Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “asymptotic”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Analytical Modeling of Metal Foam Composite Phase Change Materials (PCM) in Thermal Energy Storage Using Asymptotic Analysis

The use of phase change materials (PCMs) for thermal energy storage can release or absorb a significant amount of latent heat during the freezing or melting process, offering a higher energy storage density. One of the main drawbacks of PCMs is their low thermal conductivity, resulting in poor thermal performance. Recent research has attempted to enhance heat transfer and increase the thermal conductivity of PCMs, including the use of metal foams. However, modeling the metal foam composite PCM using conventional methods is computationally expensive. This paper proposes an asymptotic solution for a Stefan-like problem subject to a convective boundary for outward solidification in a hollow cylinder, capable of predicting the freeze-melt cycle of the metal foam composite PCM. Specifically, three temporal regimes and four spatial layers are considered in the asymptotic analysis for each phase change process. The thermal conductivity is calculated by a theoretical three-dimensional tetrakaidecahedron model, while other thermophysical properties are obtained using the method of volume averaging. The results are verified with numerical data and validated against experimental data in the literature. The presented analytical modeling framework could have the potential to be applied to other types of composite PCMs with considerably lower computational costs compared with conventional methods.

analytical model↗
DOE OSTI2024

An Asymptotic Preserving Discontinuous Galerkin Method for a Linear Boltzmann Semiconductor Model

A key property of the linear Boltzmann semiconductor model is that as the collision frequency tends to infinity, the phase space density $f$ = $f$ ($x, v, t$) converges to an isotropic function $M (v)$$ρ$$(x, t)$, called the drift-diffusion limit, where $M$ is a Maxwellian and the physical density $ρ$ satisfies a second-order parabolic PDE known as the drift-diffusion equation. Numerical approximations that mirror this property are said to be asymptotic preserving. In this paper we build a discontinuous Galerkin method to the semiconductor model, and we show this scheme is both uniformly stable in $ε$, where 1/$ε$ is the scale of the collision frequency, and asymptotic preserving. Here in particular, we discuss what properties the discrete Maxwellian must satisfy in order for the schemes to converge in $ε$ to an accurate $h$-approximation of the drift-diffusion limit. Discrete versions of the drift-diffusion equation and error estimates in several norms with respect to $ε$ and the spacial resolution are also included.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Perturbatively exact $w_{1+∞}$ asymptotic symmetry of quantum self-dual gravity

The infinite tower of positive-helicity soft gravitons in any minimally coupled, tree-level, asymptotically flat four-dimensional (4D) gravity was recently shown to generate a w 1+∞ asymptotic symmetry algebra. It is natural to ask whether this classical algebra acquires quantum corrections at loop level. We explore this in quantum self-dual gravity, whose amplitudes acquire known one-loop exact all-plus helicity quantum corrections. We show using collinear splitting formulae that, remarkably, the w 1+∞ algebra persists in quantum self-dual gravity without corrections.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Open string amplitudes: singularities, asymptotics and new representations

Open string amplitudes at tree level have been studied for over fifty years. However, there is no known analytic form for general n-point amplitudes, and their conventional representation in terms of worldsheet integrals does not make many of their most basic physical properties manifest. Recently, a formulation of these amplitudes exposing the underlying “binary geometry” via the use of “u” variables has given us many insights into their basic features. In this paper, we initiate a systematic exploration of fundamental aspects of open string amplitudes from this new point of view. We begin by finding explicit expressions for the factorization of amplitudes at general massive levels, which are seen to be determined by products of lower-point massless amplitudes with shifted kinematics. We then study the asymptotic behavior when subsets of kinematic variables become large, delineating regimes with exponential (generalized hard scattering) and power-law (generalized Regge) behavior. We also give precise expressions for the asymptotics, which reveal another example of the recently observed property of factorization away from poles. We derive new recursion relations for the amplitude, which when repeatedly applied reduce to infinite series representations with a wider domain of convergence than the usual integral representations. For the five-point case, we present a new closed-form expression for the amplitude that for the first time gives its analytic continuation to all of kinematic space. We also discuss novel relations between amplitudes at different kinematic points following from the recently observed “split” factorizations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Asymptotic behavior of meson transition form factors

