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NASA NTRS2021

Framework for Coordinated Efforts in the Exploration of Volatiles in the South Polar Region of the Moon

The exploration of the lunar south polar region and the ground truthing of polar volatiles is one of the top priorities for several space agencies and private partners. Here we use Moon Mineralogy Mapper surficial water ice detections to investigate the location of water ice-bearing permanently shaded regions near the south pole. We extract a variety of parameters such as their temperature regime, slope, hydrogen content, number of ice detections, depth stability for water ice and dry ice, and mobility aspects. We identify 169 water ice-bearing PSRs and use their characteristics to identify sites that allow to access the highest abundances of volatiles, sites that can be visited to characterize the lateral or vertical distribution of volatiles (water ice and dry ice), and sites that allow for the fastest recovery of a scientifically interesting sample. Collectively, 37 PSRs are identified as sites of interest, including 11 that would address more than one mission objective and may be, for that reason, higher priority targets of exploration. These PSRs are found in Shoemaker, Faustini, Cabeus, Malapert, Nobile, Sverdrup, Wiechert J and Haworth craters, as well as 3 unnamed craters (PSRs 57, 120, 89). These sites are all located within 6 degrees of the south pole. We present case studies for a relatively short traverse mission (20 to 50 km) to PSR 89, a medium length traverse (~100 km) to Sverdrup 1, and a longer traverse (~300 km) to Cabeus that can serve as a guide in planning upcoming exploration missions.

Myriam Lemelin↗

NASA NTRS2020

A Reinforcement Learning Framework for Space Missions in Unknown Environments

A land-and-traverse mission to icy worlds such as Europa and Enceladus is challenging due to lack of prior knowledge regarding the terrain conditions. Previous work [1] showed that rovers with high degrees of freedom (DoF) can achieve robust traversal by leveraging redundant modes for mobility to counter terrain uncertainty (e.g. walking, driving, or inch-worming). This paper presents a generic and scalable reinforcement learning scheme for enabling on-board decision making on rovers to automatically switch between modes of traversal based on online performance feedback. The objective is to maximize energy efficiency, minimize operator input and successfully negotiate unstructured terrain conditions without relying on exhaustive prior knowledge. The proposed methodology is well grounded in the literature on reinforcement learning and has been adapted to address conformance to validation and verification requirements and JPL flight operations history of using per-sol prescribed sequences for a space mission.

Tavallali, Peyman↗

NASA NTRS2021

Machine Learning Based Path Planning for Improved Rover Navigation

Enhanced AutoNav (ENav), the baseline surface navigation software for NASA’s Perseverance rover, sorts a list of candidate paths for the rover to traverse, then uses the Approximate Clearance Evaluation (ACE) algorithm to evaluate whether the most highly ranked paths are safe. ACE is crucial for maintaining the safety of the rover, but is computationally expensive. If the most promising candidates in the list of paths are all found to be infeasible, ENav must continue to search the list and run time-consuming ACE evaluations until a feasible path is found. In this paper, we present two heuristics that, given a terrain heightmap around the rover, produce cost estimates that more effectively rank the candidate paths before ACE evaluation. The first heuristic uses Sobel operators and convolution to incorporate the cost of traversing high-gradient terrain. The second heuristic uses a machine learning (ML) model to predict areas that will be deemed untraversable by ACE. We used physics simulations to collect training data for the ML model and to run Monte Carlo trials to quantify navigation performance across a variety of terrains with various slopes and rock distributions. Compared to ENav's baseline performance, integrating the heuristics can lead to a significant reduction in ACE evaluations and average computation time per planning cycle, increase path efficiency, and maintain or improve the rate of successful traverses. This strategy of targeting specific bottlenecks with ML while maintaining the original ACE safety checks provides an example of how ML can be infused into planetary science missions and other safety-critical software.

