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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 1,171 records · Page 65

Molecular Dynamics of Combustion Reactions in Supercritical Carbon Dioxide. Part 5: Computational Study of Ethane Dissociation and Recombination Reactions C 2 H 6 ⇌ CH 3 + CH 3

Fossil fuel oxy-combustion is an emerging technology where the habitual nitrogen diluent is replaced by high-pressure supercritical CO 2 (sCO 2 ), which increases the efficiency of energy conversion. In this study, the chemical kinetics of the combustion reaction C 2 H 6 ⇌ CH 3 + CH 3 in the sCO 2 environment is predicted at 30–1000 atm and 1000–2000 K. We adopt a multiscale approach, where the reactive complex is treated quantum mechanically in rigid rotor/harmonic oscillator approximation, while environment effects at different densities are taken into account by the potential of mean force, produced with classical molecular dynamics (MD). Here, we used boxed MD, where enhanced sampling of infrequent events of barrier crossing is accomplished without application of the bias potential. The multistate empirical valence bond model is applied to describe free radical formation accurately at the cost of the classical force field. Predicted rates at low densities agree well with the literature data. In conclusion, rate constants at 300 atm are 2.41 × 10 14 T –0.20 exp(–77.03 kcal/mol/RT) 1/s for ethane dissociation and 8.44 × 10 –19 T 1.42 exp(19.89 kcal/mol/RT) cm 3 /molecule/s for methyl–methyl recombination.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Microwave-based laboratory experiments for internally-heated mantle convection

The thermal evolution of terrestrial planets is mainly controlled by the amount of radioactive heat sources in their mantle, and by the geometry and efficiency of solid state thermo-chemical convection within. So far, these systems have been studied using numerical methods only and cross validation by laboratory analogous experiments has not been conducted yet. To fill this gap we perform the first laboratory experiments of mantle convection driven by microwave-generated internal heating. We use a 30×30×5 cm{sup 3} experimental tank filled with 0.5 % Natrosol in water mixture (viscosity 0.6 Pa.s at 20°C). The fluid is heated from within by a microwave device that delivers a uniform volumetric heating from 10 to 70 kW/m{sup 3}; the upper boundary of the fluid is kept at constant temperature, whereas the lower boundary is adiabatic. The velocity field is determined with particle image velocimetry and the temperature field is measured using thermochromic liquid crystals which enable us to charaterize the geometry of the convective regime as well as its bulk thermal evolution. Numerical simulations, conducted using Stag-3D in 3D cartesian geometry, reproduce the experimental setup (i.e., boundary conditions, box aspect ratio, temperature dependence of physical parameters, internal heating rate). The successful comparison between the experimental and numerical results validates our approach of modelling internal heating using microwaves.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Algebraic Multigrid Preconditioners for Multiphase Flow in Porous Media

Multiphase flow is a critical process in a wide range of applications, including carbon sequestration, contaminant remediation, and groundwater management. Typically, this process is modeled by a nonlinear system of partial differential equations derived by considering the mass conservation of each phase (e.g., oil, water), along with constitutive laws for the relationship of phase velocity to phase pressure. In this study, we develop and study efficient solution algorithms for solving the algebraic systems of equations derived from a fully coupled and time-implicit treatment of models of multiphase flow. We explore the performance of several preconditioners based on algebraic multigrid (AMG) for solving the linearized problem, including “black-box” AMG applied directly to the system, a new version of constrained pressure residual multigrid (CPR-AMG) preconditioning, and a new preconditioner derived using an approximate Schur complement arising from the block factorization of the Jacobian. Finally, we show that the new methods are the most robust with respect to problem character, as determined by varying effects of capillary pressures, and we show that the block factorization preconditioner both is efficient and scales optimally with problem size.

97 MATHEMATICS AND COMPUTING↗

Verdant Power Gen5 KHPS and TriFrame System Content Models

This submission includes the Component Content Model for Verdant Power TriFrame and the System Content Model for Verdant Power TriFrame + 3 Gen5 KHPS Turbines. The TriFrame is the foundation component of the system, which consists of a TriFrame + 3 Gen5 KHPS Turbines (TF+3T).

