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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Double Kerr-Schild spacetimes and the Newman-Penrose map

The Newman-Penrose map, which is closely related to the classical double copy, associates certain exact solutions of Einstein’s equations with self-dual solutions of the vacuum Maxwell equations. Here we initiate an extension of the Newman-Penrose map to a broader class of spacetimes. As an example, we apply principles from the Newman-Penrose map to associate a self-dual gauge field to the Kerr-Taub-NUT-(A)dS spacetime and we show that the result agrees with previously studied examples of classical double copies. The corresponding field strength exhibits a discrete electric-magnetic duality that is distinct from its (Hodge star) self-dual property.

scattering amplitudes↗
DOE OSTI2024

2D Dilaton Gravity and the Weil–Petersson Volumes with Conical Defects

We derive the Weil-Petersson measure on the moduli space of hyperbolic surfaces with defects of arbitrary opening angles and use this to compute its volume. We conjecture a matrix integral computing the corresponding volumes and confirm agreement in simple cases. Here, we combine this mathematical result with the equivariant localization approach to Jackiw-Teitelboim gravity to justify a proposed exact solution of pure 2d dilaton gravity for a large class of dilaton potentials.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

hr-Adaptivity for nonconforming high-order meshes with the target matrix optimization paradigm

In this study, we present an \(hr\) -adaptivity framework for optimization of high-order meshes. This work extends the r -adaptivity method by Dobrev et al. (Comput Fluids, 2020), where we utilized the Target-Matrix Optimization Paradigm (TMOP) to minimize a functional that depends on each element’s current and target geometric parameters: element aspect-ratio , size , skew , and rotation . Since fixed mesh topology limits the ability to achieve the target size and aspect-ratio at each position, in this paper, we augment the r -adaptivity framework with nonconforming adaptive mesh refinement to further reduce the error with respect to the target geometric parameters. The proposed formulation, referred to as \(hr\) -adaptivity, introduces TMOP-based quality estimators to satisfy the aspect-ratio target via anisotropic refinements and size target via isotropic refinements in each element of the mesh. The methodology presented is purely algebraic, extends to both simplices and hexahedra/quadrilaterals of any order, and supports nonconforming isotropic and anisotropic refinements in 2D and 3D. Using a problem with a known exact solution, we demonstrate the effectiveness of \(hr\) -adaptivity over both r - and \(h\) -adaptivity in obtaining similar accuracy in the solution with significantly fewer mesh nodes. We also present several examples that show that \(hr\) -adaptivity can help satisfy geometric targets even when \(r\) -adaptivity fails to do so, due to the topology of the initial mesh.

42 ENGINEERING↗
DOE OSTI2026

Dynamics of McMillan mappings III. Symmetric map with mixed nonlinearity

This article extends the study of the dynamical properties of the symmetric McMillan map, emphasizing its utility in understanding and modeling complex nonlinear systems. Although the map features six parameters, we demonstrate that only two are irreducible: the linearized rotation number at the fixed point and a nonlinear parameter representing the ratio of terms in the biquadratic invariant. Through a detailed analysis, we classify regimes of stable motion, provide exact solutions to the mapping equations, and derive a canonical set of action-angle variables, offering analytical expressions for the rotation number and nonlinear tune shift. We further establish connections between general standard-form mappings and the symmetric McMillan map, using the area-preserving Hénon map and accelerator lattices with thin sextupole magnet as representative case studies. Our results show that, despite being a second-order approximation, the symmetric McMillan map provides a highly accurate depiction of dynamics across a wide range of system parameters, demonstrating its practical relevance in both theoretical and applied contexts.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Topological order in Mott insulators

Here in this commemorative issue for Phil Anderson, I reproduce parts of a joint unpublished paper that first got me thinking about topological order in Mott insulators. With Phil, we explored aspects of the momentum distribution function and the non-classical rotational inertia in the Bose Hubbard model close to the quantum phase transition. My interest on this question continued, and later in the article I take up the question of topological order in the Kitaev Mott insulator on the honeycomb lattice with bond-dependent interactions in a finite magnetic field. Kitaev obtained the exact solution for zero field that demonstrated an exotic Z 2 quantum spin liquid phase with topological order. In a finite magnetic field, we discovered a new intermediate U(1) gapless quantum spin liquid phase, sandwiched between the known gapped Kitaev spin liquid and a polarized phase, that harbors fractionalized neutral fermionic excitations, dubbed spinons, that remarkably form a Fermi surface in a Mott insulator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A priori error analysis of high-order LL* (FOSLL*) finite element methods

