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At least 235 records · Page 13

A Comprehensive Comparison of Methods for Evaluating Dispatch of Long-Duration Energy Storage in Power Systems Models

Long-duration energy storage (LDES) could play a pivotal role in the transformation of electricity grids with high shares of variable renewable energy (VRE) such as solar and wind. However, the weather-dependent nature of VRE introduces challenges for grid balancing and stability, which LDES - along with short-duration energy storage (SDES) - can help address. However, modeling LDES in production cost models (PCMs) is particularly challenging due to the need for high temporal resolution over extended optimization windows while preserving chronology, which ensures the alignment of energy storage operations with VRE generation over multi-day periods. This report compares traditional dispatch methods with advanced LDES dispatch strategies, such as the extended horizon approach, across different PCM platforms and examines tradeoffs and scalability. The comparison reveals that the traditional 1-day optimization horizon within the PCM leads to inefficient utilization of LDES. In contrast, extending the optimization horizon as much as possible significantly reduces curtailment and improves storage dispatch, especially in renewable-dense systems. There is also promise in using state-of-charge or end volume targets set by an external model, however this requires an additional modeling set and generally increases computational burden. This paper presents a comparison of these various methods in a number of power systems, showing algorithms initially in small test systems and scaling up to large, country-wide simulations. Overall, the research presents the trade-offs of various computational methods and illustrates how LDES may play an essential role in power systems of the future.

14 SOLAR ENERGY↗

Polarimetric Geometric Modeling for mm-VLBI Observations of Black Holes

The Event Horizon Telescope (EHT) is a millimeter very long baseline interferometry (VLBI) array that has imaged the apparent shadows of the supermassive black holes M87* and Sagittarius A*. Polarimetric data from these observations contain a wealth of information on the black hole and accretion flow properties. In this work, we develop polarimetric geometric modeling methods for mm-VLBI data, focusing on approaches that fit data products with differing degrees of invariance to broad classes of calibration errors. We establish a fitting procedure using a polarimetric “m-ring” model to approximate the image structure near a black hole. By fitting this model to synthetic EHT data from general relativistic magnetohydrodynamic models, we show that the linear and circular polarization structure can be successfully approximated with relatively few model parameters. We then fit this model to EHT observations of M87* taken in 2017. In total intensity and linear polarization, the m-ring fits are consistent with previous results from imaging methods. In circular polarization, the m-ring fits indicate the presence of event-horizon-scale circular polarization structure, with a persistent dipolar asymmetry and orientation across several days. The same structure was recovered independently of observing band, used data products, and model assumptions. Despite this broad agreement, imaging methods do not produce similarly consistent results. Our circular polarization results, which imposed additional assumptions on the source structure, should thus be interpreted with some caution. Polarimetric geometric modeling provides a useful and powerful method to constrain the properties of horizon-scale polarized emission, particularly for sparse arrays like the EHT.

79 ASTRONOMY AND ASTROPHYSICS↗

Quantum fate of the Choptuik naked singularity

Classical critical collapse provides a dynamical route from smooth initial data to a naked singularity, representing a sharper violation of predictability than ordinary black hole singularities. We argue that this distinction is erased by quantum backreaction. Building on the semiclassical interior analysis, where quantum self-energy of the collapsing matter generates a universal growing mode and a finite mass gap, we study the exterior naked singularity region that determines global visibility in the Einstein-scalar system. We analyze controlled exterior models in both $2+1$ and $3+1$ dimensions. In the former, smooth matching and physical boundary conditions analytically select a vacuum polarization state, whose backreaction cloaks the classically naked region by a quantum trapped branch. In the latter, numerical horizon tracing shows that near a quantum-shifted threshold the exterior develops finite-mass marginally trapped surfaces rather than a zero-mass naked endpoint. These results suggest a global quantum picture in which the Choptuik naked singularity shares the fate of an ordinary black hole singularity: quantum effects push the putative Cauchy horizon behind a quantum-generated horizon, thereby reducing the loss of predictability to the standard black hole evaporation problem.

