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All sources NASA NTRS DOE OSTI

DOE OSTI2026

A parametric study of slow dynamic nonlinear elasticity with comparisons to models

Several phenomenological models that aspire to quantitative description of anomalous nonlinear mesoscopic elasticity are reviewed and compared with laboratory measurements. This class of nonlinearity, best known perhaps for slow dynamics and aging, is seen widely in imperfectly consolidated granular solids but is not well understood. Typical slow dynamic tests show that a modest conditioning oscillatory "pump" strain depresses material stiffness, which then recovers like the logarithm of time after conditioning ceases. Several phenomenological models based on physical arguments have been proposed that predict the material stiffness response to arbitrary pump strain histories during conditioning and recovery. Approximate closed form and numerical solutions to the models are presented that predict the quantitative influence of three key pump parameters: the pump's strain amplitude, the pump's strain rate, and the pump’s duration. Laboratory measurements on Berea sandstone, concrete and a confined single aluminum bead find that slow dynamic responses are linear in pump strain and independent of pump frequency. Measurements also show that, after pump-off, stiffness recovers over times far longer than the pump duration. These observations and others are compared to model predictions. One of the considered models, based on a picture of fast brittle damage and slow healing, successfully matches all these behaviors.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Effect of Biomass Water Dynamics in Cosmic-Ray Neutron Sensor Observations: A Long-Term Analysis of Maize–Soybean Rotation in Nebraska

Precise soil water content (SWC) measurement is crucial for effective water resource management. This study utilizes the Cosmic-Ray Neutron Sensor (CRNS) for area-averaged SWC measurements, emphasizing the need to consider all hydrogen sources, including time-variable plant biomass and water content. Near Mead, Nebraska, three field sites (CSP1, CSP2, and CSP3) growing a maize–soybean rotation were monitored for 5 (CSP1 and CSP2) and 13 (CSP3) years. Data collection included destructive biomass water equivalent (BWE) biweekly sampling, epithermal neutron counts, atmospheric meteorological variables, and point-scale SWC from a sparse time domain reflectometry (TDR) network (four locations and five depths). In 2023, dense gravimetric SWC surveys were collected eight (CSP1 and CSP2) and nine (CSP3) times over the growing season (April to October). The N0 parameter exhibited a linear relationship with BWE, suggesting that a straightforward vegetation correction factor may be suitable (fb). Results from the 2023 gravimetric surveys and long-term TDR data indicated a neutron count rate reduction of about 1% for every 1 kg m−2 (or mm of water) increase in BWE. This reduction factor aligns with existing shorter-term row crop studies but nearly doubles the value previously reported for forests. This long-term study contributes insights into the vegetation correction factor for CRNS, helping resolve a long-standing issue within the CRNS community.

Chemistry↗

DOE OSTI2026

Large Language Model for Validation, Optical Calibration, and Learning (VOCAL) Distributed Temperature Sensing Interface

Distributed temperature sensing (DTS) using fiber optic sensors (FOS) offers a promising method for temperature measurements in advanced reactors, such as sodium fast reactors and molten salt cooled reactors. To support the calibration and validation of DTS measurements, Argonne National Laboratory developed the Validation, Optical Calibration, and Learning (VOCAL) software package. This report describes the integration of a local large language model (LLM) with a retrieval-augmented generation (RAG) system into the VOCAL interface to serve as an interactive user assistant. The LLM framework enhances the VOCAL platform’s accessibility to users by explaining interface components, clarifying inputs and outputs, and answering user queries dynamically in real-time. The accuracy of the LLM assistant performance was evaluated with 20 queries regarding the interface and its parameters using experimental data from the Thermal Hydraulic Experimental Test Article (THETA) facility. Results demonstrate that the LLM achieved a 95% accuracy rate, with a BERTScore of 0.8816 and SBERT value of 0.7417. Furthermore, validation of the RAG system within the LLM framework showed optimal accuracy with k-values between 1 and 2 using the k-refinement convergence test. The prompt perturbation analysis demonstrated good initial consistency for the RAG system, exhibiting the highest accuracy under punctuation variations and the greatest sensitivity under query reordering. Notably, the model’s errors were limited to data retrieval failures rather than factual hallucinations, reinforcing its baseline reliability. The integration of LLM provides a highly accurate, userfriendly enhancement to the VOCAL platform without disrupting its core computational capabilities for FOS calibration and validation.

