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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 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Flow Field Measurement of Mixing Driven by Buoyancy

Mixing driven by buoyancy-induced flows inside a cavity consists of stretching and folding of an interface. Measurement of the flow field using particle imaging velocimetry shows that during stretching the flow field has a single elliptic point, thus dominated by a single vortex. However, global bifurcation that results in folding introduces a hyperbolic point whereby the flow field degenerates to multiple vortex interactions. The short-lived coherent structure observed during mixing which results in the Rayleigh- Taylor morphology is attributed to vortex interactions. The mixing characteristics of non-homogeneous fluids driven by buoyancy are important towards understanding transport phenomenon in a microgravity environment. Mixing consists of stretching and folding of an interface due to a flow field whose intensity depends on the body force. For miscible liquids, the characteristic of the flow field determines whether mass transport is governed by diffusion or bulk stirring which induces mixing. For technologically important processes, transport of mass is governed by the coupling of the body force to scalar gradients such as concentration and or temperature' 2 3 . In order to lend insight into these classes of problems we consider a model experimental system to study mixing driven by buoyancy-induced flows. The characteristics of mixing is addressed from detail measurements of the flow field using particle imaging velocimetry (PIV), and its corresponding interface dynamics using image processing techniques.

Batur, C.↗
NASA NTRSDate not supplied

Rocket Lab Venus - Enabling Low-Cost Interplanetary Missions

Rocket Lab’s mission to Venus [1], launching in January 2025, aims to demonstrate that small launch vehicles, such as Electron, and high-energy small spacecraft, such as Photon, can enable a new paradigm of regular, low-cost interplanetary missions. The Electron launch vehicle will deliver the Photon spacecraft carrying the entry probe into low earth orbit, at which point Photon will take over and put both itself and the attached probe on an Earth-Venus transfer trajectory, with assistance from a Lunar flyby. The primary science objective of the mission is to sample the Venusian cloud layers between atitudes of 45 and 60 km above the surface with an autofluorescing nephelometer. The ~1kg scientific instrument will be carried by a small ~17 kg direct entry probe which will separate from the Photon spacecraft approximately 30 minutes prior to atmospheric entry. The probe outer mould line is a scaled down version of the Deep Space 2 probes [2]. NASA’s newly developed 3D Woven Carbon Phenolic, a derivative of the Heatshield for Extreme Entry Environment Technology (HEEET) material [3], is an enabling technology for this mission, and it will comprise the probe forebody heat shield.The probe will communicate directly back to the Earth during its descent via a small on-board radio frequency (RF) antenna. The hyperbolic Venus encounter will see the probe enter the Venusia atmosphere at approximately 11 km/s with an entry flight path angle (EFPA) of about 10°. This relatively low entry angle was selected to increase the duration of the descent phase, reduce the peak deceleration, and reduce the sensitivity of the nominal entry environments to navigational errors. For reference, the Pioneer Venus probes entered at EFPAs varying from about 25° to 70°, resulting in peak decelerations between around 220 and 450 g’s and peak stagnation point heat fluxes ranging from about 40 to 75 MW/m2 [4]. In comparison, the Rocket Lab Venus probe will experience a lower preak deceleration of around 60 g’s and a lower peak stagnation point heat flux of about 15 MW/m2, at the cost of a greater total heat load and correspondingly higher thermal protection system (TPS) mass fraction. This paper recounts the development history of the TPS for the Rocket Lab Venus probe, with a focus on the unique requirements of the mission. In particular, the effect on the TPS design of the mission’s tight budget, short development timeline, slim mass and RF link margins, and mild but long duration entry heating. Rocket Lab’s initial investigations into a ‘hybrid’ TPS [5] based on a scaled version of the Pioneer Venus full-density carbon phenolic forebody shield, and the abandonment of this approach in favour of NASA’s 3D Woven Carbon Phenolic is presented. Additionally, the leveraging of previous testing under the HEEET project at higher conditions and the associated TPS margining strategy that was adopted to avoid the need for extensive mission-specific arc jet testing is discussed. Finally, this paper concludes with a brief consideration of the feasibility of a future low-cost aerocapture technology demonstrator mission based on the 2025 Rocket Lab Venus mission and entry probe.

