑑 𝑥 2 −𝑦 2 -wave channels are strongly competing in the high-order niceklates based on our random-phase approximation calculations. In general, at the level of the random-phase approximation treatment, the superconducting transition temperature 𝑇 𝑐 decreases in stoichiometric bulk systems from the bilayer La 3 Ni 2 O 7 to the six-layer La 7 Ni 6 O 19 , despite the 𝑚-dependent dominant pairing. Both in-plane and out-of-plane magnetic correlations are found to be quite complex. Within the in-plane direction, we obtained the peak of the magnetic susceptibility at 𝐪 = (0.6𝜋, 0.6𝜋) for La 5 Ni 4 O 13 (𝑚 = 4) and La 7 Ni 6 O 19 (𝑚 = 6) and at 𝐪 = (0.7𝜋, 0.7𝜋) for La 6 Ni 5 O 16 (𝑚 = 5). Along the out-of-plane direction, four layers are coupled as ↓−↑−↑−↓ in La 5 Ni 4 O 13 , five layers are coupled as ↑−↑−↓−↑−↑ in La 6 Ni 5 O 16 , and six layers are coupled as ↑−↓−↓−↑−↑−↓ in La 7 Ni 6 O 19 .
Zhang, Yang [Univ. of Tennessee, Knoxville, TN (Un↗
Catalytic disproportionation on carbon superstructures enables long-life, high-loading Li–S batteries
Electrocatalysis has been widely explored as an effective strategy to accelerate polysulfide (PS) conversion and suppress the shuttle effect in lithium–sulfur (Li–S) batteries. However, the underlying mechanisms remain elusive, and electrocatalytic reactions are inactive during cell resting. In this work, we reveal and quantitatively analyze a previously unrecognized sulfur reduction route (SRR) driven by catalytic disproportionation at the carbon cathode surface—fundamentally distinct from conventional electrocatalysis. Unlike conventional stepwise pathways, this SRR enables high-order polysulfides (Sₓ²⁻, x = 5–8) to directly convert into S₈ and Li₂S₂, bypassing low-order intermediates. This sulfur-reduction shortcut is systematically elucidated through high-performance liquid chromatography, revealing the intrinsic catalytic contribution of carbon frameworks and the dynamic evolution of PS species. We demonstrate that carbon superstructures (CSS-0.5), assembled from nanosheet subunits with abundant N/O functionalities and interconnected charge-migration channels, synergistically promote this catalytic process. Benefiting from these features, CSS-0.5 delivers superior electrochemical performance under practical conditions, enabling high sulfur loading (6.0 mg cm⁻²) pouch cells with 80.5% capacity retention over 210 cycles. This study provides the first quantitative evidence of electrocatalytic disproportionation in Li–S batteries, offering mechanistic insights and design principles for advanced sulfur cathodes.
25 ENERGY STORAGE↗
Higher symmetry breaking and nonreciprocity in a driven-dissipative Dicke model
Higher symmetries in interacting many-body systems often give rise to new phases and unexpected dynamical behavior. Here, we theoretically investigate a variant of the Dicke model with higher-order discrete symmetry, resulting from complex-valued coupling coefficients between quantum emitters and a bosonic mode. We propose a driven-dissipative realization of this model focusing on optomechanical response of a driven atom tweezer array comprised of 𝑛 subensembles and placed within an optical cavity, with the phase of the driving field advancing stepwise between subensembles. Examining stationary points and their dynamical stability, we identify a phase diagram for 𝑛≥3 with three distinctive features: a ℤ 𝑛 (ℤ 2𝑛 ) symmetry-breaking superradiant phase for even (odd) 𝑛, a normal unbroken-symmetry phase that is dynamically unstable due to nonreciprocal forces between emitters, and a first-order phase transition separating these phases. This 𝑛-phase Dicke model may be equivalently realized in a variety of optomechanical or optomagnonic settings, where it can serve as a test bed for studying high-order symmetry breaking and nonreciprocal interactions in open systems.
Non-reciprocal propagation↗
Stabilization of large-scale systems - A spinning flexible spacecraft
Stabilization of high-order constant systems by multilevel control is proposed in the framework of the decomposition-aggregation method for stability analysis of large-scale systems. An 11-order linear model of a spinning flexible spacecraft is stabilized by the method using both the passive and the active stabilization devices. The method can take advantage of the special structural features of the model to provide the best estimate of the stability region for an important parameter which couples the wobble and the spin motion of the spacecraft.
Siljak, D. D.↗
A high-order language for a system of closely coupled processing elements
The research reported in this paper was occasioned by the requirements on part of the Real-Time Digital Simulator (RTDS) project under way at NASA Lewis Research Center. The RTDS simulation scheme employs a network of CPUs running lock-step cycles in the parallel computations of jet airplane simulations. Their need for a high order language (HOL) that would allow non-experts to write simulation applications and that could be implemented on a possibly varying network can best be fulfilled by using the programming language Ada. We describe how the simulation problems can be modeled in Ada, how to map a single, multi-processing Ada program into code for individual processors, regardless of network reconfiguration, and why some Ada language features are particulary well-suited to network simulations.
Feyock, S.↗
Counterrotating prop-fan simulations which feature a relative-motion multiblock grid decomposition enabling arbitrary time-steps
Improvements are presented of a computer algorithm developed for the time-accurate flow analysis of rotating machines. The flow model is a finite volume method utilizing a high-resolution approximate Riemann solver for interface flux definitions. The numerical scheme is a block LU implicit iterative-refinement method which possesses apparent unconditional stability. Multiblock composite gridding is used to orderly partition the field into a specified arrangement of blocks exhibiting varying degrees of similarity. Block-block relative motion is achieved using local grid distortion to reduce grid skewness and accommodate arbitrary time step selection. A general high-order numerical scheme is applied to satisfy the geometric conservation law. An even-blade-count counterrotating unducted fan configuration is chosen for a computational study comparing solutions resulting from altering parameters such as time step size and iteration count. The solutions are compared with measured data.
Janus, J. Mark↗
Understanding transition and turbulence through direct simulations
Direct simulations consist in solving the full Navier-Stokes equations, without any turbulence model, and describing all the detailed features of the flow. Usually the flows are three-dimensional and time-dependent and contain both coarse and fine structures, which makes the numerical task very challenging in terms of both the algorithm and the computational effort. Most of the work until now has involved spectral methods, which are highly accurate but not very flexible in terms of geometry or complex equations. For that reason, future work will also rely on high-order finite-difference or other methods. Direct simulations complement experimental work, and both contribute to the theory and the empirical knowledge of turbulence. Once such a simulation has been shown to be accurate, the flow field is completely known in three dimensions and time, including the pressure, the vorticity and any other quantity. On the other hand, most simulations to date solved the incompressible equations in rather simple geometries, and direct simulations will always be limited to moderate Reynolds numbers. Extensive simulations have been conducted in homogeneous turbulence, channel flows, boundary layers, and mixing layers. Much effort is devoted to addressing flows with compressibility and chemical reactions, and to new geometries such as a backward-facing step.
Spalart, P. R.↗