Hong, Evan↗

NASA NTRS2019

Rewet Temperature Correlations for Liquid-Nitrogen Boiling Pipe Flows Across Varying Flow Conditions and Orientations

In many convective liquid-vapor phase change heat transfer engineering applications, cryogenic fluids are widely used in industrial processes, spacecraft and cryosurgery systems, and so on. For example, cryogens are usually used as liquid fuels such as liquid hydrogen and oxygen in the rocket industry, liquid nitrogen (LN2) and helium are frequently used to cool superconducting magnetic device for medical applications. In these systems, proper transport, handling, and storage of cryogenic fluids are of extreme importance. Among all the cryogenic transport processes performed in room temperatures, quenching, also termed chilldown, is a unavoidable initial, transient phase-change heat transfer process that brings the system down to the cryogenic condition. The Leidenfrost temperature or rewet temperature that signals the end of film boiling is practically considered the completion point of a quenching process. Therefore, rewet temperature has been considered the most important parameter for the engineering design of cryogenic thermal management systems. As most of the previous correlations for predicting the Leidenfrost temperature and the rewet temperature have been basically developed for water, they are shown to disagree with recent liquid nitrogen pipe chilldown experiments in upward and downward flow directions over a wide range of flow rates, pressures, and degrees of inlet subcooling. In addition to a complete review of the literature, two new correlations are presented in this work, one based on bubble growth and another based on the theoretical maximum limit of superheat. Each correlation performs well over the entire data set.

liquid nitrogen↗

DOE OSTI2026

Heavy long-lived dark vector via a gluonic portal

We study a dark gauge boson Z′ that exclusively couples to the QCD gluons through higher dimensional operators. These operators are generated from integrating out of heavy ultraviolet resonances carrying both QCD and dark gauge charges. With SU(3)C gauge invariance, charge and parity symmetries preserved, we find that the leading effective operators are restricted to have the form of Z′GGG and Z′Z′GG at dimension-eight, which can naturally render the Z′ particle long-lived, and serve as a viable dark matter candidate. We investigate the phenomenology of these operators with both collider experiments and cosmological observation, without and with the assumption that this dark gauge boson plays the role of the dominant dark matter component. For an unstable Z′, we show that depending on its lifetime, it can be probed by various observables up to ultraviolet physics scale around 10 9 GeV. For Z′ being dark matter, we find that $m_{Z'}$ ≳ 1 TeV is consistent with the thermal freeze-out scenario. In contrast, in the freeze-in scenario, the extremely small couplings leave the relevant parameter space largely unconstrained by current experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Fracture Analysis of Cohesive Zone Models for Modeling Residual Stress Induced Delamination in Composite Structures

A fracture study of coupon-scale composite cylinders with embedded defects was conducted with an objective to assess and validate a modeling approach using two available cohesive material models. The study included experimental and simulation evaluations of initiation of crack growth and progression. Interrupted thermal experiments used acoustic emissions monitoring to identify the onset of crack progression during each cooling interval and ultrasonic scanning provided images of defect growth. Verification, validation, and uncertainty quantification (VVUQ) processes were performed in the assessment of the simulation predicted temperature at which crack propagation begins (quantity of interest). The Sobol sensitivity analysis identified the hoop direction elastic modulus in the carbon fiber reinforced polymer (CFRP) plies as the most influential parameter for simulations using both cohesive models, accounting for at least 70% of the variation in the temperature at crack propagation. The UQ temperature range for the Tvergaard-Hutchinson model was higher (more conservative) than the experimental acoustic measurement indicators of crack progression, while the temperature range for the Thouless-Parmigiani model enveloped the experimental data points for the primary defect size of 0.75 x 1 in. The simulations could not capture the stable crack growth indicated in the experiments. This is likely due to the models’ inability to represent anisotropic fracture toughness attributed to the structure of the orthotropic fiber weave in a woven composite laminate.