Lyle Campbell↗
NASA NTRS1993

User's manual for the HYPGEN hyperbolic grid generator and the HGUI graphical user interface

The HYPGEN program is used to generate a 3-D volume grid over a user-supplied single-block surface grid. This is accomplished by solving the 3-D hyperbolic grid generation equations consisting of two orthogonality relations and one cell volume constraint. In this user manual, the required input files and parameters and output files are described. Guidelines on how to select the input parameters are given. Illustrated examples are provided showing a variety of topologies and geometries that can be treated. HYPGEN can be used in stand-alone mode as a batch program or it can be called from within a graphical user interface HGUI that runs on Silicon Graphics workstations. This user manual provides a description of the menus, buttons, sliders, and typein fields in HGUI for users to enter the parameters needed to run HYPGEN. Instructions are given on how to configure the interface to allow HYPGEN to run either locally or on a faster remote machine through the use of shell scripts on UNIX operating systems. The volume grid generated is copied back to the local machine for visualization using a built-in hook to PLOT3D.

Chan, William M.↗
DOE OSTI2025

Gradient flow based phase-field modeling using separable neural networks

Allen–Cahn equation is a reaction–diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen–Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space–time approach. To overcome these challenges, we propose solving the gradient flow of the Ginzburg–Landau free energy functional, which is equivalent to the Allen–Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen–Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space–time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulation and computational implementation, several case studies illustrate the applicability of the proposed method.

42 ENGINEERING↗
NASA NTRS1990

An investigation of design optimization using a 2-D viscous flow code with multigrid

Computational fluid dynamics (CFD) codes have advanced to the point where they are effective analytical tools for solving flow fields around complex geometries. There is also a need for their use as a design tool to find optimum aerodynamic shapes. In the area of design, however, a difficulty arises due to the large amount of computer resources required by these codes. It is desired to streamline the design process so that a large number of design options and constraints can be investigated without overloading the system. There are several techniques which have been proposed to help streamline the design process. The feasibility of one of these techniques is investigated. The technique under consideration is the interaction of the geometry change with the flow calculation. The problem of finding the value of camber which maximizes the ratio of lift over drag for a particular airfoil is considered. In order to test out this technique, a particular optimization problem was tried. A NACA 0012 airfoil was considered at free stream Mach number of 0.5 with a zero angle of attack. Camber was added to the mean line of the airfoil. The goal was to find the value of camber for which the ratio of lift over drag is a maximum. The flow code used was FLOMGE which is a two dimensional viscous flow solver which uses multigrid to speed up convergence. A hyperbolic grid generation program was used to construct the grid for each value of camber.

Doria, Michael L.↗
DOE OSTI2022

Plasma thermal transport with a generalized 8-moment distribution function

Moment equations that model plasma transport require an ansatz distribution function to close the system of equations. The resulting transport is sensitive to the specific closure used, and several options have been proposed in the literature. Two different 8-moment distribution functions can be generalized to form a single-parameter family of distribution functions. The transport coefficients resulting from this generalized distribution function can be expressed in terms of this free parameter. This provides the flexibility of matching the 8-moment model to some validating result at a given magnetization value, such as Braginskii’s transport, or the more recent results of Davies et al. [Physics of Plasma, 28, 012305 (2021)]. Here, this process can be thought of as solving for the 8-moment distribution function that matches the value of a transport coefficient given by a Chapman-Enskog expansion, while retaining the improved physical properties, such as finite propagation speeds and time dependence which belong to the hyperbolic moment models. Since the presented generalized distribution function only has a single free parameter, only a single transport coefficient can be matched at a time. However, this generalization process may be extended to provide multiple free parameters. The focus of this Brief Communication is on the dramatically improved thermal conductivity of the proposed model compared to the two base moment models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1994

System for locating the sources of wideband dE/dt from lightning

A system has been developed to measure wideband electic field derivatives (dE/dt) at five ground stations in a 15 km x 15 km network at Kennedy Space Center. Individual station responses are normalized using digital filters. Pulse-timing resolution is improved to much less than 50-ns sample interval by interpolation using packing in the frequency domain. A time tag for each pulse is defined as the mean of the times of the rising-edge half peak, peak, and falling-edge half peak. The standard deviation in these times defines the timing error and is shown to be a function of noise and bandwidth rather than digitization rate. Each of the four unknowns for a pulse source location (x,y,z) and time of occurrence (t) is found from the five time-tag measurements using different weightings for all five combinations of the four-station hyperbolic equations. Weighting factors and errors in x,y,z and t are estimated using error propagation techniques.

