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At least 73 records · Page 4
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DOE OSTI2025

Orientation reversal and the Chern-Simons natural boundary

We show that the fundamental property of preservation of relations, underlying resurgent analysis, provides a new perspective on crossing a natural boundary, an important general problem in theoretical and mathematical physics. This reveals a deeper rigidity aspect of resurgence in a quantum field theory path integral. The physical context here is the non-perturbative completion of complex Chern-Simons theory that associates to a 3-manifold a collection of q-series invariants labeled by Spinc structures, for which crossing the natural boundary corresponds to orientation reversal of the 3-manifold. Our new resurgent perspective leads to a practical numerical algorithm that generates q-series which are dual to unary q-series composed of false theta functions. Until recently, these duals were only known in a limited number of cases, essentially based on Ramanujan’s mock theta functions, and the common belief was that the duals might not even exist in the general case. Resurgence analysis identifies as primary objects Mordell integrals: up to changes of variables, they are Laplace transforms of resurgent functions. Their unique Borel summed transseries decomposition on either side of the Stokes line is simply the unique decomposition into real and imaginary parts. In turn, the latter are combinations of unary q-series in terms of q and its modular counterpart $\overset{\sim }{q}$ , and are resurgent by construction. The Mordell integral is analytic across the natural boundary of the q and $\overset{\sim }{q}$ series, and uniqueness of a similar decomposition which preserves algebraic relations on the other side of the boundary defines the unique boundary crossing of the q series. We demonstrate that this continuation can be efficiently implemented numerically. In the cases where unique mock modular identities are known, they are found by this numerical procedure, but the procedure can go well beyond the known list of identities. A particularly interesting feature of the resurgent approach is that it reveals new aspects, and is very different from other known approaches based on indefinite theta series, Appell-Lerch sums, and representation theory of logarithmic vertex operator algebras.

Chern-Simons theories↗
DOE OSTI2024

Helicity evolution at small x : quark to gluon and gluon to quark transition operators

We include the quark to gluon and gluon to quark shock-wave transition operators into the small Bjorken-x evolution equations for helicity in the flavor-singlet channel derived earlier in [1,2,3]. While such transitions do not affect the large-N c version of the evolution equations for helicity, the large-N c & N f equations are affected. (N c and N f are the numbers of quark colors and flavors, respectively.) We derive the corresponding corrected large-N c & N f equations for the polarized dipole amplitudes contributing to the flavor-singlet quark and gluon helicity distributions in the double-logarithmic approximation (DLA), resumming powers of α s ln 2 (1/x) with αs the strong coupling constant. We solve these equations iteratively and extract the polarized splitting functions up to four loops. We show that our splitting functions agree with the fixed-order perturbative calculations up to and including the existing three-loops results [4,5,6,7]. Similar to the large-Nc helicity evolution in the shock-wave approach [8], our large-N c & N f small-x splitting functions agree with those obtained in the infrared evolution equations framework from [9, 10] up to three loops, but appear to slightly disagree at four loops.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

2-loop scattering on superstring and supermembrane in flat space

We consider the S-matrix of transverse scalar excitations on an infinite D = 10 GS superstring and D = 11 supermembrane in flat target space. We compute the 4-particle scattering amplitude in the 2-loop approximation and demonstrate that, like in the Nambu string case, the D = 10 GS string S-matrix does not contain non-trivial 2d UV divergences (UV pole not accompanied by terms with logarithms of momenta is an artifact of dimensional regularization). This is consistent with underlying integrability of this model which is maintaining by adding appropriate local counterterms. In the supermembrane case there are no 1-loop divergences but we find a genuine 2-loop UV pole. This demonstrates non-finiteness of the world-volume S-matrix of the M2 brane theory.