One of the open issues in evaluations of the contribution from hadronic light-by-light scattering to the anomalous magnetic moment of the muon (g - 2)µ concerns the role of heavier scalar, axial-vector, and tensormeson intermediate states. The coupling of axial vectors to virtual photons is suppressed for small virtualities by the Landau–Yang theorem, but otherwise there are few rigorous constraints on the corresponding form factors. In this paper, we first derive the Lorentz decomposition of the two-photon matrix elements into scalar functions following the general recipe by Bardeen, Tung, and Tarrach. Based on this decomposition, we then calculate the asymptotic behavior of the meson transition form factors from a light-cone expansion in analogy to the asymptotic limits for the pseudoscalar transition form factor derived by Brodsky and Lepage. Finally, we compare our results to existing data as well as previous models employed in the literature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Islands in asymptotically flat 2D gravity

The large-$\textit{N}$ limit of asymptotically flat two-dimensional dilaton gravity coupled to $\textit{N}$ free matter fields provides a useful toy model for semiclassical black holes and the information paradox. Analyses of the asymptotic information flux as given by the entanglement entropy show that it follows the Hawking curve, indicating that information is destroyed in these models. Recently, motivated by developments in AdS/CFT, a semiclassical island rule for entropy has been proposed. We define and compute the island rule entropy for black hole formation and evaporation in the large-$\textit{N}$ RST model of dilaton gravity and show that, in contrast, it follows the unitary Page curve. The relation of these two observations, and interesting properties of the dilaton gravity island rule, are discussed.

2D Gravity↗
DOE OSTI2022

On the questions of asymptotic recoverability of information and subsystems in quantum gravity

A longstanding question in quantum gravity regards the localization of quantum information; one way to formulate this question is to ask how subsystems can be defined in quantum-gravitational systems. The gauge symmetry and necessity of solving the gravitational constraints appear to imply that the answers to this question here are different than in finite quantum systems, or in local quantum field theory. Specifically, the constraints can be solved by providing a “gravitational dressing” for the underlying field-theory operators, but this modifies their locality properties. It has been argued that holography itself may be explained through this role of the gauge symmetry and constraints, at the nonperturbative level, but there are also subtleties in constructing a holographic map in this approach. There are also claims that holography is implied even by perturbative solution of the constraints. This short note provides further examination of these questions, and in particular investigates to what extent perturbative or nonperturbative solution of the constraints implies that information naïvely thought to be localized can be recovered by asymptotic measurements, and the relevance of this in defining subsystems. In the leading perturbative case, the relevant effects are seen to be exponentially suppressed and asymptotically vanishing, for massive fields. These questions are, for example, important in sharply characterizing the unitarity problem for black holes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Asymptotic scalar field cosmology in string theory

Asymptotic (late-time) cosmology depends on the asymptotic (infinite-distance) limits of scalar field space in string theory. Such limits feature an exponentially decaying potential V ~ exp(–c$\phi$) with corresponding Hubble scale H ~ $\sqrt{{\dot{\phi}}^2+2V}$ ~ exp(–λ H$\phi$ ), and at least one tower of particles whose masses scale as m ~ exp(–λΦ), as required by the Distance Conjecture. In this paper, we provide evidence that these coefficients satisfy the inequalities $\sqrt{\left(d-1\right)/\left(d-2\right)}$ ≥ λ H ≥ λ lightest ≥ 1/$\sqrt{d-2}$ in d spacetime dimensions, where λ lightest is the λ coefficient of the lightest tower. This means that at late times, as the scalar field rolls to $\phi$ → ∞, the low-energy theory remains a d-dimensional FRW cosmology with decelerated expansion, the light towers of particles predicted by the Distance Conjecture remain at or above the Hubble scale, and both the strong energy condition and the dominant energy condition are satisfied.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Asymptotic vacuum solution at tokamak X-point tip

In the H-mode regime of diverted tokamaks, the presence of strong pressure gradients in the pedestal gives rise to a sizable bootstrap current, together with the Ohmic and Pfirsch–Schlueter currents, close to the separatrix. For such equilibria, the presence of finite current density close to the separatrix requires the reexamination of equilibrium properties. It is almost universally assumed that the two branches of the separatrix (the stable and unstable manifolds) are straight as they cross at the X-point. However, the opposite angles of the plasma-filled segment and vacuum one cannot be equal if the current density does not vanish at the separatrix on the plasma side. We solve this difficulty by chipping off a thin layer of plasma edge so that the sharp corner of the plasma-filled segment becomes a hyperbola. Using the conformal transformation, we found that in the assumption of a hyperbolic boundary, the X point moves beyond the plasma boundary to fall in the vacuum region. An acute angle of the plasma-filled segment leads to an obtuse opposite angle of vacuum segment and vice versa. In the case of an acute angle of the plasma-filled segment, the new X point shifts inside the X point formed by the asymptotes of a hyperbolic boundary; in the case of an obtuse angle of the plasma-filled segment, the new X point shifts outside the X point formed by the asymptotes of a hyperbolic plasma boundary. Furthermore, the results are important for understanding the X point features, which affect the tokamak edge stability and transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Computation of generalised magnetic coordinates asymptotically close to the separatrix

