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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Charge Conservation beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids

Nonlinear electromagnetic response functions have reemerged as a crucial tool for studying quantum materials, due to recently appreciated connections between optical response functions, quantum geometry, and band topology. Most attention has been paid to responses to spatially uniform electric fields, relevant to low-energy optical experiments in conventional solid state materials. However, magnetic and magnetoelectric phenomena are naturally connected by responses to spatially varying electric fields due to Maxwell’s equations. Furthermore, in the emerging field of moiré materials, characteristic lattice scales are much longer, allowing spatial variation of optical electric fields to potentially have a measurable effect in experiments. In order to address these issues, we develop a formalism for computing linear and nonlinear responses to spatially inhomogeneous electromagnetic fields. Starting with the continuity equation, we derive an expression for the second-quantized current operator that is manifestly conserved and model independent. Crucially, our formalism makes no assumptions on the form of the microscopic Hamiltonian and so is applicable to model Hamiltonians derived from tight-binding or calculations. We then develop a diagrammatic Kubo formalism for computing the wave vector dependence of linear and nonlinear conductivities, using Ward identities to fix the value of the diamagnetic current order by order in the vector potential. We apply our formula to compute the magnitude of the Kerr effect at oblique incidence for a model of a moiré-Chern insulator and demonstrate the experimental relevance of spatially inhomogeneous fields in these systems. We further show how our formalism allows us to compute the (orbital) magnetic multipole moments and magnetic susceptibilities in insulators. Turning to nonlinear response, we use our formalism to compute the second-order transverse response to spatially varying transverse electric fields in our moiré-Chern insulator model, with an eye toward the next generation of experiments in these systems. Published by the American Physical Society 2024

Physics↗
DOE OSTI2022

Design optimization of an additively manufactured prototype recuperator for supercritical CO 2 power cycles

Supercritical CO 2 (sCO 2 ) power cycles are being developed due to their potential for high efficiency and reduced capital cost. It is necessary that these recuperators operate at high pressures and temperatures, up to 30 MPa and 900 K, with effectiveness values > 95% and pressure drops <1% to achieve high cycle efficiencies. Moreover, it is also necessary to have reasonable cost recuperators to control the capital costs of the sCO 2 power cycles. In this study, a Plate Pin-Fin (PPF) heat exchanger has been proposed as an sCO 2 recuperator. This preliminary recuperator design leverages capabilities enabled by additive manufacturing. Although the PPF design has characteristics similar to those of a plate heat exchanger, small diameter and relatively long fins are used to increase surface area, enhance heat transfer, and provide structural support for the partition plates that separate the fluid streams. Existing correlations for heat transfer and pressure drop were adapted for the PPF heat exchanger. These correlations were implemented in a 1D analytical model and used for the optimization of a 5-kW th high temperature recuperator for an indirect sCO 2 cycle by varying the design parameters to minimize the quantity of material required. A 3D conjugate heat transfer numerical simulations were conducted to validate the heat transfer and pressure loss correlations. A steepest descent method was used to minimize heat exchanger mass for a 5-kW prototype recuperator subject to a maximum specified pressure drop. Additionally, the design analysis indicated that an optimum PPF recuperator would be attained for the minimum allowable pin transverse spacing, minimum pin width, minimum pin height and near maximum cell aspect ratio. Moreover, at a low material requirement of 0.216 kg/kW and a pressure drop, which is almost five times lower than the allowable pressure drop design target, the optimized PPF heat exchanger has the high potential to be an alternative to a printed circuit heat exchanger, which is a conservative design basis for the current state-of-the-art sCO 2 recuperators.

42 ENGINEERING↗
DOE OSTI2025

Noninvertible chiral symmetry and axions under electromagnetic duality

We study the implications of noninvertible chiral symmetry in a four-dimensional U(1) gauge theory coupled to massless fermions with electromagnetic 𝑆⁢𝐿⁡(2,ℤ) duality. This is done by deriving the Adler-Bell-Jackiw anomaly of massless QED in the dual frame that is used to explicitly construct the symmetry defect operator as well as the conserved two-form symmetry current. As expected, the noninvertible chiral symmetry is covariant under the duality transformation. This has implications for understanding the nature of kinetic and topological terms in the dual frame and for axion electrodynamics. In particular, we show that to generate an axion potential from a dyon loop, the one-form magnetic symmetry must be explicitly broken by a mutually nonlocal charged state with nonzero pairwise helicity.