AdS-CFT Correspondence↗
DOE OSTI2024

Integrating the full four-loop negative geometries and all-loop ladder-type negative geometries in ABJM theory

The decomposition of the four-point ABJM amplituhedron into negative geometries produces compact integrands of logarithmic of amplitudes such that the infrared divergence only comes from the last loop integration, from which we can compute the cusp anomalous dimension of the ABJM theory. In this note, we integrate L – 1 loop momenta of the L-loop negative geometries for all four-loop negative geometries and a special class of all-loop ladder-type negative geometries by a method based on Mellin transformation, and from these finite quantities we extract the corresponding contribution to the cusp anomalous dimension. We find that the infrared divergence of a box-type negative geometry at L = 4 is weaker than other negative geometries, then only tree-type negative geometries contribute to the cusp anomalous dimension at L = 4. For the all-loop ladder-type negative geometries, we prove and conjecture some recursive structures as integral equations in Mellin space and find that they cannot contribute zeta values like ζ 3 , ζ 5 to the cusp anomalous dimension.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Advancing the understanding of energy-energy correlators in heavy-ion collisions

We investigate the collinear limit of the energy-energy correlator (EEC) in a heavy-ion context. First, we revisit the leading-logarithmic (LL) resummation of this observable in vacuum following a diagrammatic approach. We argue that this route allows to naturally incorporate medium-induced effects into the all-orders structure systematically. As an example, we show how the phase-space constraints imposed by the static medium on vacuum-like emissions can be incorporated into the LL result by modifying the anomalous dimensions. On the fixed-order side, we calculate the $\mathcal{O}$(α s ) expansion of the in-medium EEC for a γ → $q\overline{q}$ splitting with arbitrary kinematics including, for the first time, subleading colour corrections. When comparing this result to previously used approximations in the literature, we find up to $\mathcal{O}$(1) deviations in the regime of interest for jet quenching signatures. Energy loss effects are also quantified and further suppress the EEC at large angles. These semi-analytic studies are complemented with a phenomenological study using the jet quenching Monte Carlo JetMed. Finally, we argue that the imprint of medium-induced effects in energy-energy correlators can be enhanced by using an alternative definition that takes as input Lund primary declusterings instead of particles.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Extracting the asymptotic behavior of S-matrix elements from their phases

The asymptotic kinematic limits of S-matrices are dominated by large logarithms which, roughly speaking, fall into two categories: those which are controlled by a renormalization group (RG) scale, which we may think of as logs involving ratios of invariant mass scales, and those which are functions of ratios of rapidities, so called “rapidity logs”. It has been pointed out by Caron-Huot and Wilhlem [1] that RG anomalous dimension can be extracted from the phase of the S-matrix, which can greatly simplify calculations via unitarity methods. In this paper we generalize the results of [1] to show that the phase can be used to reconstruct rapidity anomalous dimensions, by performing a special type of complex boost. The methodology introduced allows one to calculate without the need for a rapidity regulator which can lead to significant simplifications. We demonstrate the use of this method to derive the rapidity anomalous dimensions in the Sudakov form factor and the two parton soft function at two loops order.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

EFT approach to the endpoint of muon decay-in-orbit

As upcoming experiments aim to probe muon conversion with unprecedented precision, equally precise theoretical predictions are crucial to maximize discovery potential. This applies not only to the new physics signal, muon-electron conversion, but also to its only irreducible background, muon decay-in-orbit (DIO) near the endpoint. Accurate computation of higher-order corrections in bound states is a long-standing challenge due to the difficulty of systematically organizing contributions. In previous work, we developed an Effective Field Theory framework to address this issue and applied it to muon conversion. Here, we extend this approach to the DIO endpoint, a more complex problem due to the presence of a neutrino-antineutrino pair in the final state. We present the most precise prediction to date of the background spectrum relevant for future muon conversion searches, achieving next-to-leading logarithmic prime accuracy for QED corrections.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Efficient Quantum Gibbs Samplers with Kubo–Martin–Schwinger Detailed Balance Condition