A number of non-standard finite element methods have been proposed in recent years, each of which derives from a specific class of PDE-constrained norm minimization problems. The most notable examples are LL* methods. In this work, we argue that all high-order methods in this class should be expected to deliver substandard uniform h-refinement convergence rates. In fact, one may not even see rates proportional to the polynomial order p > 1 when the exact solution is a constant function. Here, we show that the convergence rate is limited by the regularity of an extraneous Lagrange multiplier variable which naturally appears via a saddle-point analysis. In turn, limited convergence rates appear because the regularity of this Lagrange multiplier is determined, in part, by the geometry of the domain. Numerical experiments support our conclusions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Optimization of battery swapping infrastructure for e-commerce drone delivery

Drone delivery is widely-researched to alter the current e-commerce delivery convention for providing short delivery lead times. Yet, flight range of drones, constrained by the available battery technology, sets a milestone toward realizing the sole-drone delivery. To tackle with the flight range limitation, locating automated battery swapping machines (ABSM) have been proposed and a few studies modeled the problem. Using the ABSMs, drones can be loaded with fully-charged batteries along the route to a demand location. Here, we introduce a mixed-integer nonlinear program to model the problem. The objective of the program is to optimally select ABSM locations, determine the delivery-mode choices (drone-only, truck-only, and mixed delivery) of demand locations, find drone delivery routes, and approximate the baseline requirements for the number of drones and batteries needed. The program minimizes the overall delivery system costs including: ABSM, delivery, drone ownership, battery inventory, and service congestion. A cutting-plane method is developed to find exact solutions in finite iterations. Computational experiments showed that the method quickly yields the optimal solution to instances with less than 60 ABSM candidates and 20 demand locations. A case study shows that the optimal drone delivery infrastructure can save almost 20% cost compared to the conventional truck-only delivery. Sensitivity analyses were conducted to reveal the impact of key parameters in the decision-making and found that a decrease in the ABSM and drone costs highly affect the system cost.

25 ENERGY STORAGE↗
DOE OSTI2020

Designing a drone delivery network with automated battery swapping machines

Drones are projected to alter last-mile delivery, but their short travel range is a concern. In this study, we propose a drone delivery network design using automated battery swapping machines (ABSMs) to extend ranges. The design minimizes the long-term delivery costs, including ABSM investment, drone ownership, and cost of the delivery time, and locates ABSMs to serve a set of customers. We build a mixed-integer nonlinear program that captures the nonlinear waiting time of drones at ABSMs. To solve the problem, we create an exact solution algorithm that finds the globally optimal solution using a derivative-supported cutting-plane method. To validate the applicability of our program, we conduct a case study on the Chicago Metropolitan area using cost data from leading ABSM manufacturer and geographical data from the planning and operations language for agent-based regional integrated simulation (more commonly known as POLARIS). A sensitivity analysis identifies that ABSM service times and costs are the key parameters impacting the long-term adoption of drone delivery.

25 ENERGY STORAGE↗
DOE OSTI2020

Fibonacci fast convergence for neutrino oscillations in matter

Understanding neutrino oscillations in matter requires a non-trivial diagonalization of the Hamiltonian. As the exact solution is very complicated, many approximation schemes have been pursued. Here we show that one scheme, systematically applying rotations to change to a better basis, converges exponentially fast wherein the rate of convergence follows the Fibonacci sequence. We find that the convergence rate of this procedure depends very sensitively on the initial choices of the rotations as well as the mechanism of selecting the pivots. We then apply this scheme for neutrino oscillations in matter and discover that the optimal convergence rate is found using the following simple strategy: first apply the vacuum (2-3) rotation and then use the largest off-diagonal element as the pivot for each of the following rotations. The Fibonacci convergence rate presented here may be extendable to systems beyond neutrino oscillations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Delivery drone route planning over a battery swapping network

Many enterprises invest on drone delivery research and development to drop off packages at consumers’ doorsteps in a matter of minutes. We study delivery drone route planning over a battery swapping network allowing farther reach by penetrating current battery capacity constraints. A mixed-integer nonlinear programming model is created to plan efficient drone routing over the swapping machines by minimizing the delivery lead time. We develop an exact solution method, evaluate its performance, and compare it with a straightforward nonlinear solver application. A case study highlights the applicability of the model. Data and source code to the solver are publicly shared.

drone battery swapping↗
DOE OSTI2024

Richtmyer–Meshkov instability when a shock is reflected for fluids with arbitrary equation of state