Yue, Yisong↗

NASA NTRS2023

Developing a Hybrid Space Suit Simulator as a Research Tool for Assessing Extravehicular Activity Relevant Workload

Suited testing time is limited and hard to come by, expensive, and requires a whole team to operate and monitor the suit; however, pressurized spacesuits are not always necessary for initial developmental efforts or assessment of informatics. The Human Physiology, Performance, Protection & Operations Laboratory (H-3PO) at NASA Johnson Space Center (JSC) is developing a Hybrid Space Suit Simulator (HS3) to support characterization of human performance during planetary surface exploration analogs. The primary goal of HS3 is to create a low cost, modular, and unpressurized suit simulator for use as a research tool which provides relevant physical and cognitive workload approximations with EVA-like immersion during planetary extravehicular activity (EVA) simulations. HS3 consists of a soft suit, communication, thermal control, gloves, boots, helmet, and integrated bioinformatics/sensors. The modular design of HS3 allows it to be modified to support test objectives as needed. HS3 enables H-3PO and NASA to complete critical human health and performance testing to address open risks and knowledge gaps in a timely, repeatable, and controlled manner. Four engineering runs were completed with HS3 as a baseline for capability. General workload was assessed while traversing on a passive treadmill and conducting geology tasks. Liquid cooling temperature, suit temperature, and metabolic rates were collected during one extended three-hour engineering run. For the duration of the engineering run the suit temperature was 26.6 ± 1.58 °C while suit humidity was 53.7 ± 5.11 %. Helmet temperature was higher than suit temperature at 27.8 ± 1.58 °C. Helmet humidity was lower than average suit humidity at 50.12 ± 11.3 °C. The liquid cooling temperature remained stable at 22.4 ± 1.62 °C. Resting metabolic rate was 597 ± 88 BTU/hr while metabolic rate increased during traverse tasks at 1500 ± 319 BTU/hr and geology tasks at 921 ± 129 BTU/hr. Following the engineering runs, a characterization study will be conducted. The subjects will perform EVA-like scenarios in both a shirtsleeve only and donned HS3, consisting of EVA task circuit focused on traversing, geological rock sampling, and task board manipulation. The characterization study will provide data capability for implementing HS3 in analog EVA testing environments.

Monica Hew↗

NASA NTRS2024

Core Body Temperature Predictions Using Metabolic Energy Expenditure and Heart Rate During Simulated Extravehicular Activity

Long duration spaceflight missions will require crew to become more autonomous in conducting extravehicular activities (EVA) without direct communication with Mission Control for biomedical support. To enable such autonomy, we are developing a Crew State and Risk Model (CSRM) as a collection of key physiology domains that drive EVA crew capabilities and workloads. One model component of CSRM is human thermal regulation. In this paper, customized development of a baseline model to predict core body temperature is presented using physiology inputs of heart rate and metabolic rate. The model development dataset included a baseline study where participants (n=6, equal male and female) performed a 5-hour EVA in a two-part session while wearing a hybrid space suit simulator (HS3). The first session included an end-to-end EVA traversing 1500 meters to a geology site and traversing back to a habitat conducting geology, payload relocation, and maintenance operations every 500 meters. The second session included standalone tasks of a 2000-meter traverse followed by geology tasks. Thermal measures of core body temperature, local skin temperature, liquid cooling garment temperature, heart rate, and metabolic rate were collected through the test duration. Multiple regression was used to build a linear equation to predict core body temperature from inputs of heart rate and metabolic rate. Heat storage was calculated via predicted core body temperature plus LCG and skin temperatures. The model was tested against a dataset from a pressurized suited test (n=6, equal male and female) in the NASA Active Response Gravity Offload System (ARGOS) conducting similar end-to-end EVA and standalone tasks. Predicted error of the model against the raw test cases was 0.2±0.15 °C. The baseline prediction of core body temperature using heart rates and metabolic rates allows for simple real-time tracking from data collected in-flight to monitor crew consumables and thermal flight limits during EVA.