Anomalies↗
DOE OSTI2024

Initial Assessment of CTF for Time-at-Temperature Applications

The US nuclear industry is interested in improving the economics of their fleet of light-water reactors (LWRs) by uprating US plants. One option being considered is to regain lost margin from overly conservative fuel safety limits. The current limit requires avoidance of critical heat flux (CHF) and prevents further operation of fuel that experiences a dry-out in boiling water reactors (BWRs) or departure from nucleate boiling (DNB) in pressurized water reactors (PWRs); however, it has been shown that temporary, mild dry-out of the fuel does not necessarily increase the risk of fuel failure during its normal anticipated operating life. Such mild dry-out or DNB events may occur during a plant anticipated operational occurrence (AOO), such as a locked rotor in a PWR or a pump trip in a BWR. The time-at-temperature (TAT) approach to regulating fuel operation aims to demonstrate that the fuel rod’s integrity is not challenged during such a mild transient that leads to CHF in which the fuel operates at an elevated temperature for a brief period of time. However, implementing this approach will require extensive fuel material experimental data, as well as supporting modeling and simulation (M&S) predictions, to ensure that the predicted fuel response during AOOs, with all applicable uncertainty considered, will not threaten the safety of the fuel during the transient or the remainder of its anticipated lifecycle. To address this need, a comprehensive effort is being proposed that includes generating cladding material data under TAT conditions, assessment of available code capabilities for TAT conditions, development of new mechanistic models, and demonstration of the M&S capabilities for AOOs of interest. This will require a joint effort between the Nuclear Energy Advanced Modeling and Simulation (NEAMS) and Advanced Fuels Campaign (AFC) programs, as well as close collaboration with nuclear industry stakeholders. The outcome of this collaboration will result in development and assessment of capabilities that can be used by the nuclear industry to support qualification of a TAT-based fuel failure criteria safety limit. This report focuses on the thermal hydraulics (T/H) modeling capabilities and summarizes currently available data for validating the T/H subchannel code CTF for TAT conditions, as well as preliminary assessment results of the code. The initial assessment also resulted in implementation of an alternative post-CHF heat transfer package, which has been shown to significantly improve accuracy. This report is not a final assessment and does not consider all available validation data; it is intended that a future assessment will more fully validate the code for this application.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

HPC Resource Allocation Under Energy Constraints

We discuss the new problem faced by High-Performance Computing (HPC) facilities in allocating resources to users of their facilities: while facilities once allocated a single finite resource—node-hours—now facilities must also concurrently allocate a second scarce resource: electrical energy, which is bounded within each facility's annual operations budget. Current application optimization practices encourage conservation of the first resource, but can be potentially unaffordably wasteful of the second. We describe a framework for reasoning about such allocations that can be utilized by facilities to articulate policy, while encouraging scientific application developers to write code mindfully of both constraints. We outline the requirements on facilities, on developers, and on hardware vendors and integrators that are necessary to enable the implementation of this framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A genoscape–network model for conservation prioritization in a migratory bird

Migratory animals are declining worldwide and coordinated conservation efforts are needed to reverse current trends. We devised a novel genoscape-network model that combines genetic analyses with species distribution modeling and demographic data to overcome challenges with conceptualizing alternative risk factors in migratory species across their full annual cycle. We applied our method to the long distance, Neotropical migratory bird, Wilson's Warbler (Cardellina pusilla). Despite a lack of data from some wintering locations, we demonstrated how the results can be used to help prioritize conservation of breeding and wintering areas. For example, we showed that when genetic, demographic, and network modeling results were considered together it became clear that conservation recommendations will differ depending on whether the goal is to preserve unique genetic lineages or the largest number of birds per unit area. More specifically, if preservation of genetic lineages is the goal, then limited resources should be focused on preserving habitat in the California Sierra, Basin Rockies, or Coastal California, where the 3 most vulnerable genetic lineages breed, or in western Mexico, where 2 of the 3 most vulnerable lineages overwinter. Alternatively, if preservation of the largest number of individuals per unit area is the goal, then limited conservation dollars should be placed in the Pacific Northwest or Central America, where densities are estimated to be the highest. Overall, our results demonstrated the utility of adopting a genetically based network model for integrating multiple types of data across vast geographic scales and better inform conservation decision-making for migratory animals.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Collective dynamics of polarized spin-half fermions in relativistic heavy-ion collisions