Lindblad dynamics and other open-system dynamics provide a promising path towards efficient Gibbs sampling on quantum computers. In these proposals, the Lindbladian is obtained via an algorithmic construction akin to designing an artificial thermostat in classical Monte Carlo or molecular dynamics methods, rather than being treated as an approximation to weakly coupled system-bath unitary dynamics. Recently, Chen, Kastoryano, and Gilyén (arXiv:2311.09207) introduced the first efficiently implementable Lindbladian satisfying the Kubo–Martin–Schwinger (KMS) detailed balance condition, which ensures that the Gibbs state is a fixed point of the dynamics and is applicable to non-commuting Hamiltonians. This Gibbs sampler uses a continuously parameterized set of jump operators, and the energy resolution required for implementing each jump operator depends only logarithmically on the precision and the mixing time. In this work, we build upon the structural characterization of KMS detailed balanced Lindbladians by Fagnola and Umanità, and develop a family of efficient quantum Gibbs samplers using a finite set of jump operators (the number can be as few as one), akin to the classical Markov chain-based sampling algorithm. Compared to the existing works, our quantum Gibbs samplers have a comparable quantum simulation cost but with greater design flexibility and a much simpler implementation and error analysis. Moreover, it encompasses the construction of Chen, Kastoryano, and Gilyén as a special instance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Advantages of the Samarskii-type schemes on the Shishkin mesh

The schemes of the Samarskii type are simple modifications of the upwind scheme. We use them on the Shishkin mesh and discuss their advantages over the upwind scheme when applied to the linear one-dimensional singularly perturbed convection–diffusion problem. One of the advantages is that the Samarskii-type schemes have exact first-order accuracy uniform in the perturbation parameter, as opposed to the upwind scheme which is almost first-order uniformly accurate because its accuracy is diminished by logarithmic factors. Although this is not a new result, we re-emphasize it in the paper. We also demonstrate another advantage, that the Samarskii-type schemes are almost second-order uniformly accurate on the layer component of the solution. Motivated by this fact, we present a further improvement of the numerical method.

Convection–diffusion↗
DOE OSTI2024

Hydrothermal solubility of Dy hydroxide as a function of pH and stability of Dy hydroxyl aqueous complexes from 25 to 250 °C

The rare earth elements (REE) have important applications in green energy technologies. The formation of mineral deposits in geologic systems commonly involves hydrothermal fluids which can mobilize the REE. However, the REE speciation is not well known as a function of pH. The thermodynamic properties of REE hydroxyl complexes used in geochemical models are based on the Helgeson-Kirkham-Flowers (HKF) equation of state parameters which were derived by extrapolation of low temperature experimental and estimated data. In this study, Dy hydroxide solubility experiments are combined with available literature data to improve these models from 25 to 250 °C and optimize the thermodynamic properties of Dy 3+ and Dy hydroxyl complexes using GEMSFITS. Batch-type solubility experiments were conducted from 150 to 250 °C and at saturated water vapor pressure in perchloric acid solutions with initial pH values of 2 to 5 in 0.5 pH unit increments. The measured solubility of Dy hydroxide is retrograde with temperature and decreases with pH. The logarithm of total dissolved Dy molality ranges from –2.3 to –5.3 at 150 °C (pH 4.7–5.5), from –2.4 to –5.6 at 200 °C (pH 3.9–5.1), and from –3.7 to –6.9 at 250 °C (pH of 3.4 and 5.0). The optimized standard partial molal Gibbs energies of formation (Δ f G° T ) derived for Dy 3+ and DyOH 2+ display a close to linear relationship with temperature, fitting with previous optimizations based on DyPO 4 solubility data in the literature. A comparison of the optimized ΔfG°T values for aqueous Dy species with predictions from available HKF parameters indicates significant differences ranging from +11 to –26 kJ/mol between 25 and 250 °C. The experimental fits are used to derive the Dy hydroxide solubility products (K s0 ) and formation constants for the hydrolysis of Dy (β n with n = 1 to 3; Dy 3+ + nOH – = DyOH n 3-n ) as a function of temperature. The optimization method presented yields accurate thermodynamic properties for the Dy 3+ aqua ions and the DyOH 2+ species at the acidic to mildly acidic pH studied whereas more experimental work is needed at near-neutral and alkaline conditions to better constrain the other hydroxyl complexes. Furthermore, the optimized thermodynamic data have a significant impact on geochemical modeling of the mobility and solubility of REE minerals in acidic hydrothermal fluids.