FOS: Physical sciences↗

Iron and Phosphorus Geochemistry in High-Centered and Low-Centered Polygon Soils from the Barrow Environmental Observatory, Utqiagvik, Alaska, 2015

This dataset provides chemical characterization of soil cores obtained in triplicate from center and trough positions of a high-centered polygon and center, ridge, and trough positions of a low-centered polygon in the NGEE Arctic research area within the Barrow Environmental Observatory, Utqiagvik, Alaska. Photographs of the 15 collected cores are provided. Cores were collected to thaw depth in early October 2015 and subsequently divided into subsamples for analysis, which included bulk soil horizons (organic or mineral) and finer scale depth increments (minimum 4 cm thickness per increment). Bulk horizons and depth increments were characterized using sequential chemical extractions for Fe and P and with Fe K-edge x-ray absorption spectroscopy. Additional soil parameters such as loss-on-ignition, gravimetric water content, and carbon and nitrogen concentrations were also quantified for bulk horizons. This dataset includes four csv files, one pdf user guide, and one zip folder of *.jpg photos.The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research.The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska.Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

54 ENVIRONMENTAL SCIENCES↗

Predictive performance of multi-model ensemble forecasts of COVID-19 across European nations

Background: Short-term forecasts of infectious disease burden can contribute to situational awareness and aid capacity planning. Based on best practice in other fields and recent insights in infectious disease epidemiology, one can maximise the predictive performance of such forecasts if multiple models are combined into an ensemble. Here, we report on the performance of ensembles in predicting COVID-19 cases and deaths across Europe between 08 March 2021 and 07 March 2022. Methods: We used open-source tools to develop a public European COVID-19 Forecast Hub. We invited groups globally to contribute weekly forecasts for COVID-19 cases and deaths reported by a standardised source for 32 countries over the next 1–4 weeks. Teams submitted forecasts from March 2021 using standardised quantiles of the predictive distribution. Each week we created an ensemble forecast, where each predictive quantile was calculated as the equally-weighted average (initially the mean and then from 26th July the median) of all individual models’ predictive quantiles. We measured the performance of each model using the relative Weighted Interval Score (WIS), comparing models’ forecast accuracy relative to all other models. We retrospectively explored alternative methods for ensemble forecasts, including weighted averages based on models’ past predictive performance. Results: Over 52 weeks, we collected forecasts from 48 unique models. We evaluated 29 models’ forecast scores in comparison to the ensemble model. We found a weekly ensemble had a consistently strong performance across countries over time. Across all horizons and locations, the ensemble performed better on relative WIS than 83% of participating models’ forecasts of incident cases (with a total N=886 predictions from 23 unique models), and 91% of participating models’ forecasts of deaths (N=763 predictions from 20 models). Across a 1–4 week time horizon, ensemble performance declined with longer forecast periods when forecasting cases, but remained stable over 4 weeks for incident death forecasts. In every forecast across 32 countries, the ensemble outperformed most contributing models when forecasting either cases or deaths, frequently outperforming all of its individual component models. Among several choices of ensemble methods we found that the