42 ENGINEERING↗

NASA NTRSDate not supplied

On-Orbit Calibration Assessment of NOAA-21 VIIRS Thermal Emissive Bands and Implications for JPSS-4 VIIRS

The Visible Infrared Imaging Radiometer Suite (VIIRS) instrument onboard the NOAA-21 (N21) satellite has been successfully operating for over three years collecting valuable scientific measurements. A large suite of weather forecasting models and scientific research applications are supported with the VIIRS measurements from N21 combined with those acquired from the VIIRS instrument onboard the S-NPP and NOAA-20 spacecraft. Among the 22 VIIRS spectral bands, there are seven thermal emissive bands (TEB) covering the 3.7 to 12.2 µm spectral range at two different spatial resolutions. The VIIRS TEB detectors are calibrated onboard using a blackbody at a controlled temperature and a space view for background signal measurement. In this paper, we discuss the on-orbit performance of the N21 VIIRS TEB using various parameters such as the detector gain, noise, and offset. This on-orbit assessment provides critical insights into instrument behavior and calibration performance that will inform pre-launch testing and post-launch validation strategies for the upcoming JPSS-4 VIIRS mission scheduled for launch in 2027. The methodologies and lessons learned from characterizing the N21 TEB performance will enable more efficient and comprehensive radiometric assessment of the next VIIRS instrument. Specific focus is placed on identifying performance trends and anomaly signatures observed during the N21 commissioning phase that can enhance the JPSS4 instrument checkout procedures and accelerate the transition to routine on-orbit operations. The established performance baselines and uncertainty estimates will serve as an acceptance criterion for the JPSS-4 commissioning activities, ensuring mission readiness and data continuity for operational users.

Amit Angal↗

DOE OSTI2026

From Bricks to Clicks: Mapping the White Space in Building Innovation

It is a critical national imperative to transform the buildings sector, yet innovation is impeded by deployment failures that leave promising technologies stranded. Conventional market reports and techno-economic analysis provide an insufficient understanding of markets and resource allocation for emerging building technologies. They omit crucial commercialization factors such as ecosystem maturity and adoption friction, where the coordinated participation of a network of suppliers, contractors, financiers, regulators, and integrators is required to scale solutions. This study addresses these gaps by introducing an evaluation framework grounded in front-line data from six years of the DOE's IMPEL incubator, comprising experience from 300 building-sector innovators and the adjacent, complex ecosystem. Our methodology synthesizes top-down market analysis with bottom-up, practitioner-level data across five megatrends: (M1) Affordable materials and industrialized construction; (M2) Healthy and efficient mechanical systems; (M3) Intelligent building operations; (M4) Buildings as grid assets; and (M5) High-density power and cooling for data centers and therein identify twelve "white space" technology opportunities. Next, we develop a multi-criteria scoring rubric to rank these opportunities based on parameters, i.e., Affordability, Quality of Life, Reliability, and Security, yielding composite ‘Demand’ and ‘Maturity’ indices. Our results indicate that the most significant white spaces may not be incremental products but a new class of ‘Ecosystem Enablers’, such as logistics platforms, orchestration layers, and automated compliance software that solve structural deployment gaps. This paper summarizes this transparent, evidence-based, practitioner-informed evaluation framework for policymakers and investors to re-evaluate policy and resource allocation and unlock scalable market transformation.

Singh, Reshma↗

DOE OSTI2023

Challenges and Prospects of Sodium‐Ion and Potassium‐Ion Batteries for Mass Production

The exponential growth of the lithium‐ion (LIB) market is causing a significant disparity between the supply chain and demand for its resources. In this regard, sodium‐ion and potassium‐ion batteries are promising alternatives to LIBs due to their low cost. However, the larger sizes of Na + and K + ions create challenges that prevent them from achieving energy densities comparable to LIBs while maintaining an acceptable cycle life. Here, in this perspective, the aim is to evaluate the status of Na‐ion and K‐ion batteries and the challenges associated with them on both fundamental and commercial levels. The focus is on the structural instability arising from phase transitions during cycling, intricate chemical degradation processes, and potential avenues for enhancing their performance with a specific goal of improving their viability for grid‐scale energy storage. Materials production and abundance limitations for the chemistries of the state‐of‐the‐art materials and account for critical parameters from both the perspective of researchers and investors are analyzed. This analysis aims to provide insights into the strategic trade‐offs required to effectively implement the technology in real‐world applications, such as grid‐scale storage and other areas. Furthermore, the utilization of metals with low or no supply‐chain problems as an important aspect of these trade‐offs is considered.

