Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Polynomial models”

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 325 records · Page 18

A fully Lagrangian, non-parametric bias model for dark matter halos

Here, we present a non-parametric Lagrangian biasing model and fit the ratio of the halo and mass densities at the field level using the mass-weighted halo field in the AbacusSummit simulations at z=0.5. Unlike the perturbative halo bias model that has been widely used in interpreting the observed large-scale structure traced by galaxies, we find a non-negative halo-to-mass ratio that increases monotonically with the linear overdensity δ 1 in the initial Lagrangian space. The bias expansion, however, does not guarantee non-negativity of the halo counts, and may lead to rising halo number counts at negative overdensities. The shape of the halo-to-mass ratio is unlikely to be described by a polynomial function of δ 1 and other quantities. Especially for massive halos with 6×10 12 h -1 M ⊙ , the halo-to-mass ratio starts soaring up at δ 1 >0, substantially different from the predictions of the bias expansion. We show that for the halo masses we consider (M>3×10 11 h -1 M ⊙ ) a non-parametric halo-to-mass ratio as a function of δ 1 and its local derivative ∇^2δ 1 can recover the halo power spectra to sub-percent level accuracy for wavenumbers k=0.01-0.1 h Mpc -1 given a proper smoothing scale to filter the initial density field, even though we do not fit the power spectrum directly. However, there is mild dependence of the recovery of the halo power spectrum on the smoothing scale and other input parameters. At k<0.01 h Mpc -1 and for massive halos with M>6x10 12 h -1 M ⊙ , our non-parametric model leads to a few percent overestimation of the halo power spectrum, indicating the need for larger or multiple smoothing scales. The halo-to-mass ratios obtained qualitatively agree with intuitions from extended Press-Schechter theory. We compare our framework to the bias expansion and discuss possible extensions.

79 ASTRONOMY AND ASTROPHYSICS↗

PolyODENet: Deriving mass-action rate equations from incomplete transient kinetics data

Kinetics of a reaction network that follows mass-action rate laws can be described with a system of ordinary differential equations (ODEs) with polynomial right-hand side. However, it is challenging to derive such kinetic differential equations from transient kinetic data without knowing the reaction network, especially when the data are incomplete due to experimental limitations. We introduce a program, PolyODENet, toward this goal. Based on the machine-learning method Neural ODE, PolyODENet defines a generative model and predicts concentrations at arbitrary time. As such, it is possible to include unmeasurable intermediate species in the kinetic equations. Importantly, we have implemented various measures to apply physical constraints and chemical knowledge in the training to regularize the solution space. Here, using simple catalytic reaction models, we demonstrate that PolyODENet can predict reaction profiles of unknown species and doing so even reveal hidden parts of reaction mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Software Verification of VARPOW

The VARPOW program is a post-processing utility program for DIF3D, specifically DIF3DVARIANT, and it was developed to provide interface files for the thermal analysis program DASSH. The basic methodology of VARPOW is to take the neutron and gamma flux (moments) calculated by DIF3D (or GAMSOR) and combine them with the heating (coefficient) cross sections to calculate the spatial power distributions using the DIF3DVARIANT spatial basis. VARPOW can use the output from GAMSOR (both steady state neutron and gamma flux calculations) or standard DIF3D/REBUS calculations (neutron flux only). The correct approach for defining the power distribution is to use GAMSOR as its purpose was to properly compute the gamma heating throughout the modeled domain. The power densities calculated by VARPOW are broken into fuel, cladding and coolant terms for which isotope-wise categorization is needed. VARPOW has built in options the user can select for the isotope categorization or VARPOW can import a file that details the isotope categorization. VARPOW can export the solution in the polynomial basis of DIF3D-VARIANT or the monomial basis of DIF3D-VARIANT. The purpose of this work is to verify the power distribution results calculated by VARPOW from both the GAMSOR and DIF3D input options and verify that the input and output options are consistent with the manual. Hand calculation and independent numerical calculation are used for this verification work.