most influential and best choice was to use a median average of models instead of using the mean, regardless of methods of weighting component forecast models. Conclusions: Our results support the use of combining forecasts from individual models into an ensemble in order to improve predictive performance across epidemiological targets and populations during infectious disease epidemics. Our findings further suggest that median ensemble methods yield better predictive performance more than ones based on means. Our findings also highlight that forecast consumers should place more weight on incident death forecasts than incident case forecasts at forecast horizons greater than 2 weeks. Funding: AA, BH, BL, LWa, MMa, PP, SV funded by National Institutes of Health (NIH) Grant 1R01GM109718, NSF BIG DATA Grant IIS-1633028, NSF Grant No.: OAC-1916805, NSF Expeditions in Computing Grant CCF-1918656, CCF-1917819, NSF RAPID CNS-2028004, NSF RAPID OAC-2027541, US Centers for Disease Control and Prevention 75D30119C05935, a grant from Google, University of Virginia Strategic Investment Fund award number SIF160, Defense Threat Reduction Agency (DTRA) under Contract No. HDTRA1-19-D-0007, and respectively Virginia Dept of Health Grant VDH-21-501-0141, VDH-21-501-0143, VDH-21-501-0147, VDH-21-501-0145, VDH-21-501-0146, VDH-21-501-0142, VDH-21-501-0148. AF, AMa, GL funded by SMIGE - Modelli statistici inferenziali per governare l'epidemia, FISR 2020-Covid-19 I Fase, FISR2020IP-00156, Codice Progetto: PRJ-0695. AM, BK, FD, FR, JK, JN, JZ, KN, MG, MR, MS, RB funded by Ministry of Science and Higher Education of Poland with grant 28/WFSN/2021 to the University of Warsaw. BRe, CPe, JLAz funded by Ministerio de Sanidad/ISCIII. BT, PG funded by PERISCOPE European H2020 project, contract number 101016233. CP, DL, EA, MC, SA funded by European Commission - Directorate-General for Communications Networks, Content and Technology through the contract LC-01485746, and Ministerio de Ciencia, Innovacion y Universidades and FEDER, with the project PGC2018-095456-B-I00. DE., MGu funded by Spanish Ministry of Health / REACT-UE (FEDER). DO, GF, IMi, LC funded by Laboratory Directed Research and Development program of Los Alamos National Laboratory (LANL) under project number 20200700ER. DS, ELR, GG, NGR, NW, YW funded by National Institutes of General Medical Sciences (R35GM119582; the content is solely the responsibility of the authors and does not necessarily represent the official views of NIGMS or the National Institutes of Health). FB, FP funded by InPresa, Lombardy Region, Italy. HG, KS funded by European Centre for Disease Prevention and Control. IV funded by Agencia de Qualitat i Avaluacio Sanitaries de Catalunya (AQuAS) through contract 2021-021OE. JDe, SMo, VP funded by Netzwerk Universitatsmedizin (NUM) project egePan (01KX2021). JPB, SH, TH funded by Federal Ministry of Education and Research (BMBF; grant 05M18SIA). KH, MSc, YKh funded by Project SaxoCOV, funded by the German Free State of Saxony. Presentation of data, model results and simulations also funded by the NFDI4Health Task Force COVID-19 ( https://www.nfdi4health.de/task-force-covid-19-2 ) within the framework of a DFG-project (LO-342/17-1). LP, VE funded by Mathematical and Statistical modelling project (MUNI/A/1615/2020), Online platform for real-time monitoring, analysis and management of epidemic situations (MUNI/11/02202001/2020); VE also supported by RECETOX research infrastructure (Ministry of Education, Youth and Sports of the Czech Republic: LM2018121), the CETOCOEN EXCELLENCE (CZ.02.1.01/0.0/0.0/17-043/0009632), RECETOX RI project (CZ.02.1.01/0.0/0.0/16-013/0001761). NIB funded by Health Protection Research Unit (grant code NIHR200908). SAb, SF funded by Wellcome Trust (210758/Z/18/Z).