58 GEOSCIENCES↗
DOE OSTI2025

An end-to-end deep learning method for solving nonlocal Allen–Cahn and Cahn–Hilliard phase-field models

Here, we propose an efficient end-to-end deep learning method for solving nonlocal Allen–Cahn (AC) and Cahn–Hilliard (CH) phase-field models. One motivation for this effort emanates from the fact that discretized partial differential equation-based AC or CH phase-field models result in diffuse interfaces between phases, with the only recourse for remediation is to severely refine the spatial grids in the vicinity of the true moving sharp interface whose width is determined by a grid-independent parameter that is substantially larger than the local grid size. In this work, we introduce non-mass conserving nonlocal AC or CH phase-field models with regular, logarithmic, or obstacle double-well potentials. Because of non-locality, some of these models feature totally sharp interfaces separating phases. The discretization of such models can lead to a transition between phases whose width is only a single grid cell wide. Another motivation is to use deep learning approaches to ameliorate the otherwise high cost of solving discretized nonlocal phase-field models. To this end, loss functions of the customized neural networks are defined using the residual of the fully discrete approximations of the AC or CH models, which results from applying a Fourier collocation method and a temporal semi-implicit approximation. To address the long-range interactions in the models, we tailor the architecture of the neural network by incorporating a nonlocal kernel as an input channel to the neural network model. We then provide the results of extensive computational experiments to illustrate the accuracy, predictive capabilities, and cost reductions of the proposed method.

42 ENGINEERING↗
DOE OSTI2025

Parallel diffusion operator for magnetized plasmas with improved spectral fidelity

Diffusive transport processes in magnetized plasmas are highly anisotropic, with fast parallel transport along the magnetic field lines sometimes faster than perpendicular transport by orders of magnitude. This constitutes a major challenge for describing non-grid-aligned magnetic structures in Eulerian (grid-based) simulations. Here, the present paper describes and validates a new method for parallel diffusion in magnetized plasmas based on the anti-symmetry representation [Halpern and Waltz, Phys. Plasmas 25, 060703 (2018)]. In the anti-symmetry formalism, diffusion manifests as a flow operator involving the logarithmic derivative of the transported quantity. Qualitative plane wave analysis shows that the new operator naturally yields better discrete spectral resolution compared to its conventional counterpart. Numerical simulations comparing the new method against existing finite difference methods are carried out, showing significant improvement. In particular, we find that combining anti-symmetry with finite differences in diagonally staggered grids essentially eliminates the so-called “artificial numerical diffusion” that affects conventional finite difference and finite volume methods.

Anisotropic diffusion↗
DOE OSTI2026

The solubility of ErPO 4 and Er speciation in hydrothermal fluids at varying pH and salinity between 350 and 450 °C