Integrals to calculate generalised magnetic coordinates from an input magnetic flux function asymptotically close to the separatrix are presented, and implemented in the GPEC/DCON code suite. These integrals allow characterisation of the magnetic equilibrium of a diverted tokamak, in magnetic coordinates, arbitrarily close to the last closed flux surface, avoiding the numerical issues associated with calculating diverging field-line integrals near a magnetic x-point. Finally, these methods may assist ongoing efforts to develop robust asymptotic equilibrium behaviour for spectral 3D MHD codes at the separatrix.

equilibrium edge truncation↗
DOE OSTI2021

Asymptotic reversibility of thermal operations for interacting quantum spin systems via generalized quantum Stein’s lemma

Abstract For quantum spin systems in any spatial dimension with a local, translation-invariant Hamiltonian, we prove that asymptotic state convertibility from a quantum state to another one by a thermodynamically feasible class of quantum dynamics, called thermal operations, is completely characterized by the Kullback–Leibler (KL) divergence rate, if the state is translation-invariant and spatially ergodic. Our proof consists of two parts and is phrased in terms of a branch of the quantum information theory called the resource theory. First, we prove that any states, for which the min and max Rényi divergences collapse approximately to a single value, can be approximately reversibly converted into one another by thermal operations with the aid of a small source of quantum coherence. Second, we prove that these divergences collapse asymptotically to the KL divergence rate for any translation-invariant ergodic state. We show this via a generalization of the quantum Stein’s lemma for quantum hypothesis testing beyond independent and identically distributed situations. Our result implies that the KL divergence rate serves as a thermodynamic potential that provides a complete characterization of thermodynamic convertibility of ergodic states of quantum many-body systems in the thermodynamic limit, including out-of-equilibrium and fully quantum situations.

Physics↗
DOE OSTI2026

Large-momentum effective theory’s asymptotic extrapolation vs the inverse problem

Large-momentum effective theory is a physics-guided systematic expansion to calculate light-cone parton distributions, including collinear (PDFs) and transverse-momentum-dependent ones, at any fixed momentum fraction 𝑥 within a range of [𝑥 min , 𝑥 max ]. It theoretically solves the ill-posed inverse problem that afflicts other theoretical approaches to collinear PDFs, such as short-distance factorizations. Recently, Dutrieux et al. raised practical concerns about whether current or even future lattice data will have sufficient precision in the subasymptotic correlation region to support an error-controlled extrapolation—and if not, whether it becomes an inverse problem where the relevant uncertainties cannot be properly quantified. While we agree that not all current lattice data have the desired precision to qualify for an asymptotic extrapolation, some calculations do, and more are expected in the future. We comment on the analysis and results in Dutrieux et al. and argue that a physics-based systematic extrapolation still provides the most reliable error estimates, even when the data quality is not ideal. In contrast, reframing the long-distance asymptotic extrapolation as a data-driven-only inverse problem with ad hoc mathematical conditioning could lead to unnecessarily conservative errors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Small-𝑥 asymptotics of the leading-twist flavor-singlet quark TMDs

In this paper, we investigate the small-𝑥 behavior of the flavor-singlet, leading-twist quark transverse-momentum-dependent parton distribution functions (TMDs) using the light-cone operator treatment. This formalism allows us to express TMD operators at small 𝑥 in terms of polarized dipole amplitudes, enabling a systematic approach to their small-𝑥 evolution. We derive the evolution equations for these TMDs and solve them within the large-𝑁 𝑐 approximation under the linearized, double-logarithmic approximation, where 𝑁 𝑐 represents the number of quark colors. Expanding on previous work on unpolarized and helicity TMDs, we present the small-𝑥 asymptotics for a comprehensive set of TMDs, including the Sivers function, helicity worm-gear, transversity, pretzelosity, Boer-Mulders, and transversity worm-gear distributions. Our results provide a complete picture of the small-𝑥 asymptotic behavior for all leading-twist flavor-singlet quark TMDs. We also discuss the implications of our findings for phenomenological applications and outline potential avenues for further research, particularly in understanding nonlinear effects and extending beyond the double-logarithmic approximation and large-𝑁 𝑐 approximations.