97 MATHEMATICS AND COMPUTING↗

Software Verification of VARPOW

The VARPOW program is a post-processing utility program for DIF3D, specifically DIF3DVARIANT, and it was developed to provide interface files for the thermal analysis program DASSH. The basic methodology of VARPOW is to take the neutron and gamma flux (moments) calculated by DIF3D (or GAMSOR) and combine them with the heating (coefficient) cross sections to calculate the spatial power distributions using the DIF3DVARIANT spatial basis. VARPOW can use the output from GAMSOR (both steady state neutron and gamma flux calculations) or standard DIF3D/REBUS calculations (neutron flux only). The correct approach for defining the power distribution is to use GAMSOR as its purpose was to properly compute the gamma heating throughout the modeled domain. The power desnities calculated by VARPOW are broken into fuel, cladding and coolant terms for which isotope-wise categorization is needed. VARPOW has built in options the user can select for the isotope categorization or VARPOW can import a file that details the isotope categorization. VARPOW can export the solution in the polynomial basis of DIF3D-VARIANT or the monomial basis of DIF3D-VARIANT. The purpose of this work is to verify the power distribution results calculated by VARPOW from both the GAMSOR and DIF3D input options and verify that the input and output options are consistent with the manual. Hand calculation and independent numerical calculation are used for this verification work.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Software Verification of VARPOW

The VARPOW program is a post-processing utility program for DIF3D, specifically DIF3DVARIANT, and it was developed to provide interface files for the thermal analysis program DASSH. The basic methodology of VARPOW is to take the neutron and gamma flux (moments) calculated by DIF3D (or GAMSOR) and combine them with the heating (coefficient) cross sections to calculate the spatial power distributions using the DIF3DVARIANT spatial basis. VARPOW can use the output from GAMSOR (both steady state neutron and gamma flux calculations) or standard DIF3D/REBUS calculations (neutron flux only). The correct approach for defining the power distribution is to use GAMSOR as its purpose was to properly compute the gamma heating throughout the modeled domain. The power desnities calculated by VARPOW are broken into fuel, cladding and coolant terms for which isotope-wise categorization is needed. VARPOW has built in options the user can select for the isotope categorization or VARPOW can import a file that details the isotope categorization. VARPOW can export the solution in the polynomial basis of DIF3D-VARIANT or the monomial basis of DIF3D-VARIANT. Recently the clad neutron damage calculation capability was introduced into VARPOW, and it now allows a pathway to get distributions of clad DPA. The purpose of this work is to verify the power distribution, fast neutron flux and clad DPA results calculated by VARPOW from both the GAMSOR and DIF3D input options and verify that the input and output options are consistent with the manual. Hand calculation and independent numerical calculation are used for this verification work.

Zhong, Zhaopeng [Argonne National Laboratory (ANL)↗

Total kinetic energy release in the fast neutron induced fission of actinide nuclei

The total kinetic energy release and fission mass distributions for the fast neutron (En = 3–100 MeV) induced fission of 232 Th, 233 U, 235 U, 237 Np, 239 Pu, 240 Pu, and 242 Pu have been measured using the LANSCE facility. The neutron energies were deduced from time-of- flight measurements. The fission fragments were detected using Si PIN diode detectors, giving us the fragment energies. The actinide targets were made by vapor deposition leading to high-quality targets, that were thin and uniform with reduced impurities. Corrections were made to the data for pulse height defect and the fragment energy loss in the target and its backing. The TKE distributions were Gaussian in shape and their mean value as a function of incoming neutron energy could be fitted with second order polynomials. In the case of 233 U and 235 U, our measurements agree with prior work. Our measurements for 232 Th are unique. Our data agree with Viola scaling. The constant position of the heavy mass peak is interpreted as being due to the influence of the N = 88 and Z = 50 shells. The GEF model predictions agree with the data in general as do the CGMF model predictions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

PolyODENet

Kinetics of a reaction network that follows mass-action rate laws can be described with a system of ordinary differential equations (ODEs) with polynomial right-hand side. However, it is challenging to derive such kinetic differential equations from transient kinetic data without knowing the reaction network, especially when the data are incomplete due to experimental limitations. We introduce a program, PolyODENet, toward this goal. Based on the machine-learning method Neural ODE, PolyODENet defines a generative model and predicts concentrations at arbitrary time. As such, it is possible to include unmeasurable intermediate species in the kinetic equations. Importantly, we have implemented various measures to apply physical constraints and chemical knowledge in the training to regularize the solution space.