Bradley Hoffmann↗

NASA NTRSDate not supplied

Simplifying Analysis of Hierarchical HDF5 and NetCDF4 Files with Xarray-Datatree

NASA’s Earth Observing System Data and Information System (EOSDIS) contains thousands of Earth science datasets from satellites, models, and field campaigns. EOSDIS data are stored in formats that are well supported by the Earth Science community. These formats include the Hierarchical Data Format (HDF), with derivative flavors such as HDF-5 and the Network Common Data Format (NetCDF-4). The HDF specification allows for a directory-like hierarchy within a single file, known as "groups". Observational data and associated metadata within a single file can be distributed amongst multiple internal groups, which can also be nested to multiple levels. Working with datasets that have a group hierarchical structure can be difficult because of the nested structure of groups. Widely used packages, such as xarray, have data models that do not accommodate the hierarchical structure within HDF files, requiring users to traverse the file and open different HDF groups as separate, unrelated objects. Xarray-datatree is a Python package developed to solve the difficulty of traversing HDFs with a hierarchical group structure by creating a tree-like hierarchical data structure in xarray. The tree-like structure allows each group to be accessed once a DataTree object is instantiated. The migration of xarray-datatree into the xarray core library will reduce barriers to accessing Earth science data by eliminating the need to understand and traverse the specific hierarchy of a grouped HDF file.

Eni Awowale↗

DOE OSTI2020

Inspection Tools for Hanford Tanks and Waste Transport Systems - 20444

Recent integrity issues in the double-shell tanks (DST) at Hanford have motivated the need for developing innovative tools that can provide information regarding the health of the tanks. These issues include the primary linear failure of AY-102 and recent concerns of thinning in the DST secondary liners. Other concerns include erosion or corrosion on transfer lines and processing pipes. In recent years, Florida International University (FIU) has supported DOE-EM by developing tools that can assist in understanding the health of tanks and waste transport system at Hanford. More specifically, FIU has developed a miniature rover that can be deployed through small risers and gain access to refractory slots in the Hanford DSTs. It traverses through the slots on the primary liner upside down via magnets to avoid debris in the slots. Recent modifications include a spring loaded magnetic arm that allows the unit to traverse over large weld seams but does not reduce the overall functionality of the system. The system has also incorporated a control capsule that will sit within the annulus of the tank and improves on issues related to signal and voltage loss over long tether lines. Lastly, the unit is also being augmented with a second module that will include a means to prep the tank surface and obtain a thickness measurement using a dual element ultrasonic sensor. FIU has also developed a 6-inch peristaltic pipe crawler that operates similar to the previous pipe crawlers developed at FIU. This crawler is a marsupial type crawler that will navigate through the 6-inch drain lines, and deploy a small rover at the entrance of the drain slots. This rover will also traverse upside down on the secondary liner and provide information regarding the health of the liner. An initial prototype for the crawler unit has been developed, assembled and tested. The system is pneumatic and consists of three modules - two grippers and one extender. The validation tests are conducted in a mockup of the drain lines and demonstrate the system's ability to navigate through long pipe lengths and elbows. In this paper, a general overview of each of the aforementioned systems is presented along with results from testing and demonstrations that shows the applicability of each system. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

Progressive Tree-Based Compression of Large-Scale Particle Data

Scientific simulations and observations using particles have been creating large datasets that require effective and efficient data reduction to store, transfer, and analyze. However, current approaches either compress only small data well while being inefficient for large data, or handle large data but with insufficient compression. Toward effective and scalable compression/decompression of particle positions, we introduce new kinds of particle hierarchies and corresponding traversal orders that quickly reduce reconstruction error while being fast and low in memory footprint. Our solution to compression of large-scale particle data is a flexible block-based hierarchy that supports progressive, random-access, and error-driven decoding, where error estimation heuristics can be supplied by the user. For low-level node encoding, we introduce new schemes that effectively compress both uniform and densely structured particle distributions. Our proposed methods thus target all three phases of a tree-based particle compression pipeline, namely tree construction, tree traversal, and node encoding. In conclusion, the improved efficacy and flexibility of these methods over existing compressors are demonstrated through extensive experimentation, using a wide range of scientific particle datasets.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Data Center Waste Heat as an Emerging Urban Thermal Hazard: First Field Measurements of Neighborhood-Scale Air Temperature Impacts