16 TIDAL AND WAVE POWER↗

Synthesizing a protocol converter from executable protocol traces

Communicating finite state machines (CFSM's) with FIFO (first in, first out) queues are used to model a protocol converter. A protocol conversion algorithm is developed and presented for the CSFM model of the protocols A and B. A converter H for protocols A = (A0, A1) and B = (B0, B1) is viewed as a black box such that H is between sender A0 and receiver B1. This gives a resulting protocol X = (A0, H, B1). The conversion algorithm requires a specification of the message relationships between the messages of protocols A and B. It is assumed that protocols A and B have the required progress properties. The algorithm includes a search for related messages from the two protocols in an FIFO from a composite space formed by a Cartesian cross-product of state spaces A1 and B0. The search produces finite-length traces which are combined to form a state machine H, which is examined for freedom from unspecified receptions, deadlocks, and livelocks. A protocol conversion example demonstrates the applicability of the algorithm.

Rajagopal, Murali↗

Evaluation of Load Analysis Methods for NASAs GIII Adaptive Compliant Trailing Edge Project

The Air Force Research Laboratory (AFRL), NASA Armstrong Flight Research Center (AFRC), and FlexSys Inc. (Ann Arbor, Michigan) have collaborated to flight test the Adaptive Compliant Trailing Edge (ACTE) flaps. These flaps were installed on a Gulfstream Aerospace Corporation (GAC) GIII aircraft and tested at AFRC at various deflection angles over a range of flight conditions. External aerodynamic and inertial load analyses were conducted with the intention to ensure that the change in wing loads due to the deployed ACTE flap did not overload the existing baseline GIII wing box structure. The objective of this paper was to substantiate the analysis tools used for predicting wing loads at AFRC. Computational fluid dynamics (CFD) models and distributed mass inertial models were developed for predicting the loads on the wing. The analysis tools included TRANAIR (full potential) and CMARC (panel) models. Aerodynamic pressure data from the analysis codes were validated against static pressure port data collected in-flight. Combined results from the CFD predictions and the inertial load analysis were used to predict the normal force, bending moment, and torque loads on the wing. Wing loads obtained from calibrated strain gages installed on the wing were used for substantiation of the load prediction tools. The load predictions exhibited good agreement compared to the flight load results obtained from calibrated strain gage measurements.

Aerodynamic Loads↗

Moving Beyond 2% Uncertainty: A New Framework for Quantifying Lidar Uncertainty

Remote sensing of wind using lidar is revolutionizing wind energy. However, current generations of wind lidar are ascribed a climatic value of uncertainty, which is based on a poor description of lidar sensitivity to external conditions. In this presentation, we show how it is important to consider the complete lidar measurement process to define the measurement uncertainty, which in turn offers the ability to define a much more granular and dynamic measurement uncertainty. This approach is a progression from the 'white box' lidar uncertainty method.

17 WIND ENERGY↗

ADEPT: A Pedagogical Framework for Integrating Agentic AI with Deterministic Scientific Workflows

The integration of Large Language Models (LLMs) into scientific research promises to accelerate discovery, yet a significant gap remains between the dynamic reasoning of Artificial Intelligence (AI) agents and the static, deterministic nature of canonical scientific workflows. This paper introduces ADEPT (Agentic Discovery and Exploration Platform for Tools), a reference architecture and pedagogical framework explicitly designed to bridge this gap. ADEPT's primary mission is to provide a transparent, "glass-box" environment where researchers and engineers can learn to effectively wrap established scientific software (e.g., BLAST, Nextflow pipelines) and compose it into reliable, agent-driven workflows. We describe its modular, multi-server architecture, which leverages the Model Context Protocol (MCP) for tool serving, LangGraph for robust agentic orchestration, and a secure nsjail-based sandbox for safe code execution. By prioritizing architectural clarity, safety, and modularity, ADEPT serves as an extensible blueprint for building trustworthy AI-augmented systems and fosters the collaborative development necessary to responsibly employ agentic AI for science. We provide practical examples of how to adapt and extend this framework, highlighting its utility in workforce development and AI-readiness capabilities across research and development projects.