The rare earth elements (REE) are important for the green-energy transition and can be incorporated into the REE phosphates, such as xenotime-(Y), which also hosts heavy REE (Tb– Lu). Xenotime-(Y) is a common accessory mineral in metamorphic rocks and a range of mineral deposits where it controls the mobility of heavy REE, however, the impact of high temperature aqueous fluids on the behavior of heavy REE is largely unknown. Thermodynamic modeling can be utilized as a tool to predict the mobility of REE in hydrothermal aqueous fluids, but must be supported by accurate experimental data. Here, we measured the solubility of endmember synthetic xenotime-structured ErPO4 in NaCl-HCl-NaOH-bearing aqueous solutions at 350 °C and water vapor saturation pressure, at 400 and at 450 °C and 500 bar using batch-type Inconel reactors. Erbium speciation was investigated as a function of pH from 2.8 to 8, where Er chloride species are predominant at acidic conditions (pH <3) and Er hydroxyl complexes are predominant at near- neutral to alkaline conditions (pH >3). At pH 7–9, the measured ErPO 4 solubility (-9.8 to -7.5 log m Er ) is up to 2.5 orders of magnitude lower than thermodynamic predictions (-9.4 to -6.7 log m Er ) using existing thermodynamic databases. At pH 2–3, the predicted ErPO 4 solubility is ~0.5 orders of magnitude higher at 350 °C and ~1 order of magnitude lower at 450 °C compared to experimentally measured Er concentrations. The thermodynamic properties of aqueous Er species were therefore revised in this study. The partial molal Gibbs energy of formation (Δ f G 0 T,P ) for aqueous Er hydroxyl and chloride species are optimized using GEMSFITS and the logarithmic formation constants (logβ n ( Cl,OH) ) were derived at each experimental temperature and pressure. The updated thermodynamic properties for Er hydroxyl species (Er(OH) +2 , Er(OH) 2 + , and Er(OH) 3 0 ) show that their stability shifts to more acidic conditions at and below 400 °C. The Er chloride species (ErCl +2 and ErCl 2 + ) show increased stability compared to Er hydroxyl species at temperatures of 450 °C and 0.01 mol/kg NaCl. The updated thermodynamic properties are implemented into the GEM-Selektor modeling package to investigate the mobility of Er in saline hydrothermal fluids in equilibrium with alkaline rocks. Importantly, the updated properties for Er hydroxyl species result in low Er solubility at rock equilibrated pH conditions due to an expanded hydroxyl predominance zone, but lower aqueous complex stability overall, whereas previous models suggest greater stability for aqueous Er species. Furthermore, ErPO 4 solubility increases with decreasing temperature due to the deprotonation of HCl, which increases the acidity of hydrothermal fluids and the availability of Cl - to complex with the REE. These simulations highlight how fluid-rock reaction and temperature affect the mobility of REE in hydrothermal ore-forming systems.

58 GEOSCIENCES↗
DOE OSTI2025

Stochastic room temperature creep of 316 L stainless steel

The creep behavior of 316 L stainless steel at room temperature was evaluated as a function of time and applied stress using a new high-throughput approach. Several common creep models were evaluated against the observations, leading to deeper analysis of a stress-dependent modified logarithmic creep model. Within this model, multiple sources of uncertainty were compared. Aleatoric stochastic variation between samples under nominally identical conditions was identified as the primary contributor to uncertainty in creep response. Under any particular set of conditions, the sample-to-sample variability in creep strain was as high as a factor of two, highlighting the engineering importance of characterizing large statistical datasets. The model's extrapolation capabilities were assessed by comparing predictions derived from calibration on partial, shorter-duration subsets of the data. In conclusion, these findings underscore the importance of accounting for stochastic effects in predictive modeling of aging phenomena.

High-throughput↗
DOE OSTI2025

A Monte-Carlo method for Coulomb collisions in moderately coupled plasmas

Here, we introduce a new approach for coupling cumulative and single-scattering distributions, extending Monte Carlo methods for Coulomb collisions in weakly coupled plasmas into the moderately coupled regime. Using time steps typical of cumulative-scattering methods, we show that this approach not only recovers leading-order corrections proportional to the inverse Coulomb logarithm but also solves the full Boltzmann collision integral. A key feature of the method is its simplicity: it can be integrated into cumulative-scattering methods for weakly coupled plasmas with only ~ 10 additional lines of code.