Wu, Qin [Brookhaven National Lab. (BNL), Upton, NY↗

Chiral-odd generalized parton distributions in the large-𝑁 𝑐 limit of QCD: Spin-flavor structure, polynomiality, and sum rules

We study the nonperturbative properties of the nucleon’s chiral-odd generalized parton distributions (transversity GPDs) in the large-𝑁 𝑐 limit of QCD. This includes the parametric ordering of the spin-flavor components, the polynomiality property of the moments, and the sum rules connecting the GPDs with the tensor form factors. A multipole expansion in the transverse momentum transfer is used to enumerate and interpret the structures in the nucleon matrix element of the chiral-odd partonic operator, including monopole, dipole and quadrupole terms. The 1/𝑁 𝑐 expansion of the GPDs is performed using the abstract mean-field picture of baryons in the large-𝑁 𝑐 limit and its symmetries. We derive a large-𝑁 𝑐 relation between the flavor-nonsinglet GPDs 𝐸$^{𝑢−𝑑}_𝑇$ and $\tilde{𝐻}^{𝑢−𝑑}_𝑇$ and test it with recent lattice QCD results. We show that the polynomiality property and sum rules of the GPDs are fulfilled with the restricted realization of translational and rotational invariance in the mean-field picture. The results provide a basis for the phenomenological analysis of chiral-odd GPDs and hard exclusive processes in the large-𝑁 𝑐 limit, and for calculations in specific dynamical models.

generalized parton distributions↗

Empirically Driven multiwavelength K-c orrections at low redshift

K -corrections – a necessary ingredient for converting between flux in observed bands to flux in rest-frame bands – are critical for comparing galaxies at differing redshifts. These corrections often rely on fits to empirical or theoretical spectral energy distribution (SED) templates of galaxies. However, templates can only produce reliable K-corrections in regimes where SED models are robust. For instance, the templates utilized in some popular software packages are not well-constrained in some bands (e.g. WISE W4 in KCORRECT ), which results in ill-behaved K -corrections. We address this shortcoming by developing an empirically driven approach to K -corrections that limits the dependence on SED templates. We perform a polynomial fit for the K -correction as a function of a galaxy’s rest-frame colour determined in a pair of well-constrained bands (e.g. 0 (g − r)) and redshift, exploiting the fact that galaxy SEDs can be approximated as a one-parameter family at low redshift. For bands well-constrained by SED templates, our empirically driven K -corrections yield results comparable to the SED fitting methods used by KCORRECT and the GSWLC-M2 catalogue (the updated medium-deep GALEX–SDSS–WISE Legacy Catalogue). However, our method dramatically outperforms Kcorrect derived K -corrections for WISE W4 . Our method is also robust to incorrect template assumptions outside of the optical bands and enforces that the K -correction must be zero at z = 0. Our K -corrected photometry and code are publicly available.