Standard relativistic hydrodynamics has been successful in describing the properties of the strongly interacting matter produced in the heavy-ion collision experiments. Recently, there has been a significant theoretical advancement in this field to explain spin polarization of hadrons emitted in these processes. Although current models have successfully explained some of the experimental data based on the coupling between spin polarization and vorticity of the medium, they still lack a clear understanding of the differential measurements. This is commonly interpreted as an indication that the spin needs to be treated as an independent degree of freedom whose dynamics is not entirely bound to flow circulation. In particular, if the spin is a macroscopic property of the system, in equilibrium its dynamics should follow hydrodynamic laws. Here, we develop a framework of relativistic hydrodynamics which includes spin degrees of freedom from the quantum kinetic theory for Dirac fermions and use it for modeling the dynamics of matter. Following experimental observations, we assume that the polarization effects are small and derive conservation laws for the net baryon current, the energy–momentum tensor and the spin tensor based on the de Groot–van Leeuwen–van Weert definitions of these currents. We present various properties of the spin polarization tensor and its components, analyze the propagation properties of the spin polarization components, and derive the spin-wave velocity for arbitrary statistics. We find that only the transverse spin components propagate, analogously to the electromagnetic waves. Finally, using our framework, we study the space–time evolution of the spin polarization for the systems respecting certain space–time symmetries and calculate the mean spin polarization per particle, which can be compared to the experimental data. We find that, for some observables, our spin polarization results agree qualitatively with the experimental findings and other model calculations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Assisted migration in a warmer and drier climate: less climate buffering capacity, less facilitation and more fires at temperate latitudes?

Assisted tree migration has been proposed as a conceptual solution to mitigate lags in biotic responses to anthropogenic climate change. The rationale behind this concept is that tree species currently growing under warmer and drier climates will be more resistant and resilient to the new climatic conditions than tree species naturally growing in currently wetter and colder climates. However, we hypothesize that, by being more stress‐tolerant to warmer and drier conditions, translocated species should exhibit different functional attributes, which could induce important ecological and societal costs and overcome the desired benefits of maintaining wood production and other ecosystem services. We used principal component analysis (PCA) to analyze variation in seven traits of 106 tree and tall shrub species from contrasting latitudinal distributions in western North America and Europe to predict the potential functional changes of forest ecosystems due to the translocation of tree species from low to high latitudes. We show that species from both continents differed primarily by their position on the leaf economy spectrum (LES) and their size traits. Even though, in Europe, differences in LES were significantly correlated to species southern latitudinal positions, in both continents differences in size traits were significantly correlated to latitude. These results suggest that assisted migration by translocating more conservative species of shorter stature in currently cooler climates should decrease the buffering capacity of forest canopies, decrease facilitation for understory species, and increase wildfire risks, whose effects have the potential to accelerate climate warming through negative atmospheric feedback processes. As an alternative solution to assisted migration that may accelerate rather than mitigate climate change, we recommend that foresters gradually diversify the vertical structure and layering of the existing forest canopy to maintain a sustainable water cycle and energy balance between the soil, the tree and the atmosphere without increasing the wildfire risk.