97 MATHEMATICS AND COMPUTING↗

Radiative Flux Measurements from ARISE: A Comparison with CERES Top-of-Atmosphere Radiative Fluxes

Uncertainty in top-of-atmosphere (TOA) radiation fluxes observations are larger in the Arctic than in other regions. These uncertainties are due to the low sun angles and the highly reflective, anisotropic, and heterogeneous surface conditions. Quantifying, attributing, and reducing Arctic TOA radiative flux uncertainty enables a better understanding of the rapidly changing Arctic. To advance this goal, we compare the Cloud and Earth’s Radiant Energy System (CERES) TOA radiative fluxes with Arctic Radiation-IceBridge Sea and Ice Experiment (ARISE) campaign measurements collected in September 2014. We compare CERES TOA and aircraft radiative flux measurements using two complementary approaches: grid box average fluxes and instantaneously matched footprints. The grid box mean flux comparison indicates an agreement between CERES and aircraft measurements within 2 uncertainty (calibration and inversion) in the longwave for all five grid boxes and for four-of-five grid boxes in the shortwave; shortwave and longwave mean differences are -7.9 and +2.3 Wm‑2, respectively. The comparison of 36 instantaneously matched footprints with aircraft measurements reveals mean differences of -10.5 and 0.4 Wm‑2 in the shortwave and longwave, respectively. To further explore the persistent negative difference in the shortwave, we further quantify the effects of temporal and spatial sampling differences, angular distribution models, and scene identification to CERES-aircraft differences. Our analysis indicates that sampling differences (including scene evolution) account for an additional 1.8 and 1.7% uncertainty in the shortwave and longwave, respectively and indicates no bias. After accounting for this sampling uncertainty, all CERES-aircraft grid box mean fluxes agree within 2 uncertainty. Scene identification errors due to sea ice concentration data set differences exhibit no bias in the shortwave flux difference and indicate the possibility of substantial differences in the CERES fluxes in specific cases with large spatial heterogeneity. Considering the instantaneously matched footprints, we find that the angular distribution models account may account for up to ‑7.3 Wm-2 of the persistent CERES-aircraft shortwave flux difference due to systematic differences in the anisotropy for sea ice partly cloudy scenes. Additional analysis using a special scan model with the CERES FM2 instrument suggests a significant view zenith angle dependence of the CERES fluxes for sea ice partly cloudy scenes where shortwave fluxes systematically decrease with increasing view zenith angle; no dependence is found for other scene types. We conclude that (1) spatial heterogeneity and scene temporal evolution substantially limit our ability to use aircraft measurements to place strong constraints on CERES TOA fluxes and (2) that the representation of anisotropy in sea ice partly cloudy scenes is a significant factor contributing to the persistent negative CERES-aircraft shortwave flux difference in this comparison and require additional data to analysis fully quantify the potential bias.

Patrick C Taylor↗

The Borg Cube Simulation: Cosmological Hydrodynamics with CRK-SPH

A challenging requirement posed by next-generation observations is a firm theoretical grasp of the impact of baryons on structure formation. Cosmological hydrodynamic simulations modeling gas physics are vital in this regard. A high degree of modeling flexibility exists in this space, making it important to explore a range of methods in order to gauge the accuracy of simulation predictions. We present results from the first cosmological simulation using Conservative Reproducing Kernel Smoothed Particle Hydrodynamics (CRK-SPH). We employ two simulations: one evolved purely under gravity, and the other with nonradiative hydrodynamics. Each contains 2 × 2304 3 cold dark matter plus baryon particles in an 800 h -1 Mpc box. We compare statistics to previous nonradiative simulations including power spectra, mass functions, baryon fractions, and concentration. We find self-similar radial profiles of gas temperature, entropy, and pressure and show that a simple analytic model recovers these results to better than 40% over two orders of magnitude in mass. We quantify the level of nonthermal pressure support in halos and demonstrate that hydrostatic mass estimates are biased low by 24% (10%) for halos of mass 10 15 (10 13 ) h -1 M⊙. Here, we compute angular power spectra for the thermal and kinematic Sunyaev–Zel’dovich effects and find good agreement with the low-ℓ Planck measurements. Finally, artificial scattering between particles of unequal mass is shown to have a large impact on the gravity-only run, and we highlight the importance of better understanding this issue in hydrodynamic applications. This is the first in a simulation campaign using CRK-SPH, with future work including subresolution gas treatments.