60 APPLIED LIFE SCIENCES↗

Integrated solution techniques for security constrained unit commitment problem

Apparatus and methods are disclosed for solving Mixed Integer Programming (MIP) problems, such as Security Constrained Unit Commitment (SCUC) problems used by power grid authorities to perform day-ahead market clearing. In certain examples, a plurality of threads of a software tool implementing a concurrent optimizer can be executed concurrently and sequentially to generate new solutions to a SCUC problem for an upcoming planning horizon. Data can be shared among the concurrently executing threads, such as intermediate/incumbent solutions and hints regarding the fixing of variables and constraints to reduce the size of the SCUC problem. In some examples, the threads are seeded with historical solutions from prior planning horizons. The software tool can select a best solution from the solutions generated by the threads, and determine dispatch instructions for a device coupled to the power grid for the upcoming planning horizon based at least in part on the selected solution.

Pan, Feng↗

Predicting Initial Trans-Membrane Pressure for Optimized Operations in UF Unit Using Random Forest

With the growing scarcity of freshwater, innovative process design mechanisms like Reverse Osmosis (RO) are increasingly gaining attention among water treatment utilities to address the rising demand. Ensuring reliable water production necessitates efficient resource utilization, minimizing downtime in (ultra-filtration) UF systems. Recent advancements in machine learning (ML) have enabled the development of accurate data-driven models for Model Predictive Control (MPC), often requiring minimal prior knowledge of underlying physical processes. In this study, we present predictive regression models based on Random Forest (RF) and Auto-Regressive (AR) approaches to forecast the initial Trans-Membrane Pressure (TMP) for each filtration cycle in data generated by Direct Potable Reuse (DPR) systems. The proposed RF-based model demonstrates superior performance compared to baseline methods, including historical mean, Last Observation Carried Forward (LOCF), and naïve AR models, across various forecasting horizons in terms of root mean square error (RMSE) metric. To evaluate how different classes of process variables contribute to TMP dynamics over time, we examine the feature importance of independent covariates across multiple forecast horizons. This analysis provides insight into the temporal relevance of operational and sensor-derived features, guiding control and monitoring strategies. Additionally, the impact of hyperparameter tuning on TMP prediction performance is studied for both direct and recursive RF modelling approaches across increasing forecast horizons. Accurate prediction of initial TMP is critical for optimizing RO operations, as it enables the development of robust modelling frameworks by accurately estimating membrane fouling trends, thereby enhancing process efficiency and long-term reliability. The demonstrated efficacy of the RF-based approach highlights its potential as a tool for real-time decision-making in water treatment systems, paving the way for advanced process optimization and sustainable water resource management.

Mukherjee, Subrata [ORNL] (ORCID:0000000309930338)↗

Real-time hybrid controls of energy storage and load shedding for integrated power and energy systems of ships

This paper presents an original energy management methodology to enhance the resilience of ship power systems. The integration of various energy storage systems (ESS), including battery energy storage systems (BESS) and super-capacitor energy storage systems (SCESS), in modern ship power systems poses challenges in designing an efficient energy management system (EMS). The EMS proposed in this paper aims to achieve multiple objectives. The primary objective is to minimize shed loads, while the secondary objective is to effectively manage different types of ESS. Considering the diverse ramp-rate characteristics of generators, SCESS, and BESS, the proposed EMS exploits these differences to determine an optimal long-term schedule for minimizing shed loads. Furthermore, the proposed EMS balances the state-of-charge (SoC) of ESS and prioritizes the SCESS’s SoC levels to ensure the efficient operation of BESS and SCESS. For better computational efficiency, we introduce the receding horizon optimization method, enabling real-time EMS implementation. Further, a comparison with the fixed horizon optimization (FHO) validates its effectiveness. Simulation studies and results demonstrate that the proposed EMS efficiently manages generators, BESS, and SCESS, ensuring system resilience under generation shortages. Additionally, the proposed methodology significantly reduces the computational burden compared to the FHO technique while maintaining acceptable resilience performance.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Integrated charging infrastructure planning and charging scheduling for battery electric bus systems

We report studies on the electric bus system planning problem have typically focused exclusively on either the deployment of charging infrastructure or the scheduling of charging events; few have examined the impact of charging facility deployment on charging activities. Considering the interdependence of system design and operational strategies, this study proposes a two-phase optimization framework for charging infrastructure planning and charging scheduling for battery electric bus systems. An integrated optimization model is first developed to simultaneously optimize charger deployment, on-board battery capacity, and charging schedules. A charging scheduling model is further proposed and a rolling horizon approach is utilized in the second phase to optimize the real-time charging scheduling of electric buses. Compared to existing electric bus system planning methods, the proposed integrated model can reduce the total system cost by 19.5%. In addition, compared to uncontrolled charging, the proposed rolling horizon-based charging strategy can reduce the total charging cost by 68.3%.

25 ENERGY STORAGE↗

U.S. Department of Energy (DOE) Enabling Extreme Real-Time Grid Integration of Solar Energy (ENERGISE) Project: Multiday and Intraday Energy Availability Product [Slides]

This presentation will provide an overview of the development of a Multi-Day Energy Availability Product under the DOE ENERGISE project, conducted in collaboration with Southwest Power Pool (SPP), the National Laboratory of the Rockies, Polaris, and the Electric Power Research Institute (EPRI). Existing market clearing processes are limited to day-ahead and real-time horizons, which may result in insufficient pricing signals and compensation for resource availability over multi-day timeframes (e.g., incentives for fuel procurement and energy-limited resource preparedness). This effort aims to develop a new market product and associated clearing process to value and procure resource energy availability over a multi-day horizon. The team will present progress to date and solicit advisory group feedback on proposed methodologies and preliminary findings.