First predicted by Richtmyer in 1960 and experimentally confirmed by Meshkov in 1969, the Richtmyer–Meshkov instability (RMI) is crucial in fields such as physics, astrophysics, inertial confinement fusion and high-energy-density physics. These disciplines often deal with strong shocks moving through condensed materials or high-pressure plasmas that exhibit non-ideal equations of state (EoS), thus requiring theoretical models with realistic fluid EoS for accurate RMI simulations. Approximate formulae for asymptotic growth rates, like those proposed by Richtmyer, are helpful but rely on heuristic prescriptions for compressible materials. These prescriptions can sometimes approximate the RMI growth rate well, but their accuracy remains uncertain without exact solutions, as the fully compressible RMI growth rate is influenced by both vorticity deposited during shock refraction and multiple sonic wave refractions. This study advances previous work by presenting an analytic, fully compressible theory of RMI for reflected shocks with arbitrary EoS. It compares theoretical predictions with heuristic prescriptions using ideal gas, van der Waals gas and three-term constitutive equations for simple metals, the latter being analysed with detailed and simplified ideal-gas-like EoS. We additionally offer an alternative explicit approximate formula for the asymptotic growth rate. The comprehensive model also incorporates the effects of constant-amplitude acoustic waves at the interface, associated with the D'yakov–Kontorovich instability in shocks.

Napieralski, Mario (ORCID:0009000692344901)↗
DOE OSTI2021

Multiple fermion scattering in the weakly coupled spin-chain compound YbAlO 3

The Heisenberg antiferromagnetic spin-1/2 chain, originally introduced almost a century ago, is one of the best studied models in quantum mechanics due to its exact solution, but nevertheless it continues to present new discoveries. Its low-energy physics is described by the Tomonaga-Luttinger liquid of spinless fermions, similar to the conduction electrons in one-dimensional metals. In this work we investigate the Heisenberg spin-chain compound YbAlO3 and show that the weak interchain coupling causes Umklapp scattering between the left- and right-moving fermions and stabilizes an incommensurate spin-density wave order at q = 2k F under finite magnetic fields. These Umklapp processes open a route to multiple coherent scattering of fermions, which results in the formation of satellites at integer multiples of the incommensurate fundamental wavevector Q = nq. Our work provides surprising and profound insight into bandstructure control for emergent fermions in quantum materials, and shows how neutron diffraction can be applied to investigate the phenomenon of coherent multiple scattering in metals through the proxy of quantum magnetic systems.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Dynamic gain and frequency comb formation in exceptional-point lasers

Abstract Exceptional points (EPs)—singularities in the parameter space of non-Hermitian systems where two nearby eigenmodes coalesce—feature unique properties with applications such as sensitivity enhancement and chiral emission. Existing realizations of EP lasers operate with static populations in the gain medium. By analyzing the full-wave Maxwell–Bloch equations, here we show that in a laser operating sufficiently close to an EP, the nonlinear gain will spontaneously induce a multi-spectral multi-modal instability above a pump threshold, which initiates an oscillating population inversion and generates a frequency comb. The efficiency of comb generation is enhanced by both the spectral degeneracy and the spatial coalescence of modes near an EP. Such an “EP comb” has a widely tunable repetition rate, self-starts without external modulators or a continuous-wave pump, and can be realized with an ultra-compact footprint. We develop an exact solution of the Maxwell–Bloch equations with an oscillating inversion, describing all spatiotemporal properties of the EP comb as a limit cycle. We numerically illustrate this phenomenon in a 5-μm-long gain-loss coupled AlGaAs cavity and adjust the EP comb repetition rate from 20 to 27 GHz. This work provides a rigorous spatiotemporal description of the rich laser behaviors that arise from the interplay between the non-Hermiticity, nonlinearity, and dynamics of a gain medium.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Bose–Einstein condensation of a two-magnon bound state in a spin-1 triangular lattice

In ordered magnets, the elementary excitations are spin waves (magnons), which obey Bose–Einstein statistics. Similarly to Cooper pairs in superconductors, magnons can be paired into bound states under attractive interactions. The Zeeman coupling to a magnetic field is able to tune the particle density through a quantum critical point, beyond which a ‘hidden order’ is predicted to exist. Here, in this work, we report direct observation of the Bose–Einstein condensation of the two-magnon bound state in Na 2 BaNi(PO 4 ) 2 . Comprehensive thermodynamic measurements confirmed the two-dimensional Bose–Einstein condensation quantum critical point at the saturation field. Inelastic neutron scattering experiments were performed to establish the microscopic model. An exact solution revealed stable two-magnon bound states that were further confirmed by electron spin resonance and nuclear magnetic resonance experiments, demonstrating that the quantum critical point is due to the pair condensation, and the phase below the saturation field is likely the long-sought-after spin nematic phase.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