79 ASTRONOMY AND ASTROPHYSICS↗

On-line estimation of error covariance parameters for atmospheric data assimilation

A simple scheme is presented for on-line estimation of covariance parameters in statistical data assimilation systems. The scheme is based on a maximum-likelihood approach in which estimates are produced on the basis of a single batch of simultaneous observations. Simple-sample covariance estimation is reasonable as long as the number of available observations exceeds the number of tunable parameters by two or three orders of magnitude. Not much is known at present about model error associated with actual forecast systems. Our scheme can be used to estimate some important statistical model error parameters such as regionally averaged variances or characteristic correlation length scales. The advantage of the single-sample approach is that it does not rely on any assumptions about the temporal behavior of the covariance parameters: time-dependent parameter estimates can be continuously adjusted on the basis of current observations. This is of practical importance since it is likely to be the case that both model error and observation error strongly depend on the actual state of the atmosphere. The single-sample estimation scheme can be incorporated into any four-dimensional statistical data assimilation system that involves explicit calculation of forecast error covariances, including optimal interpolation (OI) and the simplified Kalman filter (SKF). The computational cost of the scheme is high but not prohibitive; on-line estimation of one or two covariance parameters in each analysis box of an operational bozed-OI system is currently feasible. A number of numerical experiments performed with an adaptive SKF and an adaptive version of OI, using a linear two-dimensional shallow-water model and artificially generated model error are described. The performance of the nonadaptive versions of these methods turns out to depend rather strongly on correct specification of model error parameters. These parameters are estimated under a variety of conditions, including uniformly distributed model error and time-dependent model error statistics.

Dee, Dick P.↗

A comparison between CERES TOA Radiative Fluxes and Airborne Radiative Flux Measurements from ARISE

Uncertainty in top-of-atmosphere (TOA) radiation fluxes observations are larger in the Arctic than in other regions. These uncertainties are due to the low sun angles and the highly reflective, anisotropic, and heterogeneous surface conditions. Quantifying, attributing, and reducing Arctic TOA radiative flux uncertainty enables a better understanding of the rapidly changing Arctic. To advance this goal, we compare the Cloud and Earth’s Radiant Energy System (CERES) TOA radiative fluxes with Arctic Radiation-IceBridge Sea and Ice Experiment (ARISE) campaign measurements collected in September 2014. We compare CERES TOA and aircraft radiative flux measurements using two complementary approaches: grid box average fluxes and instantaneously matched footprints. The grid box mean flux comparison indicates an agreement between CERES and aircraft measurements within 2σ uncertainty (calibration and inversion) in the longwave for all five grid boxes and for four-of-five grid boxes in the shortwave; shortwave and longwave mean differences are -7.9 and +2.3 Wm 2, respectively. The comparison of 36 40 instantaneously matched footprints with aircraft measurements reveals mean differences of -120.25 and -1.00.4 Wm 2 in the shortwave and longwave, respectively. To further explore the persistent negative difference in the shortwave, Wwe further quantify the effects of temporal and spatial sampling differences, angular distribution models, and scene identification to CERES-aircraft differences. Our analysis indicates that sampling differences (including scene evolution) account for an additional 1.8 and 1.7% uncertainty in the shortwave and longwave, respectively and , but indicates no bias. After accounting for this sampling uncertainty, all CERES-aircraft grid box mean fluxes agree within 2σ uncertainty. Scene identification errors due to sea ice concentration data set differences exhibit no bias in the shortwave flux difference and indicate the possibility of substantial differences in the CERES fluxes in specific cases with large spatial heterogeneity. Considering the instantaneously matched footprints, we find that the angular distribution models account may account for up to 7.3 Wm-2 of the persistent CERES-aircraft shortwave flux difference due to systematic differences in the anisotropy for sea ice partly cloudy scenes. Additional analysis using a special programmable scan model with the CERES FM2 instrument suggests a significant view zenith angle dependence of the CERES fluxes for sea ice partly cloudy scenes where shortwave fluxes systematically decrease with increasing view zenith angle; no dependence is found for other scene types. We conclude that (1) spatial heterogeneity and scene temporal evolution substantially limit our ability to use aircraft measurements to place strong constraints on CERES TOA fluxes and (2) that the representation of anisotropy in sea ice partly cloudy scenes is likely a significant factor contributing to the persistent negative CERES-aircraft shortwave flux difference in this comparison and require additional data to analysis fully quantify the potential bias.