Environmental Sciences & Ecology↗
DOE OSTI2022

Axion anomalies

We study fermions derivatively coupled to axion-like or pseudoscalar fields, and show that the axial vector current of the fermions is not conserved in the limit where the fermion is massless. This apparent violation of the classical chiral symmetry is due to the background axion field. We compute the contributions to this anomalous Ward identity due to the pseudoscalar field alone, which arise in Minkowski space, as well as the effects due to an interaction with an external gravitational field. For the case of massless fermions, these interactions induce terms in the axion effective action that can be removed by the addition of local counterterms. We demonstrate that these counterterms are generated by the transformation of the path integral measure when transforming the theory from a form where the chiral symmetry is manifest to one where the symmetry is only apparent after using the classical equations of motion. We work perturbatively in Minkowski space and include the effects of interactions with a linearized gravitational field. Using the heat kernel method, we study the transformation properties of the path integral measure, and include the effects of non-linear gravity as well as interactions with gauge fields. Finally, we verify our relation by considering derivatively coupled fermions during pseudoscalar-driven inflation and computing the divergence of the axial current in de Sitter spacetime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

$\mathcal{N}$ = (1, 0) anomaly multiplet relations in six dimensions

We consider conformal and ’t Hooft anomalies in six-dimensional $\mathcal{N}$ = (1, 0) superconformal field theories, focusing on those conformal anomalies that determine the two- and three-point functions of conserved flavor and SU(2) R currents, as well as stress tensors. By analyzing these correlators in superspace, we explain why the number of independent conformal anomalies is reduced in supersymmetric theories. For instance, non- supersymmetric CFTs in six dimensions have three independent conformal c-anomalies, which determine the stress-tensor two- and three-point functions, but in superconformal theories the three c-anomalies are subject to a linear constraint. We also describe anomaly multiplet relations, which express the conformal anomalies of a superconformal theory in terms of its ’t Hooft anomalies. Following earlier work on the conformal a-anomaly, we argue for these relations by considering the supersymmetric dilaton effective action on the tensor branch of such a theory. We illustrate the utility of these anomaly multiplet relations by presenting exact results for conformal anomalies, and hence current and stress-tensor correlators, in several interacting examples.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Upcycling Mixed Spent Ni-Lean Cathodes into Ni-Rich Polycrystalline Cathodes

Sustainable battery recycling is vital for conserving resources and reducing environmental impacts. Current open- and closed-loop recycling strategies often focus on recovering individual components, making the reuse of mixed cathode materials a complex challenge. Meanwhile, the research on upcycling has been limited to using pristine cathode feedstocks and virgin materials for synthesis. Here, to address this issue, we present an upcycling approach for spent Ni-lean mixed cathode materials that integrate an upcycling hydrometallurgical recycling process with traditional hydrometallurgical methods. This strategy achieves a utilization of 92.31 mol % of recycled materials, enabling the regeneration of Ni-rich cathode materials while significantly reducing the reliance on virgin resources. The regenerated 83Ni cathode materials demonstrate physical properties comparable to those produced from virgin materials. Electrochemical evaluations using single-layer pouch cells show that both recycled and virgin cathodes exhibit initial specific capacity close to 201.1 mAh/g and maintain approximately 88 % capacity retention after 500 cycles. Additionally, 2Ah cells confirmed these findings, delivering 85 % capacity retention after about 900 cycles. Techno-economic analysis demonstrates notable environmental benefits, including reductions in greenhouse gas emissions and energy consumption, achieving 232.75 MJ/kg of product, which is 8.6 % lower than traditional methods and comparable to direct upcycling. Furthermore, the upcycling hydrometallurgical recycling process generates the highest profit, proving its economic viability. This scalable and versatile process is adaptable to varying transition metal compositions, facilitating a closed-loop recycling system that bridges mixed spent cathodes with next-generation cathode materials, and offers a sustainable solution for managing waste battery materials.