25 ENERGY STORAGE↗

NASA NTRSDate not supplied

Pragmatic Stress Prediction on Additively Manufactured Coupons

Prediction of residual stresses from process parameters for additively manufactured large metal parts is computationally expensive. NASA is currently developing meter-scale parts with direct energy deposition. Practically, the predictive computational methods need to efficiently scale-up to meter-scale parts. Coupled thermal-mechanical multi-physics simulations have been developed with the pragmatic method using ABAQUS, COMSOL Multiphysics, ALE3D software. The residual stresses are a result of the manufacturing process which creates thermal cycling of the build layers. The pragmatic method uses lumped thermal layers for stress predictions to reduce computational costs. The stress predictions as well as deformations of the different codes are compared with each other and with ANSYS Additive using identical material models, boundary and initial conditions. The codes were used to simulate three different geometries: a thin wall, hollow cylinder and twin-cantilever part. The coupon parts were then manufactured with Inconel-625. The residual stresses in these parts were measured using X-ray diffraction as well as neutron beam diffraction at NIST. The stress measurements for the two technologies are compared. The pragmatic stress prediction method enabled predictions of the multi-centimeter scale parts using desktop computer workstations in only a few hours for each coupon. The results of the simulated stress predictions compared favorably with the measured stresses even though thermally lumped layers were employed. Finally, a two-meter scale nozzle was simulated using ANSYS Additive. The simulations were used to examine the build orientation trade-space with respect to resulting geometric deformation. The predicted deformations were compared to measurements of an actual subscale part manufactured with direct energy deposition.

pragmatic method↗

DOE OSTI2026

Quality and Loss Factor Characterization of YBCO Superconducting Transmission Lines for Axion Dark Matter Detection

Axion haloscope experiments aim to detect the conversion of axions into microwave photons under a strong magnetic field through resonant cavity techniques. The conversion produces an extremely small signal, requiring a cryogenic environment to reduce thermal noise, and low-loss superconducting transmission lines for minimal attenuation in the readout chain. Yttrium barium copper oxide (YBCO) cables are a promising candidate. Unlike commonly used low-loss cryogenic cables such as niobium (Nb) and niobium titanium (NbTi), which have low critical fields, YBCO is a high-temperature superconductor that can remain stable in strong magnetic fields. We characterized the quality and loss of five stripline resonators from the Brookhaven Technology Group: three YBCO, a copper reference, and a silver reference. Experimental methodology included collecting scattering parameter data on a vector network analyzer for the samples at 77 K along with room temperature baseline measurements, and employing both Lorentzian-fit and circle-fitting techniques to confirm the coupling regime and corroborate results. We achieved quality factors on the order of $10^3$ with corresponding loss factors on the order of $10^{-1}$ dB/m. Trends were comparable with literature data on Nb and NbTi at 4 K, which did have lower loss under these conditions, but suggested similar or perhaps better loss for YBCO when accounting for the temperature difference. We also developed a cryogenic probe for future measurements in a 14 T applied field at 30 mK. This will serve to directly evaluate YBCO's durability in magnetic fields, and we expect significantly improved performance at millikelvin temperatures.

Marinos, Z. [UCLA]↗

DOE OSTI2024

Understanding the origin of early-type dwarfs: the spectrophotometric study of CGCG014−074

ABSTRACT Early-type dwarf galaxies constitute a prevalent population in the central regions of rich groups and clusters in the local Universe. These low-luminosity and low-mass stellar systems play a fundamental role in the assembly of the luminous galaxies observed today, according to the Lambda cold dark matter hierarchical theory. The origin of early-type dwarfs has been linked to the transformation of disc galaxies interacting with the intracluster medium, especially in dense environments. However, the existence of low-luminosity early-type galaxies in low-density environments presents a challenge to this scenario. This study presents a comprehensive photometric and spectroscopic analysis of the early-type dwarf galaxy CGCG014−074 using deep Gemini GMOS (Gemini Multi-Object Spectrograph) data, focusing on its peculiarities and evolutionary implications. CGCG014−074 exhibits distinct features, including a rotating inner disc, an extended stellar formation with a quiescent phase since about 2 Gyr ago, and the presence of boxy isophotes. From the kinematic analysis, we confirm CGCG014−074 as a nucleated early-type dwarf galaxy with embedded disc. The study of its stellar population parameters using different methods provides significant insights into the galaxy’s evolutionary history. These results show an old and metal-poor nucleus (${\sim}9.3$ Gyr and $\mathrm{[Z/H]}\sim -0.84$ dex), while the stellar disc is younger (${\sim}4.4$ Gyr) with a higher metallicity ($\mathrm{[Z/H]}\sim -0.40$ dex). These distinctive features collectively position CGCG014−074 as a likely building block galaxy that has evolved passively throughout its history.