Patrick C. Taylor↗

Use of the Long Duration Exposure Facility's thermal measurement system for the verification of thermal models

Results are presented of the comparison between the Long Duration Exposure Facility (LDEF) Thermal Measurements Systems (THERM) recorded temperature data and the predicted values as calculated prior to the LDEF deployment. The postflight thermal model was verified and calculated temperature uncertainties were reduced to under + or - 18 F from the preflight uncertainties of + or - 40 F. The THERM consisted of 8 temperature sensors, a shared tape recorder, a standard LDEF flight battery, and an electronics control box. The temperatures were measured at selected locations on the LDEF structure interior during the first 490 days of flight and recorded for postflight analysis. After the recorder was recovered from space, the tape recorder was recovered and the data reduced for comparison to the LDEF predicted temperatures. By comparing the calculated values to the measured data, a verified thermal model that presents the best agreement with the THERM data was obtained. The THERM experiment provided an economical way of performing a postflight verification of the LDEF Thermal Model by recording a limited number of flight temperatures on typical locations of the LDEF structure.

Berrios, William M.↗

REIONIZATION ON LARGE SCALES. I. A PARAMETRIC MODEL CONSTRUCTED FROM RADIATION-HYDRODYNAMIC SIMULATIONS

We present a new method for modeling inhomogeneous cosmic reionization on large scales. Utilizing high-resolution radiation-hydrodynamic simulations with 2048{sup 3} dark matter particles, 2048{sup 3} gas cells, and 17 billion adaptive rays in a L = 100 Mpc h {sup –1} box, we show that the density and reionization redshift fields are highly correlated on large scales (∼> 1 Mpc h {sup –1}). This correlation can be statistically represented by a scale-dependent linear bias. We construct a parametric function for the bias, which is then used to filter any large-scale density field to derive the corresponding spatially varying reionization redshift field. The parametric model has three free parameters that can be reduced to one free parameter when we fit the two bias parameters to simulation results. We can differentiate degenerate combinations of the bias parameters by combining results for the global ionization histories and correlation length between ionized regions. Unlike previous semi-analytic models, the evolution of the reionization redshift field in our model is directly compared cell by cell against simulations and performs well in all tests. Our model maps the high-resolution, intermediate-volume radiation-hydrodynamic simulations onto lower-resolution, larger-volume N-body simulations (∼> 2 Gpc h {sup –1}) in order to make mock observations and theoretical predictions.

79 ASTRONOMY AND ASTROPHYSICS↗

On interfacial properties of tetrahydrofuran: Atomistic and coarse-grained models from molecular dynamics simulation

We have determined the interfacial properties of tetrahydrofuran (THF) from direct simulation of the vapor-liquid interface. The molecules are modeled using six different molecular models, three of them based on the united-atom approach and the other three based on a coarse-grained (CG) approach. In the first case, THF is modeled using the transferable parameters potential functions approach proposed by Chandrasekhar and Jorgensen [J. Chem. Phys. 77, 5073 (1982)] and a new parametrization of the TraPPE force fields for cyclic alkanes and ethers [S. J. Keasler et al., J. Phys. Chem. B 115, 11234 (2012)]. In both cases, dispersive and coulombic intermolecular interactions are explicitly taken into account. In the second case, THF is modeled as a single sphere, a diatomic molecule, and a ring formed from three Mie monomers according to the SAFT-γ Mie top-down approach [V. Papaioannou et al., J. Chem. Phys. 140, 054107 (2014)]. Simulations were performed in the molecular dynamics canonical ensemble and the vapor-liquid surface tension is evaluated from the normal and tangential components of the pressure tensor along the simulation box. In addition to the surface tension, we have also obtained density profiles, coexistence densities, critical temperature, density, and pressure, and interfacial thickness as functions of temperature, paying special attention to the comparison between the estimations obtained from different models and literature experimental data. The simulation results obtained from the three CG models as described by the SAFT-γ Mie approach are able to predict accurately the vapor-liquid phase envelope of THF, in excellent agreement with estimations obtained from TraPPE model and experimental data in the whole range of coexistence. However, Chandrasekhar and Jorgensen model presents significant deviations from experimental results. We also compare the predictions for surface tension as obtained from simulation results for all the models with experimental data. The three CG models predict reasonably well (but only qualitatively) the surface tension of THF, as a function of temperature, from the triple point to the critical temperature. On the other hand, only the TraPPE united-atoms models are able to predict accurately the experimental surface tension of the system in the whole temperature range.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Machine learning-assisted upscaling analysis of reservoir rock core properties based on micro-computed tomography imagery