Adamiak, Daniel [Thomas Jefferson National Acceler↗
DOE OSTI2024

Fast explicit solutions for neutrino-electron scattering: Explicit asymptotic methods

Here, we present results of explicit asymptotic approximations applied to neutrino-electron scattering in a representative model of neutrino population evolution under conditions characteristic of core-collapse supernova explosions or binary neutron star mergers. It is shown that this approach provides stable solutions of these stiff systems of equations, with accuracy and time stepping comparable to that for standard implicit treatments such as backward Euler, fixed point iteration, and Anderson-accelerated fixed point iteration. Because each time step can be computed more rapidly with the explicit asymptotic approximation than with implicit methods, this suggests that algebraically stabilized explicit integration methods could be used to compute neutrino evolution coupled to hydrodynamics more efficiently in stellar explosions and mergers than the methods currently in use.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Asymptotic optimality of twist-untwist protocols for Heisenberg scaling in atom-based sensing

Twist-untwist protocols for quantum metrology consist of a serial application of (1) unitary nonlinear dynamics (e.g., spin squeezing or Kerr nonlinearity), (2) parameterized dynamics U ( φ ) (e.g., a collective rotation or phase space displacement), and (3) time reversed application of step 1. Such protocols are known to produce states that allow Heisenberg scaling for experimentally accessible estimators of φ even when the nonlinearities are applied for times much shorter than required to produce Schrödinger cat states. In this work, we prove that, asymptotically in the number of particles, twist-untwist protocols provide the lowest estimation error among quantum metrology protocols that utilize two calls to a weakly nonlinear evolution and a readout involving only first and second moments of a total spin operator n → · J → . We consider the following physical settings: all-to-all interactions generated by one-axis twisting J z 2 (e.g., interacting Bose gases), constant finite range spin-spin interactions of distinguishable or bosonic atoms (e.g., trapped ions or Rydberg atoms, or lattice bosons). In these settings, we further show that the optimal twist-untwist protocols asymptotically achieve 85% and 92% of the respective quantum Cramér-Rao bounds. We show that the error of a twist-untwist protocol can be decreased by a factor of L without an increase in the noise of the spin measurement if the twist-untwist protocol can be noiselessly iterated as an L layer quantum alternating operator ansatz.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Asymptotic gauge symmetry and UV extension of the nonperturbative coupling in holographic QCD

We extend our recent analytic study of the strong coupling 𝛼 eff in the nonperturbative and near-perturbative regimes [Phys. Rev. Lett. 133, 181901 (2024)] by imposing rigorous renormalization-group constraints from asymptotically free gauge theories at 𝑄 2 → ∞. The asymptotic boundary conditions modify the scaling properties of 𝛼eff at large values of the momentum transfer 𝑄 2 and lead to a scale-dependent confinement strength 𝜅⁡(𝑄 2 ). This requires that both 𝜅⁡(𝑄 2 ) and 𝛼 eff⁡ (𝑄 2 , 𝜅⁡(𝑄 2 )) remain holomorphic in the complex 𝑄 2 plane, except at the physical cuts associated with the heavy-quark thresholds and the singularity flow trajectory studied in our previous Letter. For color SU(3), a precise connection is found between the scaling exponent of 𝜅⁡(𝑄 2 ) in the ultraviolet, the value of the infrared fixed point of the strong coupling, and the number of flavors in agreement with observations. The nonperturbative analytic model gives an accurate description of the strong coupling across all scales, up to the highest available data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Method of Moving Asymptotes Optimization Algorithm in Python

Python implementation of the Method of Moving Asymptotes optimization algorithm described in[Svanberg, K., The method of moving asymptotes- a new method for structural optimization. International journal for numerical methods in engineering, 1987. 24(2): p.359 (https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.1620240207). Originally implemented in[GetDP](https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=717799) [project](https://gitlab.onelab.info/getdp/getdp), although it has been deleted in their repository.

Salazar De Troya, Miguel↗
DOE OSTI2021

EFT asymptotics: the growth of operator degeneracy

We establish formulae for the asymptotic growth (with respect to the scaling dimension) of the number of operators in effective field theory, or equivalently the number of S-matrix elements, in arbitrary spacetime dimensions and with generic field content. This we achieve by generalising a theorem due to Meinardus and applying it to Hilbert series---partition functions for the degeneracy of (subsets of) operators. Although our formulae are asymptotic, numerical experiments reveal remarkable agreement with exact results at very low orders in the EFT expansion, including for complicated phenomenological theories such as the standard model EFT. Our methods also reveal phase transition-like behaviour in Hilbert series. We discuss prospects for tightening the bounds and providing rigorous errors to the growth of operator degeneracy, and of extending the analytic study and utility of Hilbert series to EFT.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