14 SOLAR ENERGY↗

First Very Long Baseline Interferometry Detections at 870μm

The first very long baseline interferometry (VLBI) detections at 870$\mu$m wavelength (345$\,$GHz frequency) are reported, achieving the highest diffraction-limited angular resolution yet obtained from the surface of the Earth, and the highest-frequency example of the VLBI technique to date. These include strong detections for multiple sources observed on inter-continental baselines between telescopes in Chile, Hawaii, and Spain, obtained during observations in October 2018. The longest-baseline detections approach 11$\,$G$\lambda$ corresponding to an angular resolution, or fringe spacing, of 19$\mu$as. The Allan deviation of the visibility phase at 870$\mu$m is comparable to that at 1.3$\,$mm on the relevant integration time scales between 2 and 100$\,$s. The detections confirm that the sensitivity and signal chain stability of stations in the Event Horizon Telescope (EHT) array are suitable for VLBI observations at 870$\mu$m. Operation at this short wavelength, combined with anticipated enhancements of the EHT, will lead to a unique high angular resolution instrument for black hole studies, capable of resolving the event horizons of supermassive black holes in both space and time.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Alternating salt and freshwater floods of coastal soils impact soil structure, hydraulic properties, and oxygen dynamics

Coastal soils are increasingly impacted by hydrologic intensification in the form of rising sea level and flooding from storm surges and precipitation. Alternating saltwater (SW) and freshwater (FW) exposure has the potential to disperse colloids, which can lead to disintegration of soil structure, clogging of pore spaces, and reduction in ecologically and biogeochemically important functions like infiltration or gas exchange. To investigate how hydrologic intensification affects soil structure and oxygen dynamics, we conducted a series of laboratory-based flood simulations. Intact soil cores of the A and B horizons (22 total) from the toe slope of an upland coastal forest along the western shore of Chesapeake Bay. We subjected the cores to 24 h of saturation with either FW or alternating brackish SW and FW, with a 24-h draining event in between flood events. Oxygen diffusion into soil during draining was reduced by up to 30% for soils flooded alternating SW-FW compared to soils flooded only with FW. We attributed the reduced oxygen diffusion to clogging of smaller pores by colloids, with colloid redistribution observed as an increase in specific surface area down the core profile of up to 59%. After three SW-FW floods (six floods total), there were significant changes in pore size distribution, significant redistribution of colloids, and the A horizon became sodic. We concluded that a small number of SW flooding events can induce a measurable change in soil physical properties that directly impacts the biogeochemical dynamics.

Rod, Kenton A. [Pacific Northwest National Laborat↗

Proper time to the black hole singularity from thermal one-point functions

We argue that the proper time from the event horizon to the black hole singularity can be extracted from the thermal expectation values of certain operators outside the horizon. This works for fields which couple to higher-curvature terms, so that they can decay into two gravitons. To extract this proper time, it is necessary to vary the mass of the field.

79 ASTRONOMY AND ASTROPHYSICS↗

Absorptive effects and classical black hole scattering

Abstract We describe an approach to incorporating the physical effects of the absorption of energy by the event horizon of black holes in the scattering amplitudes based post-Minkowskian, point-particle effective description. Absorptive dynamics are incorporated in a model-independent way by coupling the usual point-particle description to an invisible sector of gapless internal degrees-of-freedom. The leading order dynamics of this sector are encoded in the low-energy expansion of a spectral density function obtained by matching an absorption cross section in the ultraviolet description. This information is then recycled using the scattering amplitudes based Kosower-Maybee-O’Connell in-in formalism to calculate the leading absorptive contribution to the impulse and change in rest mass of a Schwarzschild black hole scattering with a second compact body sourcing a massless scalar, electromagnetic or gravitational field. The results obtained are in complete agreement with previous worldline Schwinger-Keldysh calculations and provide an alternative on-shell scattering amplitudes approach to incorporating horizon absorption effects in the gravitational two-body problem.