Optimum solutions for geologic modeling and reservoir simulation in industries such as oil and gas recovery and carbon capture and storage require accurate characterization of reservoir properties, which are often heterogeneous. In this study, high-quality micro-computed tomography (CT) images (1.475-μm/pixel resolution) of a sandstone core acquired from the Bell Creek oil field, USA, were used to provide nondestructive analysis of pore- and core-scale heterogeneity across measurement scales of 94–566 μm. In addition to characterizing the as-received sample, the core sample was flooded with brine to evaluate the capacity of the core sample to receive injected fluids. The micro-CT images were systematically segmented into pore spaces and grains via machine learning (ML) steps including image preprocessing, label creation using a traditional ML method based on limited manual image annotation, and finally U-Net segmentation. The segmented image stacks were reconstructed into digital cubes of various scales of voxel lengths. The 3D porosity values were calculated for all the digital cubes, and the fractal dimensions of the cubes were estimated using a box-counting method. The results showed that smaller cubes had greater heterogeneity and that the porosity values could be accurately estimated by fractal dimension and voxel lengths using ML models. For the core sample with brine flooding, the ratio of pores filled by brine to the total pore space was related to the porosity and could also be accurately estimated by porosity, fractal dimension, and voxel lengths using ML models. In conclusion, the results of this study demonstrate that the concept of fractal dimension can be a useful vector to perform upscaling analysis of sandstone rock heterogeneity from the pore to core scale and that fractal dimensions can be used to estimate porosity values and pore space-filling capacity across those scales.

58 GEOSCIENCES↗

Revealing multiscale competing processes in the solid-state synthesis of single-crystalline layered oxide positive electrodes

Solid-state synthesis involves a web of coupled chemical reactions and physical changes that unfold across multiple scales. Efforts to fine-tune its parameters have historically followed heuristic, trial-driven workflows that demand significant time and resources. In this study, we aimed to open this black box by employing multiscale in situ synchrotron imaging and diffraction. Using LiNi 0.5 Mn 0.3 Co 0.2 O 2 battery positive electrode material as a model system and Ba-based sintering aids, we reveal dopant segregation, intergranular mass transport, and porosity evolution as key drivers of single-crystalline particle formation. Notably, we uncovered a dynamic competition between particle-level grain coalescence and atomic-scale cation disordering, both of which are thermally activated yet have opposing impacts on battery performance. These findings highlight the coupled, multiscale nature of structure development and offer a mechanistic basis for optimizing the solid-state synthesis process. This framework provides a path toward more controlled, efficient, and scalable production of high-performance battery positive electrode materials.

36 MATERIALS SCIENCE↗

Cosmic Reionization on Computers: Physical Origin of Long Dark Gaps in Quasar Absorption Spectra

I explore the properties of “dark gaps” - regions in quasar absorption spectra without significant transmission - with several simulations from the Cosmic Reionization On Computers (CROC) project. The CROC simulations in the largest available boxes (120 cMpc) come close to matching both the distribution of mean opacities and the frequency of dark gaps, but alas not in the same model: the run that matches the mean opacities fails to contain enough dark gaps and vice versa. Nevertheless, the run that matches the dark gap distributions serves as a counterexample to claims in the literature that the dark gap statistics requires a late end to reionization - in that run reionization ends at z = 6.7 (likely too early). While multiple factors contribute to the frequency of large dark gaps in the simulations, the primary factor that controls the overall shape of the dark gap distribution is the ionization level in voids—the lowest-density regions produce the highest transmission spikes that terminate long gaps. As the result, the dark gap distribution correlates strongly with the fraction of the spectrum above the gap detection threshold and the observed distribution is matched by the simulation in which this fraction is 2%. Hence, the gap distribution by itself does not constrain the timing of reionization, although it may do so in combination with the distribution of mean opacities.

79 ASTRONOMY AND ASTROPHYSICS↗