Data centers are among the fastest-growing sources of concentrated anthropogenic heat in urban environments. Despite heat flux densities that exceed peak solar irradiance by a factor of 2–6, their thermal impacts on adjacent communities have never been directly measured or reported in the peer-reviewed literature. This short communication addresses that gap by presenting the first vehicle-based traverse measurements of air temperature in residential neighborhoods downwind of operational data centers. Five traverses at four facilities in the Phoenix, Arizona metropolitan area, ranging from a 36 MW single-building data center in Mesa to a 169 MW colocation campus in Chandler, reveal downwind air temperature warming as high as 2.2 °C, with average downwind air temperatures 0.7–0.9 °C warmer than corresponding upwind areas. Thermal signatures were detectable at distances up to 500 m from facility perimeters. The 36 MW Mesa facility rejects waste heat equivalent to the electricity consumption of approximately 40,000 households, while the 169 MW Chandler campus is equivalent to over 180,000 households, both concentrated into footprints smaller than a single residential subdivision. With U.S. data center capacity projected to more than double by 2030, these findings establish data center anthropogenic waste heat as a previously undocumented urban thermal hazard demanding attention from the data center and urban planning communities.

Phoenix↗

DOE OSTI2022

Delaunay walk for fast nearest neighbor: accelerating correspondence matching for ICP

Point set registration algorithms such as Iterative Closest Point (ICP) are commonly utilized in time-constrained environments like robotics. Finding the nearest neighbor of a point in a reference 3D point set is a common operation in ICP and frequently consumes at least 90% of the computation time. We introduce a novel approach to performing the distance-based nearest neighbor step based on Delaunay triangulation. This greedy algorithm finds the nearest neighbor of a query point by traversing the edges of the Delaunay triangulation created from a reference 3D point set. Our work integrates the Delaunay traversal into the correspondences search of ICP and exploits the iterative aspect of ICP by caching previous correspondences to expedite each iteration. An algorithmic analysis and comparison is conducted showing an order of magnitude speedup for both serial and vector processor implementation.

3d point cloud processing↗

DOE OSTI2021

Non-local entanglement and fast scrambling in de-Sitter holography

We study holographic entanglement and information scrambling in de-Sitter (dS) space in the context of the DS/dS correspondence. We find that our previously identified non-local entanglement structure of dS vacua can be extended out of the time-reflection symmetric slice. We extend the geometry to a two-sided configuration and calculate the zero-time mutual information between two intervals on different sides when there is a localized shock wave in the bulk. Interestingly, we find that the information scrambling time saturates the fast scrambler bound proposed by Sekino and Susskind and that the shock wave renders a wormhole to be traversable. Furthermore, we calculate a two-sided out-of-time-ordered correlator (OTOC) in the late time regime and we see that, before scrambling, it exponentially grows with an exponent whose value saturates the maximal bound of chaos proposed by Maldacena, Shenker and Stanford. At the end, we provide an explanation why the exponential growing of the late-time OTOC with the maximal bound of chaos saturated and the traversability of the wormhole are simple results of the non-local entanglement structure and we point out that this is a realization of the ER=EPR proposal.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Sinter formation during directed energy deposition of titanium alloy powders

During directed energy deposition (DED) additive manufacturing, powder agglomeration and sintering can occur outside of the melt pool when using titanium alloy powders. Using in situ synchrotron radiography we investigate the mechanisms by which sintering of Ti6242 powder occurs around the pool, performing a parametric study to determine the influence of laser power and stage traverse speed on sinter build-up. The results reveal that detrimental sinter can be reduced using a high laser power or increased stage traverse speed, although the latter also reduces deposition layer thickness. The mechanism of sinter formation during DED was determined to be in-flight heating of the powder particles in the laser beam. Calculations of particle heating under the processing conditions explored in this study confirm that powder particles can reasonably exceed 700 °C, the threshold for Ti surface oxide dissolution, and thus the powder is prone to sintering if not incorporated into the melt pool. The build-up of sinter powder layer on deposit surfaces led to lack of fusion pores. To mitigate sinter formation and its detrimental effects on DED component quality, it is essential that the powder delivery spot area is smaller than the melt pool, ensuring most powder lands in the melt pool.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Meshfree simulation and prediction of recrystallized grain size in friction stir processed 316L stainless steel