Thomson, E. M.↗
DOE OSTI2021

Transport barriers to self-propelled particles in fluid flows

Here, we present theory and experiments demonstrating the existence of invariant manifolds that impede the motion of microswimmers in two-dimensional fluid flows. One-way barriers are apparent in a hyperbolic fluid flow that block the swimming of both smooth-swimming and run-and-tumble Bacillus subtilis bacteria. We identify key phase-space structures, called swimming invariant manifolds (SwIMs), that serve as separatrices between different regions of long-time swimmer behavior. When projected into xy space, the edges of the SwIMs act as one-way barriers, consistent with the experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A REDUCED ORDER MODELING APPROACH TO PROBABILISTIC CREEP-DAMAGE PREDICTIONS IN FINITE ELEMENT ANALYSIS

This paper introduces a computationally efficient Reduced Order Modeling (ROM) approach for the probabilistic prediction of creep-damage failure. Component-level probabilistic simulations are needed to assess the reliability and safety of high-temperature components. Full-scale probabilistic creep-damage modeling in finite element (FE) approach is computationally expensive requiring many hundreds of simulations to replicate the uncertainty of component failure. To that end, ROM is proposed to minimize the elevated computational cost while controlling the loss of accuracy. It is proposed that full-scale probabilistic simulations can be completed in 1D at a reduced cost, the extremum conditions extracted, and those conditions applied for lower-cost 2D/3D probabilistic simulations of components that capture the mean and uncertainty of failure. The probabilistic Sine-hyperbolic (Sinh) model is selected which in previous work was calibrated to alloy 304 stainless steel. The Sinh model includes probability density functions (pdfs) for test condition (stress and temperature), initial damage (i.e. microstructure), and material properties uncertainty. The Sinh model is programmed into ANSYS finite element software using the USERCREEP.F material subroutine. First, the Sinh model and FE code are subject to verification and validation to ensure the accuracy of the simulations. Numerous Monte Carlo simulations are executed in a 1D model to generate probabilistic creep deformation, damage, and rupture data. This data is analyzed and the probabilistic parameters corresponding to extreme creep response are extracted. The ROM concept is applied where only the extreme conditions are applied in the 2D probabilistic prediction of a component. The probabilistic predictions between the 1D and 2D geometry is compared to assess ROM for creep. The accuracy of the probabilistic prediction employing the ROM approach will potentially reduce the time and cost of simulating complex engineering systems. Future studies will introduce multi-stage Sinh, stochasticity, and spatial uncertainty for improved prediction.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting

Fully implicit Runge--Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly used in practice with numerical PDEs due to the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic preconditioning framework for solving the systems of equations that arise from IRK methods applied to linear numerical PDEs (without algebraic constraints). Additionally, this framework also naturally applies to discontinuous Galerkin discretizations in time. Under quite general assumptions on the spatial discretization that yield stable time integration, the preconditioned operator is proven to have condition number bounded by a small, order-one constant, independent of the spatial mesh and time-step size, and with only weak dependence on number of stages/polynomial order; for example, the preconditioned operator for 10th-order Gauss IRK has condition number less than two, independent of the spatial discretization and time step. The new method can be used with arbitrary existing preconditioners for backward Euler-type time-stepping schemes and is amenable to the use of three-term recursion Krylov methods when the underlying spatial discretization is symmetric. The new method is demonstrated to be effective on various high-order finite-difference and finite element discretizations of linear parabolic and hyperbolic problems, demonstrating fast, scalable solution of up to 10th-order accuracy. The new method consistently outperforms existing block preconditioning approaches, and in several cases, the new method can achieve 4th-order accuracy using Gauss integration with roughly half the number of preconditioner applications and wallclock time as required using standard diagonally IRK methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2016

