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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

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

Piecewise linear approximation with minimum number of linear segments and minimum error: A fast approach to tighten and warm start the hierarchical mixed integer formulation

In several areas of economics and engineering, it is often necessary to fit discrete data points or approximate nonlinear functions with continuous functions. Piecewise linear (PWL) functions are a convenient way to achieve this. PWL functions can be modeled in mathematical problems using only linear and integer variables. Moreover, there is a computational benefit in using PWL functions that have the least possible number of segments. This work proposes a novel hierarchical mixed integer linear programming (MILP) formulation that identifies a continuous PWL approximation with minimum number of linear segments for a given target maximum error. The proposed MILP formulation also identifies the solution with the least maximum error among the solutions with minimum number of segments. Then, this work proposes a fast iterative algorithm that identifies non necessarily continuous PWL approximations by solving O(S log N) linear programming (LP) problems, where N is the number of data points and S is the minimum number of segments in the non necessarily continuous case. This work demonstrates that tight bounds for the MILP problem can be derived from these approximations. Next, a fast algorithm is introduced to transform a non necessarily continuous PWL approximation into a continuous one. Finally, the tight bounds and the continuous PWL approximations are used to tighten and warm start the MILP problem. The tightened formulation is shown in experimental results to be more efficient, especially for large data sets, with a solution time that is up to two orders of magnitude less than the existing literature.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Definability of semifields of continuous positive functions by the lattices of their subalgebras

We consider the lattice A(U(X)) of subalgebras of a semifield U(X) of continuous positive functions on an arbitrary topological space X and its sublattice A{sub 1}(U(X)) of subalgebras with unity. The main result of the paper is the proof of the definability of any semifield U(X) both by the lattice A(U(X)) and by its sublattice A{sub 1}(U(X)). Bibliography: 12 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Spread of Values of a Cantor-Type Fractal Continuous Nonmonotone Function

By using the Q{sub 5}{sup ∗}-representation of numbers[0,1]∋x=β{sub α{sub 1(x)1}}+∑{sub k=2}{sup ∞}(β{sub α{sub k(x)k}}∏{sub j=1}{sup k−1}q{sub α{sub j(x)j}})=Δ{sub α{sub 1(x)α{sub 2(x)…α{sub k(x)…}{sup Q{sub 5}{sup ∗}}}}} determined by the quinary alphabet A{sub 5} ≡ {0, 1, 2, 3, 4} and an infinite stochastic matrix ‖q{sub ik}‖, i ∈ A{sub 5}, k ∈ N, with positive elements (q{sub 0k} + q{sub 1k} + q{sub 2k} + q{sub 3k} + q{sub 4k} = 1) such that ∏{sub k=1}{sup ∞}max{sub i}{q_i_k}=0 and β{sub 0k} = 0, β{sub i + 1, k} = β{sub ik} + q{sub ik}, i= (0,4)-bar , we define a continuous Cantor-type function by the equalityf(Δ{sub α{sub 1…α{sub k…}{sup Q{sub 5}{sup ∗}}}})=δ{sub α{sub 1(x)1}}+∑{sub k=2}{sup ∞}(δ{sub α{sub k(x)k}}∑{sub j=1}{sup k−1}g{sub α{sub j(x)j}})≡Δ{sub α{sub 1(x)…α{sub k(x)…}{sup G}}}, where δ{sub 0n} = 0, δ{sub 1n}=((2+ε{sub n})/4), δ{sub 2n}=(2/4)=δ{sub 3n}, and δ{sub 4n}=((2−ε{sub n})/4), i.e., δ{sub i + 1, n} = δ{sub in} + g{sub in}, n ∈ N, and (ε{sub n}) is a given sequence of real numbers such that 0 ≤ ε{sub n} ≤ 1. We prove that this function is well defined and continuous. Moreover, it does not have intervals of monotonicity, except the intervals where it is constant. A criterion of bounded variation of the function is also established. We are especially interested in the problem of level sets of the function and in the topological and metric properties of the images of Cantor-type sets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Structural and chemical ordering of Heusler C o x M n y G e z epitaxial films on Ge (111): Quantitative study using traditional and anomalous x-ray diffraction techniques