79 ASTRONOMY AND ASTROPHYSICS↗

Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth

Matrix chain multiplication -- computing $\mathcal{W} = M^{(0)}\cdots M^{(K-1)}$ where $M^{(k)} \in \mathbb{R}^{P_k \times P_{k+1}}$-- arises in scientific computing, machine learning, and graph analysis. Despite the importance of this problem, for chains of distinct matrices, the classical number of operations grows linearly with the chain length $K$ and polynomially in the matrix dimensions. We present \emph{Two-Tower Matrix Multiplication}, a quantum subroutine that encodes the product $\mathcal{W}$ of the $K$ matrices into a quantum state in circuit depth $\mathcal{O}(\max_{k} \mathrm{polylog} (P_k P_{k+1}))$, which is independent of~$K$ within the QRAM-based state-preparation model, whereas the qubit count is $\mathcal{O}\bigl(\sum_{k} \log P_k \bigr)$; the total gate count remains linear in $K$, so the gain is in the circuit depth. The construction interleaves state-preparation operators across two layers; within each layer, all operators act on disjoint registers and execute in parallel. This subroutine can be specialized for the chain-vector case, which computes the product of $K-1$ matrices applied to a vector. We prove the correctness of the subroutine for all $K$ and provide two implementations using the Qiskit and QCLAB frameworks. The subroutine is applicable to any downstream quantum algorithm that operates on a matrix encoded in the statevector, including norm estimation, graph-matrix powers, linear system solving, and quantum machine learning kernels.

Antonioli, Giacomo [Pisa U.] (ORCID:00090000668703↗

Insights on the continuous representations of piecewise-smooth nonlinear systems: limits of applicability and effectiveness

Dynamical systems subject to intermittent contact are often modeled with piecewise-smooth contact forces. However, the discontinuous nature of the contact can cause inaccuracies in numerical results or failure in numerical solvers. Representing the piecewise contact force with a continuous and smooth function can mitigate these problems, but not all continuous representations may be appropriate for this use. Here, five representations used by previous researchers (polynomial, rational polynomial, hyperbolic tangent, arctangent, and logarithm-arctangent functions) are studied to determine which ones most accurately capture nonlinear behaviors including super- and subharmonic resonances, multiple solutions, and chaos. The test case is a single-DOF forced Duffing oscillator with freeplay nonlinearity, solved using direct time integration. This work intends to expand on past studies by determining the limits of applicability for each representation and what numerical problems may occur.

42 ENGINEERING↗

Correlation of Surface Acoustic Wave (SAW) force myography sensor output with elbow joint torque

Accurate assessment of skeletal muscle forces and net joint torque is essential for preventing fatigue-related injuries, optimizing physical training, and monitoring disease progression in neuromuscular conditions. However, existing joint torque evaluation techniques are hindered by limited portability and high operational costs, confining their use to controlled laboratory or clinical settings. Despite substantial advances in wearable joint torque estimation systems, ongoing challenges such as power constraints, bulky wired setups, and susceptibility to environmental or motion artifacts underscore the urgent need for truly batteryless, wireless solutions deployable in real-world settings. This paper proposes a novel surface acoustic wave (SAW)-based force myography (FMG) system for noninvasive measurement of joint torque, validated against a gold-standard electromechanical dynamometer. The approach uses a single SAW sensor embedded in an armband to detect volumetric biceps brachii changes, with a second-order polynomial mapping sensor output and elbow angle to torque. Seven participants were tested in both isometric (15°–90°) and isokinetic (10°/s and 20°/s) supinated elbow flexion tasks. Under isometric conditions, subject-specific calibration achieved a normalized root-mean-square error (NRMSE) of 13.6% ± 6.0% and R 2 = 0.834 ± 0.180, while a group-level model yielded 14.4% ± 6.8% and 0.808 ± 0.208, respectively. For isokinetic trials, the group model produced an NRMSE of 24.1% ± 6.6% at 10°/s and 24.9% ± 08.9% at 20°/s, highlighting the feasibility of using a single-sensor SAW-FMG setup across different speeds. Because SAW devices support wireless, battery-free operation, the proposed system offers a pathway to portable, real-time monitoring for sports medicine, rehabilitation, and clinical diagnostics.