Optimizing Mars Sphere of Influence Maneuvers for NASA's Evolvable Mars Campaign

NASA's Human Spaceflight Architecture Team is refining human exploration architectures that will extend human presence to the Martian surface. For both Mars orbital and surface missions, NASA's Evolvable Mars Campaign assumes that cargo and crew can be delivered repeatedly to the same destination. Up to this point, interplanetary trajectories have been optimized to minimize the total propulsive requirements of the in-space transportation systems, while the pre-deployed assets and surface systems are optimized to minimize their respective propulsive requirements separate from the in-space transportation system. There is a need to investigate the coupled problem of optimizing the interplanetary trajectory and optimizing the maneuvers within Mars's sphere of influence. This paper provides a description of the ongoing method development, analysis and initial results of the effort to resolve the discontinuity between the interplanetary trajectory and the Mars sphere of influence trajectories. Assessment of Phobos and Deimos orbital missions shows the in-space transportation and crew taxi allocations are adequate for missions in the 2030s. Because the surface site has yet to be selected, the transportation elements must be sized to provide enough capability to provide surface access to all landing sites under consideration. Analysis shows access to sites from elliptical parking orbits with a lander that is designed for sub-periapsis landing location is either infeasible or requires expensive orbital maneuvers for many latitude ranges. In this case the locus of potential arrival perigee vectors identifies the potential maximum north or south latitudes accessible. Higher arrival velocities can decrease reorientation costs and increase landing site availability. Utilizing hyperbolic arrival and departure vectors in the optimization scheme will increase transportation site accessibility and provide more optimal solutions.

Merrill, Raymond G.↗
DOE OSTI2022

Rigorous justification for the space–split sensitivity algorithm to compute linear response in Anosov systems

Ruelle gave a formula for linear response of transitive Anosov diffeomorphisms. Recently, practically computable realizations of Ruelle's formula have emerged that potentially enable sensitivity analysis of certain high-dimensional chaotic numerical simulations encountered in the applied sciences. In this paper, we provide full mathematical justification for the convergence of one such efficient computation, the space–split sensitivity, or S3, algorithm. In S3, Ruelle's formula is computed as a sum of two terms obtained by decomposing the perturbation vector field into a coboundary and a remainder that is parallel to the unstable direction. Such a decomposition results in a splitting of Ruelle's formula that is amenable to efficient computation. Here, we prove the existence of the S3 decomposition and the convergence of the computations of both resulting components of Ruelle's formula.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations: Global Asymptotic Behavior of Time Discretizations - 2

The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.

Yee, H. C.↗
NASA NTRS1995

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations: Global Asymptotic Behavior of Time Discretizations - Part 2

The global asymptotic nonlinear behavior of 11 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDEs.

Yee, H. C.↗
DOE OSTI2025

Development of a thermal creep model for aluminum alloy 6061 cladding in U-10Mo monolithic fuel plates

Plate-type fuel elements consisting of a high-density, low-enriched uranium (LEU) U–10Mo-based fuel foil encapsulated in an aluminum alloy (AA) cladding are fabricated using the hot isostatic pressing (HIP) technique. During the HIP process, the fuel plate system is heated to 560 °C, then cooled to room temperature. This heat cycle significantly affects the mechanical properties of the aluminum cladding, and experimental investigations have shown that, post-HIP bonding, the mechanical properties of the aluminum cladding transition from those of AA 6061-T6 to something closer to the O temper. More specifically, the ultimate strength of the cladding decreases while its ductility increases, making it challenging to capture the changes in mechanical behavior and material properties. Understanding the residual stresses generated during the HIP process is critical for assessing the fuel plate’s integrity under various temperature, pressure, and irradiation. To simulate the HIP bonding process, the elastic, plastic, and thermal properties of the cladding are assumed to be similar to those of AA 6061-O temper. However, the primary challenge lies in the lack of available data for the creep model of the AA 6061 cladding during this transient process of HIP. The present study focuses on developing a computational model that predicts the creep behavior of the aluminum cladding in the fuel plates during the HIP process, as cladding creep significantly influences the residual stresses generated in U-10Mo fuel plates during HIP fabrication. Furthermore, as HIP bonding occurs at high temperatures that are nearing the melting point of aluminum, the present work considered a temperature-dependent Arrhenius-type creep model. In particular, a hyperbolic sine creep model is employed to estimate the creep properties of the as-fabricated aluminum cladding. In conclusion, the residual stresses predicted in the U-10Mo fuel when using the newly calibrated creep model closely align with the experimental measurements, validating the model’s accuracy.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Conservative DG method for the micro-macro decomposition of the Vlasov–Poisson–Lenard–Bernstein model