Friction stir processing (FSP) is a promising solid-phase microstructural modification technique that can repair and enhance damaged stainless steel surfaces exposed to harsh environments. The quality of the repaired material is closely correlated to the recrystallized grain size in the stir zone (SZ), which is influenced by the thermomechanical conditions dictated by FSP process parameters. Thus, establishing a reliable relationship between these parameters and recrystallized grain size in the SZ is crucial for optimizing repair quality. However, existing experimental approaches often rely on indirect temperatures measured far from the SZ, along with rough strain rate estimations, which are imprecise and time-consuming. Meanwhile, existing mesh-based modeling methods usually face numerical challenges when dealing with the large material deformations inherent in FSP. Here, to address these issues, this study introduces a meshfree process model for FSP based on the smoothed particle hydrodynamics (SPH) method, aimed at predicting process conditions under different parameters. The model is validated using experimental data from 11 combinations of tool traverse and rotation speeds on 316 L stainless steel. Correlations between process parameters, material flow, temperature, strain, strain rate, and recrystallized grain size are revealed through SPH simulations and electron backscatter diffraction (EBSD) imaging. The results show that in situ SZ temperatures range from 1071 to 1322°C, which exceed the tool temperature by over 300°C. Furthermore, SZ temperature, strain rate, and grain size increase monotonically with higher tool temperature and faster traverse speed. A relationship is then established between the model-predicted Zener-Hollomon parameter and the recrystallized grain size based on EBSD data, expressed as ln(d) = -0.364 ln(Z) + 14.673. Finally, this relationship exhibits satisfactory accuracy with errors of less than 26.9% in predicting grain sizes at various SZ locations, which offers valuable insights for optimizing FSP repair processes for 316 L stainless steel.

316L stainless steel↗

DOE OSTI2026

Enhancing fatigue life of aluminum alloy castings through cavitation water jet peening: Experiments and simulations

This study presents an investigation into the enhancement of the fatigue life of aluminum castings through the application of cavitation water-jet peening (CWJP). CWJP harnesses the impacts of water cavitation to induce surface compressive residual stress within metallic materials. In this work, CWJP was applied to a high pressure die-cast (HPDC) Al–Si alloy A380 with three different water-jet traverse velocities. The fatigue-life improvement, evaluated in a 4-point bending configuration (stress ratio R = 0.1), was found to vary with applied stress level and ranges from 1.6 to 10 times that of the parent alloy. The data also shows that decreasing the traverse velocity results in greater compressive residual stresses within the surface layer and a concurrent increase in surface roughness. This residual stress layer extends to a depth of 400 μm below the surface, as confirmed by through-thickness residual stress and microhardness measurements. CWJP treatment effectively slows down fatigue crack propagation, as evidenced by microstructural observations of narrower striation spacing. Simulations reveal that compressive residual stresses, in addition to surface hardening during CWJP, are key to improving fatigue life. A 20% increase in surface hardness and 150 MPa compressive residual stress imposed by CWJP process provides an average 5-fold enhancement of fatigue life across different stress levels. This study demonstrates the potential of CWJP as an effective surface treatment to enhance the fatigue life of aluminum castings, such as HPDC components for automotive applications.

Al casting↗

DOE OSTI2026

Citizen science coupled with machine learning to quantify green-blue infrastructure cooling potential in Maricopa County, Arizona

Here, this study investigates the spatiotemporal cooling performance of green and blue infrastructure (GBI) in the Dobson Ranch urban neighborhood in Phoenix, Arizona. We leveraged citizen science near-surface (2 m) air temperature (Tair) measurements to train a highly accurate Tair predicting LightGBM machine learning model (R 2 : 0.986, MAE: 0.251 °C, RMSE: 0.585 °C). On June 16, 2024, the park area exhibited approximately 1 °C cooling effect (relative to the neighborhood mean) during both day and night. In contrast, the nearby artificial lake exhibited a stronger cooling effect of 2.4 °C during the day but a slight warming of 0.3 °C at night. At 00:00, locations 50 m downwind of the park were 0.3 °C warmer than the park, while locations 50 m upwind were 0.8 °C warmer. At 11:00, we observed that the downwind area is 0.8 °C cooler and the upwind area is 0.6 °C warmer—at the same 50 m distances relative to the park. We also observed 1 °C cooler and warmer effects respectively at the same 50 m downwind and upwind locations at 19:00 on June 17, 2024. Our data-driven analysis highlights potential limitations of car-traverse measurements, showing that failure to account for temporal variations during the traverse can lead to overestimation of Tair at night and underestimation during the day. Our analysis also showed only a weak correlation (coefficient: 0.48) between Landsat-derived land surface temperature (LST) and model predicted Tair at the time of the local Landsat overpass (∼11.00). This highlights the potential error of relying solely on LST for human thermal exposure analysis—particularly within the heterogenous built-environment.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Laser glazing of cold sprayed coatings for the mitigation of stress corrosion cracking in light water reactor (LWR) applications