Astronomy & Astrophysics↗

NASA NTRS2026

Modeling Study of Hatch Spacing’s Effect on Grain Morphology in Repairing Damaged Metal Parts with Welding and Hatch Spacing’s Potential Use in Lunar Exploration

The welding process is a potential way of repairing a damaged metal component, especially cavity damage caused by a harsh environment like the lunar environment, which is characterized by large temperature differences and reduced gravity. The adjustment of welding parameter (e.g., hatch spacing) can improve production efficiency in the repair process. Seen from the microstructural level, hatch spacing sensitivity affects the metallic grain evolution and morphology in the welding process, which can further influence a repaired part’s mechanical properties; however, the study of hatch spacing’s effect on microstructure is challenging. Traditional experimental procedures are costly and time-consuming, and any change in hatch spacing value needs roll-back of experimental procedure. A modeling study can address the above challenges in experimental observation. In this research, a modeling approach based on the Kinetic Monte Carlo (KMC) Potts theory was used to simulate grain evolution and morphology with three hatch spacings. Through quantifying and analyzing the predicted grain morphologies, the effect of hatch spacing on microstructure in a welding-fabricated part was investigated. The predicted grain morphologies were validated with an EBSD image of welding microstructure, which has been published before. The primary grain morphologies were columnar grains with a small amount of fine equiaxed grains formed in the scanning path centerline. When increasing the hatch spacing, the columnar grains become larger and more lengthy, while the effect of hatch spacing on the equiaxed grains is not obvious.

Welding for repairing↗

DOE OSTI2024

Trust-Based Detection and Mitigation of Cyber Attacks in Distributed Cooperative Control of Islanded AC Microgrids

In this study, we address the challenge of detecting and mitigating cyber attacks in the distributed cooperative control of islanded AC microgrids, with a particular focus on detecting False Data Injection Attacks (FDIAs), a significant threat to the Smart Grid (SG). The SG integrates traditional power systems with communication networks, creating a complex system with numerous vulnerable links, making it a prime target for cyber attacks. These attacks can lead to the disclosure of private data, control network failures, and even blackouts. Unlike machine learning-based approaches that require extensive datasets and mathematical models dependent on accurate system modeling, our method is free from such dependencies. To enhance the microgrid’s resilience against these threats, we propose a resilient control algorithm by introducing a novel trustworthiness parameter into the traditional cooperative control algorithm. Our method evaluates the trustworthiness of distributed energy resources (DERs) based on their voltage measurements and exchanged information, using Kullback-Leibler (KL) divergence to dynamically adjust control actions. We validated our approach through simulations on both the IEEE-34 bus feeder system with eight DERs and a larger microgrid with twenty-two DERs. The results demonstrated a detection accuracy of around 100%, with millisecond range mitigation time, ensuring rapid system recovery. Additionally, our method improved system stability by up to almost 100% under attack scenarios, showcasing its effectiveness in promptly detecting attacks and maintaining system resilience. These findings highlight the potential of our approach to enhance the security and stability of microgrid systems in the face of cyber threats.