Epitaxial films of C o x M n y G e z grown on Ge (111) substrates by molecular-beam-epitaxy techniques have been investigated as a continuous function of composition using combinatorial synchrotron x-ray diffraction (XRD) and x-ray fluorescence (XRF) spectroscopy techniques. A high-resolution ternary epitaxial phase diagram is obtained, revealing a small number of structural phases stabilized over large compositional regions. Ordering of the constituent elements in the compositional region near the full Heusler alloy C o 2 MnGe has been examined in detail using both traditional XRD and a new multiple-edge anomalous diffraction (MEAD) technique. Multiple-edge anomalous diffraction involves analyzing the energy dependence of multiple reflections across each constituent absorption edge in order to detect and quantify the elemental distribution of occupation in specific lattice sites. Results of this paper show that structural and chemical ordering are very sensitive to the Co : Mn atomic ratio, such that the ordering is the highest at an atomic ratio of 2 but significantly reduced even a few percent off this ratio. The in-plane lattice is nearly coherent with that of the Ge substrate, while the approximately 2% lattice mismatch is accommodated by the out-of-plane tetragonal strain. The quantitative MEAD analysis further reveals no detectable amount (<0.5%) of Co-Mn site swapping, but instead high levels (26%) of Mn-Ge site swapping. Increasing Ge concentration above the Heusler stoichiometry ( C o 0.5 M n 0.25 G e 0.25 ) is shown to correlate with increased lattice vacancies, antisites, and stacking faults, but reduced lattice relaxation. The highest degree of chemical ordering is observed off the Heusler stoichiometry with a Ge enrichment of 5 at.%.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

FunDiff: diffusion models over function spaces for physics-informed generative modeling

Recent advances in generative modeling-particularly diffusion models and flow matching-have been widely used for synthesizing discrete data such as images and videos. However, adapting these models to physical applications remains challenging, as the quantities of interest are continuous functions governed by complex physical laws. To address this, we introduce FunDiff, an efficient and robust framework for generative modeling in function spaces. FunDiff combines a latent diffusion process with a function autoencoder architecture to handle input functions with varying discretizations, generates continuous functions that can be evaluated at arbitrary locations, and seamlessly incorporate physical priors. These priors are enforced through architectural constraints or physics-informed loss functions, ensuring that generated samples satisfy fundamental physical laws. We theoretically establish minimax optimality guarantees for density estimation in function spaces, demonstrating that diffusion-based estimators achieve optimal convergence rates under suitable regularity conditions. We further demonstrate the practical effectiveness of FunDiff across diverse applications in fluid dynamics and solid mechanics. Empirical results indicate that our method can generate physically consistent samples with high fidelity to the target distribution, and exhibit robustness to noisy and low-resolution data.

Wang, Sifan [Yale University, New Haven, CT (Unite↗
DOE OSTI2015

Adaptive Multilinear Tensor Product Wavelets

Many foundational visualization techniques including isosurfacing, direct volume rendering and texture mapping rely on piecewise multilinear interpolation over the cells of a mesh. However, there has not been much focus within the visualization community on techniques that efficiently generate and encode globally continuous functions defined by the union of multilinear cells. Wavelets provide a rich context for analyzing and processing complicated datasets. In this paper, we exploit adaptive regular refinement as a means of representing and evaluating functions described by a subset of their nonzero wavelet coefficients. We analyze the dependencies involved in the wavelet transform and describe how to generate and represent the coarsest adaptive mesh with nodal function values such that the inverse wavelet transform is exactly reproduced via simple interpolation (subdivision) over the mesh elements. This allows for an adaptive, sparse representation of the function with on-demand evaluation at any point in the domain. In conclusion, we focus on the popular wavelets formed by tensor products of linear B-splines, resulting in an adaptive, nonconforming but crack-free quadtree (2D) or octree (3D) mesh that allows reproducing globally continuous functions via multilinear interpolation over its cells.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Semirings of Continuous (0,∞]-Valued Functions

The semiring C{sup ∞}(X) of all continuous functions on an arbitrary topological space X with values in the topological semiring (0,∞] is studied. General properties of semirings C{sup ∞}(X) are considered. Properties of lattices of ideals and congruences of semirings C{sup ∞}(X) over the P-spaces X, the F-spaces X, and the finite discrete spaces are proved.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Towards determination of the strong coupling $α_s(m_Z)$ from four-flavor lattice QCD using the continuous $β$-function method

The precise value of the strong coupling $α_s(m_{Z})$ at the $Z$-boson mass $m_{Z}$ is essential for high-energy phenomenology and precision tests of quantum chromodynamics (QCD). We present the status of a program targeting a $\sim 0.3\%$ determination of $α_s(m_{Z})$ using the renormalization group $β$-function in the infinite volume gradient flow scheme based on lattice QCD simulations of degenerate four-flavor highly improved staggered quark (HISQ) ensembles. In particular, we analyze both tree-level cutoff effects and finite-mass effects. We also outline the next steps of the analysis, including the infinite-volume and continuum extrapolations required for a precise determination of $α_s(m_Z)$.