The micro-macro (mM) decomposition approach is considered for the numerical solution of the Vlasov– Poisson–Lenard–Bernstein (VPLB) system, which is relevant for plasma physics applications. In the mM approach, the kinetic distribution function is decomposed as $f$ = $\mathscr{E}$[$ρ_f$] + g , where $\mathscr{E}$ is a local equilibrium distribution, depending on the macroscopic moments $ρ_f$ = $∫_{\mathbb{R}}$ $efdv$ = $\langle$$ef$$\rangle$$_{\mathbb{R}}$, where e = (1, $v$, $\frac{1}{2}$ $v^2$) T , and $g$, the microscopic distribution, is defined such that $\langle$$eg$$\rangle$$_{\mathbb{R}}$ = 0. We aim to design numerical methods for the mM decomposition of the VPLB system, which consists of coupled equations for $ρ_f$ and $g$. To this end, we use the discontinuous Galerkin (DG) method for phase-space discretization, and implicit-explicit (IMEX) time integration, where the phase-space advection terms are integrated explicitly and the collision operator is integrated implicitly. We give special consideration to ensure that the resulting mM method maintains the $\langle$$eg$$\rangle$$_{\mathbb{R}}$ = 0 constraint, which may be necessary for obtaining (i) satisfactory results in the collision dominated regime with coarse velocity resolution, and (ii) unambiguous conservation properties. The constraint-preserving property is achieved through a consistent discretization of the equations governing the micro and macro components. Here, we present numerical results that demonstrate the performance of the mM method. The mM method is also compared against a corresponding DG-IMEX method solving directly for $f$.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Insights into hyperbolic phonon polaritons in h – BN using Raman scattering from encapsulated transition metal dichalcogenide layers

Alternative techniques for probing hyperbolic phonon polaritons (HPPs) in two-dimensional materials will support the development of the emerging technologies in this field. Previous reports have shown that it is possible for W Se 2 monolayers in contact with the hexagonal boron nitride (h– BN) to generate HPPs in the h– BN via Raman scattering. In this paper, we set out our results on HPP Raman scattering induced in h– BN by W Se 2 and Mo Se 2 monolayers including multiple resonances at which the Raman scattering is enhanced. Analysis of the observed Raman line shapes demonstrates that Raman scattering allows HPPs with wave vectors with magnitudes significantly in excess of 15 000 cm –1 to be probed. Finally, we present evidence that the Raman scattering can probe HPPs with frequencies less than the expected lower bound on the reststrahlen band, suggesting new HPP physics still waits to be discovered.

2-dimensional systems↗
DOE OSTI2022

A precision test of averaging in AdS/CFT

We reconsider the role of wormholes in the AdS/CFT correspondence. We focus on Euclidean wormholes that connect two asymptotically AdS or hyperbolic regions with $\mathbb{S}$ 1 × $\mathbb{S}$ d-1 boundary. There is no solution to Einstein’s equations of this sort, as the wormholes possess a modulus that runs to infinity. To find on-shell wormholes we must stabilize this modulus, which we can do by fixing the total energy on the two boundaries. Such a wormhole gives the saddle point approximation to a non-standard problem in quantum gravity, where we fix two asymptotic boundaries and constrain the common energy. Crucially the dual quantity does not factorize even when the bulk is dual to a single CFT, on account of the fixed energy constraint. From this quantity we extract a smeared version of the microcanonical spectral form factor. For a chaotic theory this quantity is self-averaging, i.e. well-approximated by averaging over energy windows, or over coupling constants. We go on to give a precision test involving the microcanonical spectral form factor where the two replicas have slightly different coupling constants. In chaotic theories this form factor is known to smoothly decay at a rate universally predicted in terms of one replica physics, provided that there is an average either over a window or over couplings. We compute the expected decay rate for holographic theories, and the form factor from a wormhole, and the two exactly agree for a wide range of two-derivative effective field theories in AdS. This gives a precision test of averaging in AdS/CFT. Our results interpret a number of confusing facts about wormholes and factorization in AdS and suggest that we should regard gravitational effective field theory as a mesoscopic description, analogous to semiclassical mesoscopic descriptions of quantum chaotic systems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