The transition from field emission to collisional space-charge limited current with nonzero initial velocity

Abstract Multiple electron emission mechanisms often contribute in electron devices, motivating theoretical studies characterizing the transitions between them. Previous studies unified thermionic and field emission, defined by the Richardson-Laue-Dushman (RLD) and Fowler–Nordheim (FN) equations, respectively, with the Child-Langmuir (CL) law for vacuum space-charge limited current (SCLC); another study unified FN and CL with the Mott-Gurney (MG) law for collisional SCLC. However, thermionic emission, which introduces a nonzero injection velocity, may also occur in gas, motivating this analysis to unify RLD, FN, CL, and MG. We exactly calculate the current density as a function of applied voltage over a range of injection velocity (i.e., temperature), mobility, and gap distance. This exact solution approaches RLD, FN, and generalized CL (GCL) and MG (GMG) for nonzero injection velocity under appropriate limits. For nonzero initial velocity, GMG approaches zero for sufficiently small applied voltage and mobility, making these gaps always space-charge limited by either GMG at low voltage or GCL at high voltage. The third-order nexus between FN, GMG, and GCL changes negligibly from the zero initial velocity calculation over ten orders of magnitude of applied voltage. These results provide a closed form solution for GMG and guidance on thermionic emission in a collisional gap.

42 ENGINEERING↗
DOE OSTI2020

Modeling of surface mechanical behaviors of soft elastic solids: theory and examples

Surfaces of soft solids can have significant surface stress, extensional modulus and bending stiffness. Previous theoretical studies have usually examined cases in which both the surface stress and bending stiffness are constant, assuming small deformation. In this work we consider a general formulation in which the surface can support large deformation and carry both surface stresses and surface bending moments. We show that the large deformation theory can be reduced to the classical linear theory (Shuttleworth equation). We obtain exact solutions for problems of an inflated cylindrical shell and bending of a plate with a finite thickness. Our analysis illustrates the different manners in which surface stiffening and surface bending stabilize these structures. We discuss how the complex surface constitutive behaviors affect the stress field of the bulk. Our calculation provides insights into effects of strain-dependent surface stress and surface bending in the large deformation regime, and can be used as a model to implement surface finite elements to study large deformation of complex structures.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Stability analysis of the Eulerian–Lagrangian finite volume methods for nonlinear hyperbolic equations in one space dimension

In this paper, we construct a novel Eulerian–Lagrangian finite volume (ELFV) method for nonlinear scalar hyperbolic equations in one space dimension. It is well known that the exact solutions to such problems may contain shocks though the initial conditions are smooth, and direct numerical methods may suffer from restricted time step sizes. To relieve the restriction, we propose an ELFV method, where the space-time domain was separated by the partition lines originated from the cell interfaces whose slopes are obtained following the Rakine–Hugoniot junmp condition. Unfortunately, to avoid the intersection of the partition lines, the time step sizes are still limited. To fix this gap, we detect effective troubled cells (ETCs) and carefully design the influence region of each ETC, within which the partitioned space-time regions are merged together to form a new one. Then with the new partition of the space-time domain, we theoretically prove that the proposed first-order scheme with Euler forward time discretization is total-variation-diminishing and maximum-principle-preserving with at least twice larger time step constraints than the classical first order Eulerian method for Burgers’ equation. Numerical experiments verify the optimality of the designed time step sizes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Driving a magnetized domain wall in an antiferromagnet by magnons

We theoretically study the interaction of magnons, quanta of spin waves, and a domain wall in a one-dimensional easy-axis antiferromagnet in the presence of an external magnetic field applied along the easy axis. To this end, we begin by obtaining the exact solution for spin waves in the background of a domain wall magnetized by an external field. The finite magnetization inside the domain wall is shown to give rise to reflection of magnons scattering off the domain wall, deviating from the well-known result of reflection-free magnons in the absence of a magnetic field. For practical applications of the predicted reflection of magnons, we show that the magnon reflection contributes to the thermally driven domain-wall motion. Our work leads us to envision that inducing a finite magnetization in antiferromagnetic solitons such as vortices and skyrmions can be used to engender phenomena that do not occur in the absence of magnetization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