Mandlecha, Yash (ORCID:000000020587962X)↗
DOE OSTI2026

Towards determination of the strong coupling $α_s(m_Z)$ from four-flavor lattice QCD using the continuous $β$-function method

The precise value of the strong coupling $α_s(m_{Z})$ at the $Z$-boson mass $m_{Z}$ is essential for high-energy phenomenology and precision tests of quantum chromodynamics (QCD). We present the status of a program targeting a $\sim 0.3\%$ determination of $α_s(m_{Z})$ using the renormalization group $β$-function in the infinite volume gradient flow scheme based on lattice QCD simulations of degenerate four-flavor highly improved staggered quark (HISQ) ensembles. In particular, we analyze both tree-level cutoff effects and finite-mass effects. We also outline the next steps of the analysis, including the infinite-volume and continuum extrapolations required for a precise determination of $α_s(m_Z)$.

Mandlecha, Yash [Michigan State U.; Michigan State↗
DOE OSTI2023

A unified and constructive framework for the universality of neural networks

Abstract One of the reasons why many neural networks are capable of replicating complicated tasks or functions is their universal approximation property. Though the past few decades have seen tremendous advances in theories of neural networks, a single constructive and elementary framework for neural network universality remains unavailable. This paper is an effort to provide a unified and constructive framework for the universality of a large class of activation functions including most of the existing ones. At the heart of the framework is the concept of neural network approximate identity (nAI). The main result is as follows: any nAI activation function is universal in the space of continuous functions on compacta. It turns out that most of the existing activation functions are nAI, and thus universal. The framework induces several advantages over the contemporary counterparts. First, it is constructive with elementary means from functional analysis, probability theory, and numerical analysis. Second, it is one of the first unified and constructive attempts that is valid for most of the existing activation functions. Third, it provides new proofs for most activation functions. Fourth, for a given activation and error tolerance, the framework provides precisely the architecture of the corresponding one-hidden neural network with a predetermined number of neurons and the values of weights/biases. Fifth, the framework allows us to abstractly present the first universal approximation with a favorable non-asymptotic rate. Sixth, our framework also provides insights into the developments, and hence providing constructive derivations, of some of the existing approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Dynamic subcanopy leaf traits drive resistance of net primary production across a disturbance severity gradient

Across the globe, the forest carbon sink is increasingly vulnerable to an expanding array of low- to moderate-severity disturbances. However, some forest ecosystems exhibit functional resistance (i.e., the capacity of ecosystems to continue functioning as usual) following disturbances such as extreme weather events and insect or fungal pathogen outbreaks. Unlike severe disturbances (e.g., stand-replacing wildfires), moderate severity disturbances do not always result in near-term declines in forest production because of the potential for compensatory growth, including enhanced subcanopy production. Community-wide shifts in subcanopy plant functional traits, prompted by disturbance-driven environmental change, may play a key mechanistic role in resisting declines in net primary production (NPP) up to thresholds of canopy loss. However, the temporal dynamics of these shifts, as well as the upper limits of disturbance for which subcanopy production can compensate, remain poorly characterized. In this study, we leverage a 4-year dataset from an experimental forest disturbance in northern Michigan to assess subcanopy community trait shifts as well as their utility in predicting ecosystem NPP resistance across a wide range of implemented disturbance severities. Through mechanical girdling of stems, we achieved a gradient of severity from 0% (i.e., control) to 45, 65, and 85% targeted gross canopy defoliation, replicated across four landscape ecosystems broadly representative of the Upper Great Lakes ecoregion. We found that three of four examined subcanopy community weighted mean (CWM) traits including leaf photosynthetic rate (p = 0.04), stomatal conductance (p = 0.07), and the red edge normalized difference vegetation index (p < 0.0001) shifted rapidly following disturbance but before widespread changes in subcanopy light environment triggered by canopy tree mortality. Surprisingly, stimulated subcanopy production fully compensated for upper canopy losses across our gradient of experimental severities, achieving complete resistance (i.e., no significant interannual differences from control) of whole ecosystem NPP even in the 85% disturbance treatment. Additionally, we identified a probable mechanistic switch from nutrient-driven to light-driven trait shifts as disturbance progressed. Our findings suggest that remotely sensed traits such as the red edge normalized difference vegetation index (reNDVI) could be particularly sensitive and robust predictors of production response to disturbance, even across compositionally diverse forests. The potential of leaf spectral indices to predict post-disturbance functional resistance is promising given the capabilities of airborne to satellite remote sensing. We conclude that dynamic functional trait shifts following disturbance can be used to predict production response across a wide range of disturbance severities.