Computer Science↗

NASA NTRS2012

General Purpose Data-Driven System Monitoring for Space Operations

Modern space propulsion and exploration system designs are becoming increasingly sophisticated and complex. Determining the health state of these systems using traditional methods is becoming more difficult as the number of sensors and component interactions grows. Data-driven monitoring techniques have been developed to address these issues by analyzing system operations data to automatically characterize normal system behavior. The Inductive Monitoring System (IMS) is a data-driven system health monitoring software tool that has been successfully applied to several aerospace applications. IMS uses a data mining technique called clustering to analyze archived system data and characterize normal interactions between parameters. This characterization, or model, of nominal operation is stored in a knowledge base that can be used for real-time system monitoring or for analysis of archived events. Ongoing and developing IMS space operations applications include International Space Station flight control, spacecraft vehicle system health management, launch vehicle ground operations, and fleet supportability. As a common thread of discussion this paper will employ the evolution of the IMS data-driven technique as related to several Integrated Systems Health Management (ISHM) elements. Thematically, the projects listed will be used as case studies. The maturation of IMS via projects where it has been deployed or is currently being integrated to aid in fault detection will be described. The paper will also explain how IMS can be used to complement a suite of other ISHM tools, providing initial fault detection support for diagnosis and recovery

Space Propulsion↗

DOE OSTI2024

Investigating two-dimensional adjoint QCD on the lattice

We present our investigations of SU(N) adjoint QCD in two dimensions with one Majorana fermion on the lattice. We determine the relevant parameter range for the simulations with Wilson fermions and present results for Polyakov loop, chiral condensate, and string tension. In the theory with massive fermions, all observables we checked show qualitative agreement between numerical lattice data and theory, while the massless limit is more subtle since chiral and non-invertible symmetry of the continuum theory are explicitly broken by lattice regularization. In thermal compactification, we observe N perturbative vacua for the holonomy potential at high-T with instanton events connecting them, and a unique vacuum at low-T. At finite-N, this is a cross-over and it turns to a phase transition at large-N thermodynamic limit. In circle compactification with periodic boundary conditions, we observe a unique center-symmetric minimum at any radius. In continuum, the instantons in the thermal case carry zero modes (for even N) and indeed, in the lattice simulations, we observe that chiral condensate is dominated by instanton centers, where zero modes are localized. We present lattice results on the issue of confinement vs. screening in the theory and comment on the roles of chiral symmetry and non-invertible symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Stellar Population Properties in the Stellar Streams around SPRC047

Abstract We have investigated the properties (e.g., age, metallicity) of the stellar populations of a ringlike tidal stellar stream (or streams) around the edge-on galaxy SPRC047 (z= 0.031) using spectral energy distribution (SED) fits to integrated broadband aperture flux densities. We used visual images in six different bands and Spitzer/IRAC 3.6μm data. We have attempted to derive best-fit stellar population parameters (metallicity, age) in three noncontiguous segments of the stream. Due to the very low surface brightness of the stream, we have performed a deconvolution with a Richardson–Lucy–type algorithm of the low spatial resolution 3.6μm IRAC image, thereby reducing the effect of the point-spread function aliasedemissionfrom the bright edge-on central galaxy at the locations of our three stream segments. Our SED fits that used several different star formation (SF) history priors, from an exponentially decaying SF burst to continuous SF, indicate that the age–metallicity–dust degeneracy is not resolved, most likely because of inadequate wavelength coverage and low signal-to-noise ratios of the low surface brightness features. We also discuss how future deep visual–near-infrared observations, combined with absolute flux calibration uncertainties at or below the 1% level, complemented by equally well absolute flux-calibrated observations in ultraviolet and mid-infrared bands, would improve the accuracy of broadband SED fitting results for low surface brightness targets, such as stellar streams around nearby galaxies that are not resolved into stars.

Astronomy & Astrophysics↗

DOE OSTI2024

Λ polarization from vortex rings as the medium response for jet thermalization

We performed a systematic study on the formation of vorticity rings as the process for jet thermalization in the medium created in high-energy nuclear collisions. In this work, we expanded our previous analysis to a more realistic framework by considering noncentral events and fluctuations in the initial condition. We simulate the formation and evolution of the flow vortex structure in a relativistic viscous hydrodynamic model and study the sensitivity of the proposed “ring observable” (ℛ$^{𝑡}_{Λ}$) that can be measured experimentally through the polarization of Λ hyperons. We show that this observable is robust with respect to fluctuating initial conditions to capture the jet-induced vortex flow signal and further study its dependence on different model parameters, such as the jet's velocity, position, the fluid's shear viscosity, and the collision centrality. The proposed observable is associated with the formation of vorticity in a quark-gluon plasma, showing that the measurement of particle polarization can be a powerful tool to probe different properties of jet-medium interactions and to understand better the polarization induced by the transverse and longitudinal expansions of the medium.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