36 MATERIALS SCIENCE↗

Accelerated basis adaptation in homogeneous chaos spaces

Polynomial chaos expansions (PCE) provide an efficient approach to uncertainty quantification (UQ) and have been adapted to diverse applications across the spectrum of science and engineering. For situations involving large stochastic parameterizations, the curse of dimensionality renders PCE-based methods computationally prohibitive. A basis adaptation approach for PCE was proposed by Tipireddy and Ghanem (2014) which transforms the input random variables through an isometry such that sufficient probabilistic characterization of specific quantities of interest (QoI) is concentrated in an algebraic manifold embedded in the linear span of the dominant transformed variables. While quite versatile, that original version of the PCE basis adaptation exhibited slow convergence for a number of problems of practical significance. In the present paper, we propose two novel methods to accelerate the convergence of the original basis adaptation approach, thus expanding its reach while also providing insight into its performance. In the first method, information gained from a pilot PCE representation is used to correct the mean and Gaussian coefficients in the adapted space. By taking advantages of probabilistic information in higher dimensional adaptation gleaned from an initial adaptation, the second method updates the rotation matrix used to identify the dominant transformed variables. In this manner, the new rotation matrix concentrates even more probabilistic information in its first few dimensions. These two method can be combined to achieve even better performance, the combined method is referred to as sequentially optimized adaptation method. Here, the methods are demonstrated on an analytical test function and a model of a space structure with several sub-components and a non-smooth quantity of interest representing the maximum acceleration over time. Both methods achieve accelerated convergence of the basis adaptation approach with negligible additional costs.

Accelerated convergence↗

Scalable Tensor Methods for Nonuniform Hypergraphs

While multilinear algebra appears natural for studying the multiway interactions modeled by hypergraphs, tensor methods for general hypergraphs have been stymied by theoretical and practical barriers. A recently proposed adjacency tensor is applicable to nonuniform hypergraphs, but is prohibitively costly to form and analyze in practice. We develop tensor times same vector (TTSV) algorithms for this tensor which improve complexity from $O(n^r)$ to a low-degree polynomial in $r$, where $n$ is the number of vertices and $r$ is the maximum hyperedge size. Our algorithms are implicit, avoiding formation of the order $r$ adjacency tensor. Here, we demonstrate the flexibility and utility of our approach in practice by developing tensor-based hypergraph centrality and clustering algorithms. We also show these tensor measures offer complementary information to analogous graph-reduction approaches on data, and are also able to detect higher-order structure that many existing matrix-based approaches provably cannot.

97 MATHEMATICS AND COMPUTING↗

NEAMS Technical Area Support in MOOSE

The MOOSE framework is a foundational capability used by the NEAMS program to create over 15 different simulation tools for advanced nuclear reactors. Due to this ubiquity, improvements to the framework in support of modeling and simulation goals are critical to the program. These improvements can take many forms including optimization, improved user experience, streamlined application programming interfaces (APIs), parallelism, and other new capabilities. The work transcribed in this report was conducted in direct support of the simulation tools and has already been deployed. The capabilities outlined in this report include enabling selective polynomial basis refinement, implementing a custom convergence system, building a scalable preconditioner for saddle-point problems, and much more.

97 MATHEMATICS AND COMPUTING↗

Quantum algorithms from fluctuation theorems: Thermal-state preparation

Fluctuation theorems provide a correspondence between properties of quantum systems in thermal equilibrium and a work distribution arising in a non-equilibrium process that connects two quantum systems with Hamiltonians H 0 and H 1 = H 0 + V. Building upon these theorems, we present a quantum algorithm to prepare a purification of the thermal state of H 1 at inverse temperature β ≥ 0 starting from a purification of the thermal state of H 0 . The complexity of the quantum algorithm, given by the number of uses of certain unitaries, is $\mathcal{O}$ (e β(ΔA - w l )/2 ), where ΔA is the free-energy difference between H 1 and H 0 , and w l is a work cutoff that depends on the properties of the work distribution and the approximation error ϵ > 0. If the non-equilibrium process is trivial, this complexity is exponential i β∥V∥, where ∥V∥ is the spectral norm of V. This represents a significant improvement of prior quantum algorithms that have complexity exponential in β∥H 1 ∥ in the regime where ∥V∥$\ll$ ∥H 1 ∥. The dependence of the complexity in ϵ varies according to the structure of the quantum systems. It can be exponential in 1/ϵ in general, but we show it to be sublinear in 1/ϵ if H 0 and H 1 commute, or polynomial in 1/ϵ if H 0 and H 1 are local spin systems. The possibility of applying a unitary that drives the system out of equilibrium allows one to increase the value of w l and improve the complexity even further. To this end, we analyze the complexity for preparing the thermal state of the transverse field Ising model using different non-equilibrium unitary processes and see significant complexity improvements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Equations of state, phase relations, and oxygen fugacity of the Ru-RuO 2 buffer at high pressures and temperatures