The effect of laser power, traverse speed, and cold spray coating thickness were examined with the goal of mitigating and repairing stress corrosion cracking (SCC) in light water reactor (LWR) environment. For this purpose, SCC-susceptible Alloy 600 substrate material was coated with SCC-resistant Alloy 690 via the cold spray technique. The cold spray coated substrate was then laser-glazed using various laser parameters. Single pass and multiple pass laser glazed regions were created to determine the effects. For this purpose, the area of the fusion zone, depth of the fusion zone, and elemental composition of the cross section were examined by optical microscopy, scanning electron microscopy, and energy dispersive spectroscopy. Additionally, it was shown that chromium dilution from the laser glazed region into the substrate is not a significant factor in laser glazed cold spray coated samples. Separate laser glazed samples were subjected to ASTM 633C to determine coating adhesion. Finally, by using interrupted SCC crack growth rate tests, it was shown that low traverse speeds and high laser powers produce deep fusion zones within the cold sprayed coating and substrate that can be used to seal pre-existing cracks, thus stopping SCC growth.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Effect of feed-rod tilting on friction surfacing of steel

During the friction surfacing process, the forge-axial force, rotation rate, and traverse speed of the consumable feed-rod play crucial roles in determining the deposition rate and layer morphology. Although some researchers have studied the enhancement of deposition by introducing a backward tilt relative to the traverse direction, there has been limited investigation into the effects of other tilt orientations. Therefore, this study aims to provide a more comprehensive understanding of feed-rod tilting in friction surfacing. In this investigation, the consumable feed-rod undergoes tilting in four distinct directions: forward, backward, advancing side, and retreating side, each tested at two different tilt angles (1.5° and 3.0°). The results reveal that the feed-rod tilting can influence the deposition dynamics by altering the location and area of the rubbing interface situated between the feed-rod and the substrate. Moreover, the feed-rod tilting can significantly enhance the bond width, deposition rate, and deposition efficiency. The enhancement in deposition efficiency signifies a successful reduction in flash formation. Furthermore, a distinct layered microstructure is evident within each deposition layer, regardless of tilt conditions, indicating the unique deposition process inherent to friction surfacing. Finally, the innovative approach proposed in this study not only offers a straightforward and feasible means to improve deposition rate and efficiency but also expands the potential for constructing more intricate geometries or authentic surfaces.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Sonic horizons and causality in phase transition dynamics

A system gradually driven through a symmetry-breaking phase transition is subject to the Kibble-Zurek mechanism (KZM). As a consequence of the critical slowing down, its state cannot follow local equilibrium, and its evolution becomes nonadiabatic near the critical point. In the simplest approximation, that stage can be regarded as an “impulse” where the state of the system remains unchanged. It leads to the correct KZM scaling laws. However, such a “freeze-out” might suggest that the coherence length of the nascent order parameter remains unchanged as the critical region is traversed. By contrast, the original causality-based discussion emphasized the role of the sonic horizon: Domains of the broken symmetry phase can expand with a velocity limited by the speed of the relevant sound. This effect was demonstrated in the quantum Ising chain where the dynamical exponent z = 1 and quasiparticles excited by the transition have a fixed speed of sound. To elucidate the role of the sonic horizon, in this paper we study two systems with z > 1 where the speed of sound is no longer fixed, and the fastest excited quasiparticles set the size of the sonic horizon. Their effective speed decays with increasing transition time. In the extreme case, the dynamical exponent z can diverge such as in the Griffiths region of the random Ising chain where the localization of excited quasiparticles freezes the growth of the correlation range when the critical region is traversed. Of particular interest is an example with z < 1 , the long-range extended Ising chain, where there is no upper limit to the velocity of excited quasiparticles with small momenta. Initially, the power-law tail of the correlation function grows adiabatically, but in the nonadiabatic stage it lags behind the adiabatic evolution.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