Hydrometallurgical recycling↗
DOE OSTI2021

Transport in helical Luttinger liquids in the fractional quantum Hall regime

Abstract Domain walls in fractional quantum Hall ferromagnets are gapless helical one-dimensional channels formed at the boundaries of topologically distinct quantum Hall (QH) liquids. Naïvely, these helical domain walls (hDWs) constitute two counter-propagating chiral states with opposite spins. Coupled to an s-wave superconductor, helical channels are expected to lead to topological superconductivity with high order non-Abelian excitations 1–3 . Here we investigate transport properties of hDWs in the ν = 2/3 fractional QH regime. Experimentally we found that current carried by hDWs is substantially smaller than the prediction of the naïve model. Luttinger liquid theory of the system reveals redistribution of currents between quasiparticle charge, spin and neutral modes, and predicts the reduction of the hDW current. Inclusion of spin-non-conserving tunneling processes reconciles theory with experiment. The theory confirms emergence of spin modes required for the formation of fractional topological superconductivity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Protection of U.S. streams is insufficient to safeguard stream diversity and prevent habitat impairment

Despite covering a small portion of Earth’s surface, streams support a disproportionate amount of biodiversity. Here, we measure progress against the Global Biodiversity Framework 30×30 protection target for streams within the conterminous U.S., in terms of quantity, representation, and effectiveness of habitat protection under primarily land-based protection strategies. We evaluated the geophysical and biogeographical diversity of streams falling under protection measures. Additionally, we expose a paradox of streams being protected yet simultaneously impaired from human disturbances. Without considering impairment, approximately 30% of streams are currently protected through land-based conservation of their local or upstream watersheds; when considering impairment, only 9% to 28% of streams are truly protected from disturbances depending on impairment thresholds and protection criteria. Furthermore, despite protection approaching 30×30 targets, only 5% of the most prevalent physical stream habitat types are protected. We provide a targeted protection strategy, overcoming the impairment paradox and ensuring adequate representation of streams.

Biogeography↗
DOE OSTI2026

Entity—Hardware-agnostic Particle-in-cell Code for Plasma Astrophysics. I. Curvilinear Special Relativistic Module

Entity is a new-generation, fully open-source particle-in-cell (PIC) code developed to overcome key limitations in astrophysical plasma modeling, particularly the extreme separation of scales and the performance challenges associated with evolving, GPU-centric computing infrastructures. It achieves hardware-agnostic performance portability across various GPU and CPU architectures using the Kokkos library. Crucially, Entity maintains a high standard for usability, clarity, and customizability, offering a robust and easy-to-use framework for developing new algorithms and grid geometries, which allows extensive control without requiring edits to the core source code. This paper details the core general-coordinate special relativistic module. Entity is the first PIC code designed to solve the Vlasov–Maxwell system in general coordinates, enabling a coordinate-agnostic framework that provides the foundational structure for straightforward extension to arbitrary coordinate geometries. The core methodology achieves numerical stability by solving particle equations of motion in the global orthonormal Cartesian basis, despite using generalized coordinates like Cartesian, axisymmetric spherical, and quasi-spherical grids. Charge conservation is ensured via a specialized current deposition technique using conformal currents. The code exhibits robust scalability and performance portability on major GPU platforms (AMD MI250X, NVIDIA A100, and Intel Max Series), with the 3D particle pusher and the current deposition operating efficiently at about 2 ns per particle per time step. Functionality is validated through a comprehensive suite of standard Cartesian plasma tests and the accurate modeling of relativistic magnetospheres in curvilinear axisymmetric geometries.

Hakobyan, Hayk [Flatiron Institute, New York, NY (↗
DOE OSTI2021

A NICER View of the Massive Pulsar PSR J0740+6620 Informed by Radio Timing and XMM-Newton Spectroscopy

We report on Bayesian estimation of the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740+6620, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray Timing Instrument event data. We condition on informative pulsar mass, distance, and orbital inclination priors derived from the joint North American Nanohertz Observatory for Gravitational Waves and Canadian Hydrogen Intensity Mapping Experiment/Pulsar wideband radio timing measurements of Fonseca et al. We use XMM-Newton European Photon Imaging Camera spectroscopic event data to inform our X-ray likelihood function. The prior support of the pulsar radius is truncated at 16 km to ensure coverage of current dense matter models. We assume conservative priors on instrument calibration uncertainty. We constrain the equatorial radius and mass of PSR J0740+6620 to be ${12.39}_{-0.98}^{+1.30}$ km and ${2.072}_{-0.066}^{+0.067}$ M ⊙ respectively, each reported as the posterior credible interval bounded by the 16% and 84% quantiles, conditional on surface hot regions that are non-overlapping spherical caps of fully ionized hydrogen atmosphere with uniform effective temperature; a posteriori, the temperature is ${\mathrm{log}}_{10}(T\,[{\rm{K}}])={5.99}_{-0.06}^{+0.05}$ for each hot region. All software for the X-ray modeling framework is open-source and all data, model, and sample information is publicly available, including analysis notebooks and model modules in the Python language. Furthermore, our marginal likelihood function of mass and equatorial radius is proportional to the marginal joint posterior density of those parameters (within the prior support) and can thus be computed from the posterior samples.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