Physics↗

Electromagnetic entrapment in gravity

Abstract We derive specific properties of electromagnetism when gravitational effects are not negligible and analyze their impact on new physics at the horizons of black holes. We show that a neutral configuration of charges in a region of high redshift, characterized by a largeg tt , produces a highly localized electromagnetic field that vanishes just beyond that region. This phenomenon implies the existence of extensive families of spacetime structures generated by electromagnetic degrees of freedom that are as compact as black holes. We construct neutral bound states of extremal black holes in four dimensions and in five dimensions, where one direction is compact. These geometries are indistinguishable from a neutral black hole, referred to asdistorted Schwarzschild, except in an infinitesimal region near its horizon where the entrapped electromagnetic structures start to manifest. The five-dimensional solutions satisfy various criteria for describing black hole microstructure: they increase in size with the Newton constant, are as compact as the Schwarzschild black hole, and have an entropy that scales likeM 2 .

Physics↗

Universal entropy and hawking radiation of near-extremal AdS4 black holes

We compute the Bekenstein-Hawking entropy of near-extremal asymptotically AdS 4 electrically charged rotating black holes using three different methods: (i) from the gravity solution, (ii) from the near-horizon Kerr/CFT correspondence and (iii) from the boundary conformal field theory. The results from these three different approaches match exactly, giving us a unique and universal expression for the entropy and the microstate counting of near-extremal AdS black holes via the AdS/CFT correspondence. In the second method, we extend the Kerr/CFT correspondence to the near-extremal case to compute the left and right central charges. We also use hidden conformal symmetry of the near-horizon geometry to compute the Frolov-Thorne temperatures. From the results of the near-extremal AdS 4 black hole entropy, we provide a microscopic foundation for Hawking radiation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Scattering in black hole backgrounds and higher-spin amplitudes. Part II

We continue to investigate correspondences between, on the one hand, scattering amplitudes for massive higher-spin particles and gravitons in appropriate quantum-to-classical limits, and on the other hand, classical gravitational interactions of spinning black holes according to general relativity. We first construct an ansatz for a gravitational Compton amplitude, at tree level, constrained only by locality, crossing symmetry, unitarity and consistency with the linearized-Kerr 3-point amplitude, to all orders in the black hole’s spin. We then explore the extent to which a unique classical Compton amplitude can be identified by comparing with the results of the classical process of scattering long-wavelength gravitational waves off an exact Kerr black hole, determined by appropriate solutions of the Teukolsky equation. Up to fourth order in spin, we find complete agreement with a previously conjectured exponential form of the tree-level Compton amplitude. At higher orders, we extract tree-level contributions from the Teukolsky amplitude by an analytic continuation from a physical (a/GM < 1) to a particle-like (a/GM > 1) regime. Up to the sixth order in spin, we identify a unique conservative part of the amplitude which is insensitive both to the choice of boundary conditions at the black hole horizon and to branch choices in the analytic continuation. The remainder of the amplitude is determined modulo an overall sign from a branch choice, with the sign flipping under exchanging purely ingoing and purely outgoing boundary conditions at the horizon. Along the way, we make contact with novel applications of massive spinor-helicity variables pertaining to their relation to EFT operators and (spinning) partial amplitudes.

79 ASTRONOMY AND ASTROPHYSICS↗

Thermalization in the D1D5 CFT

It is generally agreed that black hole formation in gravity corresponds to thermalization in the dual CFT. It is sometimes argued that if the CFT evolution shows evidence of large redshift in gravity, then we have seen black hole formation in the CFT. We argue that this is not the case: a clock falling towards the horizon increases its redshift but remains intact as a clock; thus it is not `thermalized'. Instead, thermalization should correspond to a new phase after the phase of large redshift, where the infalling object turns into fuzzballs on reaching within planck distance of the horizon. We compute simple examples of the scattering vertex in the D1D5 CFT which, after many iterations, would lead to thermalization. An initial state made of two left-moving and two right-moving excitations corresponds, in gravity, to two gravitons heading towards each other. The thermalization vertex in the CFT breaks these excitations into multiple excitations on the left and right sides; we compute the amplitudes for several of these processes. We find secular terms that grow as $t^2$ instead of oscillating with $t$; we conjecture that this may be a feature of processes leading to thermalization.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