Boltzmann collision integral↗
DOE OSTI2026

An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations

We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator as a weighted sum of Hamiltonian evolutions, thereby emulating a dissipative problem by mixing various time scales. We introduce an efficient encoding of the LCHS into a quantum circuit based on a simple coordinate transformation that turns the dependence on the summation index into a trigonometric function. Classically, this method is equivalent to the use of a highly accurate Fejér-Clenshaw-Curtis quadrature formula. Quantumly, this significantly simplifies block-encoding of a dissipative problem and allows one to perform an exponential number of Hamiltonian simulations by a single Quantum Signal Processing (QSP) circuit. The resulting LCHS circuit has high success probability and the selector scales logarithmically with the number of terms in the LCHS sum and linearly with time. Careful analysis of error convergence proves that this method is more efficient than other LCHS circuits that have recently appeared in the literature. We verify the quantum circuit and its scaling by simulating it on a digital emulator of fault-tolerant quantum computers and, as a test problem, solve the advection-diffusion equation. The proposed algorithm can be used for simulating a wide class of nonunitary initial-value problems including the Liouville equation with added dissipation and linear embeddings of nonlinear systems, such as the Koopman-von Neumann and Carleman embeddings.

Novikau, I [Lawrence Livermore National Laboratory↗
DOE OSTI2026

A parametric study of slow dynamic nonlinear elasticity with comparisons to models

Several phenomenological models that aspire to quantitative description of anomalous nonlinear mesoscopic elasticity are reviewed and compared with laboratory measurements. This class of nonlinearity, best known perhaps for slow dynamics and aging, is seen widely in imperfectly consolidated granular solids but is not well understood. Typical slow dynamic tests show that a modest conditioning oscillatory "pump" strain depresses material stiffness, which then recovers like the logarithm of time after conditioning ceases. Several phenomenological models based on physical arguments have been proposed that predict the material stiffness response to arbitrary pump strain histories during conditioning and recovery. Approximate closed form and numerical solutions to the models are presented that predict the quantitative influence of three key pump parameters: the pump's strain amplitude, the pump's strain rate, and the pump’s duration. Laboratory measurements on Berea sandstone, concrete and a confined single aluminum bead find that slow dynamic responses are linear in pump strain and independent of pump frequency. Measurements also show that, after pump-off, stiffness recovers over times far longer than the pump duration. These observations and others are compared to model predictions. One of the considered models, based on a picture of fast brittle damage and slow healing, successfully matches all these behaviors.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Determining reference standard strength for neutron-irradiated reduced activation ferritic/martensitic steel F82H by Bayesian method

The deterministic approach widely adopted in the design of structural components relies on systematically defined design limits using empirically determined safety factors. However, this approach is not always appropriate because structures are subjected to a variety of loads in the practical environment, which may result in excessively conservative design limits. In recent years, a more rigorous probabilistic approach that incorporates material strength distributions has become an important solution. In the probabilistic approach, the probability density functions of material strength properties underpin the design criteria. Here, the objective of this study is to identify the density distribution functions that best describe tensile properties of irradiated F82H to define a reference strength for DEMO design. Due to the limited number of existing data, this study specifically employs a Bayesian prediction method based on Monte Carlo simulations to determine a material reference value with statistical reliability and to investigate its effectiveness. For example, the dependence of tensile properties of 300 °C irradiated materials on irradiation damage and the range predicted by 95% Bayesian estimation was evaluated. As a statistical model for the dose dependence of statistical parameters, the normal distribution exhibited a better fit for 0.2% proof strength and tensile strength, whereas the distribution of total elongation data gave comparable reference values for both the normal and Weibull distribution models. Both models gave comparable criteria for the distribution of total elongation data. The Weibull model also gave better results for uniform elongation. The function best describing the model was a logarithmic law for both 0.2% proof strength and tensile strength, while a power law for both total and uniform elongation, which allowed for more comprehensive data prediction of irradiation data with statistical accuracy for DEMO reactor design.

36 MATERIALS SCIENCE↗