2021 Prototype Installation and Testing Awardee: XFlow Energy Company

XFlow Energy Company (XFlow Energy) aims to reduce the cost of wind energy by designing vertical-axis wind turbines (VAWTs), which have a cheaper blade manufacturing process and a mechanically simpler design than traditional wind turbines, among other cost-saving advantages. However, a lack of modeling or simulation tools that can predict the coupling between aerodynamic and structural forces poses a significant challenge to developers of VAWTs. Known as aeroelastic models, these are not just important design tools - they're critical for certifying VAWTs of 25 kilowatts (kW), which is the size of XFlow Energy's prototype wind turbine. Without certification, XFlow Energy will not be able to deliver an independently validated product to its customers, and those customers will not be eligible for state and federal incentives. An accurate aeroelastic model could provide less-conservative structural optimization tactics than are currently used, resulting in a wind turbine with lower capital costs.

CIP↗
DOE OSTI2025

Constraining non-standard neutrino interactions with neutral current events at long-baseline oscillation experiments

We explore, for the first time, neutral-curren t events at long-baseline experiments to constrain vector and axial-vector neutrino non-standard interactions (NSI) with quarks. We leverage the flavor dependence of NSIs to perform an oscillation analysis in the neutral- current channel. We first introduce a framework to parametrize the effect of NSI on the cross section. Then, as an example, we analyze NOvA neutral-current data which provides significantly improved constraints on the axial-vector NSI parameters ${\varepsilon}_{\mu \mu}^A$, ${\varepsilon}_{\tau \tau}^A$ and ${\varepsilon}_{e\mu}^A$. This is highly complementary to constraints from SNO data, which, differently from long-baseline neutral current data, is not sensitive to isospin conserving NSIs ${\varepsilon}_u^A$ = ${\varepsilon}_d^A$. Additionally, we disfavor large values of the diagonal vectorial NSI ${\varepsilon}_{\mu \mu}^{VV}$ and ${\varepsilon}_{\tau \tau}^V$ which originate from the LMA-Dark solution. We also highlight the complementarity between NSI searches at oscillation experiments using charged current and neutral current channels.

neutrino interactions↗
DOE OSTI2025

Constraining non-standard neutrino interactions with neutral current events at long-baseline oscillation experiments

We explore, for the first time, neutral-current events at long-baseline experiments to constrain vector and axial-vector neutrino non-standard interactions (NSI) with quarks. We leverage the flavor dependence of NSIs to perform an oscillation analysis in the neutral- current channel. We first introduce a framework to parametrize the effect of NSI on the cross section. Then, as an example, we analyze NOvA neutral-current data which provides significantly improved constraints on the axial-vector NSI parameters $ {\varepsilon}_{\mu \mu}^A $,$ {\varepsilon}_{\tau \tau}^A $ and $ {\varepsilon}_{e\mu}^A $. This is highly complementary to constraints from SNO data, which, differently from long-baseline neutral current data, is not sensitive to isospin conserving NSIs $ {\varepsilon}_u^A $ = $ {\varepsilon}_d^A $. Additionally, we disfavor large values of the diagonal vectorial NSI $ {\varepsilon}_{\mu \mu}^{VV} $ and $ {\varepsilon}_{\tau \tau}^V $ which originate from the LMA-Dark solution. We also highlight the complementarity between NSI searches at oscillation experiments using charged current and neutral current channels.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