resistance↗
DOE OSTI2019

Time-strain separability in medium-amplitude oscillatory shear

Here, we derive and study equations for the weakly nonlinear medium-amplitude oscillatory shear (MAOS) response of materials exhibiting time-strain separability. Results apply to constitutive models with arbitrary linear memory function $\textit{m}$(s) and for both viscoelastic liquids and viscoelastic solids. The derived equations serve as a reference to identify which models are time-strain separable (TSS) and which may appear separable but are not, in the weakly nonlinear limit. More importantly, we study how the linear viscoelastic (LVE) relaxation spectrum, H($_\tau$), affects the frequency dependence of the TSS MAOS material functions. Continuous relaxation spectra are considered that are associated with analytical functions (log-normal and asymmetric Lorentzian distributions), fractional mechanical models (Maxwell and Zener), and molecular theories (Rouse and Doi-Edwards). TSS MAOS signatures reveal much more than just the perturbation parameter A in the shear damping function small-strain expansion, $h(_γ) = 1 + \text{A}_γ$$^2 + \mathcal{O}(_γ$$^4)$. Specifically, the distribution of terminal relaxation times is significantly more apparent in the TSS MAOS functions than their LVE counterparts. We theoretically show that this occurs because TSS MAOS material functions are sensitive to higher-order moments of the relaxation spectrum, which leads to the definition of MAOS liquids. We also show the first examples of MAOS signatures that differ from the liquid-like terminal MAOS behavior predicted by the fourth-order fluid expansion. This occurs when higher moments of the relaxation spectrum are not finite. The famous corotational Maxwell model is a subset of our results here, for which A = -1/6, and any LVE relaxation spectrum could be used.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Multiscale multiphysics and multidomain models—Flexibility and rigidity

The emerging complexity of large macromolecules has led to challenges in their full scale theoretical description and computer simulation. Multiscale multiphysics and multidomain models have been introduced to reduce the number of degrees of freedom while maintaining modeling accuracy and achieving computational efficiency. A total energy functional is constructed to put energies for polar and nonpolar solvation, chemical potential, fluid flow, molecular mechanics, and elastic dynamics on an equal footing. The variational principle is utilized to derive coupled governing equations for the above mentioned multiphysical descriptions. Among these governing equations is the Poisson-Boltzmann equation which describes continuum electrostatics with atomic charges. The present work introduces the theory of continuum elasticity with atomic rigidity (CEWAR). The essence of CEWAR is to formulate the shear modulus as a continuous function of atomic rigidity. As a result, the dynamics complexity of a macromolecular system is separated from its static complexity so that the more time-consuming dynamics is handled with continuum elasticity theory, while the less time-consuming static analysis is pursued with atomic approaches. We propose a simple method, flexibility-rigidity index (FRI), to analyze macromolecular flexibility and rigidity in atomic detail. The construction of FRI relies on the fundamental assumption that protein functions, such as flexibility, rigidity, and energy, are entirely determined by the structure of the protein and its environment, although the structure is in turn determined by all the interactions. As such, the FRI measures the topological connectivity of protein atoms or residues and characterizes the geometric compactness of the protein structure. As a consequence, the FRI does not resort to the interaction Hamiltonian and bypasses matrix diagonalization, which underpins most other flexibility analysis methods. FRI's computational complexity is of O(N{sup 2}) at most, where N is the number of atoms or residues, in contrast to O(N{sup 3}) for Hamiltonian based methods. We demonstrate that the proposed FRI gives rise to accurate prediction of protein B-Factor for a set of 263 proteins. We show that a parameter free FRI is able to achieve about 95% accuracy of the parameter optimized FRI. An interpolation algorithm is developed to construct continuous atomic flexibility functions for visualization and use with CEWAR.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