Experimental studies and measurements of inclusions in diamonds show that ferric iron components are increasingly stabilized with depth in the mantle. To determine the thermodynamic stability of such components, their concentration needs to be measured at known oxygen fugacities. The metal-oxide pair Ru and RuO 2 are ideal as an internal oxygen fugacity buffer in high-pressure experiments. Both phases remain solid to high temperatures and react minimally with silicates, only exchanging oxygen. To calculate oxygen fugacities at high pressure and temperature, however, requires information on the phase relations and equation of state properties of the solid phases. We have made in situ synchrotron X-ray diffraction measurements in a multi-anvil press on mixtures of Ru and RuO 2 to 19.4 GPa and 1473 K with which we have determined phase relations of the RuO 2 phases and derived thermal equations of state (EoS) parameters for both Ru and RuO 2 . Rutile-structured RuO 2 was found to undergo two phase transformations, first at ~7 GPa to an orthorhombic structure and then above 12 GPa to a cubic structure. The phase boundary of the cubic phase was constrained for the first time at high pressure and temperature. We have derived a continuous Gibbs free energy expression for the tetragonal and orthorhombic phases of RuO 2 by fitting the second-order phase transition boundary and P-V-T data for both phases, using a model based on Landau theory. The transition between the orthorhombic and cubic phases was then used along with EoS terms derived for both phases to determine a Gibbs free energy expression for the cubic phase. We have used these data to calculate the oxygen fugacity of the Ru + O 2 = RuO 2 equilibrium, which we have parameterized as a single polynomial across the stability fields of all three phases of RuO 2 . The expression is log 10 f O 2 (Ru – RuO 2 ) = (7.782 – 0.00996P + 0.001932P 2 – 3.76 × 10 –5 P 3 ) + (–13 763 + 592P – 3.955P 2 )/T + (–1.05 × 10 6 – 4622P)/T 2 , which should be valid from room pressure up to 25 GPa and 773–2500 K, with an estimated uncertainty of 0.2 log units. Our calculated fO 2 is shown to be up to 1 log unit lower than estimates that use previous expressions or ignore EoS terms.

Armstrong, Katherine↗

On detrending stream velocity time series for robust tidal flow turbulence characterization

We investigated the impact of detrending techniques on turbulence quantities from tidal stream flow data, focusing on the autocorrelation function, $ρ_{uu}$, and velocity spectrum, $Φ(f)$. Standard detrending methods, including high-pass frequency-based and polynomial-based techniques, are examined, alongside a proposed alternative method, the empirical mode decomposition (EMD). Our results highlight that intervals of flow acceleration and deceleration, typical in tidal and riverine flows, significantly affect the estimation of turbulence quantities using high-pass frequency filtering and polynomial detrending of varying orders. These methods can strongly influence $ρ_{uu}$ and $Φ(f)$, thereby affecting the accurate estimation of derived quantities. We examine two variations of detrending data using EMD; the first removes only the EMD residue, and the second removes both the residue and the largest scale intrinsic mode function (IMF). By comparing the detrended spectra with the modeled von Kármán spectra, we demonstrate that the second variation (i.e., removing the residue and the largest scale IMF) successfully removed the large-scale trend of the data while retaining the energy of other scales.

Detrend↗